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/**
  ******************************************************************************
  * @file    stm32f4xx_hal_can.h
  * @author  MCD Application Team
  * @version V1.4.1
  * @date    09-October-2015
  * @brief   Header file of CAN HAL module.
  ******************************************************************************
  * @attention
  *
  * <h2><center>&copy; COPYRIGHT(c) 2015 STMicroelectronics</center></h2>
  *
  * Redistribution and use in source and binary forms, with or without modification,
  * are permitted provided that the following conditions are met:
  *   1. Redistributions of source code must retain the above copyright notice,
  *      this list of conditions and the following disclaimer.
  *   2. Redistributions in binary form must reproduce the above copyright notice,
  *      this list of conditions and the following disclaimer in the documentation
  *      and/or other materials provided with the distribution.
  *   3. Neither the name of STMicroelectronics nor the names of its contributors
  *      may be used to endorse or promote products derived from this software
  *      without specific prior written permission.
  *
  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
  * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  *
  ******************************************************************************
  */

/* Define to prevent recursive inclusion -------------------------------------*/
#ifndef __STM32F4xx_HAL_CAN_H
#define __STM32F4xx_HAL_CAN_H

#ifdef __cplusplus
 extern "C" {
#endif

#if defined(STM32F405xx) || defined(STM32F415xx) || defined(STM32F407xx) || defined(STM32F417xx) ||\
    defined(STM32F427xx) || defined(STM32F437xx) || defined(STM32F429xx) || defined(STM32F439xx) ||\
	defined(STM32F446xx) || defined(STM32F469xx) || defined(STM32F479xx) 
/* Includes ------------------------------------------------------------------*/
#include "stm32f4xx_hal_def.h"

/** @addtogroup STM32F4xx_HAL_Driver
  * @{
  */

/** @addtogroup CAN
  * @{
  */

/* Exported types ------------------------------------------------------------*/
/** @defgroup CAN_Exported_Types CAN Exported Types
  * @{
  */

/**
  * @brief  HAL State structures definition
  */
typedef enum
{
  HAL_CAN_STATE_RESET             = 0x00,  /*!< CAN not yet initialized or disabled */
  HAL_CAN_STATE_READY             = 0x01,  /*!< CAN initialized and ready for use   */
  HAL_CAN_STATE_BUSY              = 0x02,  /*!< CAN process is ongoing              */
  HAL_CAN_STATE_BUSY_TX           = 0x12,  /*!< CAN process is ongoing              */
  HAL_CAN_STATE_BUSY_RX           = 0x22,  /*!< CAN process is ongoing              */
  HAL_CAN_STATE_BUSY_TX_RX        = 0x32,  /*!< CAN process is ongoing              */
  HAL_CAN_STATE_TIMEOUT           = 0x03,  /*!< Timeout state                       */
  HAL_CAN_STATE_ERROR             = 0x04   /*!< CAN error state                     */

}HAL_CAN_StateTypeDef;

/**
  * @brief  CAN init structure definition
  */
typedef struct
{
  uint32_t Prescaler;  /*!< Specifies the length of a time quantum.
                            This parameter must be a number between Min_Data = 1 and Max_Data = 1024 */

  uint32_t Mode;       /*!< Specifies the CAN operating mode.
                            This parameter can be a value of @ref CAN_operating_mode */

  uint32_t SJW;        /*!< Specifies the maximum number of time quanta
                            the CAN hardware is allowed to lengthen or
                            shorten a bit to perform resynchronization.
                            This parameter can be a value of @ref CAN_synchronisation_jump_width */

  uint32_t BS1;        /*!< Specifies the number of time quanta in Bit Segment 1.
                            This parameter can be a value of @ref CAN_time_quantum_in_bit_segment_1 */

  uint32_t BS2;        /*!< Specifies the number of time quanta in Bit Segment 2.
                            This parameter can be a value of @ref CAN_time_quantum_in_bit_segment_2 */

  uint32_t TTCM;       /*!< Enable or disable the time triggered communication mode.
                            This parameter can be set to ENABLE or DISABLE. */

  uint32_t ABOM;       /*!< Enable or disable the automatic bus-off management.
                            This parameter can be set to ENABLE or DISABLE */

  uint32_t AWUM;       /*!< Enable or disable the automatic wake-up mode.
                            This parameter can be set to ENABLE or DISABLE */

  uint32_t NART;       /*!< Enable or disable the non-automatic retransmission mode.
                            This parameter can be set to ENABLE or DISABLE */

  uint32_t RFLM;       /*!< Enable or disable the receive FIFO Locked mode.
                            This parameter can be set to ENABLE or DISABLE */

  uint32_t TXFP;       /*!< Enable or disable the transmit FIFO priority.
                            This parameter can be set to ENABLE or DISABLE */
}CAN_InitTypeDef;

/**
  * @brief  CAN filter configuration structure definition
  */
typedef struct
{
  uint32_t FilterIdHigh;          /*!< Specifies the filter identification number (MSBs for a 32-bit
                                       configuration, first one for a 16-bit configuration).
                                       This parameter must be a number between Min_Data = 0x0000 and Max_Data = 0xFFFF */

  uint32_t FilterIdLow;           /*!< Specifies the filter identification number (LSBs for a 32-bit
                                       configuration, second one for a 16-bit configuration).
                                       This parameter must be a number between Min_Data = 0x0000 and Max_Data = 0xFFFF */

  uint32_t FilterMaskIdHigh;      /*!< Specifies the filter mask number or identification number,
                                       according to the mode (MSBs for a 32-bit configuration,
                                       first one for a 16-bit configuration).
                                       This parameter must be a number between Min_Data = 0x0000 and Max_Data = 0xFFFF */

  uint32_t FilterMaskIdLow;       /*!< Specifies the filter mask number or identification number,
                                       according to the mode (LSBs for a 32-bit configuration,
                                       second one for a 16-bit configuration).
                                       This parameter must be a number between Min_Data = 0x0000 and Max_Data = 0xFFFF */

  uint32_t FilterFIFOAssignment;  /*!< Specifies the FIFO (0 or 1) which will be assigned to the filter.
                                       This parameter can be a value of @ref CAN_filter_FIFO */

  uint32_t FilterNumber;          /*!< Specifies the filter which will be initialized.
                                       This parameter must be a number between Min_Data = 0 and Max_Data = 27 */

  uint32_t FilterMode;            /*!< Specifies the filter mode to be initialized.
                                       This parameter can be a value of @ref CAN_filter_mode */

  uint32_t FilterScale;           /*!< Specifies the filter scale.
                                       This parameter can be a value of @ref CAN_filter_scale */

  uint32_t FilterActivation;      /*!< Enable or disable the filter.
                                       This parameter can be set to ENABLE or DISABLE. */

  uint32_t BankNumber;            /*!< Select the start slave bank filter.
                                       This parameter must be a number between Min_Data = 0 and Max_Data = 28 */

}CAN_FilterConfTypeDef;

/**
  * @brief  CAN Tx message structure definition
  */
typedef struct
{
  uint32_t StdId;    /*!< Specifies the standard identifier.
                          This parameter must be a number between Min_Data = 0 and Max_Data = 0x7FF */

  uint32_t ExtId;    /*!< Specifies the extended identifier.
                          This parameter must be a number between Min_Data = 0 and Max_Data = 0x1FFFFFFF */

  uint32_t IDE;      /*!< Specifies the type of identifier for the message that will be transmitted.
                          This parameter can be a value of @ref CAN_Identifier_Type */

  uint32_t RTR;      /*!< Specifies the type of frame for the message that will be transmitted.
                          This parameter can be a value of @ref CAN_remote_transmission_request */

  uint32_t DLC;      /*!< Specifies the length of the frame that will be transmitted.
                          This parameter must be a number between Min_Data = 0 and Max_Data = 8 */

  uint8_t Data[8];   /*!< Contains the data to be transmitted.
                          This parameter must be a number between Min_Data = 0 and Max_Data = 0xFF */

}CanTxMsgTypeDef;

/**
  * @brief  CAN Rx message structure definition
  */
typedef struct
{
  uint32_t StdId;       /*!< Specifies the standard identifier.
                             This parameter must be a number between Min_Data = 0 and Max_Data = 0x7FF */

  uint32_t ExtId;       /*!< Specifies the extended identifier.
                             This parameter must be a number between Min_Data = 0 and Max_Data = 0x1FFFFFFF */

  uint32_t IDE;         /*!< Specifies the type of identifier for the message that will be received.
                             This parameter can be a value of @ref CAN_Identifier_Type */

  uint32_t RTR;         /*!< Specifies the type of frame for the received message.
                             This parameter can be a value of @ref CAN_remote_transmission_request */

  uint32_t DLC;         /*!< Specifies the length of the frame that will be received.
                             This parameter must be a number between Min_Data = 0 and Max_Data = 8 */

  uint8_t Data[8];      /*!< Contains the data to be received.
                             This parameter must be a number between Min_Data = 0 and Max_Data = 0xFF */

  uint32_t FMI;         /*!< Specifies the index of the filter the message stored in the mailbox passes through.
                             This parameter must be a number between Min_Data = 0 and Max_Data = 0xFF */

  uint32_t FIFONumber;  /*!< Specifies the receive FIFO number.
                             This parameter can be CAN_FIFO0 or CAN_FIFO1 */

}CanRxMsgTypeDef;

/**
  * @brief  CAN handle Structure definition
  */
typedef struct
{
  CAN_TypeDef                 *Instance;  /*!< Register base address          */

  CAN_InitTypeDef             Init;       /*!< CAN required parameters        */

  CanTxMsgTypeDef*            pTxMsg;     /*!< Pointer to transmit structure  */

  CanRxMsgTypeDef*            pRxMsg;     /*!< Pointer to reception structure */

  __IO HAL_CAN_StateTypeDef   State;      /*!< CAN communication state        */

  HAL_LockTypeDef             Lock;       /*!< CAN locking object             */

  __IO uint32_t               ErrorCode;  /*!< CAN Error code                 */

}CAN_HandleTypeDef;

/**
  * @}
  */

/* Exported constants --------------------------------------------------------*/
/** @defgroup CAN_Exported_Constants CAN Exported Constants
  * @{
  */

/** @defgroup HAL_CAN_Error_Code HAL CAN Error Code
  * @{
  */
#define   HAL_CAN_ERROR_NONE      0x00    /*!< No error             */
#define   HAL_CAN_ERROR_EWG       0x01    /*!< EWG error            */
#define   HAL_CAN_ERROR_EPV       0x02    /*!< EPV error            */
#define   HAL_CAN_ERROR_BOF       0x04    /*!< BOF error            */
#define   HAL_CAN_ERROR_STF       0x08    /*!< Stuff error          */
#define   HAL_CAN_ERROR_FOR       0x10    /*!< Form error           */
#define   HAL_CAN_ERROR_ACK       0x20    /*!< Acknowledgment error */
#define   HAL_CAN_ERROR_BR        0x40    /*!< Bit recessive        */
#define   HAL_CAN_ERROR_BD        0x80    /*!< LEC dominant         */
#define   HAL_CAN_ERROR_CRC       0x100   /*!< LEC transfer error   */
/**
  * @}
  */

/** @defgroup CAN_InitStatus CAN InitStatus
  * @{
  */
#define CAN_INITSTATUS_FAILED       ((uint8_t)0x00)  /*!< CAN initialization failed */
#define CAN_INITSTATUS_SUCCESS      ((uint8_t)0x01)  /*!< CAN initialization OK */
/**
  * @}
  */

/** @defgroup CAN_operating_mode CAN Operating Mode
  * @{
  */
#define CAN_MODE_NORMAL             ((uint32_t)0x00000000)                     /*!< Normal mode   */
#define CAN_MODE_LOOPBACK           ((uint32_t)CAN_BTR_LBKM)                   /*!< Loopback mode */
#define CAN_MODE_SILENT             ((uint32_t)CAN_BTR_SILM)                   /*!< Silent mode   */
#define CAN_MODE_SILENT_LOOPBACK    ((uint32_t)(CAN_BTR_LBKM | CAN_BTR_SILM))  /*!< Loopback combined with silent mode */
/**
  * @}
  */

/** @defgroup CAN_synchronisation_jump_width CAN Synchronisation Jump Width
  * @{
  */
#define CAN_SJW_1TQ                 ((uint32_t)0x00000000)     /*!< 1 time quantum */
#define CAN_SJW_2TQ                 ((uint32_t)CAN_BTR_SJW_0)  /*!< 2 time quantum */
#define CAN_SJW_3TQ                 ((uint32_t)CAN_BTR_SJW_1)  /*!< 3 time quantum */
#define CAN_SJW_4TQ                 ((uint32_t)CAN_BTR_SJW)    /*!< 4 time quantum */
/**
  * @}
  */

/** @defgroup CAN_time_quantum_in_bit_segment_1 CAN Time Quantum in bit segment 1
  * @{
  */
#define CAN_BS1_1TQ                 ((uint32_t)0x00000000)                                       /*!< 1 time quantum  */
#define CAN_BS1_2TQ                 ((uint32_t)CAN_BTR_TS1_0)                                    /*!< 2 time quantum  */
#define CAN_BS1_3TQ                 ((uint32_t)CAN_BTR_TS1_1)                                    /*!< 3 time quantum  */
#define CAN_BS1_4TQ                 ((uint32_t)(CAN_BTR_TS1_1 | CAN_BTR_TS1_0))                  /*!< 4 time quantum  */
#define CAN_BS1_5TQ                 ((uint32_t)CAN_BTR_TS1_2)                                    /*!< 5 time quantum  */
#define CAN_BS1_6TQ                 ((uint32_t)(CAN_BTR_TS1_2 | CAN_BTR_TS1_0))                  /*!< 6 time quantum  */
#define CAN_BS1_7TQ                 ((uint32_t)(CAN_BTR_TS1_2 | CAN_BTR_TS1_1))                  /*!< 7 time quantum  */
#define CAN_BS1_8TQ                 ((uint32_t)(CAN_BTR_TS1_2 | CAN_BTR_TS1_1 | CAN_BTR_TS1_0))  /*!< 8 time quantum  */
#define CAN_BS1_9TQ                 ((uint32_t)CAN_BTR_TS1_3)                                    /*!< 9 time quantum  */
#define CAN_BS1_10TQ                ((uint32_t)(CAN_BTR_TS1_3 | CAN_BTR_TS1_0))                  /*!< 10 time quantum */
#define CAN_BS1_11TQ                ((uint32_t)(CAN_BTR_TS1_3 | CAN_BTR_TS1_1))                  /*!< 11 time quantum */
#define CAN_BS1_12TQ                ((uint32_t)(CAN_BTR_TS1_3 | CAN_BTR_TS1_1 | CAN_BTR_TS1_0))  /*!< 12 time quantum */
#define CAN_BS1_13TQ                ((uint32_t)(CAN_BTR_TS1_3 | CAN_BTR_TS1_2))                  /*!< 13 time quantum */
#define CAN_BS1_14TQ                ((uint32_t)(CAN_BTR_TS1_3 | CAN_BTR_TS1_2 | CAN_BTR_TS1_0))  /*!< 14 time quantum */
#define CAN_BS1_15TQ                ((uint32_t)(CAN_BTR_TS1_3 | CAN_BTR_TS1_2 | CAN_BTR_TS1_1))  /*!< 15 time quantum */
#define CAN_BS1_16TQ                ((uint32_t)CAN_BTR_TS1) /*!< 16 time quantum */
/**
  * @}
  */

/** @defgroup CAN_time_quantum_in_bit_segment_2 CAN Time Quantum in bit segment 2
  * @{
  */
#define CAN_BS2_1TQ                 ((uint32_t)0x00000000)                       /*!< 1 time quantum */
#define CAN_BS2_2TQ                 ((uint32_t)CAN_BTR_TS2_0)                    /*!< 2 time quantum */
#define CAN_BS2_3TQ                 ((uint32_t)CAN_BTR_TS2_1)                    /*!< 3 time quantum */
#define CAN_BS2_4TQ                 ((uint32_t)(CAN_BTR_TS2_1 | CAN_BTR_TS2_0))  /*!< 4 time quantum */
#define CAN_BS2_5TQ                 ((uint32_t)CAN_BTR_TS2_2)                    /*!< 5 time quantum */
#define CAN_BS2_6TQ                 ((uint32_t)(CAN_BTR_TS2_2 | CAN_BTR_TS2_0))  /*!< 6 time quantum */
#define CAN_BS2_7TQ                 ((uint32_t)(CAN_BTR_TS2_2 | CAN_BTR_TS2_1))  /*!< 7 time quantum */
#define CAN_BS2_8TQ                 ((uint32_t)CAN_BTR_TS2)                      /*!< 8 time quantum */
/**
  * @}
  */

/** @defgroup CAN_filter_mode  CAN Filter Mode
  * @{
  */
#define CAN_FILTERMODE_IDMASK       ((uint8_t)0x00)  /*!< Identifier mask mode */
#define CAN_FILTERMODE_IDLIST       ((uint8_t)0x01)  /*!< Identifier list mode */
/**
  * @}
  */

/** @defgroup CAN_filter_scale CAN Filter Scale
  * @{
  */
#define CAN_FILTERSCALE_16BIT       ((uint8_t)0x00)  /*!< Two 16-bit filters */
#define CAN_FILTERSCALE_32BIT       ((uint8_t)0x01)  /*!< One 32-bit filter  */
/**
  * @}
  */

/** @defgroup CAN_filter_FIFO CAN Filter FIFO
  * @{
  */
#define CAN_FILTER_FIFO0             ((uint8_t)0x00)  /*!< Filter FIFO 0 assignment for filter x */
#define CAN_FILTER_FIFO1             ((uint8_t)0x01)  /*!< Filter FIFO 1 assignment for filter x */
/**
  * @}
  */

/** @defgroup CAN_Identifier_Type CAN Identifier Type
  * @{
  */
#define CAN_ID_STD             ((uint32_t)0x00000000)  /*!< Standard Id */
#define CAN_ID_EXT             ((uint32_t)0x00000004)  /*!< Extended Id */
/**
  * @}
  */

/** @defgroup CAN_remote_transmission_request CAN Remote Transmission Request
  * @{
  */
#define CAN_RTR_DATA                ((uint32_t)0x00000000)  /*!< Data frame */
#define CAN_RTR_REMOTE              ((uint32_t)0x00000002)  /*!< Remote frame */
/**
  * @}
  */

/** @defgroup CAN_receive_FIFO_number_constants CAN Receive FIFO Number Constants
  * @{
  */
#define CAN_FIFO0                   ((uint8_t)0x00)  /*!< CAN FIFO 0 used to receive */
#define CAN_FIFO1                   ((uint8_t)0x01)  /*!< CAN FIFO 1 used to receive */
/**
  * @}
  */

/** @defgroup CAN_flags CAN Flags
  * @{
  */
/* If the flag is 0x3XXXXXXX, it means that it can be used with CAN_GetFlagStatus()
   and CAN_ClearFlag() functions. */
/* If the flag is 0x1XXXXXXX, it means that it can only be used with
   CAN_GetFlagStatus() function.  */

/* Transmit Flags */
#define CAN_FLAG_RQCP0             ((uint32_t)0x00000500)  /*!< Request MailBox0 flag         */
#define CAN_FLAG_RQCP1             ((uint32_t)0x00000508)  /*!< Request MailBox1 flag         */
#define CAN_FLAG_RQCP2             ((uint32_t)0x00000510)  /*!< Request MailBox2 flag         */
#define CAN_FLAG_TXOK0             ((uint32_t)0x00000501)  /*!< Transmission OK MailBox0 flag */
#define CAN_FLAG_TXOK1             ((uint32_t)0x00000509)  /*!< Transmission OK MailBox1 flag */
#define CAN_FLAG_TXOK2             ((uint32_t)0x00000511)  /*!< Transmission OK MailBox2 flag */
#define CAN_FLAG_TME0              ((uint32_t)0x0000051A)  /*!< Transmit mailbox 0 empty flag */
#define CAN_FLAG_TME1              ((uint32_t)0x0000051B)  /*!< Transmit mailbox 0 empty flag */
#define CAN_FLAG_TME2              ((uint32_t)0x0000051C)  /*!< Transmit mailbox 0 empty flag */

/* Receive Flags */
#define CAN_FLAG_FF0               ((uint32_t)0x00000203)  /*!< FIFO 0 Full flag    */
#define CAN_FLAG_FOV0              ((uint32_t)0x00000204)  /*!< FIFO 0 Overrun flag */

#define CAN_FLAG_FF1               ((uint32_t)0x00000403)  /*!< FIFO 1 Full flag    */
#define CAN_FLAG_FOV1              ((uint32_t)0x00000404)  /*!< FIFO 1 Overrun flag */

/* Operating Mode Flags */
#define CAN_FLAG_WKU               ((uint32_t)0x00000103)  /*!< Wake up flag           */
#define CAN_FLAG_SLAK              ((uint32_t)0x00000101)  /*!< Sleep acknowledge flag */
#define CAN_FLAG_SLAKI             ((uint32_t)0x00000104)  /*!< Sleep acknowledge flag */
/* @note When SLAK interrupt is disabled (SLKIE=0), no polling on SLAKI is possible.
         In this case the SLAK bit can be polled.*/

/* Error Flags */
#define CAN_FLAG_EWG               ((uint32_t)0x00000300)  /*!< Error warning flag   */
#define CAN_FLAG_EPV               ((uint32_t)0x00000301)  /*!< Error passive flag   */
#define CAN_FLAG_BOF               ((uint32_t)0x00000302)  /*!< Bus-Off flag         */
/**
  * @}
  */

/** @defgroup CAN_Interrupts CAN Interrupts
  * @{
  */
#define CAN_IT_TME                  ((uint32_t)CAN_IER_TMEIE)   /*!< Transmit mailbox empty interrupt */

/* Receive Interrupts */
#define CAN_IT_FMP0                 ((uint32_t)CAN_IER_FMPIE0)  /*!< FIFO 0 message pending interrupt */
#define CAN_IT_FF0                  ((uint32_t)CAN_IER_FFIE0)   /*!< FIFO 0 full interrupt            */
#define CAN_IT_FOV0                 ((uint32_t)CAN_IER_FOVIE0)  /*!< FIFO 0 overrun interrupt         */
#define CAN_IT_FMP1                 ((uint32_t)CAN_IER_FMPIE1)  /*!< FIFO 1 message pending interrupt */
#define CAN_IT_FF1                  ((uint32_t)CAN_IER_FFIE1)   /*!< FIFO 1 full interrupt            */
#define CAN_IT_FOV1                 ((uint32_t)CAN_IER_FOVIE1)  /*!< FIFO 1 overrun interrupt         */

/* Operating Mode Interrupts */
#define CAN_IT_WKU                  ((uint32_t)CAN_IER_WKUIE)  /*!< Wake-up interrupt           */
#define CAN_IT_SLK                  ((uint32_t)CAN_IER_SLKIE)  /*!< Sleep acknowledge interrupt */

/* Error Interrupts */
#define CAN_IT_EWG                  ((uint32_t)CAN_IER_EWGIE) /*!< Error warning interrupt   */
#define CAN_IT_EPV                  ((uint32_t)CAN_IER_EPVIE) /*!< Error passive interrupt   */
#define CAN_IT_BOF                  ((uint32_t)CAN_IER_BOFIE) /*!< Bus-off interrupt         */
#define CAN_IT_LEC                  ((uint32_t)CAN_IER_LECIE) /*!< Last error code interrupt */
#define CAN_IT_ERR                  ((uint32_t)CAN_IER_ERRIE) /*!< Error Interrupt           */
/**
  * @}
  */

/** @defgroup CAN_Mailboxes_Definition CAN Mailboxes Definition
  * @{
  */
#define CAN_TXMAILBOX_0   ((uint8_t)0x00)
#define CAN_TXMAILBOX_1   ((uint8_t)0x01)
#define CAN_TXMAILBOX_2   ((uint8_t)0x02)
/**
  * @}
  */

/**
  * @}
  */

/* Exported macro ------------------------------------------------------------*/
/** @defgroup CAN_Exported_Macros CAN Exported Macros
  * @{
  */

/** @brief Reset CAN handle state
  * @param  __HANDLE__: specifies the CAN Handle.
  * @retval None
  */
#define __HAL_CAN_RESET_HANDLE_STATE(__HANDLE__) ((__HANDLE__)->State = HAL_CAN_STATE_RESET)

/**
  * @brief  Enable the specified CAN interrupts.
  * @param  __HANDLE__: CAN handle
  * @param  __INTERRUPT__: CAN Interrupt
  * @retval None
  */
#define __HAL_CAN_ENABLE_IT(__HANDLE__, __INTERRUPT__) (((__HANDLE__)->Instance->IER) |= (__INTERRUPT__))

/**
  * @brief  Disable the specified CAN interrupts.
  * @param  __HANDLE__: CAN handle
  * @param  __INTERRUPT__: CAN Interrupt
  * @retval None
  */
#define __HAL_CAN_DISABLE_IT(__HANDLE__, __INTERRUPT__) (((__HANDLE__)->Instance->IER) &= ~(__INTERRUPT__))

/**
  * @brief  Return the number of pending received messages.
  * @param  __HANDLE__: CAN handle
  * @param  __FIFONUMBER__: Receive FIFO number, CAN_FIFO0 or CAN_FIFO1.
  * @retval The number of pending message.
  */
#define __HAL_CAN_MSG_PENDING(__HANDLE__, __FIFONUMBER__) (((__FIFONUMBER__) == CAN_FIFO0)? \
((uint8_t)((__HANDLE__)->Instance->RF0R&(uint32_t)0x03)) : ((uint8_t)((__HANDLE__)->Instance->RF1R&(uint32_t)0x03)))

