/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_cfft_radix4_q15.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_q15(
q15_t * pSrc16,
uint32_t fftLen,
const q15_t * pCoef16,
uint32_t twidCoefModifier);
void arm_radix4_butterfly_inverse_q15(
q15_t * pSrc16,
uint32_t fftLen,
const q15_t * pCoef16,
uint32_t twidCoefModifier);
void arm_bitreversal_q15(
q15_t * pSrc,
uint32_t fftLen,
uint16_t bitRevFactor,
const uint16_t * pBitRevTab);
/**
@ingroup groupTransforms
*/
/**
@addtogroup ComplexFFT
@{
*/
/**
@brief Processing function for the Q15 CFFT/CIFFT.
@deprecated Do not use this function. It has been superseded by \ref arm_cfft_q15 and will be removed in the future.
@param[in] S points to an instance of the Q15 CFFT/CIFFT structure.
@param[in,out] pSrc points to the complex data buffer. 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 CFFTQ15.gif "Input and Output Formats for Q15 CFFT"
\image html CIFFTQ15.gif "Input and Output Formats for Q15 CIFFT"
*/
void arm_cfft_radix4_q15(
const arm_cfft_radix4_instance_q15 * S,
q15_t * pSrc)
{
if (S->ifftFlag == 1U)
{
/* Complex IFFT radix-4 */
arm_radix4_butterfly_inverse_q15(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier);
}
else
{
/* Complex FFT radix-4 */
arm_radix4_butterfly_q15(pSrc, S->fftLen, S->pTwiddle, S->twidCoefModifier);
}
if (S->bitReverseFlag == 1U)
{
/* Bit Reversal */
arm_bitreversal_q15(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)
* 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)
*
*/
/**
@brief Core function for the Q15 CFFT butterfly process.
@param[in,out] pSrc16 points to the in-place buffer of Q15 data type
@param[in] fftLen length of the FFT
@param[in] pCoef16 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_q15(
q15_t * pSrc16,
uint32_t fftLen,
const q15_t * pCoef16,
uint32_t twidCoefModifier)
{
#if defined (ARM_MATH_DSP)
q31_t R, S, T, U;
q31_t C1, C2, C3, out1, out2;
uint32_t n1, n2, ic, i0, j, k;
q15_t *ptr1;
q15_t *pSi0;
q15_t *pSi1;
q15_t *pSi2;
q15_t *pSi3;
q31_t xaya, xbyb, xcyc, xdyd;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2U;
/* Index for twiddle coefficient */
ic = 0U;
/* Index for input read and output write */
j = n2;
pSi0 = pSrc16;
pSi1 = pSi0 + 2 * n2;
pSi2 = pSi1 + 2 * n2;
pSi3 = pSi2 + 2 * n2;
/* Input is in 1.15(q15) format */
/* start of first stage process */
do
{
/* Butterfly implementation */
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = read_q15x2 (pSi0);
T = __SHADD16(T, 0); /* this is just a SIMD arithmetic shift right by 1 */
T = __SHADD16(T, 0); /* it turns out doing this twice is 2 cycles, the alternative takes 3 cycles */
/*
in = ((int16_t) (T & 0xFFFF)) >> 2; // alternative code that takes 3 cycles
T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
*/
/* Read yc (real), xc(imag) input */
S = read_q15x2 (pSi2);
S = __SHADD16(S, 0);
S = __SHADD16(S, 0);
/* R = packed((ya + yc), (xa + xc) ) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc) ) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = read_q15x2 (pSi1);
T = __SHADD16(T, 0);
T = __SHADD16(T, 0);
/* Read yd (real), xd(imag) input */
U = read_q15x2 (pSi3);
U = __SHADD16(U, 0);
U = __SHADD16(U, 0);
/* T = packed((yb + yd), (xb + xd) ) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
write_q15x2_ia (&pSi0, __SHADD16(R, T));
/* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */
R = __QSUB16(R, T);
/* co2 & si2 are read from SIMD Coefficient pointer */
