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diff --git a/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q31.c b/apps/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q31.c
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+/* ----------------------------------------------------------------------
+* Copyright (C) 2010 ARM Limited. All rights reserved.
+*
+* $Date: 15. February 2012
+* $Revision: V1.1.0
+*
+* Project: CMSIS DSP Library
+* Title: arm_rfft_q31.c
+*
+* Description: RFFT & RIFFT Q31 process function
+*
+*
+* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
+*
+* Version 1.1.0 2012/02/15
+* Updated with more optimizations, bug fixes and minor API changes.
+*
+* Version 1.0.10 2011/7/15
+* Big Endian support added and Merged M0 and M3/M4 Source code.
+*
+* Version 1.0.3 2010/11/29
+* Re-organized the CMSIS folders and updated documentation.
+*
+* Version 1.0.2 2010/11/11
+* Documentation updated.
+*
+* Version 1.0.1 2010/10/05
+* Production release and review comments incorporated.
+*
+* Version 1.0.0 2010/09/20
+* Production release and review comments incorporated.
+*
+* Version 0.0.7 2010/06/10
+* Misra-C changes done
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/*--------------------------------------------------------------------
+* Internal functions prototypes
+--------------------------------------------------------------------*/
+
+void arm_split_rfft_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ q31_t * pATable,
+ q31_t * pBTable,
+ q31_t * pDst,
+ uint32_t modifier);
+
+void arm_split_rifft_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ q31_t * pATable,
+ q31_t * pBTable,
+ q31_t * pDst,
+ uint32_t modifier);
+
+/**
+ * @addtogroup RFFT_RIFFT
+ * @{
+ */
+
+/**
+ * @brief Processing function for the Q31 RFFT/RIFFT.
+ * @param[in] *S points to an instance of the Q31 RFFT/RIFFT structure.
+ * @param[in] *pSrc points to the input buffer.
+ * @param[out] *pDst points to the output buffer.
+ * @return none.
+ *
+ * \par Input an output formats:
+ * \par
+ * Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
+ * Hence the output format is different for different RFFT sizes.
+ * The input and output formats for different RFFT sizes and number of bits to upscale are mentioned in the tables below for RFFT and RIFFT:
+ * \par
+ * \image html RFFTQ31.gif "Input and Output Formats for Q31 RFFT"
+ *
+ * \par
+ * \image html RIFFTQ31.gif "Input and Output Formats for Q31 RIFFT"
+ */
+
+void arm_rfft_q31(
+ const arm_rfft_instance_q31 * S,
+ q31_t * pSrc,
+ q31_t * pDst)
+{
+ const arm_cfft_radix4_instance_q31 *S_CFFT = S->pCfft;
+
+ /* Calculation of RIFFT of input */
+ if(S->ifftFlagR == 1u)
+ {
+ /* Real IFFT core process */
+ arm_split_rifft_q31(pSrc, S->fftLenBy2, S->pTwiddleAReal,
+ S->pTwiddleBReal, pDst, S->twidCoefRModifier);
+
+ /* Complex readix-4 IFFT process */
+ arm_radix4_butterfly_inverse_q31(pDst, S_CFFT->fftLen,
+ S_CFFT->pTwiddle,
+ S_CFFT->twidCoefModifier);
+ /* Bit reversal process */
+ if(S->bitReverseFlagR == 1u)
+ {
+ arm_bitreversal_q31(pDst, S_CFFT->fftLen,
+ S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
+ }
+ }
+ else
+ {
+ /* Calculation of RFFT of input */
+
+ /* Complex readix-4 FFT process */
+ arm_radix4_butterfly_q31(pSrc, S_CFFT->fftLen,
+ S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
+
+ /* Bit reversal process */
+ if(S->bitReverseFlagR == 1u)
+ {
+ arm_bitreversal_q31(pSrc, S_CFFT->fftLen,
+ S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
+ }
+
+ /* Real FFT core process */
+ arm_split_rfft_q31(pSrc, S->fftLenBy2, S->pTwiddleAReal,
+ S->pTwiddleBReal, pDst, S->twidCoefRModifier);
+ }
+
+}
+
+
+ /**
+ * @} end of RFFT_RIFFT group
+ */
+
+/**
+ * @brief Core Real FFT process
+ * @param[in] *pSrc points to the input buffer.
+ * @param[in] fftLen length of FFT.
+ * @param[in] *pATable points to the twiddle Coef A buffer.
+ * @param[in] *pBTable points to the twiddle Coef B buffer.
+ * @param[out] *pDst points to the output buffer.
+ * @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+ * @return none.
