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Diff: cmsis_dsp/TransformFunctions/arm_cfft_radix4_q31.c
- Revision:
- 1:fdd22bb7aa52
- Child:
- 2:da51fb522205
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/cmsis_dsp/TransformFunctions/arm_cfft_radix4_q31.c Wed Nov 28 12:30:09 2012 +0000
@@ -0,0 +1,891 @@
+/* ----------------------------------------------------------------------
+* Copyright (C) 2010 ARM Limited. All rights reserved.
+*
+* $Date: 15. February 2012
+* $Revision: V1.1.0
+*
+* Project: CMSIS DSP Library
+* Title: arm_cfft_radix4_q31.c
+*
+* Description: This file has function definition of Radix-4 FFT & IFFT function and
+* In-place bit reversal using bit reversal table
+*
+* 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
+ */
+
+/**
+ * @addtogroup Radix4_CFFT_CIFFT
+ * @{
+ */
+
+/**
+ * @details
+ * @brief Processing function for the Q31 CFFT/CIFFT.
+ * @param[in] *S points to an instance of the Q31 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.
+ *
+ * \par Input and 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 FFT sizes.
+ * The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
+ * \par
+ * \image html CFFTQ31.gif "Input and Output Formats for Q31 CFFT"
+ * \image html CIFFTQ31.gif "Input and Output Formats for Q31 CIFFT"
+ *
+ */
+
+void arm_cfft_radix4_q31(
+ const arm_cfft_radix4_instance_q31 * S,
+ q31_t * pSrc)
+{
+ if(S->ifftFlag == 1u)
+ {
+ /* Complex IFFT radix-4 */
+ arm_radix4_butterfly_inverse_q31(pSrc, S->fftLen, S->pTwiddle,
+ S->twidCoefModifier);
+ }
+ else
+ {
+ /* Complex FFT radix-4 */
+ arm_radix4_butterfly_q31(pSrc, S->fftLen, S->pTwiddle,
+ S->twidCoefModifier);
+ }
+
+
+ if(S->bitReverseFlag == 1u)
+ {
+ /* Bit Reversal */
+ arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
+ }
+
+}
+
+/**
+ * @} end of Radix4_CFFT_CIFFT group
+ */
+
+/*
+* Radix-4 FFT algorithm used is :
+*
+* Input real and imaginary data:
+* 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
+*
+*
+* Output real and imaginary data:
+* x(4r) = xa'+ j * ya'
+* x(4r+1) = xb'+ j * yb'
+* x(4r+2) = xc'+ j * yc'
+* x(4r+3) = xd'+ j * yd'
+*
+*
+* Twiddle factors for radix-4 FFT:
+* Wn = co1 + j * (- si1)
+* W2n = co2 + j * (- si2)
+* W3n = co3 + j * (- si3)
+*
+* Butterfly implementation:
+* xa' = xa + xb + xc + xd
+* ya' = ya + yb + yc + yd
+* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
+* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
+* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
+* yc' = (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)
+*
+*/
+
+/**
+ * @brief Core function for the Q31 CFFT butterfly process.
+ * @param[in, out] *pSrc points to the in-place buffer of Q31 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.
+ * @return none.
+ */
+
+void arm_radix4_butterfly_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ q31_t * pCoef,
+ uint32_t twidCoefModifier)
+{
+ uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
+ q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
+
+ q31_t xa, xb, xc, xd;
+ q31_t ya, yb, yc, yd;
+ q31_t xa_out, xb_out, xc_out, xd_out;
+ q31_t ya_out, yb_out, yc_out, yd_out;
+
+ q31_t *ptr1;
+ q63_t xaya, xbyb, xcyc, xdyd;
+ /* Total process is divided into three stages */
+
+ /* process first stage, middle stages, & last stage */
+
+
+ /* start of first stage process */
+
+ /* 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/2u], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* input is in 1.31(q31) format and provide 4 guard bits for the input */
+
+ /* Butterfly implementation */
+ /* xa + xc */
+ r1 = (pSrc[(2u * i0)] >> 4u) + (pSrc[(2u * i2)] >> 4u);
+ /* xa - xc */
+ r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);
+
+ /* xb + xd */
+ t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);
+
+ /* ya + yc */
+ s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
+ /* ya - yc */
+ s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2u * i0] = (r1 + t1);
+ /* (xa + xc) - (xb + xd) */
+ r1 = r1 - t1;
+ /* yb + yd */
+ t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
+
+ /* 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] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
+ /* xb - xd */
+ t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);
+
+ /* index calculation for the coefficients */
+ ia2 = 2u * ia1;
+ co2 = pCoef[ia2 * 2u];
+ si2 = pCoef[(ia2 * 2u) + 1u];
+
+ /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
+ ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;
+
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
+ ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;