C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic));
#ifndef ARM_MATH_BIG_ENDIAN
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
out1 = __SMUAD(C2, R) >> 16U;
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = __SMUSDX(C2, R);
#else
/* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out1 = __SMUSDX(R, C2) >> 16U;
/* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
out2 = __SMUAD(C2, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Reading i0+fftLen/4 */
/* T = packed(yb, xb) */
T = read_q15x2 (pSi1);
T = __SHADD16(T, 0);
T = __SHADD16(T, 0);
/* writing the butterfly processed i0 + fftLen/4 sample */
/* writing output(xc', yc') in little endian format */
write_q15x2_ia (&pSi1, (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
/* Butterfly calculations */
/* U = packed(yd, xd) */
U = read_q15x2 (pSi3);
U = __SHADD16(U, 0);
U = __SHADD16(U, 0);
/* T = packed(yb-yd, xb-xd) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __QASX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __QSAX(S, T);
#else
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __QSAX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __QASX(S, T);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* co1 & si1 are read from SIMD Coefficient pointer */
C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic));
/* Butterfly process for the i0+fftLen/2 sample */
#ifndef ARM_MATH_BIG_ENDIAN
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
out1 = __SMUAD(C1, S) >> 16U;
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
out2 = __SMUSDX(C1, S);
#else
/* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
out1 = __SMUSDX(S, C1) >> 16U;
/* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
out2 = __SMUAD(C1, S);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* writing output(xb', yb') in little endian format */
write_q15x2_ia (&pSi2, ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF));
/* co3 & si3 are read from SIMD Coefficient pointer */
C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic));
/* Butterfly process for the i0+3fftLen/4 sample */
#ifndef ARM_MATH_BIG_ENDIAN
/* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
out1 = __SMUAD(C3, R) >> 16U;
/* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
out2 = __SMUSDX(C3, R);
#else
/* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
out1 = __SMUSDX(R, C3) >> 16U;
/* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
out2 = __SMUAD(C3, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* writing output(xd', yd') in little endian format */
write_q15x2_ia (&pSi3, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
} while (--j);
/* data is in 4.11(q11) format */
/* end of first stage process */
/* start of middle stage process */
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2U;
/* Calculation of Middle stage */
for (k = fftLen / 4U; k > 4U; k >>= 2U)
{
/* Initializations for the middle stage */
n1 = n2;
n2 >>= 2U;
ic = 0U;
for (j = 0U; j <= (n2 - 1U); j++)
{
/* index calculation for the coefficients */
C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic));
C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic));
C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic));
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
pSi0 = pSrc16 + 2 * j;
pSi1 = pSi0 + 2 * n2;
pSi2 = pSi1 + 2 * n2;
pSi3 = pSi2 + 2 * n2;
/* Butterfly implementation */
