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Diffstat (limited to 'DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c')
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diff --git a/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c b/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c new file mode 100644 index 0000000..0fbb40b --- /dev/null +++ b/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c @@ -0,0 +1,1404 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010-2014 ARM Limited. All rights reserved. +* +* $Date: 19. March 2015 +* $Revision: V.1.4.5 +* +* 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 +* +* 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. +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +void arm_radix4_butterfly_inverse_q31( +q31_t * pSrc, +uint32_t fftLen, +q31_t * pCoef, +uint32_t twidCoefModifier); + +void arm_radix4_butterfly_q31( +q31_t * pSrc, +uint32_t fftLen, +q31_t * pCoef, +uint32_t twidCoefModifier); + +void arm_bitreversal_q31( +q31_t * pSrc, +uint32_t fftLen, +uint16_t bitRevFactor, +uint16_t * pBitRevTab); + +/** + * @ingroup groupTransforms + */ + +/** + * @addtogroup ComplexFFT + * @{ + */ + +/** + * @details + * @brief Processing function for the Q31 CFFT/CIFFT. + * @deprecated Do not use this function. It has been superseded by \ref arm_cfft_q31 and will be removed + * @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 ComplexFFT 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) +{ +#if defined(ARM_MATH_CM7) + 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; + } +#else + uint32_t n1, n2, ia1, ia2, ia3, i0, 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; + q31_t *pSi0; + q31_t *pSi1; + q31_t *pSi2; + q31_t *pSi3; + 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; + + ia1 = 0u; + + j = n2; + + pSi0 = pSrc; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + /* Calculation of first stage */ + do + { + /* input is in 1.31(q31) format and provide 4 guard bits for the input */ + + /* Butterfly implementation */ + /* xa + xc */ + r1 = (pSi0[0] >> 4u) + (pSi2[0] >> 4u); + /* xa - xc */ + r2 = (pSi0[0] >> 4u) - (pSi2[0] >> 4u); + + /* xb + xd */ + t1 = (pSi1[0] >> 4u) + (pSi3[0] >> 4u); + + /* ya + yc */ + s1 = (pSi0[1] >> 4u) + (pSi2[1] >> 4u); + /* ya - yc */ + s2 = (pSi0[1] >> 4u) - (pSi2[1] >> 4u); + + /* xa' = xa + xb + xc + xd */ + *pSi0++ = (r1 + t1); + /* (xa + xc) - (xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = (pSi1[1] >> 4u) + (pSi3[1] >> 4u); + + /* ya' = ya + yb + yc + yd */ + *pSi0++ = (s1 + t2); + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* yb - yd */ + t1 = (pSi1[1] >> 4u) - (pSi3[1] >> 4u); + /* xb - xd */ + t2 = (pSi1[0] >> 4u) - (pSi3[0] >> 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) */ + *pSi1++ = (((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) */ + *pSi1++ = (((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) */ + *pSi2++ = (((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) */ + *pSi2++ = (((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) */ + *pSi3++ = (((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) */ + *pSi3++ = (((int32_t) (((q63_t) s2 * co3) >> 32)) - + ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + } 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; + + pSi0 = pSrc + 2 * j; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* Butterfly implementation */ + /* xa + xc */ + r1 = pSi0[0] + pSi2[0]; + + /* xa - xc */ + r2 = pSi0[0] - pSi2[0]; + + + /* ya + yc */ + s1 = pSi0[1] + pSi2[1]; + + /* ya - yc */ + s2 = pSi0[1] - pSi2[1]; + + + /* xb + xd */ + t1 = pSi1[0] + pSi3[0]; + + + /* xa' = xa + xb + xc + xd */ + pSi0[0] = (r1 + t1) >> 2u; + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSi1[1] + pSi3[1]; + + /* ya' = ya + yb + yc + yd */ + pSi0[1] = (s1 + t2) >> 2u; + pSi0 += 2 * n1; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSi1[1] - pSi3[1]; + + /* (xb - xd) */ + t2 = pSi1[0] - pSi3[0]; + + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSi1[0] = (((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) */ + pSi1[1] = (((int32_t) (((q63_t) s1 * co2) >> 32)) - + ((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1u; + pSi1 += 2 * n1; + + /* (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) */ + pSi2[0] = (((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) */ + pSi2[1] = (((int32_t) (((q63_t) s1 * co1) >> 32)) - + ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u; + pSi2 += 2 * n1; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSi3[0] = (((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) */ + pSi3[1] = (((int32_t) (((q63_t) s2 * co3) >> 32)) - + ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u; + pSi3 += 2 * n1; + } + } + twidCoefModifier <<= 2u; + } +#endif + + /* 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) +{ +#if defined(ARM_MATH_CM7) + 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; + } +#else + uint32_t n1, n2, ia1, ia2, ia3, i0, 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; + q31_t *pSi0; + q31_t *pSi1; + q31_t *pSi2; + q31_t *pSi3; + 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; + + ia1 = 0u; + + j = n2; + + pSi0 = pSrc; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + do + { + /* Butterfly implementation */ + /* xa + xc */ + r1 = (pSi0[0] >> 4u) + (pSi2[0] >> 4u); + /* xa - xc */ + r2 = (pSi0[0] >> 4u) - (pSi2[0] >> 4u); + + /* xb + xd */ + t1 = (pSi1[0] >> 4u) + (pSi3[0] >> 4u); + + /* ya + yc */ + s1 = (pSi0[1] >> 4u) + (pSi2[1] >> 4u); + /* ya - yc */ + s2 = (pSi0[1] >> 4u) - (pSi2[1] >> 4u); + + /* xa' = xa + xb + xc + xd */ + *pSi0++ = (r1 + t1); + /* (xa + xc) - (xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = (pSi1[1] >> 4u) + (pSi3[1] >> 4u); + /* ya' = ya + yb + yc + yd */ + *pSi0++ = (s1 + t2); + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* yb - yd */ + t1 = (pSi1[1] >> 4u) - (pSi3[1] >> 4u); + /* xb - xd */ + t2 = (pSi1[0] >> 4u) - (pSi3[0] >> 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) */ + *pSi1++ = (((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) */ + *pSi1++ = (((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) */ + *pSi2++ = (((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) */ + *pSi2++ = (((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) */ + *pSi3++ = (((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) */ + *pSi3++ = (((int32_t) (((q63_t) s2 * co3) >> 32)) + + ((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + } 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; + + pSi0 = pSrc + 2 * j; + pSi1 = pSi0 + 2 * n2; + pSi2 = pSi1 + 2 * n2; + pSi3 = pSi2 + 2 * n2; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* Butterfly implementation */ + /* xa + xc */ + r1 = pSi0[0] + pSi2[0]; + + /* xa - xc */ + r2 = pSi0[0] - pSi2[0]; + + + /* ya + yc */ + s1 = pSi0[1] + pSi2[1]; + + /* ya - yc */ + s2 = pSi0[1] - pSi2[1]; + + + /* xb + xd */ + t1 = pSi1[0] + pSi3[0]; + + + /* xa' = xa + xb + xc + xd */ + pSi0[0] = (r1 + t1) >> 2u; + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + /* yb + yd */ + t2 = pSi1[1] + pSi3[1]; + + /* ya' = ya + yb + yc + yd */ + pSi0[1] = (s1 + t2) >> 2u; + pSi0 += 2 * n1; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSi1[1] - pSi3[1]; + + /* (xb - xd) */ + t2 = pSi1[0] - pSi3[0]; + + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSi1[0] = (((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) */ + pSi1[1] = + + (((int32_t) (((q63_t) s1 * co2) >> 32u)) + + ((int32_t) (((q63_t) r1 * si2) >> 32u))) >> 1u; + pSi1 += 2 * n1; + + /* (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) */ + pSi2[0] = (((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) */ + pSi2[1] = (((int32_t) (((q63_t) s1 * co1) >> 32)) + + ((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u; + pSi2 += 2 * n1; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSi3[0] = (((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) */ + pSi3[1] = (((int32_t) (((q63_t) s2 * co3) >> 32)) + + ((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u; + pSi3 += 2 * n1; + } + } + twidCoefModifier <<= 2u; + } +#endif + + /* 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 */ +} |