/** @brief  Check whether the specified CAN flag is set or not.
  * @param  __HANDLE__: CAN Handle
  * @param  __FLAG__: specifies the flag to check.
  *         This parameter can be one of the following values:
  *            @arg CAN_TSR_RQCP0: Request MailBox0 Flag
  *            @arg CAN_TSR_RQCP1: Request MailBox1 Flag
  *            @arg CAN_TSR_RQCP2: Request MailBox2 Flag
  *            @arg CAN_FLAG_TXOK0: Transmission OK MailBox0 Flag
  *            @arg CAN_FLAG_TXOK1: Transmission OK MailBox1 Flag
  *            @arg CAN_FLAG_TXOK2: Transmission OK MailBox2 Flag
  *            @arg CAN_FLAG_TME0: Transmit mailbox 0 empty Flag
  *            @arg CAN_FLAG_TME1: Transmit mailbox 1 empty Flag
  *            @arg CAN_FLAG_TME2: Transmit mailbox 2 empty Flag
  *            @arg CAN_FLAG_FMP0: FIFO 0 Message Pending Flag
  *            @arg CAN_FLAG_FF0: FIFO 0 Full Flag
  *            @arg CAN_FLAG_FOV0: FIFO 0 Overrun Flag
  *            @arg CAN_FLAG_FMP1: FIFO 1 Message Pending Flag
  *            @arg CAN_FLAG_FF1: FIFO 1 Full Flag
  *            @arg CAN_FLAG_FOV1: FIFO 1 Overrun Flag
  *            @arg CAN_FLAG_WKU: Wake up Flag
  *            @arg CAN_FLAG_SLAK: Sleep acknowledge Flag
  *            @arg CAN_FLAG_SLAKI: Sleep acknowledge Flag
  *            @arg CAN_FLAG_EWG: Error Warning Flag
  *            @arg CAN_FLAG_EPV: Error Passive Flag
  *            @arg CAN_FLAG_BOF: Bus-Off Flag
  * @retval The new state of __FLAG__ (TRUE or FALSE).
  */
#define __HAL_CAN_GET_FLAG(__HANDLE__, __FLAG__) \
((((__FLAG__) >> 8) == 5)? ((((__HANDLE__)->Instance->TSR) & (1 << ((__FLAG__) & CAN_FLAG_MASK))) == (1 << ((__FLAG__) & CAN_FLAG_MASK))): \
 (((__FLAG__) >> 8) == 2)? ((((__HANDLE__)->Instance->RF0R) & (1 << ((__FLAG__) & CAN_FLAG_MASK))) == (1 << ((__FLAG__) & CAN_FLAG_MASK))): \
 (((__FLAG__) >> 8) == 4)? ((((__HANDLE__)->Instance->RF1R) & (1 << ((__FLAG__) & CAN_FLAG_MASK))) == (1 << ((__FLAG__) & CAN_FLAG_MASK))): \
 (((__FLAG__) >> 8) == 1)? ((((__HANDLE__)->Instance->MSR) & (1 << ((__FLAG__) & CAN_FLAG_MASK))) == (1 << ((__FLAG__) & CAN_FLAG_MASK))): \
 ((((__HANDLE__)->Instance->ESR) & (1 << ((__FLAG__) & CAN_FLAG_MASK))) == (1 << ((__FLAG__) & CAN_FLAG_MASK))))

/** @brief  Clear the specified CAN pending flag.
  * @param  __HANDLE__: CAN Handle.
  * @param  __FLAG__: specifies the flag to check.
  *         This parameter can be one of the following values:
  *            @arg CAN_TSR_RQCP0: Request MailBox0 Flag
  *            @arg CAN_TSR_RQCP1: Request MailBox1 Flag
  *            @arg CAN_TSR_RQCP2: Request MailBox2 Flag
  *            @arg CAN_FLAG_TXOK0: Transmission OK MailBox0 Flag
  *            @arg CAN_FLAG_TXOK1: Transmission OK MailBox1 Flag
  *            @arg CAN_FLAG_TXOK2: Transmission OK MailBox2 Flag
  *            @arg CAN_FLAG_TME0: Transmit mailbox 0 empty Flag
  *            @arg CAN_FLAG_TME1: Transmit mailbox 1 empty Flag
  *            @arg CAN_FLAG_TME2: Transmit mailbox 2 empty Flag
  *            @arg CAN_FLAG_FMP0: FIFO 0 Message Pending Flag
  *            @arg CAN_FLAG_FF0: FIFO 0 Full Flag
  *            @arg CAN_FLAG_FOV0: FIFO 0 Overrun Flag
  *            @arg CAN_FLAG_FMP1: FIFO 1 Message Pending Flag
  *            @arg CAN_FLAG_FF1: FIFO 1 Full Flag
  *            @arg CAN_FLAG_FOV1: FIFO 1 Overrun Flag
  *            @arg CAN_FLAG_WKU: Wake up Flag
  *            @arg CAN_FLAG_SLAK: Sleep acknowledge Flag
  *            @arg CAN_FLAG_SLAKI: Sleep acknowledge Flag
  *            @arg CAN_FLAG_EWG: Error Warning Flag
  *            @arg CAN_FLAG_EPV: Error Passive Flag
  *            @arg CAN_FLAG_BOF: Bus-Off Flag
  * @retval The new state of __FLAG__ (TRUE or FALSE).
  */
#define __HAL_CAN_CLEAR_FLAG(__HANDLE__, __FLAG__) \
((((__FLAG__) >> 8) == 5)? (((__HANDLE__)->Instance->TSR) = ~((uint32_t)1 << ((__FLAG__) & CAN_FLAG_MASK))): \
 (((__FLAG__) >> 8) == 2)? (((__HANDLE__)->Instance->RF0R) = ~((uint32_t)1 << ((__FLAG__) & CAN_FLAG_MASK))): \
 (((__FLAG__) >> 8) == 4)? (((__HANDLE__)->Instance->RF1R) = ~((uint32_t)1 << ((__FLAG__) & CAN_FLAG_MASK))): \
 (((__FLAG__) >> 8) == 1)? (((__HANDLE__)->Instance->MSR) = ~((uint32_t)1 << ((__FLAG__) & CAN_FLAG_MASK))): \
 (((__HANDLE__)->Instance->ESR) = ~((uint32_t)1 << ((__FLAG__) & CAN_FLAG_MASK))))

/** @brief  Check if the specified CAN interrupt source is enabled or disabled.
  * @param  __HANDLE__: CAN Handle
  * @param  __INTERRUPT__: specifies the CAN interrupt source to check.
  *          This parameter can be one of the following values:
  *             @arg CAN_IT_TME: Transmit mailbox empty interrupt enable
  *             @arg CAN_IT_FMP0: FIFO0 message pending interrupt enable
  *             @arg CAN_IT_FMP1: FIFO1 message pending interrupt enable
  * @retval The new state of __IT__ (TRUE or FALSE).
  */
#define __HAL_CAN_GET_IT_SOURCE(__HANDLE__, __INTERRUPT__) ((((__HANDLE__)->Instance->IER & (__INTERRUPT__)) == (__INTERRUPT__)) ? SET : RESET)

/**
  * @brief  Check the transmission status of a CAN Frame.
  * @param  __HANDLE__: CAN Handle
  * @param  __TRANSMITMAILBOX__: the number of the mailbox that is used for transmission.
  * @retval The new status of transmission  (TRUE or FALSE).
  */
#define __HAL_CAN_TRANSMIT_STATUS(__HANDLE__, __TRANSMITMAILBOX__)\
(((__TRANSMITMAILBOX__) == CAN_TXMAILBOX_0)? ((((__HANDLE__)->Instance->TSR) & (CAN_TSR_RQCP0 | CAN_TSR_TXOK0 | CAN_TSR_TME0)) == (CAN_TSR_RQCP0 | CAN_TSR_TXOK0 | CAN_TSR_TME0)) :\
 ((__TRANSMITMAILBOX__) == CAN_TXMAILBOX_1)? ((((__HANDLE__)->Instance->TSR) & (CAN_TSR_RQCP1 | CAN_TSR_TXOK1 | CAN_TSR_TME1)) == (CAN_TSR_RQCP1 | CAN_TSR_TXOK1 | CAN_TSR_TME1)) :\
 ((((__HANDLE__)->Instance->TSR) & (CAN_TSR_RQCP2 | CAN_TSR_TXOK2 | CAN_TSR_TME2)) == (CAN_TSR_RQCP2 | CAN_TSR_TXOK2 | CAN_TSR_TME2)))

/**
  * @brief  Release the specified receive FIFO.
  * @param  __HANDLE__: CAN handle
  * @param  __FIFONUMBER__: Receive FIFO number, CAN_FIFO0 or CAN_FIFO1.
  * @retval None
  */
#define __HAL_CAN_FIFO_RELEASE(__HANDLE__, __FIFONUMBER__) (((__FIFONUMBER__) == CAN_FIFO0)? \
((__HANDLE__)->Instance->RF0R |= CAN_RF0R_RFOM0) : ((__HANDLE__)->Instance->RF1R |= CAN_RF1R_RFOM1))

/**
  * @brief  Cancel a transmit request.
  * @param  __HANDLE__: CAN Handle
  * @param  __TRANSMITMAILBOX__: the number of the mailbox that is used for transmission.
  * @retval None
  */
#define __HAL_CAN_CANCEL_TRANSMIT(__HANDLE__, __TRANSMITMAILBOX__)\
(((__TRANSMITMAILBOX__) == CAN_TXMAILBOX_0)? ((__HANDLE__)->Instance->TSR |= CAN_TSR_ABRQ0) :\
 ((__TRANSMITMAILBOX__) == CAN_TXMAILBOX_1)? ((__HANDLE__)->Instance->TSR |= CAN_TSR_ABRQ1) :\
 ((__HANDLE__)->Instance->TSR |= CAN_TSR_ABRQ2))

/**
  * @brief  Enable or disable the DBG Freeze for CAN.
  * @param  __HANDLE__: CAN Handle
  * @param  __NEWSTATE__: new state of the CAN peripheral.
  *          This parameter can be: ENABLE (CAN reception/transmission is frozen
  *          during debug. Reception FIFOs can still be accessed/controlled normally)
  *          or DISABLE (CAN is working during debug).
  * @retval None
  */
#define __HAL_CAN_DBG_FREEZE(__HANDLE__, __NEWSTATE__) (((__NEWSTATE__) == ENABLE)? \
((__HANDLE__)->Instance->MCR |= CAN_MCR_DBF) : ((__HANDLE__)->Instance->MCR &= ~CAN_MCR_DBF))

/**
  * @}
  */

/* Exported functions --------------------------------------------------------*/
/** @addtogroup CAN_Exported_Functions
  * @{
  */

/** @addtogroup CAN_Exported_Functions_Group1
  * @{
  */
/* Initialization/de-initialization functions ***********************************/
HAL_StatusTypeDef HAL_CAN_Init(CAN_HandleTypeDef* hcan);
HAL_StatusTypeDef HAL_CAN_ConfigFilter(CAN_HandleTypeDef* hcan, CAN_FilterConfTypeDef* sFilterConfig);
HAL_StatusTypeDef HAL_CAN_DeInit(CAN_HandleTypeDef* hcan);
void HAL_CAN_MspInit(CAN_HandleTypeDef* hcan);
void HAL_CAN_MspDeInit(CAN_HandleTypeDef* hcan);
/**
  * @}
  */

/** @addtogroup CAN_Exported_Functions_Group2
  * @{
  */
/* I/O operation functions ******************************************************/
HAL_StatusTypeDef HAL_CAN_Transmit(CAN_HandleTypeDef *hcan, uint32_t Timeout);
HAL_StatusTypeDef HAL_CAN_Transmit_IT(CAN_HandleTypeDef *hcan);
HAL_StatusTypeDef HAL_CAN_Receive(CAN_HandleTypeDef *hcan, uint8_t FIFONumber, uint32_t Timeout);
HAL_StatusTypeDef HAL_CAN_Receive_IT(CAN_HandleTypeDef *hcan, uint8_t FIFONumber);
HAL_StatusTypeDef HAL_CAN_Sleep(CAN_HandleTypeDef *hcan);
HAL_StatusTypeDef HAL_CAN_WakeUp(CAN_HandleTypeDef *hcan);
void HAL_CAN_IRQHandler(CAN_HandleTypeDef* hcan);
void HAL_CAN_TxCpltCallback(CAN_HandleTypeDef* hcan);
void HAL_CAN_RxCpltCallback(CAN_HandleTypeDef* hcan);
void HAL_CAN_ErrorCallback(CAN_HandleTypeDef *hcan);
/**
  * @}
  */

/** @addtogroup CAN_Exported_Functions_Group3
  * @{
  */
/* Peripheral State functions ***************************************************/
uint32_t HAL_CAN_GetError(CAN_HandleTypeDef *hcan);
HAL_CAN_StateTypeDef HAL_CAN_GetState(CAN_HandleTypeDef* hcan);
/**
  * @}
  */

/**
  * @}
  */

/* Private types -------------------------------------------------------------*/
/** @defgroup CAN_Private_Types CAN Private Types
  * @{
  */

/**
  * @}
  */

/* Private variables ---------------------------------------------------------*/
/** @defgroup CAN_Private_Variables CAN Private Variables
  * @{
  */

/**
  * @}
  */ 

/* Private constants ---------------------------------------------------------*/
/** @defgroup CAN_Private_Constants CAN Private Constants
  * @{
  */
#define CAN_TXSTATUS_NOMAILBOX      ((uint8_t)0x04)  /*!< CAN cell did not provide CAN_TxStatus_NoMailBox */
#define CAN_FLAG_MASK  ((uint32_t)0x000000FF)
/**
  * @}
  */

/* Private macros ------------------------------------------------------------*/
/** @defgroup CAN_Private_Macros CAN Private Macros
  * @{
  */
#define IS_CAN_MODE(MODE) (((MODE) == CAN_MODE_NORMAL) || \
                           ((MODE) == CAN_MODE_LOOPBACK)|| \
                           ((MODE) == CAN_MODE_SILENT) || \
                           ((MODE) == CAN_MODE_SILENT_LOOPBACK))
#define IS_CAN_SJW(SJW) (((SJW) == CAN_SJW_1TQ) || ((SJW) == CAN_SJW_2TQ)|| \
                         ((SJW) == CAN_SJW_3TQ) || ((SJW) == CAN_SJW_4TQ))
#define IS_CAN_BS1(BS1) ((BS1) <= CAN_BS1_16TQ)
#define IS_CAN_BS2(BS2) ((BS2) <= CAN_BS2_8TQ)
#define IS_CAN_PRESCALER(PRESCALER) (((PRESCALER) >= 1) && ((PRESCALER) <= 1024))
#define IS_CAN_FILTER_NUMBER(NUMBER) ((NUMBER) <= 27)
#define IS_CAN_FILTER_MODE(MODE) (((MODE) == CAN_FILTERMODE_IDMASK) || \
                                  ((MODE) == CAN_FILTERMODE_IDLIST))
#define IS_CAN_FILTER_SCALE(SCALE) (((SCALE) == CAN_FILTERSCALE_16BIT) || \
                                    ((SCALE) == CAN_FILTERSCALE_32BIT))
#define IS_CAN_FILTER_FIFO(FIFO) (((FIFO) == CAN_FILTER_FIFO0) || \
                                  ((FIFO) == CAN_FILTER_FIFO1))
#define IS_CAN_BANKNUMBER(BANKNUMBER) ((BANKNUMBER) <= 28)

#define IS_CAN_TRANSMITMAILBOX(TRANSMITMAILBOX) ((TRANSMITMAILBOX) <= ((uint8_t)0x02))
#define IS_CAN_STDID(STDID)   ((STDID) <= ((uint32_t)0x7FF))
#define IS_CAN_EXTID(EXTID)   ((EXTID) <= ((uint32_t)0x1FFFFFFF))
#define IS_CAN_DLC(DLC)       ((DLC) <= ((uint8_t)0x08))

#define IS_CAN_IDTYPE(IDTYPE)  (((IDTYPE) == CAN_ID_STD) || \
                                ((IDTYPE) == CAN_ID_EXT))
#define IS_CAN_RTR(RTR) (((RTR) == CAN_RTR_DATA) || ((RTR) == CAN_RTR_REMOTE))
#define IS_CAN_FIFO(FIFO) (((FIFO) == CAN_FIFO0) || ((FIFO) == CAN_FIFO1))

/**
  * @}
  */

/* Private functions ---------------------------------------------------------*/
/** @defgroup CAN_Private_Functions CAN Private Functions
  * @{
  */

/**
  * @}
  */

#endif /* STM32F405xx || STM32F415xx || STM32F407xx || STM32F417xx || STM32F427xx || STM32F437xx ||\
          STM32F429xx || STM32F439xx || STM32F446xx || STM32F469xx || STM32F479xx  */

/**
  * @}
  */

/**
  * @}
  */

#ifdef __cplusplus
}
#endif

#endif /* __STM32F4xx_CAN_H */


/************************ (C) COPYRIGHT STMicroelectronics *****END OF FILE****/
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/* ----------------------------------------------------------------------
* Copyright (C) 2010-2015 ARM Limited. All rights reserved.
*
* $Date:        19. March 2015
* $Revision: 	V.1.4.5
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_math.h
*
* Description:	Public header file for CMSIS DSP Library
*
* Target Processor: Cortex-M7/Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*   - Redistributions of source code must retain the above copyright
*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
 * -------------------------------------------------------------------- */

/**
   \mainpage CMSIS DSP Software Library
   *
   * Introduction
   * ------------
   *
   * This user manual describes the CMSIS DSP software library,
   * a suite of common signal processing functions for use on Cortex-M processor based devices.
   *
   * The library is divided into a number of functions each covering a specific category:
   * - Basic math functions
   * - Fast math functions
   * - Complex math functions
   * - Filters
   * - Matrix functions
   * - Transforms
   * - Motor control functions
   * - Statistical functions
   * - Support functions
   * - Interpolation functions
   *
   * The library has separate functions for operating on 8-bit integers, 16-bit integers,
   * 32-bit integer and 32-bit floating-point values.
   *
   * Using the Library
   * ------------
   *
   * The library installer contains prebuilt versions of the libraries in the <code>Lib</code> folder.
   * - arm_cortexM7lfdp_math.lib (Little endian and Double Precision Floating Point Unit on Cortex-M7)
   * - arm_cortexM7bfdp_math.lib (Big endian and Double Precision Floating Point Unit on Cortex-M7)
   * - arm_cortexM7lfsp_math.lib (Little endian and Single Precision Floating Point Unit on Cortex-M7)
   * - arm_cortexM7bfsp_math.lib (Big endian and Single Precision Floating Point Unit on Cortex-M7)
   * - arm_cortexM7l_math.lib (Little endian on Cortex-M7)
   * - arm_cortexM7b_math.lib (Big endian on Cortex-M7)
   * - arm_cortexM4lf_math.lib (Little endian and Floating Point Unit on Cortex-M4)
   * - arm_cortexM4bf_math.lib (Big endian and Floating Point Unit on Cortex-M4)
   * - arm_cortexM4l_math.lib (Little endian on Cortex-M4)
   * - arm_cortexM4b_math.lib (Big endian on Cortex-M4)
   * - arm_cortexM3l_math.lib (Little endian on Cortex-M3)
   * - arm_cortexM3b_math.lib (Big endian on Cortex-M3)
   * - arm_cortexM0l_math.lib (Little endian on Cortex-M0 / CortexM0+)
   * - arm_cortexM0b_math.lib (Big endian on Cortex-M0 / CortexM0+)
   *
   * The library functions are declared in the public file <code>arm_math.h</code> which is placed in the <code>Include</code> folder.
   * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single
   * public header file <code> arm_math.h</code> for Cortex-M7/M4/M3/M0/M0+ with little endian and big endian. Same header file will be used for floating point unit(FPU) variants.
   * Define the appropriate pre processor MACRO ARM_MATH_CM7 or ARM_MATH_CM4 or  ARM_MATH_CM3 or
   * ARM_MATH_CM0 or ARM_MATH_CM0PLUS depending on the target processor in the application.
   *
   * Examples
   * --------
   *
   * The library ships with a number of examples which demonstrate how to use the library functions.
   *
   * Toolchain Support
   * ------------
   *
   * The library has been developed and tested with MDK-ARM version 5.14.0.0
   * The library is being tested in GCC and IAR toolchains and updates on this activity will be made available shortly.
   *
   * Building the Library
   * ------------
   *
   * The library installer contains a project file to re build libraries on MDK-ARM Tool chain in the <code>CMSIS\\DSP_Lib\\Source\\ARM</code> folder.
   * - arm_cortexM_math.uvprojx
   *
   *
   * The libraries can be built by opening the arm_cortexM_math.uvprojx project in MDK-ARM, selecting a specific target, and defining the optional pre processor MACROs detailed above.
   *
   * Pre-processor Macros
   * ------------
   *
   * Each library project have differant pre-processor macros.
   *
   * - UNALIGNED_SUPPORT_DISABLE:
   *
   * Define macro UNALIGNED_SUPPORT_DISABLE, If the silicon does not support unaligned memory access
   *
   * - ARM_MATH_BIG_ENDIAN:
   *
   * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets.
   *
   * - ARM_MATH_MATRIX_CHECK:
   *
   * Define macro ARM_MATH_MATRIX_CHECK for checking on the input and output sizes of matrices
   *
   * - ARM_MATH_ROUNDING:
   *
   * Define macro ARM_MATH_ROUNDING for rounding on support functions
   *
   * - ARM_MATH_CMx:
   *
   * Define macro ARM_MATH_CM4 for building the library on Cortex-M4 target, ARM_MATH_CM3 for building library on Cortex-M3 target
   * and ARM_MATH_CM0 for building library on Cortex-M0 target, ARM_MATH_CM0PLUS for building library on Cortex-M0+ target, and
   * ARM_MATH_CM7 for building the library on cortex-M7.
   *
   * - __FPU_PRESENT:
   *
   * Initialize macro __FPU_PRESENT = 1 when building on FPU supported Targets. Enable this macro for M4bf and M4lf libraries
   *
   * <hr>
   * CMSIS-DSP in ARM::CMSIS Pack
   * -----------------------------
   * 
   * The following files relevant to CMSIS-DSP are present in the <b>ARM::CMSIS</b> Pack directories:
   * |File/Folder                   |Content                                                                 |
   * |------------------------------|------------------------------------------------------------------------|
   * |\b CMSIS\\Documentation\\DSP  | This documentation                                                     |
   * |\b CMSIS\\DSP_Lib             | Software license agreement (license.txt)                               |
   * |\b CMSIS\\DSP_Lib\\Examples   | Example projects demonstrating the usage of the library functions      |
   * |\b CMSIS\\DSP_Lib\\Source     | Source files for rebuilding the library                                |
   * 
   * <hr>
   * Revision History of CMSIS-DSP
   * ------------
   * Please refer to \ref ChangeLog_pg.
   *
   * Copyright Notice
   * ------------
   *
   * Copyright (C) 2010-2015 ARM Limited. All rights reserved.
   */


/**
 * @defgroup groupMath Basic Math Functions
 */

/**
 * @defgroup groupFastMath Fast Math Functions
 * This set of functions provides a fast approximation to sine, cosine, and square root.
 * As compared to most of the other functions in the CMSIS math library, the fast math functions
 * operate on individual values and not arrays.
 * There are separate functions for Q15, Q31, and floating-point data.
 *
 */

/**
 * @defgroup groupCmplxMath Complex Math Functions
 * This set of functions operates on complex data vectors.
 * The data in the complex arrays is stored in an interleaved fashion
 * (real, imag, real, imag, ...).
 * In the API functions, the number of samples in a complex array refers
 * to the number of complex values; the array contains twice this number of
 * real values.
 */

/**
 * @defgroup groupFilters Filtering Functions
 */

/**
 * @defgroup groupMatrix Matrix Functions
 *
 * This set of functions provides basic matrix math operations.
 * The functions operate on matrix data structures.  For example,
 * the type
 * definition for the floating-point matrix structure is shown
 * below:
 * <pre>
 *     typedef struct
 *     {
 *       uint16_t numRows;     // number of rows of the matrix.
 *       uint16_t numCols;     // number of columns of the matrix.
 *       float32_t *pData;     // points to the data of the matrix.
 *     } arm_matrix_instance_f32;
 * </pre>
 * There are similar definitions for Q15 and Q31 data types.
 *
 * The structure specifies the size of the matrix and then points to
 * an array of data.  The array is of size <code>numRows X numCols</code>
 * and the values are arranged in row order.  That is, the
 * matrix element (i, j) is stored at:
 * <pre>
 *     pData[i*numCols + j]
 * </pre>
 *
 * \par Init Functions
 * There is an associated initialization function for each type of matrix
 * data structure.
 * The initialization function sets the values of the internal structure fields.
 * Refer to the function <code>arm_mat_init_f32()</code>, <code>arm_mat_init_q31()</code>
 * and <code>arm_mat_init_q15()</code> for floating-point, Q31 and Q15 types,  respectively.
 *
 * \par
 * Use of the initialization function is optional. However, if initialization function is used
 * then the instance structure cannot be placed into a const data section.
 * To place the instance structure in a const data
 * section, manually initialize the data structure.  For example:
 * <pre>
 * <code>arm_matrix_instance_f32 S = {nRows, nColumns, pData};</code>
 * <code>arm_matrix_instance_q31 S = {nRows, nColumns, pData};</code>
 * <code>arm_matrix_instance_q15 S = {nRows, nColumns, pData};</code>
 * </pre>
 * where <code>nRows</code> specifies the number of rows, <code>nColumns</code>
 * specifies the number of columns, and <code>pData</code> points to the
 * data array.
 *
 * \par Size Checking
 * By default all of the matrix functions perform size checking on the input and
 * output matrices.  For example, the matrix addition function verifies that the
 * two input matrices and the output matrix all have the same number of rows and
 * columns.  If the size check fails the functions return:
 * <pre>
 *     ARM_MATH_SIZE_MISMATCH
 * </pre>
 * Otherwise the functions return
 * <pre>
 *     ARM_MATH_SUCCESS
 * </pre>
 * There is some overhead associated with this matrix size checking.
 * The matrix size checking is enabled via the \#define
 * <pre>
 *     ARM_MATH_MATRIX_CHECK
 * </pre>
 * within the library project settings.  By default this macro is defined
 * and size checking is enabled.  By changing the project settings and
 * undefining this macro size checking is eliminated and the functions
 * run a bit faster.  With size checking disabled the functions always
 * return <code>ARM_MATH_SUCCESS</code>.
 */

/**
 * @defgroup groupTransforms Transform Functions
 */

/**
 * @defgroup groupController Controller Functions
 */

/**
 * @defgroup groupStats Statistics Functions
 */
/**
 * @defgroup groupSupport Support Functions
 */