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = read_q15x2 (pSi0);
/* Read yc (real), xc(imag) input */
S = read_q15x2 (pSi2);
/* R = packed( (ya + yc), (xa + xc)) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc)) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = read_q15x2 (pSi1);
/* Read yd (real), xd(imag) input */
U = read_q15x2 (pSi3);
/* T = packed( (yb + yd), (xb + xd)) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
out1 = __SHADD16(R, T);
out1 = __SHADD16(out1, 0);
write_q15x2 (pSi0, out1);
pSi0 += 2 * n1;
/* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
R = __SHSUB16(R, T);
#ifndef ARM_MATH_BIG_ENDIAN
/* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
out1 = __SMUAD(C2, R) >> 16U;
/* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = __SMUSDX(C2, R);
#else
/* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out1 = __SMUSDX(R, C2) >> 16U;
/* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
out2 = __SMUAD(C2, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Reading i0+3fftLen/4 */
/* Read yb (real), xb(imag) input */
T = read_q15x2 (pSi1);
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
write_q15x2 (pSi1, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
pSi1 += 2 * n1;
/* Butterfly calculations */
/* Read yd (real), xd(imag) input */
U = read_q15x2 (pSi3);
/* T = packed(yb-yd, xb-xd) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __SHASX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __SHSAX(S, T);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = __SMUAD(C1, S) >> 16U;
out2 = __SMUSDX(C1, S);
#else
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __SHSAX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __SHASX(S, T);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = __SMUSDX(S, C1) >> 16U;
out2 = __SMUAD(C1, S);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
write_q15x2 (pSi2, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
pSi2 += 2 * n1;
/* Butterfly process for the i0+3fftLen/4 sample */
#ifndef ARM_MATH_BIG_ENDIAN
out1 = __SMUAD(C3, R) >> 16U;
out2 = __SMUSDX(C3, R);
#else
out1 = __SMUSDX(R, C3) >> 16U;
out2 = __SMUAD(C3, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
/* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
write_q15x2 (pSi3, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
pSi3 += 2 * n1;
}
}
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2U;
}
/* end of middle stage process */
/* data is in 10.6(q6) format for the 1024 point */
/* data is in 8.8(q8) format for the 256 point */
/* data is in 6.10(q10) format for the 64 point */
/* data is in 4.12(q12) format for the 16 point */
/* Initializations for the last stage */
j = fftLen >> 2;
ptr1 = &pSrc16[0];
/* start of last stage process */
/* Butterfly implementation */
do
{
/* Read xa (real), ya(imag) input */
xaya = read_q15x2_ia ((q15_t **) &ptr1);
/* Read xb (real), yb(imag) input */
xbyb = read_q15x2_ia ((q15_t **) &ptr1);
/* Read xc (real), yc(imag) input */
xcyc = read_q15x2_ia ((q15_t **) &ptr1);
/* Read xd (real), yd(imag) input */
xdyd = read_q15x2_ia ((q15_t **) &ptr1);
/* R = packed((ya + yc), (xa + xc)) */
R = __QADD16(xaya, xcyc);
/* T = packed((yb + yd), (xb + xd)) */
T = __QADD16(xbyb, xdyd);
/* pointer updation for writing */
ptr1 = ptr1 - 8U;
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
write_q15x2_ia (&ptr1, __SHADD16(R, T));
/* T = packed((yb + yd), (xb + xd)) */
T = __QADD16(xbyb, xdyd);
