/* ----------------------------------------------------------------------
* 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
*
* $Date: 18. March 2019
* $Revision: V1.6.0
*
* Target Processor: Cortex-M cores
* -------------------------------------------------------------------- */
/*
* Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved.
*
* SPDX-License-Identifier: Apache-2.0
*
* Licensed under the Apache License, Version 2.0 (the License); you may
* not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an AS IS BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "arm_math.h"
void arm_radix4_butterfly_inverse_q31(
q31_t * pSrc,
uint32_t fftLen,
const q31_t * pCoef,
uint32_t twidCoefModifier);
void arm_radix4_butterfly_q31(
q31_t * pSrc,
uint32_t fftLen,
const q31_t * pCoef,
uint32_t twidCoefModifier);
void arm_bitreversal_q31(
q31_t * pSrc,
uint32_t fftLen,
uint16_t bitRevFactor,
const uint16_t * pBitRevTab);
/**
@ingroup groupTransforms
*/
/**
@addtogroup ComplexFFT
@{
*/
/**
@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 It has been superseded by \ref arm_cfft_q31 and will be removed in the future.
@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:
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,
const 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;
/* 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
{
/* Read xa (real), ya(imag) input */
xa = *ptr1++;
ya = *ptr1++;
/* Read xb (real), yb(imag) input */
xb = *ptr1++;
yb = *ptr1++;
/* Read xc (real), yc(imag) input */
xc = *ptr1++;
yc = *ptr1++;
/* Read xc (real), yc(imag) input */
xd = *ptr1++;
yd = *ptr1++;
/* 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,
const 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;
/* 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
{
/* Read xa (real), ya(imag) input */
xa = *ptr1++;
ya = *ptr1++;
/* Read xb (real), yb(imag) input */
xb = *ptr1++;
yb = *ptr1++;
/* Read xc (real), yc(imag) input */
xc = *ptr1++;
yc = *ptr1++;
/* Read xc (real), yc(imag) input */
xd = *ptr1++;
yd = *ptr1++;
/* 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 */
}