/**
 * @defgroup groupInterpolation Interpolation Functions
 * These functions perform 1- and 2-dimensional interpolation of data.
 * Linear interpolation is used for 1-dimensional data and
 * bilinear interpolation is used for 2-dimensional data.
 */

/**
 * @defgroup groupExamples Examples
 */
#ifndef _ARM_MATH_H
#define _ARM_MATH_H

#define __CMSIS_GENERIC         /* disable NVIC and Systick functions */

#if defined(ARM_MATH_CM7)
  #include "core_cm7.h"
#elif defined (ARM_MATH_CM4)
  #include "core_cm4.h"
#elif defined (ARM_MATH_CM3)
  #include "core_cm3.h"
#elif defined (ARM_MATH_CM0)
  #include "core_cm0.h"
#define ARM_MATH_CM0_FAMILY
  #elif defined (ARM_MATH_CM0PLUS)
#include "core_cm0plus.h"
  #define ARM_MATH_CM0_FAMILY
#else
  #error "Define according the used Cortex core ARM_MATH_CM7, ARM_MATH_CM4, ARM_MATH_CM3, ARM_MATH_CM0PLUS or ARM_MATH_CM0"
#endif

#undef  __CMSIS_GENERIC         /* enable NVIC and Systick functions */
#include "string.h"
#include "math.h"
#ifdef	__cplusplus
extern "C"
{
#endif


  /**
   * @brief Macros required for reciprocal calculation in Normalized LMS
   */

#define DELTA_Q31 			(0x100)
#define DELTA_Q15 			0x5
#define INDEX_MASK 			0x0000003F
#ifndef PI
#define PI					3.14159265358979f
#endif

  /**
   * @brief Macros required for SINE and COSINE Fast math approximations
   */

#define FAST_MATH_TABLE_SIZE  512
#define FAST_MATH_Q31_SHIFT   (32 - 10)
#define FAST_MATH_Q15_SHIFT   (16 - 10)
#define CONTROLLER_Q31_SHIFT  (32 - 9)
#define TABLE_SIZE  256
#define TABLE_SPACING_Q31	   0x400000
#define TABLE_SPACING_Q15	   0x80

  /**
   * @brief Macros required for SINE and COSINE Controller functions
   */
  /* 1.31(q31) Fixed value of 2/360 */
  /* -1 to +1 is divided into 360 values so total spacing is (2/360) */
#define INPUT_SPACING			0xB60B61

  /**
   * @brief Macro for Unaligned Support
   */
#ifndef UNALIGNED_SUPPORT_DISABLE
    #define ALIGN4
#else
  #if defined  (__GNUC__)
    #define ALIGN4 __attribute__((aligned(4)))
  #else
    #define ALIGN4 __align(4)
  #endif
#endif	/*	#ifndef UNALIGNED_SUPPORT_DISABLE	*/

  /**
   * @brief Error status returned by some functions in the library.
   */

  typedef enum
  {
    ARM_MATH_SUCCESS = 0,                /**< No error */
    ARM_MATH_ARGUMENT_ERROR = -1,        /**< One or more arguments are incorrect */
    ARM_MATH_LENGTH_ERROR = -2,          /**< Length of data buffer is incorrect */
    ARM_MATH_SIZE_MISMATCH = -3,         /**< Size of matrices is not compatible with the operation. */
    ARM_MATH_NANINF = -4,                /**< Not-a-number (NaN) or infinity is generated */
    ARM_MATH_SINGULAR = -5,              /**< Generated by matrix inversion if the input matrix is singular and cannot be inverted. */
    ARM_MATH_TEST_FAILURE = -6           /**< Test Failed  */
  } arm_status;

  /**
   * @brief 8-bit fractional data type in 1.7 format.
   */
  typedef int8_t q7_t;

  /**
   * @brief 16-bit fractional data type in 1.15 format.
   */
  typedef int16_t q15_t;

  /**
   * @brief 32-bit fractional data type in 1.31 format.
   */
  typedef int32_t q31_t;

  /**
   * @brief 64-bit fractional data type in 1.63 format.
   */
  typedef int64_t q63_t;

  /**
   * @brief 32-bit floating-point type definition.
   */
  typedef float float32_t;

  /**
   * @brief 64-bit floating-point type definition.
   */
  typedef double float64_t;

  /**
   * @brief definition to read/write two 16 bit values.
   */
#if defined __CC_ARM
  #define __SIMD32_TYPE int32_t __packed
  #define CMSIS_UNUSED __attribute__((unused))
#elif defined __ICCARM__
  #define __SIMD32_TYPE int32_t __packed
  #define CMSIS_UNUSED
#elif defined __GNUC__
  #define __SIMD32_TYPE int32_t
  #define CMSIS_UNUSED __attribute__((unused))
#elif defined __CSMC__			/* Cosmic */
  #define __SIMD32_TYPE int32_t
  #define CMSIS_UNUSED
#elif defined __TASKING__
  #define __SIMD32_TYPE __unaligned int32_t
  #define CMSIS_UNUSED
#else
  #error Unknown compiler
#endif

#define __SIMD32(addr)  (*(__SIMD32_TYPE **) & (addr))
#define __SIMD32_CONST(addr)  ((__SIMD32_TYPE *)(addr))

#define _SIMD32_OFFSET(addr)  (*(__SIMD32_TYPE *)  (addr))

#define __SIMD64(addr)  (*(int64_t **) & (addr))

#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)
  /**
   * @brief definition to pack two 16 bit values.
   */
#define __PKHBT(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0x0000FFFF) | \
                                         (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
#define __PKHTB(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0xFFFF0000) | \
                                         (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF)  )

#endif


   /**
   * @brief definition to pack four 8 bit values.
   */
#ifndef ARM_MATH_BIG_ENDIAN

#define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) <<  0) & (int32_t)0x000000FF) |	\
                                (((int32_t)(v1) <<  8) & (int32_t)0x0000FF00) |	\
							    (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) |	\
							    (((int32_t)(v3) << 24) & (int32_t)0xFF000000)  )
#else

#define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) <<  0) & (int32_t)0x000000FF) |	\
                                (((int32_t)(v2) <<  8) & (int32_t)0x0000FF00) |	\
							    (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) |	\
							    (((int32_t)(v0) << 24) & (int32_t)0xFF000000)  )

#endif


  /**
   * @brief Clips Q63 to Q31 values.
   */
  static __INLINE q31_t clip_q63_to_q31(
  q63_t x)
  {
    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
      ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x;
  }

  /**
   * @brief Clips Q63 to Q15 values.
   */
  static __INLINE q15_t clip_q63_to_q15(
  q63_t x)
  {
    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
      ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15);
  }

  /**
   * @brief Clips Q31 to Q7 values.
   */
  static __INLINE q7_t clip_q31_to_q7(
  q31_t x)
  {
    return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ?
      ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x;
  }

  /**
   * @brief Clips Q31 to Q15 values.
   */
  static __INLINE q15_t clip_q31_to_q15(
  q31_t x)
  {
    return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ?
      ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x;
  }

  /**
   * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format.
   */

  static __INLINE q63_t mult32x64(
  q63_t x,
  q31_t y)
  {
    return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
            (((q63_t) (x >> 32) * y)));
  }


//#if defined (ARM_MATH_CM0_FAMILY) && defined ( __CC_ARM   )
//#define __CLZ __clz
//#endif

//note: function can be removed when all toolchain support __CLZ for Cortex-M0
#if defined (ARM_MATH_CM0_FAMILY) && ((defined (__ICCARM__))  )

  static __INLINE uint32_t __CLZ(
  q31_t data);


  static __INLINE uint32_t __CLZ(
  q31_t data)
  {
    uint32_t count = 0;
    uint32_t mask = 0x80000000;

    while((data & mask) == 0)
    {
      count += 1u;
      mask = mask >> 1u;
    }

    return (count);

  }

#endif

  /**
   * @brief Function to Calculates 1/in (reciprocal) value of Q31 Data type.
   */

  static __INLINE uint32_t arm_recip_q31(
  q31_t in,
  q31_t * dst,
  q31_t * pRecipTable)
  {

    uint32_t out, tempVal;
    uint32_t index, i;
    uint32_t signBits;

    if(in > 0)
    {
      signBits = __CLZ(in) - 1;
    }
    else
    {
      signBits = __CLZ(-in) - 1;
    }

    /* Convert input sample to 1.31 format */
    in = in << signBits;

    /* calculation of index for initial approximated Val */
    index = (uint32_t) (in >> 24u);
    index = (index & INDEX_MASK);

    /* 1.31 with exp 1 */
    out = pRecipTable[index];

    /* calculation of reciprocal value */
    /* running approximation for two iterations */
    for (i = 0u; i < 2u; i++)
    {
      tempVal = (q31_t) (((q63_t) in * out) >> 31u);
      tempVal = 0x7FFFFFFF - tempVal;
      /*      1.31 with exp 1 */
      //out = (q31_t) (((q63_t) out * tempVal) >> 30u);
      out = (q31_t) clip_q63_to_q31(((q63_t) out * tempVal) >> 30u);
    }

    /* write output */
    *dst = out;

    /* return num of signbits of out = 1/in value */
    return (signBits + 1u);

  }

  /**
   * @brief Function to Calculates 1/in (reciprocal) value of Q15 Data type.
   */
  static __INLINE uint32_t arm_recip_q15(
  q15_t in,
  q15_t * dst,
  q15_t * pRecipTable)
  {

    uint32_t out = 0, tempVal = 0;
    uint32_t index = 0, i = 0;
    uint32_t signBits = 0;

    if(in > 0)
    {
      signBits = __CLZ(in) - 17;
    }
    else
    {
      signBits = __CLZ(-in) - 17;
    }

    /* Convert input sample to 1.15 format */
    in = in << signBits;

    /* calculation of index for initial approximated Val */
    index = in >> 8;
    index = (index & INDEX_MASK);

    /*      1.15 with exp 1  */
    out = pRecipTable[index];

    /* calculation of reciprocal value */
    /* running approximation for two iterations */
    for (i = 0; i < 2; i++)
    {
      tempVal = (q15_t) (((q31_t) in * out) >> 15);
      tempVal = 0x7FFF - tempVal;
      /*      1.15 with exp 1 */
      out = (q15_t) (((q31_t) out * tempVal) >> 14);
    }

    /* write output */
    *dst = out;

    /* return num of signbits of out = 1/in value */
    return (signBits + 1);

  }


  /*
   * @brief C custom defined intrinisic function for only M0 processors
   */
#if defined(ARM_MATH_CM0_FAMILY)

  static __INLINE q31_t __SSAT(
  q31_t x,
  uint32_t y)
  {
    int32_t posMax, negMin;
    uint32_t i;

    posMax = 1;
    for (i = 0; i < (y - 1); i++)
    {
      posMax = posMax * 2;
    }

    if(x > 0)
    {
      posMax = (posMax - 1);

      if(x > posMax)
      {
        x = posMax;
      }
    }
    else
    {
      negMin = -posMax;

      if(x < negMin)
      {
        x = negMin;
      }
    }
    return (x);


  }

#endif /* end of ARM_MATH_CM0_FAMILY */



  /*
   * @brief C custom defined intrinsic function for M3 and M0 processors
   */
#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)

  /*
   * @brief C custom defined QADD8 for M3 and M0 processors
   */
  static __INLINE q31_t __QADD8(
  q31_t x,
  q31_t y)
  {

    q31_t sum;
    q7_t r, s, t, u;

    r = (q7_t) x;
    s = (q7_t) y;

    r = __SSAT((q31_t) (r + s), 8);
    s = __SSAT(((q31_t) (((x << 16) >> 24) + ((y << 16) >> 24))), 8);
    t = __SSAT(((q31_t) (((x << 8) >> 24) + ((y << 8) >> 24))), 8);
    u = __SSAT(((q31_t) ((x >> 24) + (y >> 24))), 8);

    sum =
      (((q31_t) u << 24) & 0xFF000000) | (((q31_t) t << 16) & 0x00FF0000) |
      (((q31_t) s << 8) & 0x0000FF00) | (r & 0x000000FF);

    return sum;

  }

  /*
   * @brief C custom defined QSUB8 for M3 and M0 processors
   */
  static __INLINE q31_t __QSUB8(
  q31_t x,
  q31_t y)
  {

    q31_t sum;
    q31_t r, s, t, u;

    r = (q7_t) x;
    s = (q7_t) y;

    r = __SSAT((r - s), 8);
    s = __SSAT(((q31_t) (((x << 16) >> 24) - ((y << 16) >> 24))), 8) << 8;
    t = __SSAT(((q31_t) (((x << 8) >> 24) - ((y << 8) >> 24))), 8) << 16;
    u = __SSAT(((q31_t) ((x >> 24) - (y >> 24))), 8) << 24;

    sum =
      (u & 0xFF000000) | (t & 0x00FF0000) | (s & 0x0000FF00) | (r &
                                                                0x000000FF);

    return sum;
  }

  /*
   * @brief C custom defined QADD16 for M3 and M0 processors
   */

  /*
   * @brief C custom defined QADD16 for M3 and M0 processors
   */
  static __INLINE q31_t __QADD16(
  q31_t x,
  q31_t y)
  {

    q31_t sum;
    q31_t r, s;

    r = (q15_t) x;
    s = (q15_t) y;

    r = __SSAT(r + s, 16);
    s = __SSAT(((q31_t) ((x >> 16) + (y >> 16))), 16) << 16;

    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

    return sum;

  }

  /*
   * @brief C custom defined SHADD16 for M3 and M0 processors
   */
  static __INLINE q31_t __SHADD16(
  q31_t x,
  q31_t y)
  {

    q31_t sum;
    q31_t r, s;

    r = (q15_t) x;
    s = (q15_t) y;

    r = ((r >> 1) + (s >> 1));
    s = ((q31_t) ((x >> 17) + (y >> 17))) << 16;

    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

    return sum;

  }

  /*
   * @brief C custom defined QSUB16 for M3 and M0 processors
   */
  static __INLINE q31_t __QSUB16(
  q31_t x,
  q31_t y)
  {

    q31_t sum;
    q31_t r, s;

    r = (q15_t) x;
    s = (q15_t) y;

    r = __SSAT(r - s, 16);
    s = __SSAT(((q31_t) ((x >> 16) - (y >> 16))), 16) << 16;

    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

    return sum;
  }

  /*
   * @brief C custom defined SHSUB16 for M3 and M0 processors
   */
  static __INLINE q31_t __SHSUB16(
  q31_t x,
  q31_t y)
  {

    q31_t diff;
    q31_t r, s;

    r = (q15_t) x;
    s = (q15_t) y;

    r = ((r >> 1) - (s >> 1));
    s = (((x >> 17) - (y >> 17)) << 16);

    diff = (s & 0xFFFF0000) | (r & 0x0000FFFF);

    return diff;
  }

  /*
   * @brief C custom defined QASX for M3 and M0 processors
   */
  static __INLINE q31_t __QASX(
  q31_t x,
  q31_t y)
  {

    q31_t sum = 0;

    sum =
      ((sum +
        clip_q31_to_q15((q31_t) ((q15_t) (x >> 16) + (q15_t) y))) << 16) +
      clip_q31_to_q15((q31_t) ((q15_t) x - (q15_t) (y >> 16)));

    return sum;
  }

  /*
   * @brief C custom defined SHASX for M3 and M0 processors
   */
  static __INLINE q31_t __SHASX(
  q31_t x,
  q31_t y)
  {

    q31_t sum;
    q31_t r, s;

    r = (q15_t) x;
    s = (q15_t) y;

    r = ((r >> 1) - (y >> 17));
    s = (((x >> 17) + (s >> 1)) << 16);

    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

    return sum;
  }


  /*
   * @brief C custom defined QSAX for M3 and M0 processors
   */
  static __INLINE q31_t __QSAX(
  q31_t x,
  q31_t y)
  {

    q31_t sum = 0;

    sum =
      ((sum +
        clip_q31_to_q15((q31_t) ((q15_t) (x >> 16) - (q15_t) y))) << 16) +
      clip_q31_to_q15((q31_t) ((q15_t) x + (q15_t) (y >> 16)));

    return sum;
  }

  /*
   * @brief C custom defined SHSAX for M3 and M0 processors
   */
  static __INLINE q31_t __SHSAX(
  q31_t x,
  q31_t y)
  {

    q31_t sum;
    q31_t r, s;

    r = (q15_t) x;
    s = (q15_t) y;

    r = ((r >> 1) + (y >> 17));
    s = (((x >> 17) - (s >> 1)) << 16);

    sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);

    return sum;
  }

  /*
   * @brief C custom defined SMUSDX for M3 and M0 processors
   */
  static __INLINE q31_t __SMUSDX(
  q31_t x,
  q31_t y)
  {

    return ((q31_t) (((q15_t) x * (q15_t) (y >> 16)) -
                     ((q15_t) (x >> 16) * (q15_t) y)));
  }

  /*
   * @brief C custom defined SMUADX for M3 and M0 processors
   */
  static __INLINE q31_t __SMUADX(
  q31_t x,
  q31_t y)
  {

    return ((q31_t) (((q15_t) x * (q15_t) (y >> 16)) +
                     ((q15_t) (x >> 16) * (q15_t) y)));
  }

  /*
   * @brief C custom defined QADD for M3 and M0 processors
   */
  static __INLINE q31_t __QADD(
  q31_t x,
  q31_t y)
  {
    return clip_q63_to_q31((q63_t) x + y);
  }

  /*
   * @brief C custom defined QSUB for M3 and M0 processors
   */
  static __INLINE q31_t __QSUB(
  q31_t x,
  q31_t y)
  {
    return clip_q63_to_q31((q63_t) x - y);
  }

  /*
   * @brief C custom defined SMLAD for M3 and M0 processors
   */
  static __INLINE q31_t __SMLAD(
  q31_t x,
  q31_t y,
  q31_t sum)
  {

    return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) +
            ((q15_t) x * (q15_t) y));
  }

  /*
   * @brief C custom defined SMLADX for M3 and M0 processors
   */
  static __INLINE q31_t __SMLADX(
  q31_t x,
  q31_t y,
  q31_t sum)
  {

    return (sum + ((q15_t) (x >> 16) * (q15_t) (y)) +
            ((q15_t) x * (q15_t) (y >> 16)));
  }

  /*
   * @brief C custom defined SMLSDX for M3 and M0 processors
   */
  static __INLINE q31_t __SMLSDX(
  q31_t x,
  q31_t y,
  q31_t sum)
  {

    return (sum - ((q15_t) (x >> 16) * (q15_t) (y)) +
            ((q15_t) x * (q15_t) (y >> 16)));
  }

  /*
   * @brief C custom defined SMLALD for M3 and M0 processors
   */
  static __INLINE q63_t __SMLALD(
  q31_t x,
  q31_t y,
  q63_t sum)
  {

    return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) +
            ((q15_t) x * (q15_t) y));
  }

  /*
   * @brief C custom defined SMLALDX for M3 and M0 processors
   */
  static __INLINE q63_t __SMLALDX(
  q31_t x,
  q31_t y,
  q63_t sum)
  {

    return (sum + ((q15_t) (x >> 16) * (q15_t) y)) +
      ((q15_t) x * (q15_t) (y >> 16));
  }

  /*
   * @brief C custom defined SMUAD for M3 and M0 processors
   */
  static __INLINE q31_t __SMUAD(
  q31_t x,
  q31_t y)
  {

    return (((x >> 16) * (y >> 16)) +
            (((x << 16) >> 16) * ((y << 16) >> 16)));
  }

  /*
   * @brief C custom defined SMUSD for M3 and M0 processors
   */
  static __INLINE q31_t __SMUSD(
  q31_t x,
  q31_t y)
  {

    return (-((x >> 16) * (y >> 16)) +
            (((x << 16) >> 16) * ((y << 16) >> 16)));
  }


  /*
   * @brief C custom defined SXTB16 for M3 and M0 processors
   */
  static __INLINE q31_t __SXTB16(
  q31_t x)
  {

    return ((((x << 24) >> 24) & 0x0000FFFF) |
            (((x << 8) >> 8) & 0xFFFF0000));
  }


#endif /* defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY) */


  /**
   * @brief Instance structure for the Q7 FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;        /**< number of filter coefficients in the filter. */
    q7_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q7_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
  } arm_fir_instance_q7;

  /**
   * @brief Instance structure for the Q15 FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;         /**< number of filter coefficients in the filter. */
    q15_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q15_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
  } arm_fir_instance_q15;

  /**
   * @brief Instance structure for the Q31 FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;         /**< number of filter coefficients in the filter. */
    q31_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q31_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps. */
  } arm_fir_instance_q31;

  /**
   * @brief Instance structure for the floating-point FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;     /**< number of filter coefficients in the filter. */
    float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
  } arm_fir_instance_f32;


  /**
   * @brief Processing function for the Q7 FIR filter.
   * @param[in] *S points to an instance of the Q7 FIR filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */
  void arm_fir_q7(
  const arm_fir_instance_q7 * S,
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q7 FIR filter.
   * @param[in,out] *S points to an instance of the Q7 FIR structure.
   * @param[in] numTaps  Number of filter coefficients in the filter.
   * @param[in] *pCoeffs points to the filter coefficients.
   * @param[in] *pState points to the state buffer.
   * @param[in] blockSize number of samples that are processed.
   * @return none
   */
  void arm_fir_init_q7(
  arm_fir_instance_q7 * S,
  uint16_t numTaps,
  q7_t * pCoeffs,
  q7_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q15 FIR filter.
   * @param[in] *S points to an instance of the Q15 FIR structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */
  void arm_fir_q15(
  const arm_fir_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Processing function for the fast Q15 FIR filter for Cortex-M3 and Cortex-M4.
   * @param[in] *S points to an instance of the Q15 FIR filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */
  void arm_fir_fast_q15(
  const arm_fir_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the Q15 FIR filter.
   * @param[in,out] *S points to an instance of the Q15 FIR filter structure.
   * @param[in] numTaps  Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
   * @param[in] *pCoeffs points to the filter coefficients.
   * @param[in] *pState points to the state buffer.
   * @param[in] blockSize number of samples that are processed at a time.
   * @return The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_ARGUMENT_ERROR if
   * <code>numTaps</code> is not a supported value.
   */

  arm_status arm_fir_init_q15(
  arm_fir_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q31 FIR filter.
   * @param[in] *S points to an instance of the Q31 FIR filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */
  void arm_fir_q31(
  const arm_fir_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Processing function for the fast Q31 FIR filter for Cortex-M3 and Cortex-M4.
   * @param[in] *S points to an instance of the Q31 FIR structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */
  void arm_fir_fast_q31(
  const arm_fir_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the Q31 FIR filter.
   * @param[in,out] *S points to an instance of the Q31 FIR structure.
   * @param[in] 	numTaps  Number of filter coefficients in the filter.
   * @param[in] 	*pCoeffs points to the filter coefficients.
   * @param[in] 	*pState points to the state buffer.
   * @param[in] 	blockSize number of samples that are processed at a time.
   * @return 		none.
   */
  void arm_fir_init_q31(
  arm_fir_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  uint32_t blockSize);

  /**
   * @brief Processing function for the floating-point FIR filter.
   * @param[in] *S points to an instance of the floating-point FIR structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */
  void arm_fir_f32(
  const arm_fir_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the floating-point FIR filter.
   * @param[in,out] *S points to an instance of the floating-point FIR filter structure.
   * @param[in] 	numTaps  Number of filter coefficients in the filter.
   * @param[in] 	*pCoeffs points to the filter coefficients.
   * @param[in] 	*pState points to the state buffer.
   * @param[in] 	blockSize number of samples that are processed at a time.
   * @return    	none.
   */
  void arm_fir_init_f32(
  arm_fir_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  uint32_t blockSize);


  /**
   * @brief Instance structure for the Q15 Biquad cascade filter.
   */
  typedef struct
  {
    int8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    q15_t *pState;            /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
    q15_t *pCoeffs;           /**< Points to the array of coefficients.  The array is of length 5*numStages. */
    int8_t postShift;         /**< Additional shift, in bits, applied to each output sample. */

  } arm_biquad_casd_df1_inst_q15;


  /**
   * @brief Instance structure for the Q31 Biquad cascade filter.
   */
  typedef struct
  {
    uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    q31_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
    q31_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
    uint8_t postShift;       /**< Additional shift, in bits, applied to each output sample. */

  } arm_biquad_casd_df1_inst_q31;

  /**
   * @brief Instance structure for the floating-point Biquad cascade filter.
   */
  typedef struct
  {
    uint32_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    float32_t *pState;          /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
    float32_t *pCoeffs;         /**< Points to the array of coefficients.  The array is of length 5*numStages. */


  } arm_biquad_casd_df1_inst_f32;



  /**
   * @brief Processing function for the Q15 Biquad cascade filter.
   * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.
   * @param[in]  *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in]  blockSize number of samples to process.
   * @return     none.
   */

  void arm_biquad_cascade_df1_q15(
  const arm_biquad_casd_df1_inst_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the Q15 Biquad cascade filter.
   * @param[in,out] *S           points to an instance of the Q15 Biquad cascade structure.
   * @param[in]     numStages    number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @param[in]     postShift    Shift to be applied to the output. Varies according to the coefficients format
   * @return        none
   */

  void arm_biquad_cascade_df1_init_q15(
  arm_biquad_casd_df1_inst_q15 * S,
  uint8_t numStages,
  q15_t * pCoeffs,
  q15_t * pState,
  int8_t postShift);


  /**
   * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
   * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.
   * @param[in]  *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in]  blockSize number of samples to process.
   * @return     none.
   */

  void arm_biquad_cascade_df1_fast_q15(
  const arm_biquad_casd_df1_inst_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q31 Biquad cascade filter
   * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.
   * @param[in]  *pSrc      points to the block of input data.
   * @param[out] *pDst      points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   * @return     none.
   */

  void arm_biquad_cascade_df1_q31(
  const arm_biquad_casd_df1_inst_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
   * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.
   * @param[in]  *pSrc      points to the block of input data.
   * @param[out] *pDst      points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   * @return     none.
   */

  void arm_biquad_cascade_df1_fast_q31(
  const arm_biquad_casd_df1_inst_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the Q31 Biquad cascade filter.
   * @param[in,out] *S           points to an instance of the Q31 Biquad cascade structure.
   * @param[in]     numStages      number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @param[in]     postShift    Shift to be applied to the output. Varies according to the coefficients format
   * @return        none
   */

  void arm_biquad_cascade_df1_init_q31(
  arm_biquad_casd_df1_inst_q31 * S,
  uint8_t numStages,
  q31_t * pCoeffs,
  q31_t * pState,
  int8_t postShift);