/* xc' = (xa-xb+xc-xd) */
/* yc' = (ya-yb+yc-yd) */
write_q15x2_ia (&ptr1, __SHSUB16(R, T));
/* S = packed((ya - yc), (xa - xc)) */
S = __QSUB16(xaya, xcyc);
/* Read yd (real), xd(imag) input */
/* T = packed( (yb - yd), (xb - xd)) */
U = __QSUB16(xbyb, xdyd);
#ifndef ARM_MATH_BIG_ENDIAN
/* xb' = (xa+yb-xc-yd) */
/* yb' = (ya-xb-yc+xd) */
write_q15x2_ia (&ptr1, __SHSAX(S, U));
/* xd' = (xa-yb-xc+yd) */
/* yd' = (ya+xb-yc-xd) */
write_q15x2_ia (&ptr1, __SHASX(S, U));
#else
/* xb' = (xa+yb-xc-yd) */
/* yb' = (ya-xb-yc+xd) */
write_q15x2_ia (&ptr1, __SHASX(S, U));
/* xd' = (xa-yb-xc+yd) */
/* yd' = (ya+xb-yc-xd) */
write_q15x2_ia (&ptr1, __SHSAX(S, U));
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
} while (--j);
/* end of last stage process */
/* output is in 11.5(q5) format for the 1024 point */
/* output is in 9.7(q7) format for the 256 point */
/* output is in 7.9(q9) format for the 64 point */
/* output is in 5.11(q11) format for the 16 point */
#else /* #if defined (ARM_MATH_DSP) */
q15_t R0, R1, S0, S1, T0, T1, U0, U1;
q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2;
uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2U;
/* Index for twiddle coefficient */
ic = 0U;
/* Index for input read and output write */
i0 = 0U;
j = n2;
/* Input is in 1.15(q15) format */
/* start of first stage process */
do
{
/* Butterfly implementation */
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* input is down scale by 4 to avoid overflow */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2U] >> 2U;
T1 = pSrc16[(i0 * 2U) + 1U] >> 2U;
/* input is down scale by 4 to avoid overflow */
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2U] >> 2U;
S1 = pSrc16[(i2 * 2U) + 1U] >> 2U;
/* R0 = (ya + yc) */
R0 = __SSAT(T0 + S0, 16U);
/* R1 = (xa + xc) */
R1 = __SSAT(T1 + S1, 16U);
/* S0 = (ya - yc) */
S0 = __SSAT(T0 - S0, 16);
/* S1 = (xa - xc) */
S1 = __SSAT(T1 - S1, 16);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* input is down scale by 4 to avoid overflow */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U] >> 2U;
T1 = pSrc16[(i1 * 2U) + 1U] >> 2U;
/* input is down scale by 4 to avoid overflow */
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U] >> 2U;
U1 = pSrc16[(i3 * 2U) + 1] >> 2U;
/* T0 = (yb + yd) */
T0 = __SSAT(T0 + U0, 16U);
/* T1 = (xb + xd) */
T1 = __SSAT(T1 + U1, 16U);
/* writing the butterfly processed i0 sample */
/* ya' = ya + yb + yc + yd */
/* xa' = xa + xb + xc + xd */
pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U);
pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U);
/* R0 = (ya + yc) - (yb + yd) */
/* R1 = (xa + xc) - (xb + xd) */
R0 = __SSAT(R0 - T0, 16U);
R1 = __SSAT(R1 - T1, 16U);
/* co2 & si2 are read from Coefficient pointer */
Co2 = pCoef16[2U * ic * 2U];
Si2 = pCoef16[(2U * ic * 2U) + 1];
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
out1 = (q15_t) ((Co2 * R0 + Si2 * R1) >> 16U);
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = (q15_t) ((-Si2 * R0 + Co2 * R1) >> 16U);
/* Reading i0+fftLen/4 */
/* input is down scale by 4 to avoid overflow */
/* T0 = yb, T1 = xb */
T0 = pSrc16[i1 * 2U] >> 2;
T1 = pSrc16[(i1 * 2U) + 1] >> 2;
/* writing the butterfly processed i0 + fftLen/4 sample */
/* writing output(xc', yc') in little endian format */
pSrc16[i1 * 2U] = out1;
pSrc16[(i1 * 2U) + 1] = out2;
/* Butterfly calculations */
/* input is down scale by 4 to avoid overflow */
/* U0 = yd, U1 = xd */
