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diff --git a/src/modules/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_f32.c b/src/modules/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_f32.c new file mode 100644 index 000000000..d51e9830b --- /dev/null +++ b/src/modules/mathlib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_f32.c @@ -0,0 +1,1236 @@ +/* ----------------------------------------------------------------------
+* Copyright (C) 2010 ARM Limited. All rights reserved.
+*
+* $Date: 15. February 2012
+* $Revision: V1.1.0
+*
+* Project: CMSIS DSP Library
+* Title: arm_cfft_radix4_f32.c
+*
+* Description: Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing 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 0.0.5 2010/04/26
+* incorporated review comments and updated with latest CMSIS layer
+*
+* Version 0.0.3 2010/03/10
+* Initial version
+* -------------------------------------------------------------------- */
+
+#include "arm_math.h"
+
+/**
+ * @ingroup groupTransforms
+ */
+
+/**
+ * @defgroup Radix4_CFFT_CIFFT Radix-4 Complex FFT Functions
+ *
+ * \par
+ * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).
+ * Computational complexity of CFFT reduces drastically when compared to DFT.
+ * \par
+ * This set of functions implements CFFT/CIFFT
+ * for Q15, Q31, and floating-point data types. The functions operates on in-place buffer which uses same buffer for input and output.
+ * Complex input is stored in input buffer in an interleaved fashion.
+ *
+ * \par
+ * The functions operate on blocks of input and output data and each call to the function processes
+ * <code>2*fftLen</code> samples through the transform. <code>pSrc</code> points to In-place arrays containing <code>2*fftLen</code> values.
+ * \par
+ * The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below.
+ * <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
+ *
+ * \par Lengths supported by the transform:
+ * \par
+ * Internally, the function utilize a radix-4 decimation in frequency(DIF) algorithm
+ * and the size of the FFT supported are of the lengths [16, 64, 256, 1024].
+ *
+ *
+ * \par Algorithm:
+ *
+ * <b>Complex Fast Fourier Transform:</b>
+ * \par
+ * Input real and imaginary data:
+ * <pre>
+ * x(n) = xa + j * ya
+ * x(n+N/4 ) = xb + j * yb
+ * x(n+N/2 ) = xc + j * yc
+ * x(n+3N 4) = xd + j * yd
+ * </pre>
+ * where N is length of FFT
+ * \par
+ * Output real and imaginary data:
+ * <pre>
+ * X(4r) = xa'+ j * ya'
+ * X(4r+1) = xb'+ j * yb'
+ * X(4r+2) = xc'+ j * yc'
+ * X(4r+3) = xd'+ j * yd'
+ * </pre>
+ * \par
+ * Twiddle factors for radix-4 FFT:
+ * <pre>
+ * Wn = co1 + j * (- si1)
+ * W2n = co2 + j * (- si2)
+ * W3n = co3 + j * (- si3)
+ * </pre>
+ *
+ * \par
+ * \image html CFFT.gif "Radix-4 Decimation-in Frequency Complex Fast Fourier Transform"
+ *
+ * \par
+ * Output from Radix-4 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.
+ * \par
+ * <b> Butterfly CFFT equations:</b>
+ * <pre>
+ * xa' = xa + xb + xc + xd
+ * ya' = ya + yb + yc + yd
+ * xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
+ * yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
+ * xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
+ * yb' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
+ * xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
+ * yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
+ * </pre>
+ *
+ *
+ * <b>Complex Inverse Fast Fourier Transform:</b>
+ * \par
+ * CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.
+ *
+ * \par
+ * <b> Modified Butterfly CIFFT equations:</b>
+ * <pre>
+ * xa' = xa + xb + xc + xd
+ * ya' = ya + yb + yc + yd
+ * xc' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
+ * yc' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
+ * xb' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
+ * yb' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
+ * xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
+ * yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
+ * </pre>
+ *
+ * \par Instance Structure
+ * A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused.
+ * There are separate instance structure declarations for each of the 3 supported data types.
+ *
+ * \par Initialization Functions
+ * There is also an associated initialization function for each data type.
+ * The initialization function performs the following operations:
+ * - Sets the values of the internal structure fields.
+ * - Initializes twiddle factor table and bit reversal table pointers
+ * \par
+ * Use of the initialization function is optional.
+ * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
+ * To place an instance structure into a const data section, the instance structure must be manually initialized.
+ * Manually initialize the instance structure as follows:
+ * <pre>
+ *arm_cfft_radix4_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen};
+ *arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
+ *arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
+ * </pre>
+ * \par
+ * where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);
+ * <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);
+ * <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table.
+ * <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;
+ * <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.
+ * <code>onebyfftLen</code> value of 1/fftLen to calculate CIFFT;
+ *
+ * \par Fixed-Point Behavior
+ * Care must be taken when using the fixed-point versions of the CFFT/CIFFT function.
+ * Refer to the function specific documentation below for usage guidelines.
+ */
+
+
+/**
+ * @addtogroup Radix4_CFFT_CIFFT
+ * @{
+ */
+
+/**
+ * @details
+ * @brief Processing function for the floating-point Radix-4 CFFT/CIFFT.
+ * @param[in] *S points to an instance of the floating-point Radix-4 CFFT/CIFFT structure.
+ * @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
+ * @return none.
+ */
+
+void arm_cfft_radix4_f32(
+ const arm_cfft_radix4_instance_f32 * S,
+ float32_t * pSrc)
+{
+
+ if(S->ifftFlag == 1u)
+ {
+ /* Complex IFFT radix-4 */
+ arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
+ S->twidCoefModifier, S->onebyfftLen);
+ }
+ else
+ {
+ /* Complex FFT radix-4 */
+ arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
+ S->twidCoefModifier);
+ }
+
+ if(S->bitReverseFlag == 1u)
+ {
+ /* Bit Reversal */
+ arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+ }
+
+}
+
+
+/**
+ * @} end of Radix4_CFFT_CIFFT group
+ */
+
+
+/* ----------------------------------------------------------------------
+** Internal helper function used by the FFTs
+** ------------------------------------------------------------------- */
+
+/*
+ * @brief Core function for the floating-point CFFT butterfly process.
+ * @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
+ * @param[in] fftLen length of the FFT.
+ * @param[in] *pCoef points to the twiddle coefficient buffer.
+ * @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+ * @return none.
+ */
+
+void arm_radix4_butterfly_f32(
+ float32_t * pSrc,
+ uint16_t fftLen,
+ float32_t * pCoef,
+ uint16_t twidCoefModifier)
+{
+
+ float32_t co1, co2, co3, si1, si2, si3;
+ uint32_t ia1, ia2, ia3;
+ uint32_t i0, i1, i2, i3;
+ uint32_t n1, n2, j, k;
+
+#ifndef ARM_MATH_CM0
+
+ /* Run the below code for Cortex-M4 and Cortex-M3 */
+
+ float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
+ float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
+ Ybminusd;
+ float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
+ float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
+ float32_t *ptr1;
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+
+ /* n2 = fftLen/4 */
+ n2 >>= 2u;
+ i0 = 0u;
+ ia1 = 0u;
+
+ j = n2;
+
+ /* Calculation of first stage */
+ do
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ xaIn = pSrc[(2u * i0)];
+ yaIn = pSrc[(2u * i0) + 1u];
+
+ xcIn = pSrc[(2u * i2)];
+ ycIn = pSrc[(2u * i2) + 1u];
+
+ xbIn = pSrc[(2u * i1)];