+ */
+
+void arm_split_rfft_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ q31_t * pATable,
+ q31_t * pBTable,
+ q31_t * pDst,
+ uint32_t modifier)
+{
+ uint32_t i; /* Loop Counter */
+ q31_t outR, outI; /* Temporary variables for output */
+ q31_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
+ q31_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
+ q31_t *pOut1 = &pDst[2], *pOut2 = &pDst[(4u * fftLen) - 1u];
+ q31_t *pIn1 = &pSrc[2], *pIn2 = &pSrc[(2u * fftLen) - 1u];
+
+ /* Init coefficient pointers */
+ pCoefA = &pATable[modifier * 2u];
+ pCoefB = &pBTable[modifier * 2u];
+
+ i = fftLen - 1u;
+
+ while(i > 0u)
+ {
+ /*
+ outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]
+ + pSrc[2 * n - 2 * i] * pBTable[2 * i] +
+ pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
+ */
+
+ /* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +
+ pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
+ pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
+
+ CoefA1 = *pCoefA++;
+ CoefA2 = *pCoefA;
+
+ /* outR = (pSrc[2 * i] * pATable[2 * i] */
+ outR = ((int32_t) (((q63_t) * pIn1 * CoefA1) >> 32));
+
+ /* outI = pIn[2 * i] * pATable[2 * i + 1] */
+ outI = ((int32_t) (((q63_t) * pIn1++ * CoefA2) >> 32));
+
+ /* - pSrc[2 * i + 1] * pATable[2 * i + 1] */
+ outR =
+ (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn1 * (-CoefA2))) >> 32);
+
+ /* (pIn[2 * i + 1] * pATable[2 * i] */
+ outI =
+ (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn1++ * (CoefA1))) >> 32);
+
+ /* pSrc[2 * n - 2 * i] * pBTable[2 * i] */
+ outR =
+ (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (-CoefA2))) >> 32);
+ CoefB1 = *pCoefB;
+
+ /* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] */
+ outI =
+ (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (-CoefB1))) >> 32);
+
+ /* pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1] */
+ outR =
+ (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefB1))) >> 32);
+
+ /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
+ outI =
+ (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (-CoefA2))) >> 32);
+
+ /* write output */
+ *pOut1++ = (outR << 1u);
+ *pOut1++ = (outI << 1u);
+
+ /* write complex conjugate output */
+ *pOut2-- = -(outI << 1u);
+ *pOut2-- = (outR << 1u);
+
+ /* update coefficient pointer */
+ pCoefB = pCoefB + (modifier * 2u);
+ pCoefA = pCoefA + ((modifier * 2u) - 1u);
+
+ i--;
+
+ }
+
+ pDst[2u * fftLen] = pSrc[0] - pSrc[1];
+ pDst[(2u * fftLen) + 1u] = 0;
+
+ pDst[0] = pSrc[0] + pSrc[1];
+ pDst[1] = 0;
+
+}
+
+
+/**
+ * @brief Core Real IFFT process
+ * @param[in] *pSrc points to the input buffer.
+ * @param[in] fftLen length of FFT.
+ * @param[in] *pATable points to the twiddle Coef A buffer.
+ * @param[in] *pBTable points to the twiddle Coef B buffer.
+ * @param[out] *pDst points to the output buffer.
+ * @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+ * @return none.
+ */
+
+void arm_split_rifft_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ q31_t * pATable,
+ q31_t * pBTable,
+ q31_t * pDst,
+ uint32_t modifier)
+{
+ q31_t outR, outI; /* Temporary variables for output */
+ q31_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
+ q31_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
+ q31_t *pIn1 = &pSrc[0], *pIn2 = &pSrc[(2u * fftLen) + 1u];
+
+ pCoefA = &pATable[0];
+ pCoefB = &pBTable[0];
+
+ while(fftLen > 0u)
+ {
+ /*
+ outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
+ pIn[2 * n - 2 * i] * pBTable[2 * i] -
+ pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
+
+ outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -
+ pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
+ pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
+
+ */
+ CoefA1 = *pCoefA++;
+ CoefA2 = *pCoefA;
+
+ /* outR = (pIn[2 * i] * pATable[2 * i] */
+ outR = ((int32_t) (((q63_t) * pIn1 * CoefA1) >> 32));
+
+ /* - pIn[2 * i] * pATable[2 * i + 1] */
+ outI = -((int32_t) (((q63_t) * pIn1++ * CoefA2) >> 32));
+
+ /* pIn[2 * i + 1] * pATable[2 * i + 1] */
+ outR =
+ (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn1 * (CoefA2))) >> 32);
+
+ /* pIn[2 * i + 1] * pATable[2 * i] */
+ outI =
+ (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn1++ * (CoefA1))) >> 32);
+
+ /* pIn[2 * n - 2 * i] * pBTable[2 * i] */
+ outR =
+ (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefA2))) >> 32);
+
+ CoefB1 = *pCoefB;
+
+ /* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] */
+ outI =
+ (q31_t) ((((q63_t) outI << 32) - ((q63_t) * pIn2-- * (CoefB1))) >> 32);
+
+ /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1] */
+ outR =
+ (q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefB1))) >> 32);
+
+ /* pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
+ outI =
+ (q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (CoefA2))) >> 32);
+
+ /* write output */
+ *pDst++ = (outR << 1u);
+ *pDst++ = (outI << 1u);
+
+ /* update coefficient pointer */
+ pCoefB = pCoefB + (modifier * 2u);
+ pCoefA = pCoefA + ((modifier * 2u) - 1u);
+
+ /* Decrement loop count */
+ fftLen--;
+
+ }
+
+
+}
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