U0 = pSrc16[i3 * 2U] >> 2;
U1 = pSrc16[(i3 * 2U) + 1] >> 2;
/* T0 = yb-yd */
T0 = __SSAT(T0 - U0, 16);
/* T1 = xb-xd */
T1 = __SSAT(T1 - U1, 16);
/* R1 = (ya-yc) + (xb- xd), R0 = (xa-xc) - (yb-yd)) */
R0 = (q15_t) __SSAT((q31_t) (S0 - T1), 16);
R1 = (q15_t) __SSAT((q31_t) (S1 + T0), 16);
/* S1 = (ya-yc) - (xb- xd), S0 = (xa-xc) + (yb-yd)) */
S0 = (q15_t) __SSAT(((q31_t) S0 + T1), 16U);
S1 = (q15_t) __SSAT(((q31_t) S1 - T0), 16U);
/* co1 & si1 are read from Coefficient pointer */
Co1 = pCoef16[ic * 2U];
Si1 = pCoef16[(ic * 2U) + 1];
/* Butterfly process for the i0+fftLen/2 sample */
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
out1 = (q15_t) ((Si1 * S1 + Co1 * S0) >> 16);
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
out2 = (q15_t) ((-Si1 * S0 + Co1 * S1) >> 16);
/* writing output(xb', yb') in little endian format */
pSrc16[i2 * 2U] = out1;
pSrc16[(i2 * 2U) + 1] = out2;
/* Co3 & si3 are read from Coefficient pointer */
Co3 = pCoef16[3U * (ic * 2U)];
Si3 = pCoef16[(3U * (ic * 2U)) + 1];
/* Butterfly process for the i0+3fftLen/4 sample */
/* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */
out1 = (q15_t) ((Si3 * R1 + Co3 * R0) >> 16U);
/* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */
out2 = (q15_t) ((-Si3 * R0 + Co3 * R1) >> 16U);
/* writing output(xd', yd') in little endian format */
pSrc16[i3 * 2U] = out1;
pSrc16[(i3 * 2U) + 1] = out2;
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1U;
} while (--j);
/* data is in 4.11(q11) format */
/* end of first stage process */
/* start of middle stage process */
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2U;
/* Calculation of Middle stage */
for (k = fftLen / 4U; k > 4U; k >>= 2U)
{
/* Initializations for the middle stage */
n1 = n2;
n2 >>= 2U;
ic = 0U;
for (j = 0U; j <= (n2 - 1U); j++)
{
/* index calculation for the coefficients */
Co1 = pCoef16[ic * 2U];
Si1 = pCoef16[(ic * 2U) + 1U];
Co2 = pCoef16[2U * (ic * 2U)];
Si2 = pCoef16[(2U * (ic * 2U)) + 1U];
Co3 = pCoef16[3U * (ic * 2U)];
Si3 = pCoef16[(3U * (ic * 2U)) + 1U];
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Butterfly implementation */
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2U];
T1 = pSrc16[(i0 * 2U) + 1U];
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2U];
S1 = pSrc16[(i2 * 2U) + 1U];
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16);
R1 = __SSAT(T1 + S1, 16);
/* S0 = (ya - yc), S1 =(xa - xc) */
S0 = __SSAT(T0 - S0, 16);
S1 = __SSAT(T1 - S1, 16);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U];
T1 = pSrc16[(i1 * 2U) + 1U];
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U];
U1 = pSrc16[(i3 * 2U) + 1U];
/* T0 = (yb + yd), T1 = (xb + xd) */
T0 = __SSAT(T0 + U0, 16);
T1 = __SSAT(T1 + U1, 16);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
out1 = ((R0 >> 1U) + (T0 >> 1U)) >> 1U;
out2 = ((R1 >> 1U) + (T1 >> 1U)) >> 1U;
pSrc16[i0 * 2U] = out1;
pSrc16[(2U * i0) + 1U] = out2;
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
R0 = (R0 >> 1U) - (T0 >> 1U);
R1 = (R1 >> 1U) - (T1 >> 1U);
/* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
out1 = (q15_t) ((Co2 * R0 + Si2 * R1) >> 16U);
/* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = (q15_t) ((-Si2 * R0 + Co2 * R1) >> 16U);
/* Reading i0+3fftLen/4 */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U];
T1 = pSrc16[(i1 * 2U) + 1U];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
pSrc16[i1 * 2U] = out1;
pSrc16[(i1 * 2U) + 1U] = out2;
