/* ----------------------------------------------------------------------
|
* 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: 27. January 2017
|
* $Revision: V.1.5.1
|
*
|
* Target Processor: Cortex-M cores
|
* -------------------------------------------------------------------- */
|
/*
|
* Copyright (C) 2010-2017 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,
|
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 It has been superseded by \ref arm_cfft_q31 and will be removed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 */
|
}
|
