mbed-os 6.10 versione
cmsis_dsp/TransformFunctions/arm_cfft_radix4_q31.c
- Committer:
- emilmont
- Date:
- 2012-11-28
- Revision:
- 1:fdd22bb7aa52
- Child:
- 2:da51fb522205
File content as of revision 1:fdd22bb7aa52:
/* ---------------------------------------------------------------------- * 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 */ }