/* Butterfly calculations */
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U];
U1 = pSrc16[(i3 * 2U) + 1U];
/* T0 = yb-yd, T1 = xb-xd */
T0 = __SSAT(T0 - U0, 16);
T1 = __SSAT(T1 - U1, 16);
/* R0 = (ya-yc) + (xb- xd), R1 = (xa-xc) - (yb-yd)) */
R0 = (S0 >> 1U) - (T1 >> 1U);
R1 = (S1 >> 1U) + (T0 >> 1U);
/* S0 = (ya-yc) - (xb- xd), S1 = (xa-xc) + (yb-yd)) */
S0 = (S0 >> 1U) + (T1 >> 1U);
S1 = (S1 >> 1U) - (T0 >> 1U);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = (q15_t) ((Co1 * S0 + Si1 * S1) >> 16U);
out2 = (q15_t) ((-Si1 * S0 + Co1 * S1) >> 16U);
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
pSrc16[i2 * 2U] = out1;
pSrc16[(i2 * 2U) + 1U] = out2;
/* Butterfly process for the i0+3fftLen/4 sample */
out1 = (q15_t) ((Si3 * R1 + Co3 * R0) >> 16U);
out2 = (q15_t) ((-Si3 * R0 + Co3 * R1) >> 16U);
/* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */
/* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */
pSrc16[i3 * 2U] = out1;
pSrc16[(i3 * 2U) + 1U] = out2;
}
}
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2U;
}
/* end of middle stage process */
/* data is in 10.6(q6) format for the 1024 point */
/* data is in 8.8(q8) format for the 256 point */
/* data is in 6.10(q10) format for the 64 point */
/* data is in 4.12(q12) format for the 16 point */
/* Initializations for the last stage */
n1 = n2;
n2 >>= 2U;
/* start of last stage process */
/* Butterfly implementation */
for (i0 = 0U; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2U];
T1 = pSrc16[(i0 * 2U) + 1U];
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2U];
S1 = pSrc16[(i2 * 2U) + 1U];
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16U);
R1 = __SSAT(T1 + S1, 16U);
/* S0 = (ya - yc), S1 = (xa - xc) */
S0 = __SSAT(T0 - S0, 16U);
S1 = __SSAT(T1 - S1, 16U);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U];
T1 = pSrc16[(i1 * 2U) + 1U];
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U];
U1 = pSrc16[(i3 * 2U) + 1U];
/* T0 = (yb + yd), T1 = (xb + xd)) */
T0 = __SSAT(T0 + U0, 16U);
T1 = __SSAT(T1 + U1, 16U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U);
pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U);
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
R0 = (R0 >> 1U) - (T0 >> 1U);
R1 = (R1 >> 1U) - (T1 >> 1U);
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U];
T1 = pSrc16[(i1 * 2U) + 1U];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd) */
/* yc' = (ya-yb+yc-yd) */
pSrc16[i1 * 2U] = R0;
pSrc16[(i1 * 2U) + 1U] = R1;
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U];
U1 = pSrc16[(i3 * 2U) + 1U];
/* T0 = (yb - yd), T1 = (xb - xd) */
T0 = __SSAT(T0 - U0, 16U);
T1 = __SSAT(T1 - U1, 16U);
/* writing the butterfly processed i0 + fftLen/2 sample */
/* xb' = (xa+yb-xc-yd) */
/* yb' = (ya-xb-yc+xd) */
pSrc16[i2 * 2U] = (S0 >> 1U) + (T1 >> 1U);
pSrc16[(i2 * 2U) + 1U] = (S1 >> 1U) - (T0 >> 1U);
/* writing the butterfly processed i0 + 3fftLen/4 sample */
/* xd' = (xa-yb-xc+yd) */
/* yd' = (ya+xb-yc-xd) */
pSrc16[i3 * 2U] = (S0 >> 1U) - (T1 >> 1U);
pSrc16[(i3 * 2U) + 1U] = (S1 >> 1U) + (T0 >> 1U);
}
/* end of last stage process */
/* output is in 11.5(q5) format for the 1024 point */
/* output is in 9.7(q7) format for the 256 point */
/* output is in 7.9(q9) format for the 64 point */
/* output is in 5.11(q11) format for the 16 point */
#endif /* #if defined (ARM_MATH_DSP) */
}
/**
@brief Core function for the Q15 CIFFT butterfly process.
