arm_cfft_radix4_q31.c
906 lines
| 27.2 KiB
| text/x-c
|
CLexer
r71 | /* ---------------------------------------------------------------------- | |||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 15. July 2011 | ||||
* $Revision: V1.0.10 | ||||
* | ||||
* 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 1.0.10 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 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 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; | ||||
/* 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); | ||||
/* 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); | ||||
/* xb + xd */ | ||||
t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 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 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/2u], pSrc[i0 + 3fftLen/4] */ | ||||
i1 = i0 + n2; | ||||
i2 = i1 + n2; | ||||
i3 = i2 + n2; | ||||
/* Butterfly implementation */ | ||||
/* xa + xb */ | ||||
r1 = pSrc[2u * i0] + pSrc[2u * i2]; | ||||
/* xa - xb */ | ||||
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); | ||||
/* (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); | ||||
/* (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; | ||||
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ | ||||
pSrc[(2u * i1) + 1u] = s1; | ||||
/* (xa+yb-xc-yd) */ | ||||
r1 = r2 + t1; | ||||
/* (xa-yb-xc+yd) */ | ||||
r2 = r2 - t1; | ||||
/* (ya-xb-yc+xd) */ | ||||
s1 = s2 - t2; | ||||
/* (ya+xb-yc-xd) */ | ||||
s2 = s2 + t2; | ||||
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ | ||||
pSrc[2u * i2] = r1; | ||||
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ | ||||
pSrc[(2u * i2) + 1u] = s1; | ||||
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ | ||||
pSrc[2u * i3] = r2; | ||||
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ | ||||
pSrc[(2u * i3) + 1u] = s2; | ||||
} | ||||
/* 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; | ||||
/* 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); | ||||
/* 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); | ||||
/* xb + xd */ | ||||
t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 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 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/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]; | ||||
/* xc + xd */ | ||||
t1 = pSrc[2u * i1] + pSrc[2u * i3]; | ||||
/* xa' = xa + xb + xc + xd */ | ||||
pSrc[2u * i0] = (r1 + t1); | ||||
/* (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); | ||||
/* (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; | ||||
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ | ||||
pSrc[(2u * i1) + 1u] = s1; | ||||
/* (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; | ||||
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ | ||||
pSrc[(2u * i2) + 1u] = s1; | ||||
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ | ||||
pSrc[2u * i3] = r2; | ||||
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ | ||||
pSrc[(2u * i3) + 1u] = s2; | ||||
} | ||||
/* 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 In-place bit reversal function. | ||||
* @param[in, out] *pSrc points to the in-place buffer of Q31 data type. | ||||
* @param[in] fftLen length of the FFT. | ||||
* @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table | ||||
* @param[in] *pBitRevTab points to bit reversal table. | ||||
* @return none. | ||||
*/ | ||||
void arm_bitreversal_q31( | ||||
q31_t * pSrc, | ||||
uint32_t fftLen, | ||||
uint16_t bitRevFactor, | ||||
uint16_t * pBitRevTable) | ||||
{ | ||||
uint32_t fftLenBy2, fftLenBy2p1, i, j; | ||||
q31_t in; | ||||
/* Initializations */ | ||||
j = 0u; | ||||
fftLenBy2 = fftLen / 2u; | ||||
fftLenBy2p1 = (fftLen / 2u) + 1u; | ||||
/* Bit Reversal Implementation */ | ||||
for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u) | ||||
{ | ||||
if(i < j) | ||||
{ | ||||
/* pSrc[i] <-> pSrc[j]; */ | ||||
in = pSrc[2u * i]; | ||||
pSrc[2u * i] = pSrc[2u * j]; | ||||
pSrc[2u * j] = in; | ||||
/* pSrc[i+1u] <-> pSrc[j+1u] */ | ||||
in = pSrc[(2u * i) + 1u]; | ||||
pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u]; | ||||
pSrc[(2u * j) + 1u] = in; | ||||
/* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */ | ||||
in = pSrc[2u * (i + fftLenBy2p1)]; | ||||
pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)]; | ||||
pSrc[2u * (j + fftLenBy2p1)] = in; | ||||
/* pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */ | ||||
in = pSrc[(2u * (i + fftLenBy2p1)) + 1u]; | ||||
pSrc[(2u * (i + fftLenBy2p1)) + 1u] = | ||||
pSrc[(2u * (j + fftLenBy2p1)) + 1u]; | ||||
pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in; | ||||
} | ||||
/* pSrc[i+1u] <-> pSrc[j+1u] */ | ||||
in = pSrc[2u * (i + 1u)]; | ||||
pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)]; | ||||
pSrc[2u * (j + fftLenBy2)] = in; | ||||
/* pSrc[i+2u] <-> pSrc[j+2u] */ | ||||
in = pSrc[(2u * (i + 1u)) + 1u]; | ||||
pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u]; | ||||
pSrc[(2u * (j + fftLenBy2)) + 1u] = in; | ||||
/* Reading the index for the bit reversal */ | ||||
j = *pBitRevTable; | ||||
/* Updating the bit reversal index depending on the fft length */ | ||||
pBitRevTable += bitRevFactor; | ||||
} | ||||
} | ||||