  /**
   * @brief Processing function for the floating-point Biquad cascade filter.
   * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.
   * @param[in]  *pSrc      points to the block of input data.
   * @param[out] *pDst      points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   * @return     none.
   */

  void arm_biquad_cascade_df1_f32(
  const arm_biquad_casd_df1_inst_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the floating-point Biquad cascade filter.
   * @param[in,out] *S           points to an instance of the floating-point Biquad cascade structure.
   * @param[in]     numStages    number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @return        none
   */

  void arm_biquad_cascade_df1_init_f32(
  arm_biquad_casd_df1_inst_f32 * S,
  uint8_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);


  /**
   * @brief Instance structure for the floating-point matrix structure.
   */

  typedef struct
  {
    uint16_t numRows;     /**< number of rows of the matrix.     */
    uint16_t numCols;     /**< number of columns of the matrix.  */
    float32_t *pData;     /**< points to the data of the matrix. */
  } arm_matrix_instance_f32;


  /**
   * @brief Instance structure for the floating-point matrix structure.
   */

  typedef struct
  {
    uint16_t numRows;     /**< number of rows of the matrix.     */
    uint16_t numCols;     /**< number of columns of the matrix.  */
    float64_t *pData;     /**< points to the data of the matrix. */
  } arm_matrix_instance_f64;

  /**
   * @brief Instance structure for the Q15 matrix structure.
   */

  typedef struct
  {
    uint16_t numRows;     /**< number of rows of the matrix.     */
    uint16_t numCols;     /**< number of columns of the matrix.  */
    q15_t *pData;         /**< points to the data of the matrix. */

  } arm_matrix_instance_q15;

  /**
   * @brief Instance structure for the Q31 matrix structure.
   */

  typedef struct
  {
    uint16_t numRows;     /**< number of rows of the matrix.     */
    uint16_t numCols;     /**< number of columns of the matrix.  */
    q31_t *pData;         /**< points to the data of the matrix. */

  } arm_matrix_instance_q31;



  /**
   * @brief Floating-point matrix addition.
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_add_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);

  /**
   * @brief Q15 matrix addition.
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_add_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst);

  /**
   * @brief Q31 matrix addition.
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_add_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);

  /**
   * @brief Floating-point, complex, matrix multiplication.
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_cmplx_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);

  /**
   * @brief Q15, complex,  matrix multiplication.
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_cmplx_mult_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst,
  q15_t * pScratch);

  /**
   * @brief Q31, complex, matrix multiplication.
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_cmplx_mult_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Floating-point matrix transpose.
   * @param[in]  *pSrc points to the input matrix
   * @param[out] *pDst points to the output matrix
   * @return 	The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_trans_f32(
  const arm_matrix_instance_f32 * pSrc,
  arm_matrix_instance_f32 * pDst);


  /**
   * @brief Q15 matrix transpose.
   * @param[in]  *pSrc points to the input matrix
   * @param[out] *pDst points to the output matrix
   * @return 	The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_trans_q15(
  const arm_matrix_instance_q15 * pSrc,
  arm_matrix_instance_q15 * pDst);

  /**
   * @brief Q31 matrix transpose.
   * @param[in]  *pSrc points to the input matrix
   * @param[out] *pDst points to the output matrix
   * @return 	The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_trans_q31(
  const arm_matrix_instance_q31 * pSrc,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Floating-point matrix multiplication
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);

  /**
   * @brief Q15 matrix multiplication
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @param[in]		 *pState points to the array for storing intermediate results
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_mult_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst,
  q15_t * pState);

  /**
   * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
   * @param[in]       *pSrcA  points to the first input matrix structure
   * @param[in]       *pSrcB  points to the second input matrix structure
   * @param[out]      *pDst   points to output matrix structure
   * @param[in]		  *pState points to the array for storing intermediate results
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_mult_fast_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst,
  q15_t * pState);

  /**
   * @brief Q31 matrix multiplication
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_mult_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);

  /**
   * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_mult_fast_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Floating-point matrix subtraction
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_sub_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);

  /**
   * @brief Q15 matrix subtraction
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_sub_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst);

  /**
   * @brief Q31 matrix subtraction
   * @param[in]       *pSrcA points to the first input matrix structure
   * @param[in]       *pSrcB points to the second input matrix structure
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_sub_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);

  /**
   * @brief Floating-point matrix scaling.
   * @param[in]  *pSrc points to the input matrix
   * @param[in]  scale scale factor
   * @param[out] *pDst points to the output matrix
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_scale_f32(
  const arm_matrix_instance_f32 * pSrc,
  float32_t scale,
  arm_matrix_instance_f32 * pDst);

  /**
   * @brief Q15 matrix scaling.
   * @param[in]       *pSrc points to input matrix
   * @param[in]       scaleFract fractional portion of the scale factor
   * @param[in]       shift number of bits to shift the result by
   * @param[out]      *pDst points to output matrix
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_scale_q15(
  const arm_matrix_instance_q15 * pSrc,
  q15_t scaleFract,
  int32_t shift,
  arm_matrix_instance_q15 * pDst);

  /**
   * @brief Q31 matrix scaling.
   * @param[in]       *pSrc points to input matrix
   * @param[in]       scaleFract fractional portion of the scale factor
   * @param[in]       shift number of bits to shift the result by
   * @param[out]      *pDst points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */

  arm_status arm_mat_scale_q31(
  const arm_matrix_instance_q31 * pSrc,
  q31_t scaleFract,
  int32_t shift,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief  Q31 matrix initialization.
   * @param[in,out] *S             points to an instance of the floating-point matrix structure.
   * @param[in]     nRows          number of rows in the matrix.
   * @param[in]     nColumns       number of columns in the matrix.
   * @param[in]     *pData	       points to the matrix data array.
   * @return        none
   */

  void arm_mat_init_q31(
  arm_matrix_instance_q31 * S,
  uint16_t nRows,
  uint16_t nColumns,
  q31_t * pData);

  /**
   * @brief  Q15 matrix initialization.
   * @param[in,out] *S             points to an instance of the floating-point matrix structure.
   * @param[in]     nRows          number of rows in the matrix.
   * @param[in]     nColumns       number of columns in the matrix.
   * @param[in]     *pData	       points to the matrix data array.
   * @return        none
   */

  void arm_mat_init_q15(
  arm_matrix_instance_q15 * S,
  uint16_t nRows,
  uint16_t nColumns,
  q15_t * pData);

  /**
   * @brief  Floating-point matrix initialization.
   * @param[in,out] *S             points to an instance of the floating-point matrix structure.
   * @param[in]     nRows          number of rows in the matrix.
   * @param[in]     nColumns       number of columns in the matrix.
   * @param[in]     *pData	       points to the matrix data array.
   * @return        none
   */

  void arm_mat_init_f32(
  arm_matrix_instance_f32 * S,
  uint16_t nRows,
  uint16_t nColumns,
  float32_t * pData);



  /**
   * @brief Instance structure for the Q15 PID Control.
   */
  typedef struct
  {
    q15_t A0;    /**< The derived gain, A0 = Kp + Ki + Kd . */
#ifdef ARM_MATH_CM0_FAMILY
    q15_t A1;
    q15_t A2;
#else
    q31_t A1;           /**< The derived gain A1 = -Kp - 2Kd | Kd.*/
#endif
    q15_t state[3];       /**< The state array of length 3. */
    q15_t Kp;           /**< The proportional gain. */
    q15_t Ki;           /**< The integral gain. */
    q15_t Kd;           /**< The derivative gain. */
  } arm_pid_instance_q15;

  /**
   * @brief Instance structure for the Q31 PID Control.
   */
  typedef struct
  {
    q31_t A0;            /**< The derived gain, A0 = Kp + Ki + Kd . */
    q31_t A1;            /**< The derived gain, A1 = -Kp - 2Kd. */
    q31_t A2;            /**< The derived gain, A2 = Kd . */
    q31_t state[3];      /**< The state array of length 3. */
    q31_t Kp;            /**< The proportional gain. */
    q31_t Ki;            /**< The integral gain. */
    q31_t Kd;            /**< The derivative gain. */

  } arm_pid_instance_q31;

  /**
   * @brief Instance structure for the floating-point PID Control.
   */
  typedef struct
  {
    float32_t A0;          /**< The derived gain, A0 = Kp + Ki + Kd . */
    float32_t A1;          /**< The derived gain, A1 = -Kp - 2Kd. */
    float32_t A2;          /**< The derived gain, A2 = Kd . */
    float32_t state[3];    /**< The state array of length 3. */
    float32_t Kp;               /**< The proportional gain. */
    float32_t Ki;               /**< The integral gain. */
    float32_t Kd;               /**< The derivative gain. */
  } arm_pid_instance_f32;



  /**
   * @brief  Initialization function for the floating-point PID Control.
   * @param[in,out] *S      points to an instance of the PID structure.
   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   * @return none.
   */
  void arm_pid_init_f32(
  arm_pid_instance_f32 * S,
  int32_t resetStateFlag);

  /**
   * @brief  Reset function for the floating-point PID Control.
   * @param[in,out] *S is an instance of the floating-point PID Control structure
   * @return none
   */
  void arm_pid_reset_f32(
  arm_pid_instance_f32 * S);


  /**
   * @brief  Initialization function for the Q31 PID Control.
   * @param[in,out] *S points to an instance of the Q15 PID structure.
   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   * @return none.
   */
  void arm_pid_init_q31(
  arm_pid_instance_q31 * S,
  int32_t resetStateFlag);


  /**
   * @brief  Reset function for the Q31 PID Control.
   * @param[in,out] *S points to an instance of the Q31 PID Control structure
   * @return none
   */

  void arm_pid_reset_q31(
  arm_pid_instance_q31 * S);

  /**
   * @brief  Initialization function for the Q15 PID Control.
   * @param[in,out] *S points to an instance of the Q15 PID structure.
   * @param[in] resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   * @return none.
   */
  void arm_pid_init_q15(
  arm_pid_instance_q15 * S,
  int32_t resetStateFlag);

  /**
   * @brief  Reset function for the Q15 PID Control.
   * @param[in,out] *S points to an instance of the q15 PID Control structure
   * @return none
   */
  void arm_pid_reset_q15(
  arm_pid_instance_q15 * S);


  /**
   * @brief Instance structure for the floating-point Linear Interpolate function.
   */
  typedef struct
  {
    uint32_t nValues;           /**< nValues */
    float32_t x1;               /**< x1 */
    float32_t xSpacing;         /**< xSpacing */
    float32_t *pYData;          /**< pointer to the table of Y values */
  } arm_linear_interp_instance_f32;

  /**
   * @brief Instance structure for the floating-point bilinear interpolation function.
   */

  typedef struct
  {
    uint16_t numRows;   /**< number of rows in the data table. */
    uint16_t numCols;   /**< number of columns in the data table. */
    float32_t *pData;   /**< points to the data table. */
  } arm_bilinear_interp_instance_f32;

   /**
   * @brief Instance structure for the Q31 bilinear interpolation function.
   */

  typedef struct
  {
    uint16_t numRows;   /**< number of rows in the data table. */
    uint16_t numCols;   /**< number of columns in the data table. */
    q31_t *pData;       /**< points to the data table. */
  } arm_bilinear_interp_instance_q31;

   /**
   * @brief Instance structure for the Q15 bilinear interpolation function.
   */

  typedef struct
  {
    uint16_t numRows;   /**< number of rows in the data table. */
    uint16_t numCols;   /**< number of columns in the data table. */
    q15_t *pData;       /**< points to the data table. */
  } arm_bilinear_interp_instance_q15;

   /**
   * @brief Instance structure for the Q15 bilinear interpolation function.
   */

  typedef struct
  {
    uint16_t numRows;   /**< number of rows in the data table. */
    uint16_t numCols;   /**< number of columns in the data table. */
    q7_t *pData;                /**< points to the data table. */
  } arm_bilinear_interp_instance_q7;


  /**
   * @brief Q7 vector multiplication.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst  points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_mult_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q15 vector multiplication.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst  points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_mult_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q31 vector multiplication.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_mult_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Floating-point vector multiplication.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_mult_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);






  /**
   * @brief Instance structure for the Q15 CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                 /**< length of the FFT. */
    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    q15_t *pTwiddle;                     /**< points to the Sin twiddle factor table. */
    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
  } arm_cfft_radix2_instance_q15;

/* Deprecated */
  arm_status arm_cfft_radix2_init_q15(
  arm_cfft_radix2_instance_q15 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_q15(
  const arm_cfft_radix2_instance_q15 * S,
  q15_t * pSrc);



  /**
   * @brief Instance structure for the Q15 CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                 /**< length of the FFT. */
    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    q15_t *pTwiddle;                 /**< points to the twiddle factor table. */
    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
  } arm_cfft_radix4_instance_q15;

/* Deprecated */
  arm_status arm_cfft_radix4_init_q15(
  arm_cfft_radix4_instance_q15 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix4_q15(
  const arm_cfft_radix4_instance_q15 * S,
  q15_t * pSrc);

  /**
   * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                 /**< length of the FFT. */
    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    q31_t *pTwiddle;                     /**< points to the Twiddle factor table. */
    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
  } arm_cfft_radix2_instance_q31;

/* Deprecated */
  arm_status arm_cfft_radix2_init_q31(
  arm_cfft_radix2_instance_q31 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_q31(
  const arm_cfft_radix2_instance_q31 * S,
  q31_t * pSrc);

  /**
   * @brief Instance structure for the Q31 CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                 /**< length of the FFT. */
    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    q31_t *pTwiddle;                 /**< points to the twiddle factor table. */
    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
  } arm_cfft_radix4_instance_q31;

/* Deprecated */
  void arm_cfft_radix4_q31(
  const arm_cfft_radix4_instance_q31 * S,
  q31_t * pSrc);

/* Deprecated */
  arm_status arm_cfft_radix4_init_q31(
  arm_cfft_radix4_instance_q31 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

  /**
   * @brief Instance structure for the floating-point CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
    uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
    float32_t onebyfftLen;                 /**< value of 1/fftLen. */
  } arm_cfft_radix2_instance_f32;

/* Deprecated */
  arm_status arm_cfft_radix2_init_f32(
  arm_cfft_radix2_instance_f32 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_f32(
  const arm_cfft_radix2_instance_f32 * S,
  float32_t * pSrc);

  /**
   * @brief Instance structure for the floating-point CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
    uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
    float32_t onebyfftLen;                 /**< value of 1/fftLen. */
  } arm_cfft_radix4_instance_f32;

/* Deprecated */
  arm_status arm_cfft_radix4_init_f32(
  arm_cfft_radix4_instance_f32 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix4_f32(
  const arm_cfft_radix4_instance_f32 * S,
  float32_t * pSrc);

  /**
   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    const q15_t *pTwiddle;             /**< points to the Twiddle factor table. */
    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
    uint16_t bitRevLength;             /**< bit reversal table length. */
  } arm_cfft_instance_q15;

void arm_cfft_q15( 
    const arm_cfft_instance_q15 * S, 
    q15_t * p1,
    uint8_t ifftFlag,
    uint8_t bitReverseFlag);  

  /**
   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    const q31_t *pTwiddle;             /**< points to the Twiddle factor table. */
    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
    uint16_t bitRevLength;             /**< bit reversal table length. */
  } arm_cfft_instance_q31;

void arm_cfft_q31( 
    const arm_cfft_instance_q31 * S, 
    q31_t * p1,
    uint8_t ifftFlag,
    uint8_t bitReverseFlag);  
  
  /**
   * @brief Instance structure for the floating-point CFFT/CIFFT function.
   */

  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    const float32_t *pTwiddle;         /**< points to the Twiddle factor table. */
    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
    uint16_t bitRevLength;             /**< bit reversal table length. */
  } arm_cfft_instance_f32;

  void arm_cfft_f32(
  const arm_cfft_instance_f32 * S,
  float32_t * p1,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

  /**
   * @brief Instance structure for the Q15 RFFT/RIFFT function.
   */

  typedef struct
  {
    uint32_t fftLenReal;                      /**< length of the real FFT. */
    uint8_t ifftFlagR;                        /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
    uint8_t bitReverseFlagR;                  /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
    uint32_t twidCoefRModifier;               /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    q15_t *pTwiddleAReal;                     /**< points to the real twiddle factor table. */
    q15_t *pTwiddleBReal;                     /**< points to the imag twiddle factor table. */
    const arm_cfft_instance_q15 *pCfft;       /**< points to the complex FFT instance. */
  } arm_rfft_instance_q15;

  arm_status arm_rfft_init_q15(
  arm_rfft_instance_q15 * S,
  uint32_t fftLenReal,
  uint32_t ifftFlagR,
  uint32_t bitReverseFlag);

  void arm_rfft_q15(
  const arm_rfft_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst);

  /**
   * @brief Instance structure for the Q31 RFFT/RIFFT function.
   */

  typedef struct
  {
    uint32_t fftLenReal;                        /**< length of the real FFT. */
    uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
    uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
    uint32_t twidCoefRModifier;                 /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    q31_t *pTwiddleAReal;                       /**< points to the real twiddle factor table. */
    q31_t *pTwiddleBReal;                       /**< points to the imag twiddle factor table. */
    const arm_cfft_instance_q31 *pCfft;         /**< points to the complex FFT instance. */
  } arm_rfft_instance_q31;

  arm_status arm_rfft_init_q31(
  arm_rfft_instance_q31 * S,
  uint32_t fftLenReal,
  uint32_t ifftFlagR,
  uint32_t bitReverseFlag);

  void arm_rfft_q31(
  const arm_rfft_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst);

  /**
   * @brief Instance structure for the floating-point RFFT/RIFFT function.
   */

  typedef struct
  {
    uint32_t fftLenReal;                        /**< length of the real FFT. */
    uint16_t fftLenBy2;                         /**< length of the complex FFT. */
    uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
    uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
    uint32_t twidCoefRModifier;                     /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
    float32_t *pTwiddleBReal;                   /**< points to the imag twiddle factor table. */
    arm_cfft_radix4_instance_f32 *pCfft;        /**< points to the complex FFT instance. */
  } arm_rfft_instance_f32;

  arm_status arm_rfft_init_f32(
  arm_rfft_instance_f32 * S,
  arm_cfft_radix4_instance_f32 * S_CFFT,
  uint32_t fftLenReal,
  uint32_t ifftFlagR,
  uint32_t bitReverseFlag);

  void arm_rfft_f32(
  const arm_rfft_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst);

  /**
   * @brief Instance structure for the floating-point RFFT/RIFFT function.
   */

typedef struct
  {
    arm_cfft_instance_f32 Sint;      /**< Internal CFFT structure. */
    uint16_t fftLenRFFT;                        /**< length of the real sequence */
	float32_t * pTwiddleRFFT;					/**< Twiddle factors real stage  */
  } arm_rfft_fast_instance_f32 ;

arm_status arm_rfft_fast_init_f32 (
	arm_rfft_fast_instance_f32 * S,
	uint16_t fftLen);

void arm_rfft_fast_f32(
  arm_rfft_fast_instance_f32 * S,
  float32_t * p, float32_t * pOut,
  uint8_t ifftFlag);

  /**
   * @brief Instance structure for the floating-point DCT4/IDCT4 function.
   */

  typedef struct
  {
    uint16_t N;                         /**< length of the DCT4. */
    uint16_t Nby2;                      /**< half of the length of the DCT4. */
    float32_t normalize;                /**< normalizing factor. */
    float32_t *pTwiddle;                /**< points to the twiddle factor table. */
    float32_t *pCosFactor;              /**< points to the cosFactor table. */
    arm_rfft_instance_f32 *pRfft;        /**< points to the real FFT instance. */
    arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */
  } arm_dct4_instance_f32;

  /**
   * @brief  Initialization function for the floating-point DCT4/IDCT4.
   * @param[in,out] *S         points to an instance of floating-point DCT4/IDCT4 structure.
   * @param[in]     *S_RFFT    points to an instance of floating-point RFFT/RIFFT structure.
   * @param[in]     *S_CFFT    points to an instance of floating-point CFFT/CIFFT structure.
   * @param[in]     N          length of the DCT4.
   * @param[in]     Nby2       half of the length of the DCT4.
   * @param[in]     normalize  normalizing factor.
   * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length.
   */

  arm_status arm_dct4_init_f32(
  arm_dct4_instance_f32 * S,
  arm_rfft_instance_f32 * S_RFFT,
  arm_cfft_radix4_instance_f32 * S_CFFT,
  uint16_t N,
  uint16_t Nby2,
  float32_t normalize);

  /**
   * @brief Processing function for the floating-point DCT4/IDCT4.
   * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.
   * @param[in]       *pState        points to state buffer.
   * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
   * @return none.
   */

  void arm_dct4_f32(
  const arm_dct4_instance_f32 * S,
  float32_t * pState,
  float32_t * pInlineBuffer);

  /**
   * @brief Instance structure for the Q31 DCT4/IDCT4 function.
   */

  typedef struct
  {
    uint16_t N;                         /**< length of the DCT4. */
    uint16_t Nby2;                      /**< half of the length of the DCT4. */
    q31_t normalize;                    /**< normalizing factor. */
    q31_t *pTwiddle;                    /**< points to the twiddle factor table. */
    q31_t *pCosFactor;                  /**< points to the cosFactor table. */
    arm_rfft_instance_q31 *pRfft;        /**< points to the real FFT instance. */
    arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */
  } arm_dct4_instance_q31;

  /**
   * @brief  Initialization function for the Q31 DCT4/IDCT4.
   * @param[in,out] *S         points to an instance of Q31 DCT4/IDCT4 structure.
   * @param[in]     *S_RFFT    points to an instance of Q31 RFFT/RIFFT structure
   * @param[in]     *S_CFFT    points to an instance of Q31 CFFT/CIFFT structure
   * @param[in]     N          length of the DCT4.
   * @param[in]     Nby2       half of the length of the DCT4.
   * @param[in]     normalize  normalizing factor.
   * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
   */

  arm_status arm_dct4_init_q31(
  arm_dct4_instance_q31 * S,
  arm_rfft_instance_q31 * S_RFFT,
  arm_cfft_radix4_instance_q31 * S_CFFT,
  uint16_t N,
  uint16_t Nby2,
  q31_t normalize);

  /**
   * @brief Processing function for the Q31 DCT4/IDCT4.
   * @param[in]       *S             points to an instance of the Q31 DCT4 structure.
   * @param[in]       *pState        points to state buffer.
   * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
   * @return none.
   */

  void arm_dct4_q31(
  const arm_dct4_instance_q31 * S,
  q31_t * pState,
  q31_t * pInlineBuffer);

  /**
   * @brief Instance structure for the Q15 DCT4/IDCT4 function.
   */

  typedef struct
  {
    uint16_t N;                         /**< length of the DCT4. */
    uint16_t Nby2;                      /**< half of the length of the DCT4. */
    q15_t normalize;                    /**< normalizing factor. */
    q15_t *pTwiddle;                    /**< points to the twiddle factor table. */
    q15_t *pCosFactor;                  /**< points to the cosFactor table. */
    arm_rfft_instance_q15 *pRfft;        /**< points to the real FFT instance. */
    arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */
  } arm_dct4_instance_q15;

  /**
   * @brief  Initialization function for the Q15 DCT4/IDCT4.
   * @param[in,out] *S         points to an instance of Q15 DCT4/IDCT4 structure.
   * @param[in]     *S_RFFT    points to an instance of Q15 RFFT/RIFFT structure.
   * @param[in]     *S_CFFT    points to an instance of Q15 CFFT/CIFFT structure.
   * @param[in]     N          length of the DCT4.
   * @param[in]     Nby2       half of the length of the DCT4.
   * @param[in]     normalize  normalizing factor.
   * @return		arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
   */

  arm_status arm_dct4_init_q15(
  arm_dct4_instance_q15 * S,
  arm_rfft_instance_q15 * S_RFFT,
  arm_cfft_radix4_instance_q15 * S_CFFT,
  uint16_t N,
  uint16_t Nby2,
  q15_t normalize);

  /**
   * @brief Processing function for the Q15 DCT4/IDCT4.
   * @param[in]       *S             points to an instance of the Q15 DCT4 structure.
   * @param[in]       *pState        points to state buffer.
   * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
   * @return none.
   */

  void arm_dct4_q15(
  const arm_dct4_instance_q15 * S,
  q15_t * pState,
  q15_t * pInlineBuffer);

  /**
   * @brief Floating-point vector addition.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_add_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q7 vector addition.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_add_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q15 vector addition.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_add_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q31 vector addition.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_add_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Floating-point vector subtraction.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_sub_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q7 vector subtraction.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_sub_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q15 vector subtraction.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_sub_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q31 vector subtraction.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_sub_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Multiplies a floating-point vector by a scalar.
   * @param[in]       *pSrc points to the input vector
   * @param[in]       scale scale factor to be applied
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in the vector
   * @return none.
   */

  void arm_scale_f32(
  float32_t * pSrc,
  float32_t scale,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Multiplies a Q7 vector by a scalar.
   * @param[in]       *pSrc points to the input vector
   * @param[in]       scaleFract fractional portion of the scale value
   * @param[in]       shift number of bits to shift the result by
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in the vector
   * @return none.
   */

  void arm_scale_q7(
  q7_t * pSrc,
  q7_t scaleFract,
  int8_t shift,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Multiplies a Q15 vector by a scalar.
   * @param[in]       *pSrc points to the input vector
   * @param[in]       scaleFract fractional portion of the scale value
   * @param[in]       shift number of bits to shift the result by
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in the vector
   * @return none.
   */

  void arm_scale_q15(
  q15_t * pSrc,
  q15_t scaleFract,
  int8_t shift,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Multiplies a Q31 vector by a scalar.
   * @param[in]       *pSrc points to the input vector
   * @param[in]       scaleFract fractional portion of the scale value
   * @param[in]       shift number of bits to shift the result by
   * @param[out]      *pDst points to the output vector
   * @param[in]       blockSize number of samples in the vector
   * @return none.
   */

  void arm_scale_q31(
  q31_t * pSrc,
  q31_t scaleFract,
  int8_t shift,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q7 vector absolute value.
   * @param[in]       *pSrc points to the input buffer
   * @param[out]      *pDst points to the output buffer
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_abs_q7(
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Floating-point vector absolute value.
   * @param[in]       *pSrc points to the input buffer
   * @param[out]      *pDst points to the output buffer
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_abs_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q15 vector absolute value.
   * @param[in]       *pSrc points to the input buffer
   * @param[out]      *pDst points to the output buffer
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_abs_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Q31 vector absolute value.
   * @param[in]       *pSrc points to the input buffer
   * @param[out]      *pDst points to the output buffer
   * @param[in]       blockSize number of samples in each vector
   * @return none.
   */

  void arm_abs_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Dot product of floating-point vectors.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[in]       blockSize number of samples in each vector
   * @param[out]      *result output result returned here
   * @return none.
   */

  void arm_dot_prod_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  uint32_t blockSize,
  float32_t * result);