+ ybIn = pSrc[(2u * i1) + 1u];
+
+ xdIn = pSrc[(2u * i3)];
+ ydIn = pSrc[(2u * i3) + 1u];
+
+ /* xa + xc */
+ Xaplusc = xaIn + xcIn;
+ /* xb + xd */
+ Xbplusd = xbIn + xdIn;
+ /* ya + yc */
+ Yaplusc = yaIn + ycIn;
+ /* yb + yd */
+ Ybplusd = ybIn + ydIn;
+
+ /* index calculation for the coefficients */
+ ia2 = ia1 + ia1;
+ co2 = pCoef[ia2 * 2u];
+ si2 = pCoef[(ia2 * 2u) + 1u];
+
+ /* xa - xc */
+ Xaminusc = xaIn - xcIn;
+ /* xb - xd */
+ Xbminusd = xbIn - xdIn;
+ /* ya - yc */
+ Yaminusc = yaIn - ycIn;
+ /* yb + yd */
+ Ybminusd = ybIn - ydIn;
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[(2u * i0)] = Xaplusc + Xbplusd;
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
+
+ /* (xa - xc) + (yb - yd) */
+ Xb12C_out = (Xaminusc + Ybminusd);
+ /* (ya - yc) + (xb - xd) */
+ Yb12C_out = (Yaminusc - Xbminusd);
+ /* (xa + xc) - (xb + xd) */
+ Xc12C_out = (Xaplusc - Xbplusd);
+ /* (ya + yc) - (yb + yd) */
+ Yc12C_out = (Yaplusc - Ybplusd);
+ /* (xa - xc) - (yb - yd) */
+ Xd12C_out = (Xaminusc - Ybminusd);
+ /* (ya - yc) + (xb - xd) */
+ Yd12C_out = (Xbminusd + Yaminusc);
+
+ co1 = pCoef[ia1 * 2u];
+ si1 = pCoef[(ia1 * 2u) + 1u];
+
+ /* index calculation for the coefficients */
+ ia3 = ia2 + ia1;
+ co3 = pCoef[ia3 * 2u];
+ si3 = pCoef[(ia3 * 2u) + 1u];
+
+ Xb12_out = Xb12C_out * co1;
+ Yb12_out = Yb12C_out * co1;
+ Xc12_out = Xc12C_out * co2;
+ Yc12_out = Yc12C_out * co2;
+ Xd12_out = Xd12C_out * co3;
+ Yd12_out = Yd12C_out * co3;
+
+ /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+ Xb12_out += Yb12C_out * si1;
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ Yb12_out -= Xb12C_out * si1;
+ /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+ Xc12_out += Yc12C_out * si2;
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ Yc12_out -= Xc12C_out * si2;
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ Xd12_out += Yd12C_out * si3;
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ Yd12_out -= Xd12C_out * si3;
+
+
+ /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = Xc12_out;
+
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = Yc12_out;
+
+ /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = Xb12_out;
+
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = Yb12_out;
+
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = Xd12_out;
+
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = Yd12_out;
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ /* Updating input index */
+ i0 = i0 + 1u;
+
+ }
+ while(--j);
+
+ twidCoefModifier <<= 2u;
+
+ /* Calculation of second stage to excluding last stage */
+ for (k = fftLen / 4; k > 4u; k >>= 2u)
+ {
+ /* Initializations for the first stage */
+ n1 = n2;
+ n2 >>= 2u;
+ ia1 = 0u;
+
+ /* Calculation of first stage */
+ for (j = 0u; j <= (n2 - 1u); j++)
+ {
+ /* index calculation for the coefficients */
+ ia2 = ia1 + ia1;
+ ia3 = ia2 + ia1;
+ co1 = pCoef[ia1 * 2u];
+ si1 = pCoef[(ia1 * 2u) + 1u];
+ co2 = pCoef[ia2 * 2u];
+ si2 = pCoef[(ia2 * 2u) + 1u];
+ co3 = pCoef[ia3 * 2u];
+ si3 = pCoef[(ia3 * 2u) + 1u];
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ xaIn = pSrc[(2u * i0)];
+ yaIn = pSrc[(2u * i0) + 1u];
+
+ xbIn = pSrc[(2u * i1)];
+ ybIn = pSrc[(2u * i1) + 1u];
+
+ xcIn = pSrc[(2u * i2)];
+ ycIn = pSrc[(2u * i2) + 1u];
+
+ xdIn = pSrc[(2u * i3)];
+ ydIn = pSrc[(2u * i3) + 1u];
+
+ /* xa - xc */
+ Xaminusc = xaIn - xcIn;
+ /* (xb - xd) */