+
+ /* (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;
+
+ co1 = pCoef[ia1 * 2u];
+ si1 = pCoef[(ia1 * 2u) + 1u];
+
+ /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
+ ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;
+
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
+ ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;
+
+ /* index calculation for the coefficients */
+ ia3 = 3u * ia1;
+ co3 = pCoef[ia3 * 2u];
+ si3 = pCoef[(ia3 * 2u) + 1u];
+
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
+ ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;
+
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
+ ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ /* Updating input index */
+ i0 = i0 + 1u;
+
+ } while(--j);
+
+ /* end of first stage process */
+
+ /* data is in 5.27(q27) format */
+
+
+ /* start of Middle stages process */
+
+
+ /* each stage in middle stages provides two down scaling of the input */
+
+ twidCoefModifier <<= 2u;
+
+
+ for (k = fftLen / 4u; 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/2u], 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];
+
+ /* xb + xd */
+ t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2u * i0] = (r1 + t1) >> 2u;
+ /* 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) >> 2u;
+
+ /* (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] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
+ ((int32_t) (((q63_t) s1 * si2) >> 32))) >> 1u;
+
+ /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
+ ((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1u;
+
+ /* (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] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
+ ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;
+
+ /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
+ ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
+
+ /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
+ ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;
+
+ /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
+ ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
+ }
+ }
+ twidCoefModifier <<= 2u;
+ }
+
+ /* End of Middle stages process */
+
+ /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
+ /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
+ /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
+ /* data is in 5.27(q27) format for the 16 point as there are no middle stages */
+
+
+ /* start of Last stage process */
+ /* Initializations for the last stage */
+ j = fftLen >> 2;
+ ptr1 = &pSrc[0];
+
+ /* Calculations of last stage */
+ do
+ {
+
+#ifndef ARM_MATH_BIG_ENDIAN
+
+ /* Read xa (real), ya(imag) input */
+ xaya = *__SIMD64(ptr1)++;
+ xa = (q31_t) xaya;
+ ya = (q31_t) (xaya >> 32);
+
+ /* Read xb (real), yb(imag) input */
+ xbyb = *__SIMD64(ptr1)++;
+ xb = (q31_t) xbyb;
+ yb = (q31_t) (xbyb >> 32);
+
+ /* Read xc (real), yc(imag) input */
+ xcyc = *__SIMD64(ptr1)++;
+ xc = (q31_t) xcyc;
+ yc = (q31_t) (xcyc >> 32);
+
+ /* Read xc (real), yc(imag) input */
+ xdyd = *__SIMD64(ptr1)++;
+ xd = (q31_t) xdyd;
+ yd = (q31_t) (xdyd >> 32);
+
+#else
+
+ /* Read xa (real), ya(imag) input */
+ xaya = *__SIMD64(ptr1)++;
+ ya = (q31_t) xaya;
+ xa = (q31_t) (xaya >> 32);
+
+ /* Read xb (real), yb(imag) input */
+ xbyb = *__SIMD64(ptr1)++;
+ yb = (q31_t) xbyb;
+ xb = (q31_t) (xbyb >> 32);
+
+ /* Read xc (real), yc(imag) input */
+ xcyc = *__SIMD64(ptr1)++;
+ yc = (q31_t) xcyc;
+ xc = (q31_t) (xcyc >> 32);
+
+ /* Read xc (real), yc(imag) input */
+ xdyd = *__SIMD64(ptr1)++;
+ yd = (q31_t) xdyd;
+ xd = (q31_t) (xdyd >> 32);
+
+
+#endif
+
+ /* xa' = xa + xb + xc + xd */
+ xa_out = xa + xb + xc + xd;
+
+ /* ya' = ya + yb + yc + yd */
+ ya_out = ya + yb + yc + yd;
+
+ /* pointer updation for writing */
+ ptr1 = ptr1 - 8u;
+
+ /* writing xa' and ya' */
+ *ptr1++ = xa_out;
+ *ptr1++ = ya_out;
+
+ xc_out = (xa - xb + xc - xd);
+ yc_out = (ya - yb + yc - yd);
+
+ /* writing xc' and yc' */
+ *ptr1++ = xc_out;
+ *ptr1++ = yc_out;
+
+ xb_out = (xa + yb - xc - yd);
+ yb_out = (ya - xb - yc + xd);
+
+ /* writing xb' and yb' */
+ *ptr1++ = xb_out;
+ *ptr1++ = yb_out;
+
+ xd_out = (xa - yb - xc + yd);
+ yd_out = (ya + xb - yc - xd);
+
+ /* writing xd' and yd' */
+ *ptr1++ = xd_out;
+ *ptr1++ = yd_out;
+
+
+ } while(--j);
+
+ /* output is in 11.21(q21) format for the 1024 point */
+ /* output is in 9.23(q23) format for the 256 point */
+ /* output is in 7.25(q25) format for the 64 point */
+ /* output is in 5.27(q27) format for the 16 point */
+
+ /* End of last stage process */
+
+}
+
+
+/**
+ * @brief Core function for the Q31 CIFFT butterfly process.