  /**
   * @brief Dot product of Q7 vectors.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[in]       blockSize number of samples in each vector
   * @param[out]      *result output result returned here
   * @return none.
   */

  void arm_dot_prod_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  uint32_t blockSize,
  q31_t * result);

  /**
   * @brief Dot product of Q15 vectors.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[in]       blockSize number of samples in each vector
   * @param[out]      *result output result returned here
   * @return none.
   */

  void arm_dot_prod_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  uint32_t blockSize,
  q63_t * result);

  /**
   * @brief Dot product of Q31 vectors.
   * @param[in]       *pSrcA points to the first input vector
   * @param[in]       *pSrcB points to the second input vector
   * @param[in]       blockSize number of samples in each vector
   * @param[out]      *result output result returned here
   * @return none.
   */

  void arm_dot_prod_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  uint32_t blockSize,
  q63_t * result);

  /**
   * @brief  Shifts the elements of a Q7 vector a specified number of bits.
   * @param[in]  *pSrc points to the input vector
   * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_shift_q7(
  q7_t * pSrc,
  int8_t shiftBits,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Shifts the elements of a Q15 vector a specified number of bits.
   * @param[in]  *pSrc points to the input vector
   * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_shift_q15(
  q15_t * pSrc,
  int8_t shiftBits,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Shifts the elements of a Q31 vector a specified number of bits.
   * @param[in]  *pSrc points to the input vector
   * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_shift_q31(
  q31_t * pSrc,
  int8_t shiftBits,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Adds a constant offset to a floating-point vector.
   * @param[in]  *pSrc points to the input vector
   * @param[in]  offset is the offset to be added
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_offset_f32(
  float32_t * pSrc,
  float32_t offset,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Adds a constant offset to a Q7 vector.
   * @param[in]  *pSrc points to the input vector
   * @param[in]  offset is the offset to be added
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_offset_q7(
  q7_t * pSrc,
  q7_t offset,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Adds a constant offset to a Q15 vector.
   * @param[in]  *pSrc points to the input vector
   * @param[in]  offset is the offset to be added
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_offset_q15(
  q15_t * pSrc,
  q15_t offset,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Adds a constant offset to a Q31 vector.
   * @param[in]  *pSrc points to the input vector
   * @param[in]  offset is the offset to be added
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_offset_q31(
  q31_t * pSrc,
  q31_t offset,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Negates the elements of a floating-point vector.
   * @param[in]  *pSrc points to the input vector
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_negate_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Negates the elements of a Q7 vector.
   * @param[in]  *pSrc points to the input vector
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_negate_q7(
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Negates the elements of a Q15 vector.
   * @param[in]  *pSrc points to the input vector
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_negate_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Negates the elements of a Q31 vector.
   * @param[in]  *pSrc points to the input vector
   * @param[out]  *pDst points to the output vector
   * @param[in]  blockSize number of samples in the vector
   * @return none.
   */

  void arm_negate_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);
  /**
   * @brief  Copies the elements of a floating-point vector.
   * @param[in]  *pSrc input pointer
   * @param[out]  *pDst output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_copy_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Copies the elements of a Q7 vector.
   * @param[in]  *pSrc input pointer
   * @param[out]  *pDst output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_copy_q7(
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Copies the elements of a Q15 vector.
   * @param[in]  *pSrc input pointer
   * @param[out]  *pDst output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_copy_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Copies the elements of a Q31 vector.
   * @param[in]  *pSrc input pointer
   * @param[out]  *pDst output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_copy_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);
  /**
   * @brief  Fills a constant value into a floating-point vector.
   * @param[in]  value input value to be filled
   * @param[out]  *pDst output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_fill_f32(
  float32_t value,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Fills a constant value into a Q7 vector.
   * @param[in]  value input value to be filled
   * @param[out]  *pDst output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_fill_q7(
  q7_t value,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Fills a constant value into a Q15 vector.
   * @param[in]  value input value to be filled
   * @param[out]  *pDst output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_fill_q15(
  q15_t value,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Fills a constant value into a Q31 vector.
   * @param[in]  value input value to be filled
   * @param[out]  *pDst output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_fill_q31(
  q31_t value,
  q31_t * pDst,
  uint32_t blockSize);

/**
 * @brief Convolution of floating-point sequences.
 * @param[in] *pSrcA points to the first input sequence.
 * @param[in] srcALen length of the first input sequence.
 * @param[in] *pSrcB points to the second input sequence.
 * @param[in] srcBLen length of the second input sequence.
 * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.
 * @return none.
 */

  void arm_conv_f32(
  float32_t * pSrcA,
  uint32_t srcALen,
  float32_t * pSrcB,
  uint32_t srcBLen,
  float32_t * pDst);


  /**
   * @brief Convolution of Q15 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   * @param[in]  *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @param[in]  *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).
   * @return none.
   */


  void arm_conv_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);


/**
 * @brief Convolution of Q15 sequences.
 * @param[in] *pSrcA points to the first input sequence.
 * @param[in] srcALen length of the first input sequence.
 * @param[in] *pSrcB points to the second input sequence.
 * @param[in] srcBLen length of the second input sequence.
 * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.
 * @return none.
 */

  void arm_conv_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst);

  /**
   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   * @return none.
   */

  void arm_conv_fast_q15(
			  q15_t * pSrcA,
			 uint32_t srcALen,
			  q15_t * pSrcB,
			 uint32_t srcBLen,
			 q15_t * pDst);

  /**
   * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   * @param[in]  *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @param[in]  *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).
   * @return none.
   */

  void arm_conv_fast_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);



  /**
   * @brief Convolution of Q31 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   * @return none.
   */

  void arm_conv_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);

  /**
   * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   * @return none.
   */

  void arm_conv_fast_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);


    /**
   * @brief Convolution of Q7 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
   * @return none.
   */

  void arm_conv_opt_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);



  /**
   * @brief Convolution of Q7 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   * @return none.
   */

  void arm_conv_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst);


  /**
   * @brief Partial convolution of floating-point sequences.
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_f32(
  float32_t * pSrcA,
  uint32_t srcALen,
  float32_t * pSrcB,
  uint32_t srcBLen,
  float32_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints);

    /**
   * @brief Partial convolution of Q15 sequences.
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @param[in]       * pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @param[in]       * pScratch2 points to scratch buffer of size min(srcALen, srcBLen).
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints,
  q15_t * pScratch1,
  q15_t * pScratch2);


/**
   * @brief Partial convolution of Q15 sequences.
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints);

  /**
   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_fast_q15(
				        q15_t * pSrcA,
				       uint32_t srcALen,
				        q15_t * pSrcB,
				       uint32_t srcBLen,
				       q15_t * pDst,
				       uint32_t firstIndex,
				       uint32_t numPoints);


  /**
   * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @param[in]       * pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @param[in]       * pScratch2 points to scratch buffer of size min(srcALen, srcBLen).
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_fast_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints,
  q15_t * pScratch1,
  q15_t * pScratch2);


  /**
   * @brief Partial convolution of Q31 sequences.
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints);


  /**
   * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_fast_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints);


  /**
   * @brief Partial convolution of Q7 sequences
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_opt_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints,
  q15_t * pScratch1,
  q15_t * pScratch2);


/**
   * @brief Partial convolution of Q7 sequences.
   * @param[in]       *pSrcA points to the first input sequence.
   * @param[in]       srcALen length of the first input sequence.
   * @param[in]       *pSrcB points to the second input sequence.
   * @param[in]       srcBLen length of the second input sequence.
   * @param[out]      *pDst points to the block of output data
   * @param[in]       firstIndex is the first output sample to start with.
   * @param[in]       numPoints is the number of output points to be computed.
   * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   */

  arm_status arm_conv_partial_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst,
  uint32_t firstIndex,
  uint32_t numPoints);



  /**
   * @brief Instance structure for the Q15 FIR decimator.
   */

  typedef struct
  {
    uint8_t M;                      /**< decimation factor. */
    uint16_t numTaps;               /**< number of coefficients in the filter. */
    q15_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numTaps.*/
    q15_t *pState;                   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
  } arm_fir_decimate_instance_q15;

  /**
   * @brief Instance structure for the Q31 FIR decimator.
   */

  typedef struct
  {
    uint8_t M;                  /**< decimation factor. */
    uint16_t numTaps;           /**< number of coefficients in the filter. */
    q31_t *pCoeffs;              /**< points to the coefficient array. The array is of length numTaps.*/
    q31_t *pState;               /**< points to the state variable array. The array is of length numTaps+blockSize-1. */

  } arm_fir_decimate_instance_q31;

  /**
   * @brief Instance structure for the floating-point FIR decimator.
   */

  typedef struct
  {
    uint8_t M;                          /**< decimation factor. */
    uint16_t numTaps;                   /**< number of coefficients in the filter. */
    float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numTaps.*/
    float32_t *pState;                   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */

  } arm_fir_decimate_instance_f32;



  /**
   * @brief Processing function for the floating-point FIR decimator.
   * @param[in] *S points to an instance of the floating-point FIR decimator structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data
   * @param[in] blockSize number of input samples to process per call.
   * @return none
   */

  void arm_fir_decimate_f32(
  const arm_fir_decimate_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the floating-point FIR decimator.
   * @param[in,out] *S points to an instance of the floating-point FIR decimator structure.
   * @param[in] numTaps  number of coefficients in the filter.
   * @param[in] M  decimation factor.
   * @param[in] *pCoeffs points to the filter coefficients.
   * @param[in] *pState points to the state buffer.
   * @param[in] blockSize number of input samples to process per call.
   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   * <code>blockSize</code> is not a multiple of <code>M</code>.
   */

  arm_status arm_fir_decimate_init_f32(
  arm_fir_decimate_instance_f32 * S,
  uint16_t numTaps,
  uint8_t M,
  float32_t * pCoeffs,
  float32_t * pState,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q15 FIR decimator.
   * @param[in] *S points to an instance of the Q15 FIR decimator structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data
   * @param[in] blockSize number of input samples to process per call.
   * @return none
   */

  void arm_fir_decimate_q15(
  const arm_fir_decimate_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
   * @param[in] *S points to an instance of the Q15 FIR decimator structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data
   * @param[in] blockSize number of input samples to process per call.
   * @return none
   */

  void arm_fir_decimate_fast_q15(
  const arm_fir_decimate_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);



  /**
   * @brief  Initialization function for the Q15 FIR decimator.
   * @param[in,out] *S points to an instance of the Q15 FIR decimator structure.
   * @param[in] numTaps  number of coefficients in the filter.
   * @param[in] M  decimation factor.
   * @param[in] *pCoeffs points to the filter coefficients.
   * @param[in] *pState points to the state buffer.
   * @param[in] blockSize number of input samples to process per call.
   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   * <code>blockSize</code> is not a multiple of <code>M</code>.
   */

  arm_status arm_fir_decimate_init_q15(
  arm_fir_decimate_instance_q15 * S,
  uint16_t numTaps,
  uint8_t M,
  q15_t * pCoeffs,
  q15_t * pState,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q31 FIR decimator.
   * @param[in] *S points to an instance of the Q31 FIR decimator structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data
   * @param[in] blockSize number of input samples to process per call.
   * @return none
   */

  void arm_fir_decimate_q31(
  const arm_fir_decimate_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
   * @param[in] *S points to an instance of the Q31 FIR decimator structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data
   * @param[in] blockSize number of input samples to process per call.
   * @return none
   */

  void arm_fir_decimate_fast_q31(
  arm_fir_decimate_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q31 FIR decimator.
   * @param[in,out] *S points to an instance of the Q31 FIR decimator structure.
   * @param[in] numTaps  number of coefficients in the filter.
   * @param[in] M  decimation factor.
   * @param[in] *pCoeffs points to the filter coefficients.
   * @param[in] *pState points to the state buffer.
   * @param[in] blockSize number of input samples to process per call.
   * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   * <code>blockSize</code> is not a multiple of <code>M</code>.
   */

  arm_status arm_fir_decimate_init_q31(
  arm_fir_decimate_instance_q31 * S,
  uint16_t numTaps,
  uint8_t M,
  q31_t * pCoeffs,
  q31_t * pState,
  uint32_t blockSize);



  /**
   * @brief Instance structure for the Q15 FIR interpolator.
   */

  typedef struct
  {
    uint8_t L;                      /**< upsample factor. */
    uint16_t phaseLength;           /**< length of each polyphase filter component. */
    q15_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
    q15_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
  } arm_fir_interpolate_instance_q15;

  /**
   * @brief Instance structure for the Q31 FIR interpolator.
   */

  typedef struct
  {
    uint8_t L;                      /**< upsample factor. */
    uint16_t phaseLength;           /**< length of each polyphase filter component. */
    q31_t *pCoeffs;                  /**< points to the coefficient array. The array is of length L*phaseLength. */
    q31_t *pState;                   /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
  } arm_fir_interpolate_instance_q31;

  /**
   * @brief Instance structure for the floating-point FIR interpolator.
   */

  typedef struct
  {
    uint8_t L;                     /**< upsample factor. */
    uint16_t phaseLength;          /**< length of each polyphase filter component. */
    float32_t *pCoeffs;             /**< points to the coefficient array. The array is of length L*phaseLength. */
    float32_t *pState;              /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */
  } arm_fir_interpolate_instance_f32;


  /**
   * @brief Processing function for the Q15 FIR interpolator.
   * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.
   * @param[in] *pSrc     points to the block of input data.
   * @param[out] *pDst    points to the block of output data.
   * @param[in] blockSize number of input samples to process per call.
   * @return none.
   */

  void arm_fir_interpolate_q15(
  const arm_fir_interpolate_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q15 FIR interpolator.
   * @param[in,out] *S        points to an instance of the Q15 FIR interpolator structure.
   * @param[in]     L         upsample factor.
   * @param[in]     numTaps   number of filter coefficients in the filter.
   * @param[in]     *pCoeffs  points to the filter coefficient buffer.
   * @param[in]     *pState   points to the state buffer.
   * @param[in]     blockSize number of input samples to process per call.
   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
   */

  arm_status arm_fir_interpolate_init_q15(
  arm_fir_interpolate_instance_q15 * S,
  uint8_t L,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q31 FIR interpolator.
   * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.
   * @param[in] *pSrc     points to the block of input data.
   * @param[out] *pDst    points to the block of output data.
   * @param[in] blockSize number of input samples to process per call.
   * @return none.
   */

  void arm_fir_interpolate_q31(
  const arm_fir_interpolate_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the Q31 FIR interpolator.
   * @param[in,out] *S        points to an instance of the Q31 FIR interpolator structure.
   * @param[in]     L         upsample factor.
   * @param[in]     numTaps   number of filter coefficients in the filter.
   * @param[in]     *pCoeffs  points to the filter coefficient buffer.
   * @param[in]     *pState   points to the state buffer.
   * @param[in]     blockSize number of input samples to process per call.
   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
   */

  arm_status arm_fir_interpolate_init_q31(
  arm_fir_interpolate_instance_q31 * S,
  uint8_t L,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the floating-point FIR interpolator.
   * @param[in] *S        points to an instance of the floating-point FIR interpolator structure.
   * @param[in] *pSrc     points to the block of input data.
   * @param[out] *pDst    points to the block of output data.
   * @param[in] blockSize number of input samples to process per call.
   * @return none.
   */

  void arm_fir_interpolate_f32(
  const arm_fir_interpolate_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the floating-point FIR interpolator.
   * @param[in,out] *S        points to an instance of the floating-point FIR interpolator structure.
   * @param[in]     L         upsample factor.
   * @param[in]     numTaps   number of filter coefficients in the filter.
   * @param[in]     *pCoeffs  points to the filter coefficient buffer.
   * @param[in]     *pState   points to the state buffer.
   * @param[in]     blockSize number of input samples to process per call.
   * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
   */

  arm_status arm_fir_interpolate_init_f32(
  arm_fir_interpolate_instance_f32 * S,
  uint8_t L,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  uint32_t blockSize);

  /**
   * @brief Instance structure for the high precision Q31 Biquad cascade filter.
   */

  typedef struct
  {
    uint8_t numStages;       /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    q63_t *pState;           /**< points to the array of state coefficients.  The array is of length 4*numStages. */
    q31_t *pCoeffs;          /**< points to the array of coefficients.  The array is of length 5*numStages. */
    uint8_t postShift;       /**< additional shift, in bits, applied to each output sample. */

  } arm_biquad_cas_df1_32x64_ins_q31;


  /**
   * @param[in]  *S        points to an instance of the high precision Q31 Biquad cascade filter structure.
   * @param[in]  *pSrc     points to the block of input data.
   * @param[out] *pDst     points to the block of output data
   * @param[in]  blockSize number of samples to process.
   * @return none.
   */

  void arm_biquad_cas_df1_32x64_q31(
  const arm_biquad_cas_df1_32x64_ins_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @param[in,out] *S           points to an instance of the high precision Q31 Biquad cascade filter structure.
   * @param[in]     numStages    number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @param[in]     postShift    shift to be applied to the output. Varies according to the coefficients format
   * @return        none
   */

  void arm_biquad_cas_df1_32x64_init_q31(
  arm_biquad_cas_df1_32x64_ins_q31 * S,
  uint8_t numStages,
  q31_t * pCoeffs,
  q63_t * pState,
  uint8_t postShift);



  /**
   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
   */

  typedef struct
  {
    uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
    float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
  } arm_biquad_cascade_df2T_instance_f32;



  /**
   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
   */

  typedef struct
  {
    uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 4*numStages. */
    float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
  } arm_biquad_cascade_stereo_df2T_instance_f32;



  /**
   * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
   */

  typedef struct
  {
    uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    float64_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
    float64_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
  } arm_biquad_cascade_df2T_instance_f64;


  /**
   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
   * @param[in]  *S        points to an instance of the filter data structure.
   * @param[in]  *pSrc     points to the block of input data.
   * @param[out] *pDst     points to the block of output data
   * @param[in]  blockSize number of samples to process.
   * @return none.
   */

  void arm_biquad_cascade_df2T_f32(
  const arm_biquad_cascade_df2T_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 2 channels
   * @param[in]  *S        points to an instance of the filter data structure.
   * @param[in]  *pSrc     points to the block of input data.
   * @param[out] *pDst     points to the block of output data
   * @param[in]  blockSize number of samples to process.
   * @return none.
   */

  void arm_biquad_cascade_stereo_df2T_f32(
  const arm_biquad_cascade_stereo_df2T_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
   * @param[in]  *S        points to an instance of the filter data structure.
   * @param[in]  *pSrc     points to the block of input data.
   * @param[out] *pDst     points to the block of output data
   * @param[in]  blockSize number of samples to process.
   * @return none.
   */

  void arm_biquad_cascade_df2T_f64(
  const arm_biquad_cascade_df2T_instance_f64 * S,
  float64_t * pSrc,
  float64_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
   * @param[in,out] *S           points to an instance of the filter data structure.
   * @param[in]     numStages    number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @return        none
   */

  void arm_biquad_cascade_df2T_init_f32(
  arm_biquad_cascade_df2T_instance_f32 * S,
  uint8_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);


  /**
   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
   * @param[in,out] *S           points to an instance of the filter data structure.
   * @param[in]     numStages    number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @return        none
   */

  void arm_biquad_cascade_stereo_df2T_init_f32(
  arm_biquad_cascade_stereo_df2T_instance_f32 * S,
  uint8_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);


  /**
   * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
   * @param[in,out] *S           points to an instance of the filter data structure.
   * @param[in]     numStages    number of 2nd order stages in the filter.
   * @param[in]     *pCoeffs     points to the filter coefficients.
   * @param[in]     *pState      points to the state buffer.
   * @return        none
   */

  void arm_biquad_cascade_df2T_init_f64(
  arm_biquad_cascade_df2T_instance_f64 * S,
  uint8_t numStages,
  float64_t * pCoeffs,
  float64_t * pState);



  /**
   * @brief Instance structure for the Q15 FIR lattice filter.
   */

  typedef struct
  {
    uint16_t numStages;                          /**< number of filter stages. */
    q15_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
    q15_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
  } arm_fir_lattice_instance_q15;

  /**
   * @brief Instance structure for the Q31 FIR lattice filter.
   */

  typedef struct
  {
    uint16_t numStages;                          /**< number of filter stages. */
    q31_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
    q31_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
  } arm_fir_lattice_instance_q31;

  /**
   * @brief Instance structure for the floating-point FIR lattice filter.
   */

  typedef struct
  {
    uint16_t numStages;                  /**< number of filter stages. */
    float32_t *pState;                   /**< points to the state variable array. The array is of length numStages. */
    float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numStages. */
  } arm_fir_lattice_instance_f32;

  /**
   * @brief Initialization function for the Q15 FIR lattice filter.
   * @param[in] *S points to an instance of the Q15 FIR lattice structure.
   * @param[in] numStages  number of filter stages.
   * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
   * @param[in] *pState points to the state buffer.  The array is of length numStages.
   * @return none.
   */

  void arm_fir_lattice_init_q15(
  arm_fir_lattice_instance_q15 * S,
  uint16_t numStages,
  q15_t * pCoeffs,
  q15_t * pState);


  /**
   * @brief Processing function for the Q15 FIR lattice filter.
   * @param[in] *S points to an instance of the Q15 FIR lattice structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */
  void arm_fir_lattice_q15(
  const arm_fir_lattice_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Initialization function for the Q31 FIR lattice filter.
   * @param[in] *S points to an instance of the Q31 FIR lattice structure.
   * @param[in] numStages  number of filter stages.
   * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
   * @param[in] *pState points to the state buffer.   The array is of length numStages.
   * @return none.
   */

  void arm_fir_lattice_init_q31(
  arm_fir_lattice_instance_q31 * S,
  uint16_t numStages,
  q31_t * pCoeffs,
  q31_t * pState);


  /**
   * @brief Processing function for the Q31 FIR lattice filter.
   * @param[in]  *S        points to an instance of the Q31 FIR lattice structure.
   * @param[in]  *pSrc     points to the block of input data.
   * @param[out] *pDst     points to the block of output data
   * @param[in]  blockSize number of samples to process.
   * @return none.
   */

  void arm_fir_lattice_q31(
  const arm_fir_lattice_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

/**
 * @brief Initialization function for the floating-point FIR lattice filter.
 * @param[in] *S points to an instance of the floating-point FIR lattice structure.
 * @param[in] numStages  number of filter stages.
 * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
 * @param[in] *pState points to the state buffer.  The array is of length numStages.
 * @return none.
 */

  void arm_fir_lattice_init_f32(
  arm_fir_lattice_instance_f32 * S,
  uint16_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);

  /**
   * @brief Processing function for the floating-point FIR lattice filter.
   * @param[in]  *S        points to an instance of the floating-point FIR lattice structure.
   * @param[in]  *pSrc     points to the block of input data.
   * @param[out] *pDst     points to the block of output data
   * @param[in]  blockSize number of samples to process.
   * @return none.
   */

  void arm_fir_lattice_f32(
  const arm_fir_lattice_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Instance structure for the Q15 IIR lattice filter.
   */
  typedef struct
  {
    uint16_t numStages;                         /**< number of stages in the filter. */
    q15_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
    q15_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
    q15_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
  } arm_iir_lattice_instance_q15;

  /**
   * @brief Instance structure for the Q31 IIR lattice filter.
   */
  typedef struct
  {
    uint16_t numStages;                         /**< number of stages in the filter. */
    q31_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
    q31_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
    q31_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
  } arm_iir_lattice_instance_q31;

  /**
   * @brief Instance structure for the floating-point IIR lattice filter.
   */
  typedef struct
  {
    uint16_t numStages;                         /**< number of stages in the filter. */
    float32_t *pState;                          /**< points to the state variable array. The array is of length numStages+blockSize. */
    float32_t *pkCoeffs;                        /**< points to the reflection coefficient array. The array is of length numStages. */
    float32_t *pvCoeffs;                        /**< points to the ladder coefficient array. The array is of length numStages+1. */
  } arm_iir_lattice_instance_f32;

  /**
   * @brief Processing function for the floating-point IIR lattice filter.
   * @param[in] *S points to an instance of the floating-point IIR lattice structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_iir_lattice_f32(
  const arm_iir_lattice_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Initialization function for the floating-point IIR lattice filter.
   * @param[in] *S points to an instance of the floating-point IIR lattice structure.
   * @param[in] numStages number of stages in the filter.
   * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
   * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
   * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize-1.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_iir_lattice_init_f32(
  arm_iir_lattice_instance_f32 * S,
  uint16_t numStages,
  float32_t * pkCoeffs,
  float32_t * pvCoeffs,
  float32_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q31 IIR lattice filter.
   * @param[in] *S points to an instance of the Q31 IIR lattice structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_iir_lattice_q31(
  const arm_iir_lattice_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Initialization function for the Q31 IIR lattice filter.
   * @param[in] *S points to an instance of the Q31 IIR lattice structure.
   * @param[in] numStages number of stages in the filter.
   * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
   * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
   * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_iir_lattice_init_q31(
  arm_iir_lattice_instance_q31 * S,
  uint16_t numStages,
  q31_t * pkCoeffs,
  q31_t * pvCoeffs,
  q31_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q15 IIR lattice filter.
   * @param[in] *S points to an instance of the Q15 IIR lattice structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[out] *pDst points to the block of output data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_iir_lattice_q15(
  const arm_iir_lattice_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