+ Xbminusd = xbIn - xdIn;
+ /* ya - yc */
+ Yaminusc = yaIn - ycIn;
+ /* (yb - yd) */
+ Ybminusd = ybIn - ydIn;
+
+ /* xa + xc */
+ Xaplusc = xaIn + xcIn;
+ /* xb + xd */
+ Xbplusd = xbIn + xdIn;
+ /* ya + yc */
+ Yaplusc = yaIn + ycIn;
+ /* yb + yd */
+ Ybplusd = ybIn + ydIn;
+
+ /* (xa - xc) + (yb - yd) */
+ Xb12C_out = (Xaminusc + Ybminusd);
+ /* (ya - yc) - (xb - xd) */
+ Yb12C_out = (Yaminusc - Xbminusd);
+ /* xa + xc -(xb + xd) */
+ Xc12C_out = (Xaplusc - Xbplusd);
+ /* (ya + yc) - (yb + yd) */
+ Yc12C_out = (Yaplusc - Ybplusd);
+ /* (xa - xc) - (yb - yd) */
+ Xd12C_out = (Xaminusc - Ybminusd);
+ /* (ya - yc) + (xb - xd) */
+ Yd12C_out = (Xbminusd + Yaminusc);
+
+ pSrc[(2u * i0)] = Xaplusc + Xbplusd;
+ pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
+
+ Xb12_out = Xb12C_out * co1;
+ Yb12_out = Yb12C_out * co1;
+ Xc12_out = Xc12C_out * co2;
+ Yc12_out = Yc12C_out * co2;
+ Xd12_out = Xd12C_out * co3;
+ Yd12_out = Yd12C_out * co3;
+
+ /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+ Xb12_out += Yb12C_out * si1;
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ Yb12_out -= Xb12C_out * si1;
+ /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+ Xc12_out += Yc12C_out * si2;
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ Yc12_out -= Xc12C_out * si2;
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ Xd12_out += Yd12C_out * si3;
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ Yd12_out -= Xd12C_out * si3;
+
+ /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = Xc12_out;
+
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = Yc12_out;
+
+ /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = Xb12_out;
+
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = Yb12_out;
+
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = Xd12_out;
+
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = Yd12_out;
+
+ }
+ }
+ twidCoefModifier <<= 2u;
+ }
+
+ j = fftLen >> 2;
+ ptr1 = &pSrc[0];
+
+ /* Calculations of last stage */
+ do
+ {
+
+ xaIn = ptr1[0];
+ xcIn = ptr1[4];
+ yaIn = ptr1[1];
+ ycIn = ptr1[5];
+
+ /* xa + xc */
+ Xaplusc = xaIn + xcIn;
+
+ xbIn = ptr1[2];
+
+ /* xa - xc */
+ Xaminusc = xaIn - xcIn;
+
+ xdIn = ptr1[6];
+
+ /* ya + yc */
+ Yaplusc = yaIn + ycIn;
+
+ ybIn = ptr1[3];
+
+ /* ya - yc */
+ Yaminusc = yaIn - ycIn;
+
+ ydIn = ptr1[7];
+
+ /* xb + xd */
+ Xbplusd = xbIn + xdIn;
+
+ /* yb + yd */
+ Ybplusd = ybIn + ydIn;
+
+ /* xa' = xa + xb + xc + xd */
+ ptr1[0] = (Xaplusc + Xbplusd);
+
+ /* (xb-xd) */
+ Xbminusd = xbIn - xdIn;
+
+ /* ya' = ya + yb + yc + yd */
+ ptr1[1] = (Yaplusc + Ybplusd);
+
+ /* (yb-yd) */
+ Ybminusd = ybIn - ydIn;
+
+ /* xc' = (xa-xb+xc-xd) */
+ ptr1[2] = (Xaplusc - Xbplusd);
+ /* yc' = (ya-yb+yc-yd) */
+ ptr1[3] = (Yaplusc - Ybplusd);
+ /* xb' = (xa+yb-xc-yd) */
+ ptr1[4] = (Xaminusc + Ybminusd);
+ /* yb' = (ya-xb-yc+xd) */
+ ptr1[5] = (Yaminusc - Xbminusd);
+ /* xd' = (xa-yb-xc+yd)) */
+ ptr1[6] = (Xaminusc - Ybminusd);
+ /* yd' = (ya+xb-yc-xd) */
+ ptr1[7] = (Xbminusd + Yaminusc);
+
+ /* increment pointer by 8 */
+ ptr1 = ptr1 + 8u;
+
+ } while(--j);
+
+#else
+
+ float32_t t1, t2, r1, r2, s1, s2;
+
+ /* Run the below code for Cortex-M0 */
+
+ /* Initializations for the fft calculation */
+ n2 = fftLen;
+ n1 = n2;
+ for (k = fftLen; k > 1u; k >>= 2u)
+ {
+ /* Initializations for the fft calculation */
+ n1 = n2;
+ n2 >>= 2u;
+ ia1 = 0u;
+
+ /* FFT Calculation */