+ * @param[in, out] *pSrc points to the in-place buffer of Q31 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.
+ * @return none.
+ */
+
+
+/*
+* Radix-4 IFFT algorithm used is :
+*
+* CIFFT uses same twiddle coefficients as CFFT Function
+* x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]
+*
+*
+* IFFT is implemented with following changes in equations from FFT
+*
+* Input real and imaginary data:
+* 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
+*
+*
+* Output real and imaginary data:
+* x(4r) = xa'+ j * ya'
+* x(4r+1) = xb'+ j * yb'
+* x(4r+2) = xc'+ j * yc'
+* x(4r+3) = xd'+ j * yd'
+*
+*
+* Twiddle factors for radix-4 IFFT:
+* Wn = co1 + j * (si1)
+* W2n = co2 + j * (si2)
+* W3n = co3 + j * (si3)
+
+* The real and imaginary output values for the radix-4 butterfly are
+* xa' = xa + xb + xc + xd
+* ya' = ya + yb + yc + yd
+* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
+* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
+* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
+* yc' = (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)
+*
+*/
+
+void arm_radix4_butterfly_inverse_q31(
+ q31_t * pSrc,
+ uint32_t fftLen,
+ q31_t * pCoef,
+ uint32_t twidCoefModifier)
+{
+ uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
+ q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
+ q31_t xa, xb, xc, xd;
+ q31_t ya, yb, yc, yd;
+ q31_t xa_out, xb_out, xc_out, xd_out;
+ q31_t ya_out, yb_out, yc_out, yd_out;
+
+ q31_t *ptr1;
+ q63_t xaya, xbyb, xcyc, xdyd;
+
+ /* input is be 1.31(q31) format for all FFT sizes */
+ /* Total process is divided into three stages */
+ /* process first stage, middle stages, & last stage */
+
+ /* Start of first stage process */
+
+ /* Initializations for the first stage */
+ n2 = fftLen;
+ n1 = n2;
+ /* n2 = fftLen/4 */
+ n2 >>= 2u;
+ i0 = 0u;
+ ia1 = 0u;
+
+ j = n2;
+
+ do
+ {
+
+ /* input is in 1.31(q31) format and provide 4 guard bits for the input */
+
+ /* index calculation for the input as, */
+ /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
+ i1 = i0 + n2;
+ i2 = i1 + n2;
+ i3 = i2 + n2;
+
+ /* Butterfly implementation */
+ /* xa + xc */
+ r1 = (pSrc[2u * i0] >> 4u) + (pSrc[2u * i2] >> 4u);
+ /* xa - xc */
+ r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);
+
+ /* xb + xd */
+ t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);
+
+ /* ya + yc */
+ s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
+ /* ya - yc */
+ s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2u * i0] = (r1 + t1);
+ /* (xa + xc) - (xb + xd) */
+ r1 = r1 - t1;
+ /* yb + yd */
+ t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
+ /* 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] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
+ /* xb - xd */
+ t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);
+
+ /* index calculation for the coefficients */
+ ia2 = 2u * ia1;
+ co2 = pCoef[ia2 * 2u];
+ si2 = pCoef[(ia2 * 2u) + 1u];
+
+ /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
+ pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) -
+ ((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;
+
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ pSrc[2u * i1 + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) +
+ ((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;
+
+ /* (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;
+
+ co1 = pCoef[ia1 * 2u];
+ si1 = pCoef[(ia1 * 2u) + 1u];
+
+ /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
+ pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
+ ((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;
+
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
+ ((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;
+
+ /* index calculation for the coefficients */
+ ia3 = 3u * ia1;
+ co3 = pCoef[ia3 * 2u];
+ si3 = pCoef[(ia3 * 2u) + 1u];
+
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
+ ((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;
+
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
+ ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
+
+ /* Twiddle coefficients index modifier */
+ ia1 = ia1 + twidCoefModifier;
+
+ /* Updating input index */
+ i0 = i0 + 1u;