/**
 * @brief Initialization function for the Q15 IIR lattice filter.
 * @param[in] *S points to an instance of the fixed-point Q15 IIR lattice structure.
 * @param[in] numStages  number of stages in the filter.
 * @param[in] *pkCoeffs points to reflection coefficient buffer.  The array is of length numStages.
 * @param[in] *pvCoeffs points to ladder coefficient buffer.  The array is of length numStages+1.
 * @param[in] *pState points to state buffer.  The array is of length numStages+blockSize.
 * @param[in] blockSize number of samples to process per call.
 * @return none.
 */

  void arm_iir_lattice_init_q15(
  arm_iir_lattice_instance_q15 * S,
  uint16_t numStages,
  q15_t * pkCoeffs,
  q15_t * pvCoeffs,
  q15_t * pState,
  uint32_t blockSize);

  /**
   * @brief Instance structure for the floating-point LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;    /**< number of coefficients in the filter. */
    float32_t *pState;   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    float32_t *pCoeffs;  /**< points to the coefficient array. The array is of length numTaps. */
    float32_t mu;        /**< step size that controls filter coefficient updates. */
  } arm_lms_instance_f32;

  /**
   * @brief Processing function for floating-point LMS filter.
   * @param[in]  *S points to an instance of the floating-point LMS filter structure.
   * @param[in]  *pSrc points to the block of input data.
   * @param[in]  *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in]  blockSize number of samples to process.
   * @return     none.
   */

  void arm_lms_f32(
  const arm_lms_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pRef,
  float32_t * pOut,
  float32_t * pErr,
  uint32_t blockSize);

  /**
   * @brief Initialization function for floating-point LMS filter.
   * @param[in] *S points to an instance of the floating-point LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to the coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_init_f32(
  arm_lms_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  float32_t mu,
  uint32_t blockSize);

  /**
   * @brief Instance structure for the Q15 LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;    /**< number of coefficients in the filter. */
    q15_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q15_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
    q15_t mu;            /**< step size that controls filter coefficient updates. */
    uint32_t postShift;  /**< bit shift applied to coefficients. */
  } arm_lms_instance_q15;


  /**
   * @brief Initialization function for the Q15 LMS filter.
   * @param[in] *S points to an instance of the Q15 LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to the coefficient buffer.
   * @param[in] *pState points to the state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @param[in] postShift bit shift applied to coefficients.
   * @return    none.
   */

  void arm_lms_init_q15(
  arm_lms_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  q15_t mu,
  uint32_t blockSize,
  uint32_t postShift);

  /**
   * @brief Processing function for Q15 LMS filter.
   * @param[in] *S points to an instance of the Q15 LMS filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[in] *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_q15(
  const arm_lms_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pRef,
  q15_t * pOut,
  q15_t * pErr,
  uint32_t blockSize);


  /**
   * @brief Instance structure for the Q31 LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;    /**< number of coefficients in the filter. */
    q31_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q31_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
    q31_t mu;            /**< step size that controls filter coefficient updates. */
    uint32_t postShift;  /**< bit shift applied to coefficients. */

  } arm_lms_instance_q31;

  /**
   * @brief Processing function for Q31 LMS filter.
   * @param[in]  *S points to an instance of the Q15 LMS filter structure.
   * @param[in]  *pSrc points to the block of input data.
   * @param[in]  *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in]  blockSize number of samples to process.
   * @return     none.
   */

  void arm_lms_q31(
  const arm_lms_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pRef,
  q31_t * pOut,
  q31_t * pErr,
  uint32_t blockSize);

  /**
   * @brief Initialization function for Q31 LMS filter.
   * @param[in] *S points to an instance of the Q31 LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @param[in] postShift bit shift applied to coefficients.
   * @return none.
   */

  void arm_lms_init_q31(
  arm_lms_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  q31_t mu,
  uint32_t blockSize,
  uint32_t postShift);

  /**
   * @brief Instance structure for the floating-point normalized LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;     /**< number of coefficients in the filter. */
    float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
    float32_t mu;        /**< step size that control filter coefficient updates. */
    float32_t energy;    /**< saves previous frame energy. */
    float32_t x0;        /**< saves previous input sample. */
  } arm_lms_norm_instance_f32;

  /**
   * @brief Processing function for floating-point normalized LMS filter.
   * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[in] *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_norm_f32(
  arm_lms_norm_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pRef,
  float32_t * pOut,
  float32_t * pErr,
  uint32_t blockSize);

  /**
   * @brief Initialization function for floating-point normalized LMS filter.
   * @param[in] *S points to an instance of the floating-point LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_norm_init_f32(
  arm_lms_norm_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  float32_t mu,
  uint32_t blockSize);


  /**
   * @brief Instance structure for the Q31 normalized LMS filter.
   */
  typedef struct
  {
    uint16_t numTaps;     /**< number of coefficients in the filter. */
    q31_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q31_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
    q31_t mu;             /**< step size that controls filter coefficient updates. */
    uint8_t postShift;    /**< bit shift applied to coefficients. */
    q31_t *recipTable;    /**< points to the reciprocal initial value table. */
    q31_t energy;         /**< saves previous frame energy. */
    q31_t x0;             /**< saves previous input sample. */
  } arm_lms_norm_instance_q31;

  /**
   * @brief Processing function for Q31 normalized LMS filter.
   * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[in] *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_norm_q31(
  arm_lms_norm_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pRef,
  q31_t * pOut,
  q31_t * pErr,
  uint32_t blockSize);

  /**
   * @brief Initialization function for Q31 normalized LMS filter.
   * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @param[in] postShift bit shift applied to coefficients.
   * @return none.
   */

  void arm_lms_norm_init_q31(
  arm_lms_norm_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  q31_t mu,
  uint32_t blockSize,
  uint8_t postShift);

  /**
   * @brief Instance structure for the Q15 normalized LMS filter.
   */

  typedef struct
  {
    uint16_t numTaps;    /**< Number of coefficients in the filter. */
    q15_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q15_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
    q15_t mu;            /**< step size that controls filter coefficient updates. */
    uint8_t postShift;   /**< bit shift applied to coefficients. */
    q15_t *recipTable;   /**< Points to the reciprocal initial value table. */
    q15_t energy;        /**< saves previous frame energy. */
    q15_t x0;            /**< saves previous input sample. */
  } arm_lms_norm_instance_q15;

  /**
   * @brief Processing function for Q15 normalized LMS filter.
   * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
   * @param[in] *pSrc points to the block of input data.
   * @param[in] *pRef points to the block of reference data.
   * @param[out] *pOut points to the block of output data.
   * @param[out] *pErr points to the block of error data.
   * @param[in] blockSize number of samples to process.
   * @return none.
   */

  void arm_lms_norm_q15(
  arm_lms_norm_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pRef,
  q15_t * pOut,
  q15_t * pErr,
  uint32_t blockSize);


  /**
   * @brief Initialization function for Q15 normalized LMS filter.
   * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
   * @param[in] numTaps  number of filter coefficients.
   * @param[in] *pCoeffs points to coefficient buffer.
   * @param[in] *pState points to state buffer.
   * @param[in] mu step size that controls filter coefficient updates.
   * @param[in] blockSize number of samples to process.
   * @param[in] postShift bit shift applied to coefficients.
   * @return none.
   */

  void arm_lms_norm_init_q15(
  arm_lms_norm_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  q15_t mu,
  uint32_t blockSize,
  uint8_t postShift);

  /**
   * @brief Correlation of floating-point sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_f32(
  float32_t * pSrcA,
  uint32_t srcALen,
  float32_t * pSrcB,
  uint32_t srcBLen,
  float32_t * pDst);


   /**
   * @brief Correlation of Q15 sequences
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @return none.
   */
  void arm_correlate_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch);


  /**
   * @brief Correlation of Q15 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst);

  /**
   * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_fast_q15(
			       q15_t * pSrcA,
			      uint32_t srcALen,
			       q15_t * pSrcB,
			      uint32_t srcBLen,
			      q15_t * pDst);



  /**
   * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @return none.
   */

  void arm_correlate_fast_opt_q15(
  q15_t * pSrcA,
  uint32_t srcALen,
  q15_t * pSrcB,
  uint32_t srcBLen,
  q15_t * pDst,
  q15_t * pScratch);

  /**
   * @brief Correlation of Q31 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);

  /**
   * @brief Correlation of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_fast_q31(
  q31_t * pSrcA,
  uint32_t srcALen,
  q31_t * pSrcB,
  uint32_t srcBLen,
  q31_t * pDst);



 /**
   * @brief Correlation of Q7 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
   * @return none.
   */

  void arm_correlate_opt_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst,
  q15_t * pScratch1,
  q15_t * pScratch2);


  /**
   * @brief Correlation of Q7 sequences.
   * @param[in] *pSrcA points to the first input sequence.
   * @param[in] srcALen length of the first input sequence.
   * @param[in] *pSrcB points to the second input sequence.
   * @param[in] srcBLen length of the second input sequence.
   * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   * @return none.
   */

  void arm_correlate_q7(
  q7_t * pSrcA,
  uint32_t srcALen,
  q7_t * pSrcB,
  uint32_t srcBLen,
  q7_t * pDst);


  /**
   * @brief Instance structure for the floating-point sparse FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;             /**< number of coefficients in the filter. */
    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
    float32_t *pState;            /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
    float32_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
  } arm_fir_sparse_instance_f32;

  /**
   * @brief Instance structure for the Q31 sparse FIR filter.
   */

  typedef struct
  {
    uint16_t numTaps;             /**< number of coefficients in the filter. */
    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
    q31_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
    q31_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
  } arm_fir_sparse_instance_q31;

  /**
   * @brief Instance structure for the Q15 sparse FIR filter.
   */

  typedef struct
  {
    uint16_t numTaps;             /**< number of coefficients in the filter. */
    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
    q15_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
    q15_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
  } arm_fir_sparse_instance_q15;

  /**
   * @brief Instance structure for the Q7 sparse FIR filter.
   */

  typedef struct
  {
    uint16_t numTaps;             /**< number of coefficients in the filter. */
    uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
    q7_t *pState;                 /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
    q7_t *pCoeffs;                /**< points to the coefficient array. The array is of length numTaps.*/
    uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
    int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
  } arm_fir_sparse_instance_q7;

  /**
   * @brief Processing function for the floating-point sparse FIR filter.
   * @param[in]  *S          points to an instance of the floating-point sparse FIR structure.
   * @param[in]  *pSrc       points to the block of input data.
   * @param[out] *pDst       points to the block of output data
   * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
   * @param[in]  blockSize   number of input samples to process per call.
   * @return none.
   */

  void arm_fir_sparse_f32(
  arm_fir_sparse_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  float32_t * pScratchIn,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the floating-point sparse FIR filter.
   * @param[in,out] *S         points to an instance of the floating-point sparse FIR structure.
   * @param[in]     numTaps    number of nonzero coefficients in the filter.
   * @param[in]     *pCoeffs   points to the array of filter coefficients.
   * @param[in]     *pState    points to the state buffer.
   * @param[in]     *pTapDelay points to the array of offset times.
   * @param[in]     maxDelay   maximum offset time supported.
   * @param[in]     blockSize  number of samples that will be processed per block.
   * @return none
   */

  void arm_fir_sparse_init_f32(
  arm_fir_sparse_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q31 sparse FIR filter.
   * @param[in]  *S          points to an instance of the Q31 sparse FIR structure.
   * @param[in]  *pSrc       points to the block of input data.
   * @param[out] *pDst       points to the block of output data
   * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
   * @param[in]  blockSize   number of input samples to process per call.
   * @return none.
   */

  void arm_fir_sparse_q31(
  arm_fir_sparse_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  q31_t * pScratchIn,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the Q31 sparse FIR filter.
   * @param[in,out] *S         points to an instance of the Q31 sparse FIR structure.
   * @param[in]     numTaps    number of nonzero coefficients in the filter.
   * @param[in]     *pCoeffs   points to the array of filter coefficients.
   * @param[in]     *pState    points to the state buffer.
   * @param[in]     *pTapDelay points to the array of offset times.
   * @param[in]     maxDelay   maximum offset time supported.
   * @param[in]     blockSize  number of samples that will be processed per block.
   * @return none
   */

  void arm_fir_sparse_init_q31(
  arm_fir_sparse_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q15 sparse FIR filter.
   * @param[in]  *S           points to an instance of the Q15 sparse FIR structure.
   * @param[in]  *pSrc        points to the block of input data.
   * @param[out] *pDst        points to the block of output data
   * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
   * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
   * @param[in]  blockSize    number of input samples to process per call.
   * @return none.
   */

  void arm_fir_sparse_q15(
  arm_fir_sparse_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  q15_t * pScratchIn,
  q31_t * pScratchOut,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q15 sparse FIR filter.
   * @param[in,out] *S         points to an instance of the Q15 sparse FIR structure.
   * @param[in]     numTaps    number of nonzero coefficients in the filter.
   * @param[in]     *pCoeffs   points to the array of filter coefficients.
   * @param[in]     *pState    points to the state buffer.
   * @param[in]     *pTapDelay points to the array of offset times.
   * @param[in]     maxDelay   maximum offset time supported.
   * @param[in]     blockSize  number of samples that will be processed per block.
   * @return none
   */

  void arm_fir_sparse_init_q15(
  arm_fir_sparse_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);

  /**
   * @brief Processing function for the Q7 sparse FIR filter.
   * @param[in]  *S           points to an instance of the Q7 sparse FIR structure.
   * @param[in]  *pSrc        points to the block of input data.
   * @param[out] *pDst        points to the block of output data
   * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
   * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
   * @param[in]  blockSize    number of input samples to process per call.
   * @return none.
   */

  void arm_fir_sparse_q7(
  arm_fir_sparse_instance_q7 * S,
  q7_t * pSrc,
  q7_t * pDst,
  q7_t * pScratchIn,
  q31_t * pScratchOut,
  uint32_t blockSize);

  /**
   * @brief  Initialization function for the Q7 sparse FIR filter.
   * @param[in,out] *S         points to an instance of the Q7 sparse FIR structure.
   * @param[in]     numTaps    number of nonzero coefficients in the filter.
   * @param[in]     *pCoeffs   points to the array of filter coefficients.
   * @param[in]     *pState    points to the state buffer.
   * @param[in]     *pTapDelay points to the array of offset times.
   * @param[in]     maxDelay   maximum offset time supported.
   * @param[in]     blockSize  number of samples that will be processed per block.
   * @return none
   */

  void arm_fir_sparse_init_q7(
  arm_fir_sparse_instance_q7 * S,
  uint16_t numTaps,
  q7_t * pCoeffs,
  q7_t * pState,
  int32_t * pTapDelay,
  uint16_t maxDelay,
  uint32_t blockSize);


  /*
   * @brief  Floating-point sin_cos function.
   * @param[in]  theta    input value in degrees
   * @param[out] *pSinVal points to the processed sine output.
   * @param[out] *pCosVal points to the processed cos output.
   * @return none.
   */

  void arm_sin_cos_f32(
  float32_t theta,
  float32_t * pSinVal,
  float32_t * pCcosVal);

  /*
   * @brief  Q31 sin_cos function.
   * @param[in]  theta    scaled input value in degrees
   * @param[out] *pSinVal points to the processed sine output.
   * @param[out] *pCosVal points to the processed cosine output.
   * @return none.
   */

  void arm_sin_cos_q31(
  q31_t theta,
  q31_t * pSinVal,
  q31_t * pCosVal);


  /**
   * @brief  Floating-point complex conjugate.
   * @param[in]  *pSrc points to the input vector
   * @param[out]  *pDst points to the output vector
   * @param[in]  numSamples number of complex samples in each vector
   * @return none.
   */

  void arm_cmplx_conj_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Q31 complex conjugate.
   * @param[in]  *pSrc points to the input vector
   * @param[out]  *pDst points to the output vector
   * @param[in]  numSamples number of complex samples in each vector
   * @return none.
   */

  void arm_cmplx_conj_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Q15 complex conjugate.
   * @param[in]  *pSrc points to the input vector
   * @param[out]  *pDst points to the output vector
   * @param[in]  numSamples number of complex samples in each vector
   * @return none.
   */

  void arm_cmplx_conj_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t numSamples);



  /**
   * @brief  Floating-point complex magnitude squared
   * @param[in]  *pSrc points to the complex input vector
   * @param[out]  *pDst points to the real output vector
   * @param[in]  numSamples number of complex samples in the input vector
   * @return none.
   */

  void arm_cmplx_mag_squared_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Q31 complex magnitude squared
   * @param[in]  *pSrc points to the complex input vector
   * @param[out]  *pDst points to the real output vector
   * @param[in]  numSamples number of complex samples in the input vector
   * @return none.
   */

  void arm_cmplx_mag_squared_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Q15 complex magnitude squared
   * @param[in]  *pSrc points to the complex input vector
   * @param[out]  *pDst points to the real output vector
   * @param[in]  numSamples number of complex samples in the input vector
   * @return none.
   */

  void arm_cmplx_mag_squared_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t numSamples);


 /**
   * @ingroup groupController
   */

  /**
   * @defgroup PID PID Motor Control
   *
   * A Proportional Integral Derivative (PID) controller is a generic feedback control
   * loop mechanism widely used in industrial control systems.
   * A PID controller is the most commonly used type of feedback controller.
   *
   * This set of functions implements (PID) controllers
   * for Q15, Q31, and floating-point data types.  The functions operate on a single sample
   * of data and each call to the function returns a single processed value.
   * <code>S</code> points to an instance of the PID control data structure.  <code>in</code>
   * is the input sample value. The functions return the output value.
   *
   * \par Algorithm:
   * <pre>
   *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
   *    A0 = Kp + Ki + Kd
   *    A1 = (-Kp ) - (2 * Kd )
   *    A2 = Kd  </pre>
   *
   * \par
   * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant
   *
   * \par
   * \image html PID.gif "Proportional Integral Derivative Controller"
   *
   * \par
   * The PID controller calculates an "error" value as the difference between
   * the measured output and the reference input.
   * The controller attempts to minimize the error by adjusting the process control inputs.
   * The proportional value determines the reaction to the current error,
   * the integral value determines the reaction based on the sum of recent errors,
   * and the derivative value determines the reaction based on the rate at which the error has been changing.
   *
   * \par Instance Structure
   * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure.
   * A separate instance structure must be defined for each PID Controller.
   * There are separate instance structure declarations for each of the 3 supported data types.
   *
   * \par Reset Functions
   * There is also an associated reset function for each data type which clears the state array.
   *
   * \par Initialization Functions
   * There is also an associated initialization function for each data type.
   * The initialization function performs the following operations:
   * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains.
   * - Zeros out the values in the state buffer.
   *
   * \par
   * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
   *
   * \par Fixed-Point Behavior
   * Care must be taken when using the fixed-point versions of the PID Controller functions.
   * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
   * Refer to the function specific documentation below for usage guidelines.
   */

  /**
   * @addtogroup PID
   * @{
   */

  /**
   * @brief  Process function for the floating-point PID Control.
   * @param[in,out] *S is an instance of the floating-point PID Control structure
   * @param[in] in input sample to process
   * @return out processed output sample.
   */


  static __INLINE float32_t arm_pid_f32(
  arm_pid_instance_f32 * S,
  float32_t in)
  {
    float32_t out;

    /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]  */
    out = (S->A0 * in) +
      (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]);

    /* Update state */
    S->state[1] = S->state[0];
    S->state[0] = in;
    S->state[2] = out;

    /* return to application */
    return (out);

  }

  /**
   * @brief  Process function for the Q31 PID Control.
   * @param[in,out] *S points to an instance of the Q31 PID Control structure
   * @param[in] in input sample to process
   * @return out processed output sample.
   *
   * <b>Scaling and Overflow Behavior:</b>
   * \par
   * The function is implemented using an internal 64-bit accumulator.
   * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
   * Thus, if the accumulator result overflows it wraps around rather than clip.
   * In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions.
   * After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.
   */

  static __INLINE q31_t arm_pid_q31(
  arm_pid_instance_q31 * S,
  q31_t in)
  {
    q63_t acc;
    q31_t out;

    /* acc = A0 * x[n]  */
    acc = (q63_t) S->A0 * in;

    /* acc += A1 * x[n-1] */
    acc += (q63_t) S->A1 * S->state[0];

    /* acc += A2 * x[n-2]  */
    acc += (q63_t) S->A2 * S->state[1];

    /* convert output to 1.31 format to add y[n-1] */
    out = (q31_t) (acc >> 31u);

    /* out += y[n-1] */
    out += S->state[2];

    /* Update state */
    S->state[1] = S->state[0];
    S->state[0] = in;
    S->state[2] = out;

    /* return to application */
    return (out);

  }

  /**
   * @brief  Process function for the Q15 PID Control.
   * @param[in,out] *S points to an instance of the Q15 PID Control structure
   * @param[in] in input sample to process
   * @return out processed output sample.
   *
   * <b>Scaling and Overflow Behavior:</b>
   * \par
   * The function is implemented using a 64-bit internal accumulator.
   * Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result.
   * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
   * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.
   * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.
   * Lastly, the accumulator is saturated to yield a result in 1.15 format.
   */

  static __INLINE q15_t arm_pid_q15(
  arm_pid_instance_q15 * S,
  q15_t in)
  {
    q63_t acc;
    q15_t out;

#ifndef ARM_MATH_CM0_FAMILY
    __SIMD32_TYPE *vstate;

    /* Implementation of PID controller */

    /* acc = A0 * x[n]  */
    acc = (q31_t) __SMUAD(S->A0, in);

    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
    vstate = __SIMD32_CONST(S->state);
    acc = __SMLALD(S->A1, (q31_t) *vstate, acc);

#else
    /* acc = A0 * x[n]  */
    acc = ((q31_t) S->A0) * in;

    /* acc += A1 * x[n-1] + A2 * x[n-2]  */
    acc += (q31_t) S->A1 * S->state[0];
    acc += (q31_t) S->A2 * S->state[1];

#endif

    /* acc += y[n-1] */
    acc += (q31_t) S->state[2] << 15;

    /* saturate the output */
    out = (q15_t) (__SSAT((acc >> 15), 16));

    /* Update state */
    S->state[1] = S->state[0];
    S->state[0] = in;
    S->state[2] = out;

    /* return to application */
    return (out);

  }

  /**
   * @} end of PID group
   */


  /**
   * @brief Floating-point matrix inverse.
   * @param[in]  *src points to the instance of the input floating-point matrix structure.
   * @param[out] *dst points to the instance of the output floating-point matrix structure.
   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
   */

  arm_status arm_mat_inverse_f32(
  const arm_matrix_instance_f32 * src,
  arm_matrix_instance_f32 * dst);


  /**
   * @brief Floating-point matrix inverse.
   * @param[in]  *src points to the instance of the input floating-point matrix structure.
   * @param[out] *dst points to the instance of the output floating-point matrix structure.
   * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
   * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
   */

  arm_status arm_mat_inverse_f64(
  const arm_matrix_instance_f64 * src,
  arm_matrix_instance_f64 * dst);



  /**
   * @ingroup groupController
   */


  /**
   * @defgroup clarke Vector Clarke Transform
   * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector.
   * Generally the Clarke transform uses three-phase currents <code>Ia, Ib and Ic</code> to calculate currents
   * in the two-phase orthogonal stator axis <code>Ialpha</code> and <code>Ibeta</code>.
   * When <code>Ialpha</code> is superposed with <code>Ia</code> as shown in the figure below
   * \image html clarke.gif Stator current space vector and its components in (a,b).
   * and <code>Ia + Ib + Ic = 0</code>, in this condition <code>Ialpha</code> and <code>Ibeta</code>
   * can be calculated using only <code>Ia</code> and <code>Ib</code>.
   *
   * The function operates on a single sample of data and each call to the function returns the processed output.
   * The library provides separate functions for Q31 and floating-point data types.
   * \par Algorithm
   * \image html clarkeFormula.gif
   * where <code>Ia</code> and <code>Ib</code> are the instantaneous stator phases and
   * <code>pIalpha</code> and <code>pIbeta</code> are the two coordinates of time invariant vector.
   * \par Fixed-Point Behavior
   * Care must be taken when using the Q31 version of the Clarke transform.
   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
   * Refer to the function specific documentation below for usage guidelines.
   */

  /**
   * @addtogroup clarke
   * @{
   */

  /**
   *
   * @brief  Floating-point Clarke transform
   * @param[in]       Ia       input three-phase coordinate <code>a</code>
   * @param[in]       Ib       input three-phase coordinate <code>b</code>
   * @param[out]      *pIalpha points to output two-phase orthogonal vector axis alpha
   * @param[out]      *pIbeta  points to output two-phase orthogonal vector axis beta
   * @return none.
   */

  static __INLINE void arm_clarke_f32(
  float32_t Ia,
  float32_t Ib,
  float32_t * pIalpha,
  float32_t * pIbeta)
  {
    /* Calculate pIalpha using the equation, pIalpha = Ia */
    *pIalpha = Ia;

    /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */
    *pIbeta =
      ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib);

  }

  /**
   * @brief  Clarke transform for Q31 version
   * @param[in]       Ia       input three-phase coordinate <code>a</code>
   * @param[in]       Ib       input three-phase coordinate <code>b</code>
   * @param[out]      *pIalpha points to output two-phase orthogonal vector axis alpha
   * @param[out]      *pIbeta  points to output two-phase orthogonal vector axis beta
   * @return none.
   *
   * <b>Scaling and Overflow Behavior:</b>
   * \par
   * The function is implemented using an internal 32-bit accumulator.
   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
   * There is saturation on the addition, hence there is no risk of overflow.
   */

  static __INLINE void arm_clarke_q31(
  q31_t Ia,
  q31_t Ib,
  q31_t * pIalpha,
  q31_t * pIbeta)
  {
    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */

    /* Calculating pIalpha from Ia by equation pIalpha = Ia */
    *pIalpha = Ia;

    /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */
    product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30);

    /* Intermediate product is calculated by (2/sqrt(3) * Ib) */
    product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30);

    /* pIbeta is calculated by adding the intermediate products */
    *pIbeta = __QADD(product1, product2);
  }