+ for (j = 0u; j <= (n2 - 1u); j++)
+ {
+ /* index calculation for the coefficients */
+ ia2 = ia1 + ia1;
+ ia3 = ia2 + ia1;
+ co1 = pCoef[ia1 * 2u];
+ si1 = pCoef[(ia1 * 2u) + 1u];
+ co2 = pCoef[ia2 * 2u];
+ si2 = pCoef[(ia2 * 2u) + 1u];
+ co3 = pCoef[ia3 * 2u];
+ si3 = pCoef[(ia3 * 2u) + 1u];
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* xa + xc */
+ r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
+
+ /* xa - xc */
+ r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
+
+ /* ya + yc */
+ s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
+
+ /* ya - yc */
+ s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
+
+ /* xb + xd */
+ t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2u * i0] = r1 + t1;
+
+ /* xa + xc -(xb + xd) */
+ r1 = r1 - t1;
+
+ /* yb + yd */
+ t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
+
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2u * i0) + 1u] = s1 + t2;
+
+ /* (ya + yc) - (yb + yd) */
+ s1 = s1 - t2;
+
+ /* (yb - yd) */
+ t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
+
+ /* (xb - xd) */
+ t2 = pSrc[2u * i1] - pSrc[2u * i3];
+
+ /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
+
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
+
+ /* (xa - xc) + (yb - yd) */
+ r1 = r2 + t1;
+
+ /* (xa - xc) - (yb - yd) */
+ r2 = r2 - t1;
+
+ /* (ya - yc) - (xb - xd) */
+ s1 = s2 - t2;
+
+ /* (ya - yc) + (xb - xd) */
+ s2 = s2 + t2;
+
+ /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
+
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
+
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
+
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
+ }
+ }
+ twidCoefModifier <<= 2u;
+ }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
+
+/*
+ * @brief Core function for the floating-point CIFFT butterfly process.
+ * @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
+ * @param[in] fftLen length of the FFT.
+ * @param[in] *pCoef points to twiddle coefficient buffer.
+ * @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
+ * @param[in] onebyfftLen value of 1/fftLen.
+ * @return none.
+ */
+
+void arm_radix4_butterfly_inverse_f32(
+ float32_t * pSrc,
+ uint16_t fftLen,
+ float32_t * pCoef,
+ uint16_t twidCoefModifier,
+ float32_t onebyfftLen)
+{
+ float32_t co1, co2, co3, si1, si2, si3;
+ uint32_t ia1, ia2, ia3;
+ uint32_t i0, i1, i2, i3;
+ uint32_t n1, n2, j, k;
+
+#ifndef ARM_MATH_CM0
+
+ float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
+ float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
+ Ybminusd;
+ float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
+ float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
+ float32_t *ptr1;
+
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+
+ /* n2 = fftLen/4 */
+ n2 >>= 2u;
+ i0 = 0u;
+ ia1 = 0u;
+
+ j = n2;
+
+ /* Calculation of first stage */
+ do
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Butterfly implementation */
+ xaIn = pSrc[(2u * i0)];
+ yaIn = pSrc[(2u * i0) + 1u];
+
+ xcIn = pSrc[(2u * i2)];
+ ycIn = pSrc[(2u * i2) + 1u];
+
+ xbIn = pSrc[(2u * i1)];
+ ybIn = pSrc[(2u * i1) + 1u];
+
+ xdIn = pSrc[(2u * i3)];
+ ydIn = pSrc[(2u * i3) + 1u];
+
+ /* xa + xc */
+ Xaplusc = xaIn + xcIn;
+ /* xb + xd */
+ Xbplusd = xbIn + xdIn;
+ /* ya + yc */
+ Yaplusc = yaIn + ycIn;
+ /* yb + yd */
+ Ybplusd = ybIn + ydIn;
+
+ /* index calculation for the coefficients */
+ ia2 = ia1 + ia1;