+
+ } while(--j);
+
+ /* data is in 5.27(q27) format */
+ /* each stage provides two down scaling of the input */
+
+
+ /* Start of Middle stages process */
+
+ twidCoefModifier <<= 2u;
+
+ /* Calculation of second stage to excluding last stage */
+ for (k = fftLen / 4u; k > 4u; k >>= 2u)
+ {
+ /* Initializations for the first stage */
+ n1 = n2;
+ n2 >>= 2u;
+ ia1 = 0u;
+
+ for (j = 0; 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/2u], 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];
+
+ /* xb + xd */
+ t1 = pSrc[2u * i1] + pSrc[2u * i3];
+
+ /* xa' = xa + xb + xc + xd */
+ pSrc[2u * i0] = (r1 + t1) >> 2u;
+ /* 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) >> 2u;
+
+ /* (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] = (((int32_t) (((q63_t) r1 * co2) >> 32u)) -
+ ((int32_t) (((q63_t) s1 * si2) >> 32u))) >> 1u;
+
+ /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
+ pSrc[(2u * i1) + 1u] =
+ (((int32_t) (((q63_t) s1 * co2) >> 32u)) +
+ ((int32_t) (((q63_t) r1 * si2) >> 32u))) >> 1u;
+
+ /* (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] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
+ ((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;
+
+ /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
+ pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
+ ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
+
+ /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
+ pSrc[(2u * i3)] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
+ ((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;
+
+ /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
+ pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
+ ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
+ }
+ }
+ twidCoefModifier <<= 2u;
+ }
+
+ /* End of Middle stages process */
+
+ /* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
+ /* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
+ /* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
+ /* data is in 5.27(q27) format for the 16 point as there are no middle stages */
+
+
+ /* Start of last stage process */
+
+
+ /* Initializations for the last stage */
+ j = fftLen >> 2;
+ ptr1 = &pSrc[0];
+
+ /* Calculations of last stage */
+ do
+ {
+#ifndef ARM_MATH_BIG_ENDIAN
+ /* Read xa (real), ya(imag) input */
+ xaya = *__SIMD64(ptr1)++;
+ xa = (q31_t) xaya;
+ ya = (q31_t) (xaya >> 32);
+
+ /* Read xb (real), yb(imag) input */
+ xbyb = *__SIMD64(ptr1)++;
+ xb = (q31_t) xbyb;
+ yb = (q31_t) (xbyb >> 32);
+
+ /* Read xc (real), yc(imag) input */
+ xcyc = *__SIMD64(ptr1)++;
+ xc = (q31_t) xcyc;
+ yc = (q31_t) (xcyc >> 32);
+
+ /* Read xc (real), yc(imag) input */
+ xdyd = *__SIMD64(ptr1)++;
+ xd = (q31_t) xdyd;
+ yd = (q31_t) (xdyd >> 32);
+
+#else
+
+ /* Read xa (real), ya(imag) input */
+ xaya = *__SIMD64(ptr1)++;
+ ya = (q31_t) xaya;
+ xa = (q31_t) (xaya >> 32);
+
+ /* Read xb (real), yb(imag) input */
+ xbyb = *__SIMD64(ptr1)++;
+ yb = (q31_t) xbyb;
+ xb = (q31_t) (xbyb >> 32);
+
+ /* Read xc (real), yc(imag) input */
+ xcyc = *__SIMD64(ptr1)++;
+ yc = (q31_t) xcyc;
+ xc = (q31_t) (xcyc >> 32);
+
+ /* Read xc (real), yc(imag) input */
+ xdyd = *__SIMD64(ptr1)++;
+ yd = (q31_t) xdyd;
+ xd = (q31_t) (xdyd >> 32);
+
+
+#endif
+
+ /* xa' = xa + xb + xc + xd */
+ xa_out = xa + xb + xc + xd;
+
+ /* ya' = ya + yb + yc + yd */
+ ya_out = ya + yb + yc + yd;
+
+ /* pointer updation for writing */
+ ptr1 = ptr1 - 8u;
+
+ /* writing xa' and ya' */
+ *ptr1++ = xa_out;
+ *ptr1++ = ya_out;
+
+ xc_out = (xa - xb + xc - xd);
+ yc_out = (ya - yb + yc - yd);
+
+ /* writing xc' and yc' */
+ *ptr1++ = xc_out;
+ *ptr1++ = yc_out;
+
+ xb_out = (xa - yb - xc + yd);
+ yb_out = (ya + xb - yc - xd);
+
+ /* writing xb' and yb' */
+ *ptr1++ = xb_out;
+ *ptr1++ = yb_out;
+
+ xd_out = (xa + yb - xc - yd);
+ yd_out = (ya - xb - yc + xd);
+
+ /* writing xd' and yd' */
+ *ptr1++ = xd_out;
+ *ptr1++ = yd_out;
+
+
+ } while(--j);
+
+ /* output is in 11.21(q21) format for the 1024 point */
+ /* output is in 9.23(q23) format for the 256 point */
+ /* output is in 7.25(q25) format for the 64 point */
+ /* output is in 5.27(q27) format for the 16 point */
+
+ /* End of last stage process */
+}