  /**
   * @} end of clarke group
   */

  /**
   * @brief  Converts the elements of the Q7 vector to Q31 vector.
   * @param[in]  *pSrc     input pointer
   * @param[out]  *pDst    output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_q7_to_q31(
  q7_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);




  /**
   * @ingroup groupController
   */

  /**
   * @defgroup inv_clarke Vector Inverse Clarke Transform
   * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases.
   *
   * The function operates on a single sample of data and each call to the function returns the processed output.
   * The library provides separate functions for Q31 and floating-point data types.
   * \par Algorithm
   * \image html clarkeInvFormula.gif
   * where <code>pIa</code> and <code>pIb</code> are the instantaneous stator phases and
   * <code>Ialpha</code> and <code>Ibeta</code> are the two coordinates of time invariant vector.
   * \par Fixed-Point Behavior
   * Care must be taken when using the Q31 version of the Clarke transform.
   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
   * Refer to the function specific documentation below for usage guidelines.
   */

  /**
   * @addtogroup inv_clarke
   * @{
   */

   /**
   * @brief  Floating-point Inverse Clarke transform
   * @param[in]       Ialpha  input two-phase orthogonal vector axis alpha
   * @param[in]       Ibeta   input two-phase orthogonal vector axis beta
   * @param[out]      *pIa    points to output three-phase coordinate <code>a</code>
   * @param[out]      *pIb    points to output three-phase coordinate <code>b</code>
   * @return none.
   */


  static __INLINE void arm_inv_clarke_f32(
  float32_t Ialpha,
  float32_t Ibeta,
  float32_t * pIa,
  float32_t * pIb)
  {
    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
    *pIa = Ialpha;

    /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */
    *pIb = -0.5 * Ialpha + (float32_t) 0.8660254039 *Ibeta;

  }

  /**
   * @brief  Inverse Clarke transform for Q31 version
   * @param[in]       Ialpha  input two-phase orthogonal vector axis alpha
   * @param[in]       Ibeta   input two-phase orthogonal vector axis beta
   * @param[out]      *pIa    points to output three-phase coordinate <code>a</code>
   * @param[out]      *pIb    points to output three-phase coordinate <code>b</code>
   * @return none.
   *
   * <b>Scaling and Overflow Behavior:</b>
   * \par
   * The function is implemented using an internal 32-bit accumulator.
   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
   * There is saturation on the subtraction, hence there is no risk of overflow.
   */

  static __INLINE void arm_inv_clarke_q31(
  q31_t Ialpha,
  q31_t Ibeta,
  q31_t * pIa,
  q31_t * pIb)
  {
    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */

    /* Calculating pIa from Ialpha by equation pIa = Ialpha */
    *pIa = Ialpha;

    /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */
    product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31);

    /* Intermediate product is calculated by (1/sqrt(3) * pIb) */
    product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31);

    /* pIb is calculated by subtracting the products */
    *pIb = __QSUB(product2, product1);

  }

  /**
   * @} end of inv_clarke group
   */

  /**
   * @brief  Converts the elements of the Q7 vector to Q15 vector.
   * @param[in]  *pSrc     input pointer
   * @param[out] *pDst     output pointer
   * @param[in]  blockSize number of samples to process
   * @return none.
   */
  void arm_q7_to_q15(
  q7_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);



  /**
   * @ingroup groupController
   */

  /**
   * @defgroup park Vector Park Transform
   *
   * Forward Park transform converts the input two-coordinate vector to flux and torque components.
   * The Park transform can be used to realize the transformation of the <code>Ialpha</code> and the <code>Ibeta</code> currents
   * from the stationary to the moving reference frame and control the spatial relationship between
   * the stator vector current and rotor flux vector.
   * If we consider the d axis aligned with the rotor flux, the diagram below shows the
   * current vector and the relationship from the two reference frames:
   * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame"
   *
   * The function operates on a single sample of data and each call to the function returns the processed output.
   * The library provides separate functions for Q31 and floating-point data types.
   * \par Algorithm
   * \image html parkFormula.gif
   * where <code>Ialpha</code> and <code>Ibeta</code> are the stator vector components,
   * <code>pId</code> and <code>pIq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
   * cosine and sine values of theta (rotor flux position).
   * \par Fixed-Point Behavior
   * Care must be taken when using the Q31 version of the Park transform.
   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
   * Refer to the function specific documentation below for usage guidelines.
   */

  /**
   * @addtogroup park
   * @{
   */

  /**
   * @brief Floating-point Park transform
   * @param[in]       Ialpha input two-phase vector coordinate alpha
   * @param[in]       Ibeta  input two-phase vector coordinate beta
   * @param[out]      *pId   points to output	rotor reference frame d
   * @param[out]      *pIq   points to output	rotor reference frame q
   * @param[in]       sinVal sine value of rotation angle theta
   * @param[in]       cosVal cosine value of rotation angle theta
   * @return none.
   *
   * The function implements the forward Park transform.
   *
   */

  static __INLINE void arm_park_f32(
  float32_t Ialpha,
  float32_t Ibeta,
  float32_t * pId,
  float32_t * pIq,
  float32_t sinVal,
  float32_t cosVal)
  {
    /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */
    *pId = Ialpha * cosVal + Ibeta * sinVal;

    /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */
    *pIq = -Ialpha * sinVal + Ibeta * cosVal;

  }

  /**
   * @brief  Park transform for Q31 version
   * @param[in]       Ialpha input two-phase vector coordinate alpha
   * @param[in]       Ibeta  input two-phase vector coordinate beta
   * @param[out]      *pId   points to output rotor reference frame d
   * @param[out]      *pIq   points to output rotor reference frame q
   * @param[in]       sinVal sine value of rotation angle theta
   * @param[in]       cosVal cosine value of rotation angle theta
   * @return none.
   *
   * <b>Scaling and Overflow Behavior:</b>
   * \par
   * The function is implemented using an internal 32-bit accumulator.
   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
   * There is saturation on the addition and subtraction, hence there is no risk of overflow.
   */


  static __INLINE void arm_park_q31(
  q31_t Ialpha,
  q31_t Ibeta,
  q31_t * pId,
  q31_t * pIq,
  q31_t sinVal,
  q31_t cosVal)
  {
    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */

    /* Intermediate product is calculated by (Ialpha * cosVal) */
    product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31);

    /* Intermediate product is calculated by (Ibeta * sinVal) */
    product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31);


    /* Intermediate product is calculated by (Ialpha * sinVal) */
    product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31);

    /* Intermediate product is calculated by (Ibeta * cosVal) */
    product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31);

    /* Calculate pId by adding the two intermediate products 1 and 2 */
    *pId = __QADD(product1, product2);

    /* Calculate pIq by subtracting the two intermediate products 3 from 4 */
    *pIq = __QSUB(product4, product3);
  }

  /**
   * @} end of park group
   */

  /**
   * @brief  Converts the elements of the Q7 vector to floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[out]  *pDst is output pointer
   * @param[in]  blockSize is the number of samples to process
   * @return none.
   */
  void arm_q7_to_float(
  q7_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @ingroup groupController
   */

  /**
   * @defgroup inv_park Vector Inverse Park transform
   * Inverse Park transform converts the input flux and torque components to two-coordinate vector.
   *
   * The function operates on a single sample of data and each call to the function returns the processed output.
   * The library provides separate functions for Q31 and floating-point data types.
   * \par Algorithm
   * \image html parkInvFormula.gif
   * where <code>pIalpha</code> and <code>pIbeta</code> are the stator vector components,
   * <code>Id</code> and <code>Iq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
   * cosine and sine values of theta (rotor flux position).
   * \par Fixed-Point Behavior
   * Care must be taken when using the Q31 version of the Park transform.
   * In particular, the overflow and saturation behavior of the accumulator used must be considered.
   * Refer to the function specific documentation below for usage guidelines.
   */

  /**
   * @addtogroup inv_park
   * @{
   */

   /**
   * @brief  Floating-point Inverse Park transform
   * @param[in]       Id        input coordinate of rotor reference frame d
   * @param[in]       Iq        input coordinate of rotor reference frame q
   * @param[out]      *pIalpha  points to output two-phase orthogonal vector axis alpha
   * @param[out]      *pIbeta   points to output two-phase orthogonal vector axis beta
   * @param[in]       sinVal    sine value of rotation angle theta
   * @param[in]       cosVal    cosine value of rotation angle theta
   * @return none.
   */

  static __INLINE void arm_inv_park_f32(
  float32_t Id,
  float32_t Iq,
  float32_t * pIalpha,
  float32_t * pIbeta,
  float32_t sinVal,
  float32_t cosVal)
  {
    /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */
    *pIalpha = Id * cosVal - Iq * sinVal;

    /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */
    *pIbeta = Id * sinVal + Iq * cosVal;

  }


  /**
   * @brief  Inverse Park transform for	Q31 version
   * @param[in]       Id        input coordinate of rotor reference frame d
   * @param[in]       Iq        input coordinate of rotor reference frame q
   * @param[out]      *pIalpha  points to output two-phase orthogonal vector axis alpha
   * @param[out]      *pIbeta   points to output two-phase orthogonal vector axis beta
   * @param[in]       sinVal    sine value of rotation angle theta
   * @param[in]       cosVal    cosine value of rotation angle theta
   * @return none.
   *
   * <b>Scaling and Overflow Behavior:</b>
   * \par
   * The function is implemented using an internal 32-bit accumulator.
   * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
   * There is saturation on the addition, hence there is no risk of overflow.
   */


  static __INLINE void arm_inv_park_q31(
  q31_t Id,
  q31_t Iq,
  q31_t * pIalpha,
  q31_t * pIbeta,
  q31_t sinVal,
  q31_t cosVal)
  {
    q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
    q31_t product3, product4;                    /* Temporary variables used to store intermediate results */

    /* Intermediate product is calculated by (Id * cosVal) */
    product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31);

    /* Intermediate product is calculated by (Iq * sinVal) */
    product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31);


    /* Intermediate product is calculated by (Id * sinVal) */
    product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31);

    /* Intermediate product is calculated by (Iq * cosVal) */
    product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31);

    /* Calculate pIalpha by using the two intermediate products 1 and 2 */
    *pIalpha = __QSUB(product1, product2);

    /* Calculate pIbeta by using the two intermediate products 3 and 4 */
    *pIbeta = __QADD(product4, product3);

  }

  /**
   * @} end of Inverse park group
   */


  /**
   * @brief  Converts the elements of the Q31 vector to floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[out]  *pDst is output pointer
   * @param[in]  blockSize is the number of samples to process
   * @return none.
   */
  void arm_q31_to_float(
  q31_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);

  /**
   * @ingroup groupInterpolation
   */

  /**
   * @defgroup LinearInterpolate Linear Interpolation
   *
   * Linear interpolation is a method of curve fitting using linear polynomials.
   * Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line
   *
   * \par
   * \image html LinearInterp.gif "Linear interpolation"
   *
   * \par
   * A  Linear Interpolate function calculates an output value(y), for the input(x)
   * using linear interpolation of the input values x0, x1( nearest input values) and the output values y0 and y1(nearest output values)
   *
   * \par Algorithm:
   * <pre>
   *       y = y0 + (x - x0) * ((y1 - y0)/(x1-x0))
   *       where x0, x1 are nearest values of input x
   *             y0, y1 are nearest values to output y
   * </pre>
   *
   * \par
   * This set of functions implements Linear interpolation process
   * for Q7, Q15, Q31, and floating-point data types.  The functions operate on a single
   * sample of data and each call to the function returns a single processed value.
   * <code>S</code> points to an instance of the Linear Interpolate function data structure.
   * <code>x</code> is the input sample value. The functions returns the output value.
   *
   * \par
   * if x is outside of the table boundary, Linear interpolation returns first value of the table
   * if x is below input range and returns last value of table if x is above range.
   */

  /**
   * @addtogroup LinearInterpolate
   * @{
   */

  /**
   * @brief  Process function for the floating-point Linear Interpolation Function.
   * @param[in,out] *S is an instance of the floating-point Linear Interpolation structure
   * @param[in] x input sample to process
   * @return y processed output sample.
   *
   */

  static __INLINE float32_t arm_linear_interp_f32(
  arm_linear_interp_instance_f32 * S,
  float32_t x)
  {

    float32_t y;
    float32_t x0, x1;                            /* Nearest input values */
    float32_t y0, y1;                            /* Nearest output values */
    float32_t xSpacing = S->xSpacing;            /* spacing between input values */
    int32_t i;                                   /* Index variable */
    float32_t *pYData = S->pYData;               /* pointer to output table */

    /* Calculation of index */
    i = (int32_t) ((x - S->x1) / xSpacing);

    if(i < 0)
    {
      /* Iniatilize output for below specified range as least output value of table */
      y = pYData[0];
    }
    else if((uint32_t)i >= S->nValues)
    {
      /* Iniatilize output for above specified range as last output value of table */
      y = pYData[S->nValues - 1];
    }
    else
    {
      /* Calculation of nearest input values */
      x0 = S->x1 + i * xSpacing;
      x1 = S->x1 + (i + 1) * xSpacing;

      /* Read of nearest output values */
      y0 = pYData[i];
      y1 = pYData[i + 1];

      /* Calculation of output */
      y = y0 + (x - x0) * ((y1 - y0) / (x1 - x0));

    }

    /* returns output value */
    return (y);
  }

   /**
   *
   * @brief  Process function for the Q31 Linear Interpolation Function.
   * @param[in] *pYData  pointer to Q31 Linear Interpolation table
   * @param[in] x input sample to process
   * @param[in] nValues number of table values
   * @return y processed output sample.
   *
   * \par
   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
   * This function can support maximum of table size 2^12.
   *
   */


  static __INLINE q31_t arm_linear_interp_q31(
  q31_t * pYData,
  q31_t x,
  uint32_t nValues)
  {
    q31_t y;                                     /* output */
    q31_t y0, y1;                                /* Nearest output values */
    q31_t fract;                                 /* fractional part */
    int32_t index;                               /* Index to read nearest output values */

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    index = ((x & 0xFFF00000) >> 20);

    if(index >= (int32_t)(nValues - 1))
    {
      return (pYData[nValues - 1]);
    }
    else if(index < 0)
    {
      return (pYData[0]);
    }
    else
    {

      /* 20 bits for the fractional part */
      /* shift left by 11 to keep fract in 1.31 format */
      fract = (x & 0x000FFFFF) << 11;

      /* Read two nearest output values from the index in 1.31(q31) format */
      y0 = pYData[index];
      y1 = pYData[index + 1u];

      /* Calculation of y0 * (1-fract) and y is in 2.30 format */
      y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32));

      /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */
      y += ((q31_t) (((q63_t) y1 * fract) >> 32));

      /* Convert y to 1.31 format */
      return (y << 1u);

    }

  }

  /**
   *
   * @brief  Process function for the Q15 Linear Interpolation Function.
   * @param[in] *pYData  pointer to Q15 Linear Interpolation table
   * @param[in] x input sample to process
   * @param[in] nValues number of table values
   * @return y processed output sample.
   *
   * \par
   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
   * This function can support maximum of table size 2^12.
   *
   */


  static __INLINE q15_t arm_linear_interp_q15(
  q15_t * pYData,
  q31_t x,
  uint32_t nValues)
  {
    q63_t y;                                     /* output */
    q15_t y0, y1;                                /* Nearest output values */
    q31_t fract;                                 /* fractional part */
    int32_t index;                               /* Index to read nearest output values */

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    index = ((x & 0xFFF00000) >> 20u);

    if(index >= (int32_t)(nValues - 1))
    {
      return (pYData[nValues - 1]);
    }
    else if(index < 0)
    {
      return (pYData[0]);
    }
    else
    {
      /* 20 bits for the fractional part */
      /* fract is in 12.20 format */
      fract = (x & 0x000FFFFF);

      /* Read two nearest output values from the index */
      y0 = pYData[index];
      y1 = pYData[index + 1u];

      /* Calculation of y0 * (1-fract) and y is in 13.35 format */
      y = ((q63_t) y0 * (0xFFFFF - fract));

      /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */
      y += ((q63_t) y1 * (fract));

      /* convert y to 1.15 format */
      return (y >> 20);
    }


  }

  /**
   *
   * @brief  Process function for the Q7 Linear Interpolation Function.
   * @param[in] *pYData  pointer to Q7 Linear Interpolation table
   * @param[in] x input sample to process
   * @param[in] nValues number of table values
   * @return y processed output sample.
   *
   * \par
   * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
   * This function can support maximum of table size 2^12.
   */


  static __INLINE q7_t arm_linear_interp_q7(
  q7_t * pYData,
  q31_t x,
  uint32_t nValues)
  {
    q31_t y;                                     /* output */
    q7_t y0, y1;                                 /* Nearest output values */
    q31_t fract;                                 /* fractional part */
    uint32_t index;                              /* Index to read nearest output values */

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    if (x < 0)
    {
      return (pYData[0]);
    }
    index = (x >> 20) & 0xfff;


    if(index >= (nValues - 1))
    {
      return (pYData[nValues - 1]);
    }
    else
    {

      /* 20 bits for the fractional part */
      /* fract is in 12.20 format */
      fract = (x & 0x000FFFFF);

      /* Read two nearest output values from the index and are in 1.7(q7) format */
      y0 = pYData[index];
      y1 = pYData[index + 1u];

      /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */
      y = ((y0 * (0xFFFFF - fract)));

      /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */
      y += (y1 * fract);

      /* convert y to 1.7(q7) format */
      return (y >> 20u);

    }

  }
  /**
   * @} end of LinearInterpolate group
   */

  /**
   * @brief  Fast approximation to the trigonometric sine function for floating-point data.
   * @param[in] x input value in radians.
   * @return  sin(x).
   */

  float32_t arm_sin_f32(
  float32_t x);

  /**
   * @brief  Fast approximation to the trigonometric sine function for Q31 data.
   * @param[in] x Scaled input value in radians.
   * @return  sin(x).
   */

  q31_t arm_sin_q31(
  q31_t x);

  /**
   * @brief  Fast approximation to the trigonometric sine function for Q15 data.
   * @param[in] x Scaled input value in radians.
   * @return  sin(x).
   */

  q15_t arm_sin_q15(
  q15_t x);

  /**
   * @brief  Fast approximation to the trigonometric cosine function for floating-point data.
   * @param[in] x input value in radians.
   * @return  cos(x).
   */

  float32_t arm_cos_f32(
  float32_t x);

  /**
   * @brief Fast approximation to the trigonometric cosine function for Q31 data.
   * @param[in] x Scaled input value in radians.
   * @return  cos(x).
   */

  q31_t arm_cos_q31(
  q31_t x);

  /**
   * @brief  Fast approximation to the trigonometric cosine function for Q15 data.
   * @param[in] x Scaled input value in radians.
   * @return  cos(x).
   */

  q15_t arm_cos_q15(
  q15_t x);


  /**
   * @ingroup groupFastMath
   */


  /**
   * @defgroup SQRT Square Root
   *
   * Computes the square root of a number.
   * There are separate functions for Q15, Q31, and floating-point data types.
   * The square root function is computed using the Newton-Raphson algorithm.
   * This is an iterative algorithm of the form:
   * <pre>
   *      x1 = x0 - f(x0)/f'(x0)
   * </pre>
   * where <code>x1</code> is the current estimate,
   * <code>x0</code> is the previous estimate, and
   * <code>f'(x0)</code> is the derivative of <code>f()</code> evaluated at <code>x0</code>.
   * For the square root function, the algorithm reduces to:
   * <pre>
   *     x0 = in/2                         [initial guess]
   *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
   * </pre>
   */


  /**
   * @addtogroup SQRT
   * @{
   */

  /**
   * @brief  Floating-point square root function.
   * @param[in]  in     input value.
   * @param[out] *pOut  square root of input value.
   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
   * <code>in</code> is negative value and returns zero output for negative values.
   */

  static __INLINE arm_status arm_sqrt_f32(
  float32_t in,
  float32_t * pOut)
  {
    if(in >= 0.0f)
    {

//      #if __FPU_USED
#if (__FPU_USED == 1) && defined ( __CC_ARM   )
      *pOut = __sqrtf(in);
#else
      *pOut = sqrtf(in);
#endif

      return (ARM_MATH_SUCCESS);
    }
    else
    {
      *pOut = 0.0f;
      return (ARM_MATH_ARGUMENT_ERROR);
    }

  }


  /**
   * @brief Q31 square root function.
   * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
   * @param[out]  *pOut square root of input value.
   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
   * <code>in</code> is negative value and returns zero output for negative values.
   */
  arm_status arm_sqrt_q31(
  q31_t in,
  q31_t * pOut);

  /**
   * @brief  Q15 square root function.
   * @param[in]   in     input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF.
   * @param[out]  *pOut  square root of input value.
   * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
   * <code>in</code> is negative value and returns zero output for negative values.
   */
  arm_status arm_sqrt_q15(
  q15_t in,
  q15_t * pOut);

  /**
   * @} end of SQRT group
   */






  /**
   * @brief floating-point Circular write function.
   */

  static __INLINE void arm_circularWrite_f32(
  int32_t * circBuffer,
  int32_t L,
  uint16_t * writeOffset,
  int32_t bufferInc,
  const int32_t * src,
  int32_t srcInc,
  uint32_t blockSize)
  {
    uint32_t i = 0u;
    int32_t wOffset;

    /* Copy the value of Index pointer that points
     * to the current location where the input samples to be copied */
    wOffset = *writeOffset;

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the input sample to the circular buffer */
      circBuffer[wOffset] = *src;

      /* Update the input pointer */
      src += srcInc;

      /* Circularly update wOffset.  Watch out for positive and negative value */
      wOffset += bufferInc;
      if(wOffset >= L)
        wOffset -= L;

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *writeOffset = wOffset;
  }



  /**
   * @brief floating-point Circular Read function.
   */
  static __INLINE void arm_circularRead_f32(
  int32_t * circBuffer,
  int32_t L,
  int32_t * readOffset,
  int32_t bufferInc,
  int32_t * dst,
  int32_t * dst_base,
  int32_t dst_length,
  int32_t dstInc,
  uint32_t blockSize)
  {
    uint32_t i = 0u;
    int32_t rOffset, dst_end;

    /* Copy the value of Index pointer that points
     * to the current location from where the input samples to be read */
    rOffset = *readOffset;
    dst_end = (int32_t) (dst_base + dst_length);

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the sample from the circular buffer to the destination buffer */
      *dst = circBuffer[rOffset];

      /* Update the input pointer */
      dst += dstInc;

      if(dst == (int32_t *) dst_end)
      {
        dst = dst_base;
      }

      /* Circularly update rOffset.  Watch out for positive and negative value  */
      rOffset += bufferInc;

      if(rOffset >= L)
      {
        rOffset -= L;
      }

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *readOffset = rOffset;
  }

  /**
   * @brief Q15 Circular write function.
   */

  static __INLINE void arm_circularWrite_q15(
  q15_t * circBuffer,
  int32_t L,
  uint16_t * writeOffset,
  int32_t bufferInc,
  const q15_t * src,
  int32_t srcInc,
  uint32_t blockSize)
  {
    uint32_t i = 0u;
    int32_t wOffset;

    /* Copy the value of Index pointer that points
     * to the current location where the input samples to be copied */
    wOffset = *writeOffset;

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the input sample to the circular buffer */
      circBuffer[wOffset] = *src;

      /* Update the input pointer */
      src += srcInc;

      /* Circularly update wOffset.  Watch out for positive and negative value */
      wOffset += bufferInc;
      if(wOffset >= L)
        wOffset -= L;

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *writeOffset = wOffset;
  }



  /**
   * @brief Q15 Circular Read function.
   */
  static __INLINE void arm_circularRead_q15(
  q15_t * circBuffer,
  int32_t L,
  int32_t * readOffset,
  int32_t bufferInc,
  q15_t * dst,
  q15_t * dst_base,
  int32_t dst_length,
  int32_t dstInc,
  uint32_t blockSize)
  {
    uint32_t i = 0;
    int32_t rOffset, dst_end;

    /* Copy the value of Index pointer that points
     * to the current location from where the input samples to be read */
    rOffset = *readOffset;

    dst_end = (int32_t) (dst_base + dst_length);

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the sample from the circular buffer to the destination buffer */
      *dst = circBuffer[rOffset];

      /* Update the input pointer */
      dst += dstInc;

      if(dst == (q15_t *) dst_end)
      {
        dst = dst_base;
      }

      /* Circularly update wOffset.  Watch out for positive and negative value */
      rOffset += bufferInc;

      if(rOffset >= L)
      {
        rOffset -= L;
      }

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *readOffset = rOffset;
  }


  /**
   * @brief Q7 Circular write function.
   */

  static __INLINE void arm_circularWrite_q7(
  q7_t * circBuffer,
  int32_t L,
  uint16_t * writeOffset,
  int32_t bufferInc,
  const q7_t * src,
  int32_t srcInc,
  uint32_t blockSize)
  {
    uint32_t i = 0u;
    int32_t wOffset;

    /* Copy the value of Index pointer that points
     * to the current location where the input samples to be copied */
    wOffset = *writeOffset;

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the input sample to the circular buffer */
      circBuffer[wOffset] = *src;

      /* Update the input pointer */
      src += srcInc;

      /* Circularly update wOffset.  Watch out for positive and negative value */
      wOffset += bufferInc;
      if(wOffset >= L)
        wOffset -= L;

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *writeOffset = wOffset;
  }



  /**
   * @brief Q7 Circular Read function.
   */
  static __INLINE void arm_circularRead_q7(
  q7_t * circBuffer,
  int32_t L,
  int32_t * readOffset,
  int32_t bufferInc,
  q7_t * dst,
  q7_t * dst_base,
  int32_t dst_length,
  int32_t dstInc,
  uint32_t blockSize)
  {
    uint32_t i = 0;
    int32_t rOffset, dst_end;

    /* Copy the value of Index pointer that points
     * to the current location from where the input samples to be read */
    rOffset = *readOffset;

    dst_end = (int32_t) (dst_base + dst_length);

    /* Loop over the blockSize */
    i = blockSize;

    while(i > 0u)
    {
      /* copy the sample from the circular buffer to the destination buffer */
      *dst = circBuffer[rOffset];