+ co2 = pCoef[ia2 * 2u];
+ si2 = pCoef[(ia2 * 2u) + 1u];
+
+ /* xa - xc */
+ Xaminusc = xaIn - xcIn;
+ /* xb - xd */
+ Xbminusd = xbIn - xdIn;
+ /* ya - yc */
+ Yaminusc = yaIn - ycIn;
+ /* yb - yd */
+ Ybminusd = ybIn - ydIn;
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[(2u * i0)] = Xaplusc + Xbplusd;
+
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
+
+ /* (xa - xc) - (yb - yd) */
+ Xb12C_out = (Xaminusc - Ybminusd);
+ /* (ya - yc) + (xb - xd) */
+ Yb12C_out = (Yaminusc + Xbminusd);
+ /* (xa + xc) - (xb + xd) */
+ Xc12C_out = (Xaplusc - Xbplusd);
+ /* (ya + yc) - (yb + yd) */
+ Yc12C_out = (Yaplusc - Ybplusd);
+ /* (xa - xc) + (yb - yd) */
+ Xd12C_out = (Xaminusc + Ybminusd);
+ /* (ya - yc) - (xb - xd) */
+ Yd12C_out = (Yaminusc - Xbminusd);
+
+ co1 = pCoef[ia1 * 2u];
+ si1 = pCoef[(ia1 * 2u) + 1u];
+
+ /* index calculation for the coefficients */
+ ia3 = ia2 + ia1;
+ co3 = pCoef[ia3 * 2u];
+ si3 = pCoef[(ia3 * 2u) + 1u];
+
+ Xb12_out = Xb12C_out * co1;
+ Yb12_out = Yb12C_out * co1;
+ Xc12_out = Xc12C_out * co2;
+ Yc12_out = Yc12C_out * co2;
+ Xd12_out = Xd12C_out * co3;
+ Yd12_out = Yd12C_out * co3;
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ Xb12_out -= Yb12C_out * si1;
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ Yb12_out += Xb12C_out * si1;
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ Xc12_out -= Yc12C_out * si2;
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ Yc12_out += Xc12C_out * si2;
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ Xd12_out -= Yd12C_out * si3;
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ Yd12_out += Xd12C_out * si3;
+
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = Xc12_out;
+
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = Yc12_out;
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = Xb12_out;
+
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = Yb12_out;
+
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = Xd12_out;
+
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = Yd12_out;
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ /* Updating input index */
+ i0 = i0 + 1u;
+
+ } while(--j);
+
+ twidCoefModifier <<= 2u;
+
+ /* Calculation of second stage to excluding last stage */
+ for (k = fftLen / 4; k > 4u; k >>= 2u)
+ {
+ /* Initializations for the first stage */
+ n1 = n2;
+ n2 >>= 2u;
+ ia1 = 0u;
+
+ /* Calculation of first stage */
+ for (j = 0u; j <= (n2 - 1u); j++)
+ {
+ /* index calculation for the coefficients */
+ ia2 = ia1 + ia1;
+ ia3 = ia2 + ia1;
+ co1 = pCoef[ia1 * 2u];
+ si1 = pCoef[(ia1 * 2u) + 1u];
+ co2 = pCoef[ia2 * 2u];
+ si2 = pCoef[(ia2 * 2u) + 1u];
+ co3 = pCoef[ia3 * 2u];
+ si3 = pCoef[(ia3 * 2u) + 1u];
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ xaIn = pSrc[(2u * i0)];
+ yaIn = pSrc[(2u * i0) + 1u];
+
+ xbIn = pSrc[(2u * i1)];
+ ybIn = pSrc[(2u * i1) + 1u];
+
+ xcIn = pSrc[(2u * i2)];
+ ycIn = pSrc[(2u * i2) + 1u];
+
+ xdIn = pSrc[(2u * i3)];
+ ydIn = pSrc[(2u * i3) + 1u];
+
+ /* xa - xc */
+ Xaminusc = xaIn - xcIn;
+ /* (xb - xd) */
+ Xbminusd = xbIn - xdIn;
+ /* ya - yc */
+ Yaminusc = yaIn - ycIn;
+ /* (yb - yd) */
+ Ybminusd = ybIn - ydIn;
+
+ /* xa + xc */
+ Xaplusc = xaIn + xcIn;
+ /* xb + xd */
+ Xbplusd = xbIn + xdIn;
+ /* ya + yc */
+ Yaplusc = yaIn + ycIn;
+ /* yb + yd */
+ Ybplusd = ybIn + ydIn;
+
+ /* (xa - xc) - (yb - yd) */
+ Xb12C_out = (Xaminusc - Ybminusd);
+ /* (ya - yc) + (xb - xd) */
+ Yb12C_out = (Yaminusc + Xbminusd);
+ /* xa + xc -(xb + xd) */
+ Xc12C_out = (Xaplusc - Xbplusd);
+ /* (ya + yc) - (yb + yd) */
+ Yc12C_out = (Yaplusc - Ybplusd);
+ /* (xa - xc) + (yb - yd) */
+ Xd12C_out = (Xaminusc + Ybminusd);
+ /* (ya - yc) - (xb - xd) */
+ Yd12C_out = (Yaminusc - Xbminusd);
+
+ pSrc[(2u * i0)] = Xaplusc + Xbplusd;
+ pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
+
+ Xb12_out = Xb12C_out * co1;
+ Yb12_out = Yb12C_out * co1;
+ Xc12_out = Xc12C_out * co2;
+ Yc12_out = Yc12C_out * co2;
+ Xd12_out = Xd12C_out * co3;
+ Yd12_out = Yd12C_out * co3;
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ Xb12_out -= Yb12C_out * si1;
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ Yb12_out += Xb12C_out * si1;
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ Xc12_out -= Yc12C_out * si2;
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ Yc12_out += Xc12C_out * si2;
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ Xd12_out -= Yd12C_out * si3;
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ Yd12_out += Xd12C_out * si3;
+
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = Xc12_out;
+
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = Yc12_out;
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = Xb12_out;
+
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = Yb12_out;
+
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = Xd12_out;
+
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = Yd12_out;
+
+ }
+ }
+ twidCoefModifier <<= 2u;
+ }
+ /* Initializations of last stage */
+
+ j = fftLen >> 2;
+ ptr1 = &pSrc[0];
+
+ /* Calculations of last stage */
+ do
+ {
+
+ xaIn = ptr1[0];
+ xcIn = ptr1[4];
+ yaIn = ptr1[1];
+ ycIn = ptr1[5];
+
+ /* Butterfly implementation */
+ /* xa + xc */
+ Xaplusc = xaIn + xcIn;
+
+ xbIn = ptr1[2];
+
+ /* xa - xc */
+ Xaminusc = xaIn - xcIn;
+
+ xdIn = ptr1[6];
+
+ /* ya + yc */
+ Yaplusc = yaIn + ycIn;
+
+ ybIn = ptr1[3];
+
+ /* ya - yc */
+ Yaminusc = yaIn - ycIn;
+
+ ydIn = ptr1[7];
+
+ /* xc + xd */
+ Xbplusd = xbIn + xdIn;
+
+ /* yb + yd */
+ Ybplusd = ybIn + ydIn;
+
+ /* xa' = xa + xb + xc + xd */
+ ptr1[0] = (Xaplusc + Xbplusd) * onebyfftLen;
+
+ /* (xb-xd) */
+ Xbminusd = xbIn - xdIn;
+
+ /* ya' = ya + yb + yc + yd */
+ ptr1[1] = (Yaplusc + Ybplusd) * onebyfftLen;
+
+ /* (yb-yd) */
+ Ybminusd = ybIn - ydIn;
+
+ /* xc' = (xa-xb+xc-xd) * onebyfftLen */
+ ptr1[2] = (Xaplusc - Xbplusd) * onebyfftLen;
+
+ /* yc' = (ya-yb+yc-yd) * onebyfftLen */
+ ptr1[3] = (Yaplusc - Ybplusd) * onebyfftLen;
+
+ /* xb' = (xa-yb-xc+yd) * onebyfftLen */
+ ptr1[4] = (Xaminusc - Ybminusd) * onebyfftLen;
+
+ /* yb' = (ya+xb-yc-xd) * onebyfftLen */
+ ptr1[5] = (Yaminusc + Xbminusd) * onebyfftLen;
+
+ /* xd' = (xa-yb-xc+yd) * onebyfftLen */
+ ptr1[6] = (Xaminusc + Ybminusd) * onebyfftLen;
+
+ /* yd' = (ya-xb-yc+xd) * onebyfftLen */
+ ptr1[7] = (Yaminusc - Xbminusd) * onebyfftLen;
+
+ /* increment source pointer by 8 for next calculations */
+ ptr1 = ptr1 + 8u;
+
+ } while(--j);
+
+#else
+
+ float32_t t1, t2, r1, r2, s1, s2;
+
+ /* Run the below code for Cortex-M0 */
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+
+ /* Calculation of first stage */
+ for (k = fftLen; k > 4u; k >>= 2u)
+ {
+ /* Initializations for the first stage */
+ n1 = n2;
+ n2 >>= 2u;
+ ia1 = 0u;
+
+ /* Calculation of first stage */
+ for (j = 0u; j <= (n2 - 1u); j++)
+ {