      /* Update the input pointer */
      dst += dstInc;

      if(dst == (q7_t *) dst_end)
      {
        dst = dst_base;
      }

      /* Circularly update rOffset.  Watch out for positive and negative value */
      rOffset += bufferInc;

      if(rOffset >= L)
      {
        rOffset -= L;
      }

      /* Decrement the loop counter */
      i--;
    }

    /* Update the index pointer */
    *readOffset = rOffset;
  }


  /**
   * @brief  Sum of the squares of the elements of a Q31 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_power_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q63_t * pResult);

  /**
   * @brief  Sum of the squares of the elements of a floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_power_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  /**
   * @brief  Sum of the squares of the elements of a Q15 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_power_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q63_t * pResult);

  /**
   * @brief  Sum of the squares of the elements of a Q7 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_power_q7(
  q7_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  /**
   * @brief  Mean value of a Q7 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_mean_q7(
  q7_t * pSrc,
  uint32_t blockSize,
  q7_t * pResult);

  /**
   * @brief  Mean value of a Q15 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */
  void arm_mean_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult);

  /**
   * @brief  Mean value of a Q31 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */
  void arm_mean_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  /**
   * @brief  Mean value of a floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */
  void arm_mean_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  /**
   * @brief  Variance of the elements of a floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_var_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  /**
   * @brief  Variance of the elements of a Q31 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_var_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  /**
   * @brief  Variance of the elements of a Q15 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_var_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult);

  /**
   * @brief  Root Mean Square of the elements of a floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_rms_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  /**
   * @brief  Root Mean Square of the elements of a Q31 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_rms_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  /**
   * @brief  Root Mean Square of the elements of a Q15 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_rms_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult);

  /**
   * @brief  Standard deviation of the elements of a floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_std_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult);

  /**
   * @brief  Standard deviation of the elements of a Q31 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_std_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult);

  /**
   * @brief  Standard deviation of the elements of a Q15 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output value.
   * @return none.
   */

  void arm_std_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult);

  /**
   * @brief  Floating-point complex magnitude
   * @param[in]  *pSrc points to the complex input vector
   * @param[out]  *pDst points to the real output vector
   * @param[in]  numSamples number of complex samples in the input vector
   * @return none.
   */

  void arm_cmplx_mag_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Q31 complex magnitude
   * @param[in]  *pSrc points to the complex input vector
   * @param[out]  *pDst points to the real output vector
   * @param[in]  numSamples number of complex samples in the input vector
   * @return none.
   */

  void arm_cmplx_mag_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Q15 complex magnitude
   * @param[in]  *pSrc points to the complex input vector
   * @param[out]  *pDst points to the real output vector
   * @param[in]  numSamples number of complex samples in the input vector
   * @return none.
   */

  void arm_cmplx_mag_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Q15 complex dot product
   * @param[in]  *pSrcA points to the first input vector
   * @param[in]  *pSrcB points to the second input vector
   * @param[in]  numSamples number of complex samples in each vector
   * @param[out]  *realResult real part of the result returned here
   * @param[out]  *imagResult imaginary part of the result returned here
   * @return none.
   */

  void arm_cmplx_dot_prod_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  uint32_t numSamples,
  q31_t * realResult,
  q31_t * imagResult);

  /**
   * @brief  Q31 complex dot product
   * @param[in]  *pSrcA points to the first input vector
   * @param[in]  *pSrcB points to the second input vector
   * @param[in]  numSamples number of complex samples in each vector
   * @param[out]  *realResult real part of the result returned here
   * @param[out]  *imagResult imaginary part of the result returned here
   * @return none.
   */

  void arm_cmplx_dot_prod_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  uint32_t numSamples,
  q63_t * realResult,
  q63_t * imagResult);

  /**
   * @brief  Floating-point complex dot product
   * @param[in]  *pSrcA points to the first input vector
   * @param[in]  *pSrcB points to the second input vector
   * @param[in]  numSamples number of complex samples in each vector
   * @param[out]  *realResult real part of the result returned here
   * @param[out]  *imagResult imaginary part of the result returned here
   * @return none.
   */

  void arm_cmplx_dot_prod_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  uint32_t numSamples,
  float32_t * realResult,
  float32_t * imagResult);

  /**
   * @brief  Q15 complex-by-real multiplication
   * @param[in]  *pSrcCmplx points to the complex input vector
   * @param[in]  *pSrcReal points to the real input vector
   * @param[out]  *pCmplxDst points to the complex output vector
   * @param[in]  numSamples number of samples in each vector
   * @return none.
   */

  void arm_cmplx_mult_real_q15(
  q15_t * pSrcCmplx,
  q15_t * pSrcReal,
  q15_t * pCmplxDst,
  uint32_t numSamples);

  /**
   * @brief  Q31 complex-by-real multiplication
   * @param[in]  *pSrcCmplx points to the complex input vector
   * @param[in]  *pSrcReal points to the real input vector
   * @param[out]  *pCmplxDst points to the complex output vector
   * @param[in]  numSamples number of samples in each vector
   * @return none.
   */

  void arm_cmplx_mult_real_q31(
  q31_t * pSrcCmplx,
  q31_t * pSrcReal,
  q31_t * pCmplxDst,
  uint32_t numSamples);

  /**
   * @brief  Floating-point complex-by-real multiplication
   * @param[in]  *pSrcCmplx points to the complex input vector
   * @param[in]  *pSrcReal points to the real input vector
   * @param[out]  *pCmplxDst points to the complex output vector
   * @param[in]  numSamples number of samples in each vector
   * @return none.
   */

  void arm_cmplx_mult_real_f32(
  float32_t * pSrcCmplx,
  float32_t * pSrcReal,
  float32_t * pCmplxDst,
  uint32_t numSamples);

  /**
   * @brief  Minimum value of a Q7 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *result is output pointer
   * @param[in]  index is the array index of the minimum value in the input buffer.
   * @return none.
   */

  void arm_min_q7(
  q7_t * pSrc,
  uint32_t blockSize,
  q7_t * result,
  uint32_t * index);

  /**
   * @brief  Minimum value of a Q15 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output pointer
   * @param[in]  *pIndex is the array index of the minimum value in the input buffer.
   * @return none.
   */

  void arm_min_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult,
  uint32_t * pIndex);

  /**
   * @brief  Minimum value of a Q31 vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output pointer
   * @param[out]  *pIndex is the array index of the minimum value in the input buffer.
   * @return none.
   */
  void arm_min_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult,
  uint32_t * pIndex);

  /**
   * @brief  Minimum value of a floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[in]  blockSize is the number of samples to process
   * @param[out]  *pResult is output pointer
   * @param[out]  *pIndex is the array index of the minimum value in the input buffer.
   * @return none.
   */

  void arm_min_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult,
  uint32_t * pIndex);

/**
 * @brief Maximum value of a Q7 vector.
 * @param[in]       *pSrc points to the input buffer
 * @param[in]       blockSize length of the input vector
 * @param[out]      *pResult maximum value returned here
 * @param[out]      *pIndex index of maximum value returned here
 * @return none.
 */

  void arm_max_q7(
  q7_t * pSrc,
  uint32_t blockSize,
  q7_t * pResult,
  uint32_t * pIndex);

/**
 * @brief Maximum value of a Q15 vector.
 * @param[in]       *pSrc points to the input buffer
 * @param[in]       blockSize length of the input vector
 * @param[out]      *pResult maximum value returned here
 * @param[out]      *pIndex index of maximum value returned here
 * @return none.
 */

  void arm_max_q15(
  q15_t * pSrc,
  uint32_t blockSize,
  q15_t * pResult,
  uint32_t * pIndex);

/**
 * @brief Maximum value of a Q31 vector.
 * @param[in]       *pSrc points to the input buffer
 * @param[in]       blockSize length of the input vector
 * @param[out]      *pResult maximum value returned here
 * @param[out]      *pIndex index of maximum value returned here
 * @return none.
 */

  void arm_max_q31(
  q31_t * pSrc,
  uint32_t blockSize,
  q31_t * pResult,
  uint32_t * pIndex);

/**
 * @brief Maximum value of a floating-point vector.
 * @param[in]       *pSrc points to the input buffer
 * @param[in]       blockSize length of the input vector
 * @param[out]      *pResult maximum value returned here
 * @param[out]      *pIndex index of maximum value returned here
 * @return none.
 */

  void arm_max_f32(
  float32_t * pSrc,
  uint32_t blockSize,
  float32_t * pResult,
  uint32_t * pIndex);

  /**
   * @brief  Q15 complex-by-complex multiplication
   * @param[in]  *pSrcA points to the first input vector
   * @param[in]  *pSrcB points to the second input vector
   * @param[out]  *pDst  points to the output vector
   * @param[in]  numSamples number of complex samples in each vector
   * @return none.
   */

  void arm_cmplx_mult_cmplx_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Q31 complex-by-complex multiplication
   * @param[in]  *pSrcA points to the first input vector
   * @param[in]  *pSrcB points to the second input vector
   * @param[out]  *pDst  points to the output vector
   * @param[in]  numSamples number of complex samples in each vector
   * @return none.
   */

  void arm_cmplx_mult_cmplx_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t numSamples);

  /**
   * @brief  Floating-point complex-by-complex multiplication
   * @param[in]  *pSrcA points to the first input vector
   * @param[in]  *pSrcB points to the second input vector
   * @param[out]  *pDst  points to the output vector
   * @param[in]  numSamples number of complex samples in each vector
   * @return none.
   */

  void arm_cmplx_mult_cmplx_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t numSamples);

  /**
   * @brief Converts the elements of the floating-point vector to Q31 vector.
   * @param[in]       *pSrc points to the floating-point input vector
   * @param[out]      *pDst points to the Q31 output vector
   * @param[in]       blockSize length of the input vector
   * @return none.
   */
  void arm_float_to_q31(
  float32_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Converts the elements of the floating-point vector to Q15 vector.
   * @param[in]       *pSrc points to the floating-point input vector
   * @param[out]      *pDst points to the Q15 output vector
   * @param[in]       blockSize length of the input vector
   * @return          none
   */
  void arm_float_to_q15(
  float32_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief Converts the elements of the floating-point vector to Q7 vector.
   * @param[in]       *pSrc points to the floating-point input vector
   * @param[out]      *pDst points to the Q7 output vector
   * @param[in]       blockSize length of the input vector
   * @return          none
   */
  void arm_float_to_q7(
  float32_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Converts the elements of the Q31 vector to Q15 vector.
   * @param[in]  *pSrc is input pointer
   * @param[out]  *pDst is output pointer
   * @param[in]  blockSize is the number of samples to process
   * @return none.
   */
  void arm_q31_to_q15(
  q31_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Converts the elements of the Q31 vector to Q7 vector.
   * @param[in]  *pSrc is input pointer
   * @param[out]  *pDst is output pointer
   * @param[in]  blockSize is the number of samples to process
   * @return none.
   */
  void arm_q31_to_q7(
  q31_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);

  /**
   * @brief  Converts the elements of the Q15 vector to floating-point vector.
   * @param[in]  *pSrc is input pointer
   * @param[out]  *pDst is output pointer
   * @param[in]  blockSize is the number of samples to process
   * @return none.
   */
  void arm_q15_to_float(
  q15_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Converts the elements of the Q15 vector to Q31 vector.
   * @param[in]  *pSrc is input pointer
   * @param[out]  *pDst is output pointer
   * @param[in]  blockSize is the number of samples to process
   * @return none.
   */
  void arm_q15_to_q31(
  q15_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Converts the elements of the Q15 vector to Q7 vector.
   * @param[in]  *pSrc is input pointer
   * @param[out]  *pDst is output pointer
   * @param[in]  blockSize is the number of samples to process
   * @return none.
   */
  void arm_q15_to_q7(
  q15_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @ingroup groupInterpolation
   */

  /**
   * @defgroup BilinearInterpolate Bilinear Interpolation
   *
   * Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.
   * The underlying function <code>f(x, y)</code> is sampled on a regular grid and the interpolation process
   * determines values between the grid points.
   * Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension.
   * Bilinear interpolation is often used in image processing to rescale images.
   * The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types.
   *
   * <b>Algorithm</b>
   * \par
   * The instance structure used by the bilinear interpolation functions describes a two dimensional data table.
   * For floating-point, the instance structure is defined as:
   * <pre>
   *   typedef struct
   *   {
   *     uint16_t numRows;
   *     uint16_t numCols;
   *     float32_t *pData;
   * } arm_bilinear_interp_instance_f32;
   * </pre>
   *
   * \par
   * where <code>numRows</code> specifies the number of rows in the table;
   * <code>numCols</code> specifies the number of columns in the table;
   * and <code>pData</code> points to an array of size <code>numRows*numCols</code> values.
   * The data table <code>pTable</code> is organized in row order and the supplied data values fall on integer indexes.
   * That is, table element (x,y) is located at <code>pTable[x + y*numCols]</code> where x and y are integers.
   *
   * \par
   * Let <code>(x, y)</code> specify the desired interpolation point.  Then define:
   * <pre>
   *     XF = floor(x)
   *     YF = floor(y)
   * </pre>
   * \par
   * The interpolated output point is computed as:
   * <pre>
   *  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
   *           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
   *           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
   *           + f(XF+1, YF+1) * (x-XF)*(y-YF)
   * </pre>
   * Note that the coordinates (x, y) contain integer and fractional components.
   * The integer components specify which portion of the table to use while the
   * fractional components control the interpolation processor.
   *
   * \par
   * if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output.
   */

  /**
   * @addtogroup BilinearInterpolate
   * @{
   */

  /**
  *
  * @brief  Floating-point bilinear interpolation.
  * @param[in,out] *S points to an instance of the interpolation structure.
  * @param[in] X interpolation coordinate.
  * @param[in] Y interpolation coordinate.
  * @return out interpolated value.
  */


  static __INLINE float32_t arm_bilinear_interp_f32(
  const arm_bilinear_interp_instance_f32 * S,
  float32_t X,
  float32_t Y)
  {
    float32_t out;
    float32_t f00, f01, f10, f11;
    float32_t *pData = S->pData;
    int32_t xIndex, yIndex, index;
    float32_t xdiff, ydiff;
    float32_t b1, b2, b3, b4;

    xIndex = (int32_t) X;
    yIndex = (int32_t) Y;

    /* Care taken for table outside boundary */
    /* Returns zero output when values are outside table boundary */
    if(xIndex < 0 || xIndex > (S->numRows - 1) || yIndex < 0
       || yIndex > (S->numCols - 1))
    {
      return (0);
    }

    /* Calculation of index for two nearest points in X-direction */
    index = (xIndex - 1) + (yIndex - 1) * S->numCols;


    /* Read two nearest points in X-direction */
    f00 = pData[index];
    f01 = pData[index + 1];

    /* Calculation of index for two nearest points in Y-direction */
    index = (xIndex - 1) + (yIndex) * S->numCols;


    /* Read two nearest points in Y-direction */
    f10 = pData[index];
    f11 = pData[index + 1];

    /* Calculation of intermediate values */
    b1 = f00;
    b2 = f01 - f00;
    b3 = f10 - f00;
    b4 = f00 - f01 - f10 + f11;

    /* Calculation of fractional part in X */
    xdiff = X - xIndex;

    /* Calculation of fractional part in Y */
    ydiff = Y - yIndex;

    /* Calculation of bi-linear interpolated output */
    out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;

    /* return to application */
    return (out);

  }

  /**
  *
  * @brief  Q31 bilinear interpolation.
  * @param[in,out] *S points to an instance of the interpolation structure.
  * @param[in] X interpolation coordinate in 12.20 format.
  * @param[in] Y interpolation coordinate in 12.20 format.
  * @return out interpolated value.
  */

  static __INLINE q31_t arm_bilinear_interp_q31(
  arm_bilinear_interp_instance_q31 * S,
  q31_t X,
  q31_t Y)
  {
    q31_t out;                                   /* Temporary output */
    q31_t acc = 0;                               /* output */
    q31_t xfract, yfract;                        /* X, Y fractional parts */
    q31_t x1, x2, y1, y2;                        /* Nearest output values */
    int32_t rI, cI;                              /* Row and column indices */
    q31_t *pYData = S->pData;                    /* pointer to output table values */
    uint32_t nCols = S->numCols;                 /* num of rows */


    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    rI = ((X & 0xFFF00000) >> 20u);

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    cI = ((Y & 0xFFF00000) >> 20u);

    /* Care taken for table outside boundary */
    /* Returns zero output when values are outside table boundary */
    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
    {
      return (0);
    }

    /* 20 bits for the fractional part */
    /* shift left xfract by 11 to keep 1.31 format */
    xfract = (X & 0x000FFFFF) << 11u;

    /* Read two nearest output values from the index */
    x1 = pYData[(rI) + nCols * (cI)];
    x2 = pYData[(rI) + nCols * (cI) + 1u];

    /* 20 bits for the fractional part */
    /* shift left yfract by 11 to keep 1.31 format */
    yfract = (Y & 0x000FFFFF) << 11u;

    /* Read two nearest output values from the index */
    y1 = pYData[(rI) + nCols * (cI + 1)];
    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */
    out = ((q31_t) (((q63_t) x1 * (0x7FFFFFFF - xfract)) >> 32));
    acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32));

    /* x2 * (xfract) * (1-yfract)  in 3.29(q29) and adding to acc */
    out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32));
    acc += ((q31_t) ((q63_t) out * (xfract) >> 32));

    /* y1 * (1 - xfract) * (yfract)  in 3.29(q29) and adding to acc */
    out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32));
    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));

    /* y2 * (xfract) * (yfract)  in 3.29(q29) and adding to acc */
    out = ((q31_t) ((q63_t) y2 * (xfract) >> 32));
    acc += ((q31_t) ((q63_t) out * (yfract) >> 32));

    /* Convert acc to 1.31(q31) format */
    return (acc << 2u);

  }

  /**
  * @brief  Q15 bilinear interpolation.
  * @param[in,out] *S points to an instance of the interpolation structure.
  * @param[in] X interpolation coordinate in 12.20 format.
  * @param[in] Y interpolation coordinate in 12.20 format.
  * @return out interpolated value.
  */

  static __INLINE q15_t arm_bilinear_interp_q15(
  arm_bilinear_interp_instance_q15 * S,
  q31_t X,
  q31_t Y)
  {
    q63_t acc = 0;                               /* output */
    q31_t out;                                   /* Temporary output */
    q15_t x1, x2, y1, y2;                        /* Nearest output values */
    q31_t xfract, yfract;                        /* X, Y fractional parts */
    int32_t rI, cI;                              /* Row and column indices */
    q15_t *pYData = S->pData;                    /* pointer to output table values */
    uint32_t nCols = S->numCols;                 /* num of rows */

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    rI = ((X & 0xFFF00000) >> 20);

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    cI = ((Y & 0xFFF00000) >> 20);

    /* Care taken for table outside boundary */
    /* Returns zero output when values are outside table boundary */
    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
    {
      return (0);
    }

    /* 20 bits for the fractional part */
    /* xfract should be in 12.20 format */
    xfract = (X & 0x000FFFFF);

    /* Read two nearest output values from the index */
    x1 = pYData[(rI) + nCols * (cI)];
    x2 = pYData[(rI) + nCols * (cI) + 1u];


    /* 20 bits for the fractional part */
    /* yfract should be in 12.20 format */
    yfract = (Y & 0x000FFFFF);

    /* Read two nearest output values from the index */
    y1 = pYData[(rI) + nCols * (cI + 1)];
    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */

    /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */
    /* convert 13.35 to 13.31 by right shifting  and out is in 1.31 */
    out = (q31_t) (((q63_t) x1 * (0xFFFFF - xfract)) >> 4u);
    acc = ((q63_t) out * (0xFFFFF - yfract));

    /* x2 * (xfract) * (1-yfract)  in 1.51 and adding to acc */
    out = (q31_t) (((q63_t) x2 * (0xFFFFF - yfract)) >> 4u);
    acc += ((q63_t) out * (xfract));

    /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
    out = (q31_t) (((q63_t) y1 * (0xFFFFF - xfract)) >> 4u);
    acc += ((q63_t) out * (yfract));

    /* y2 * (xfract) * (yfract)  in 1.51 and adding to acc */
    out = (q31_t) (((q63_t) y2 * (xfract)) >> 4u);
    acc += ((q63_t) out * (yfract));

    /* acc is in 13.51 format and down shift acc by 36 times */
    /* Convert out to 1.15 format */
    return (acc >> 36);

  }

  /**
  * @brief  Q7 bilinear interpolation.
  * @param[in,out] *S points to an instance of the interpolation structure.
  * @param[in] X interpolation coordinate in 12.20 format.
  * @param[in] Y interpolation coordinate in 12.20 format.
  * @return out interpolated value.
  */

  static __INLINE q7_t arm_bilinear_interp_q7(
  arm_bilinear_interp_instance_q7 * S,
  q31_t X,
  q31_t Y)
  {
    q63_t acc = 0;                               /* output */
    q31_t out;                                   /* Temporary output */
    q31_t xfract, yfract;                        /* X, Y fractional parts */
    q7_t x1, x2, y1, y2;                         /* Nearest output values */
    int32_t rI, cI;                              /* Row and column indices */
    q7_t *pYData = S->pData;                     /* pointer to output table values */
    uint32_t nCols = S->numCols;                 /* num of rows */

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    rI = ((X & 0xFFF00000) >> 20);

    /* Input is in 12.20 format */
    /* 12 bits for the table index */
    /* Index value calculation */
    cI = ((Y & 0xFFF00000) >> 20);

    /* Care taken for table outside boundary */
    /* Returns zero output when values are outside table boundary */
    if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
    {
      return (0);
    }

    /* 20 bits for the fractional part */
    /* xfract should be in 12.20 format */
    xfract = (X & 0x000FFFFF);

    /* Read two nearest output values from the index */
    x1 = pYData[(rI) + nCols * (cI)];
    x2 = pYData[(rI) + nCols * (cI) + 1u];


    /* 20 bits for the fractional part */
    /* yfract should be in 12.20 format */
    yfract = (Y & 0x000FFFFF);

    /* Read two nearest output values from the index */
    y1 = pYData[(rI) + nCols * (cI + 1)];
    y2 = pYData[(rI) + nCols * (cI + 1) + 1u];

    /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */
    out = ((x1 * (0xFFFFF - xfract)));
    acc = (((q63_t) out * (0xFFFFF - yfract)));

    /* x2 * (xfract) * (1-yfract)  in 2.22 and adding to acc */
    out = ((x2 * (0xFFFFF - yfract)));
    acc += (((q63_t) out * (xfract)));

    /* y1 * (1 - xfract) * (yfract)  in 2.22 and adding to acc */
    out = ((y1 * (0xFFFFF - xfract)));
    acc += (((q63_t) out * (yfract)));

    /* y2 * (xfract) * (yfract)  in 2.22 and adding to acc */
    out = ((y2 * (yfract)));
    acc += (((q63_t) out * (xfract)));

    /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */
    return (acc >> 40);

  }

  /**
   * @} end of BilinearInterpolate group
   */
   

//SMMLAR
#define multAcc_32x32_keep32_R(a, x, y) \
    a = (q31_t) (((((q63_t) a) << 32) + ((q63_t) x * y) + 0x80000000LL ) >> 32)

//SMMLSR
#define multSub_32x32_keep32_R(a, x, y) \
    a = (q31_t) (((((q63_t) a) << 32) - ((q63_t) x * y) + 0x80000000LL ) >> 32)

//SMMULR
#define mult_32x32_keep32_R(a, x, y) \
    a = (q31_t) (((q63_t) x * y + 0x80000000LL ) >> 32)

//SMMLA
#define multAcc_32x32_keep32(a, x, y) \
    a += (q31_t) (((q63_t) x * y) >> 32)

//SMMLS
#define multSub_32x32_keep32(a, x, y) \
    a -= (q31_t) (((q63_t) x * y) >> 32)

//SMMUL
#define mult_32x32_keep32(a, x, y) \
    a = (q31_t) (((q63_t) x * y ) >> 32)


#if defined ( __CC_ARM ) //Keil

//Enter low optimization region - place directly above function definition
    #ifdef ARM_MATH_CM4
      #define LOW_OPTIMIZATION_ENTER \
         _Pragma ("push")         \
         _Pragma ("O1")
    #else
      #define LOW_OPTIMIZATION_ENTER 
    #endif

//Exit low optimization region - place directly after end of function definition
    #ifdef ARM_MATH_CM4
      #define LOW_OPTIMIZATION_EXIT \
         _Pragma ("pop")
    #else
      #define LOW_OPTIMIZATION_EXIT  
    #endif

//Enter low optimization region - place directly above function definition
  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER

//Exit low optimization region - place directly after end of function definition
  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#elif defined(__ICCARM__) //IAR

//Enter low optimization region - place directly above function definition
    #ifdef ARM_MATH_CM4
      #define LOW_OPTIMIZATION_ENTER \
         _Pragma ("optimize=low")
    #else
      #define LOW_OPTIMIZATION_ENTER   
    #endif

//Exit low optimization region - place directly after end of function definition
  #define LOW_OPTIMIZATION_EXIT

//Enter low optimization region - place directly above function definition
    #ifdef ARM_MATH_CM4
      #define IAR_ONLY_LOW_OPTIMIZATION_ENTER \
         _Pragma ("optimize=low")
    #else
      #define IAR_ONLY_LOW_OPTIMIZATION_ENTER   
    #endif

//Exit low optimization region - place directly after end of function definition
  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#elif defined(__GNUC__)

  #define LOW_OPTIMIZATION_ENTER __attribute__(( optimize("-O1") ))

  #define LOW_OPTIMIZATION_EXIT

  #define IAR_ONLY_LOW_OPTIMIZATION_ENTER

  #define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#elif defined(__CSMC__)		// Cosmic

#define LOW_OPTIMIZATION_ENTER
#define LOW_OPTIMIZATION_EXIT
#define IAR_ONLY_LOW_OPTIMIZATION_ENTER
#define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#elif defined(__TASKING__)		// TASKING

#define LOW_OPTIMIZATION_ENTER
#define LOW_OPTIMIZATION_EXIT
#define IAR_ONLY_LOW_OPTIMIZATION_ENTER
#define IAR_ONLY_LOW_OPTIMIZATION_EXIT

#endif


#ifdef	__cplusplus
}
#endif


#endif /* _ARM_MATH_H */

/**
 *
 * End of file.
 */