+ /* index calculation for the coefficients */
+ ia2 = ia1 + ia1;
+ ia3 = ia2 + ia1;
+ co1 = pCoef[ia1 * 2u];
+ si1 = pCoef[(ia1 * 2u) + 1u];
+ co2 = pCoef[ia2 * 2u];
+ si2 = pCoef[(ia2 * 2u) + 1u];
+ co3 = pCoef[ia3 * 2u];
+ si3 = pCoef[(ia3 * 2u) + 1u];
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ for (i0 = j; i0 < fftLen; i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* xa + xc */
+ r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
+
+ /* xa - xc */
+ r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
+
+ /* ya + yc */
+ s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
+
+ /* ya - yc */
+ s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
+
+ /* xb + xd */
+ t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2u * i0] = r1 + t1;
+
+ /* xa + xc -(xb + xd) */
+ r1 = r1 - t1;
+
+ /* yb + yd */
+ t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
+
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2u * i0) + 1u] = s1 + t2;
+
+ /* (ya + yc) - (yb + yd) */
+ s1 = s1 - t2;
+
+ /* (yb - yd) */
+ t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
+
+ /* (xb - xd) */
+ t2 = pSrc[2u * i1] - pSrc[2u * i3];
+
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
+
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
+
+ /* (xa - xc) - (yb - yd) */
+ r1 = r2 - t1;
+
+ /* (xa - xc) + (yb - yd) */
+ r2 = r2 + t1;
+
+ /* (ya - yc) + (xb - xd) */
+ s1 = s2 + t2;
+
+ /* (ya - yc) - (xb - xd) */
+ s2 = s2 - t2;
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
+
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
+
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
+
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
+ }
+ }
+ twidCoefModifier <<= 2u;
+ }
+ /* Initializations of last stage */
+ n1 = n2;
+ n2 >>= 2u;
+
+ /* Calculations of last stage */
+ for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
+ {
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Butterfly implementation */
+ /* xa + xc */
+ r1 = pSrc[2u * i0] + pSrc[2u * i2];
+
+ /* xa - xc */
+ r2 = pSrc[2u * i0] - pSrc[2u * i2];
+
+ /* ya + yc */
+ s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
+
+ /* ya - yc */
+ s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
+
+ /* xc + xd */
+ t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2u * i0] = (r1 + t1) * onebyfftLen;
+
+ /* (xa + xb) - (xc + xd) */
+ r1 = r1 - t1;
+
+ /* yb + yd */
+ t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
+
+ /* ya' = ya + yb + yc + yd */
+ pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;
+
+ /* (ya + yc) - (yb + yd) */
+ s1 = s1 - t2;
+
+ /* (yb-yd) */
+ t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
+
+ /* (xb-xd) */
+ t2 = pSrc[2u * i1] - pSrc[2u * i3];
+
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = r1 * onebyfftLen;
+
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;
+
+
+ /* (xa - xc) - (yb-yd) */
+ r1 = r2 - t1;
+
+ /* (xa - xc) + (yb-yd) */
+ r2 = r2 + t1;
+
+ /* (ya - yc) + (xb-xd) */
+ s1 = s2 + t2;
+
+ /* (ya - yc) - (xb-xd) */
+ s2 = s2 - t2;
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = r1 * onebyfftLen;
+
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;
+
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = r2 * onebyfftLen;
+
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
+ }
+
+#endif /* #ifndef ARM_MATH_CM0 */
+
+}
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