@param[in,out] pSrc16 points to the in-place buffer of Q15 data type
@param[in] fftLen length of the FFT
@param[in] pCoef16 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_q15(
q15_t * pSrc16,
uint32_t fftLen,
const q15_t * pCoef16,
uint32_t twidCoefModifier)
{
#if defined (ARM_MATH_DSP)
q31_t R, S, T, U;
q31_t C1, C2, C3, out1, out2;
uint32_t n1, n2, ic, i0, j, k;
q15_t *ptr1;
q15_t *pSi0;
q15_t *pSi1;
q15_t *pSi2;
q15_t *pSi3;
q31_t xaya, xbyb, xcyc, xdyd;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2U;
/* Index for twiddle coefficient */
ic = 0U;
/* Index for input read and output write */
j = n2;
pSi0 = pSrc16;
pSi1 = pSi0 + 2 * n2;
pSi2 = pSi1 + 2 * n2;
pSi3 = pSi2 + 2 * n2;
/* Input is in 1.15(q15) format */
/* start of first stage process */
do
{
/* Butterfly implementation */
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = read_q15x2 (pSi0);
T = __SHADD16(T, 0);
T = __SHADD16(T, 0);
/* Read yc (real), xc(imag) input */
S = read_q15x2 (pSi2);
S = __SHADD16(S, 0);
S = __SHADD16(S, 0);
/* R = packed((ya + yc), (xa + xc) ) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc) ) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = read_q15x2 (pSi1);
T = __SHADD16(T, 0);
T = __SHADD16(T, 0);
/* Read yd (real), xd(imag) input */
U = read_q15x2 (pSi3);
U = __SHADD16(U, 0);
U = __SHADD16(U, 0);
/* T = packed((yb + yd), (xb + xd) ) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
write_q15x2_ia (&pSi0, __SHADD16(R, T));
/* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */
R = __QSUB16(R, T);
/* co2 & si2 are read from SIMD Coefficient pointer */
C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic));
#ifndef ARM_MATH_BIG_ENDIAN
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
out1 = __SMUSD(C2, R) >> 16U;
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = __SMUADX(C2, R);
#else
/* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out1 = __SMUADX(C2, R) >> 16U;
/* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
out2 = __SMUSD(__QSUB16(0, C2), R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Reading i0+fftLen/4 */
/* T = packed(yb, xb) */
T = read_q15x2 (pSi1);
T = __SHADD16(T, 0);
T = __SHADD16(T, 0);
/* writing the butterfly processed i0 + fftLen/4 sample */
/* writing output(xc', yc') in little endian format */
write_q15x2_ia (&pSi1, (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
/* Butterfly calculations */
/* U = packed(yd, xd) */
U = read_q15x2 (pSi3);
U = __SHADD16(U, 0);
U = __SHADD16(U, 0);
/* T = packed(yb-yd, xb-xd) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __QSAX(S, T);
/* S = packed((ya-yc) + (xb- xd), (xa-xc) - (yb-yd)) */
S = __QASX(S, T);
#else
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __QASX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __QSAX(S, T);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* co1 & si1 are read from SIMD Coefficient pointer */
C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic));
/* Butterfly process for the i0+fftLen/2 sample */
#ifndef ARM_MATH_BIG_ENDIAN
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
out1 = __SMUSD(C1, S) >> 16U;
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
out2 = __SMUADX(C1, S);
#else
/* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
out1 = __SMUADX(C1, S) >> 16U;
/* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
out2 = __SMUSD(__QSUB16(0, C1), S);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* writing output(xb', yb') in little endian format */
write_q15x2_ia (&pSi2, ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF));
/* co3 & si3 are read from SIMD Coefficient pointer */
C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic));
/* Butterfly process for the i0+3fftLen/4 sample */
#ifndef ARM_MATH_BIG_ENDIAN
/* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
out1 = __SMUSD(C3, R) >> 16U;
/* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
out2 = __SMUADX(C3, R);
#else
/* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
out1 = __SMUADX(C3, R) >> 16U;
/* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
out2 = __SMUSD(__QSUB16(0, C3), R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* writing output(xd', yd') in little endian format */
write_q15x2_ia (&pSi3, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
} while (--j);
/* data is in 4.11(q11) format */
/* end of first stage process */
/* start of middle stage process */
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2U;
/* Calculation of Middle stage */
for (k = fftLen / 4U; k > 4U; k >>= 2U)
{
/* Initializations for the middle stage */
n1 = n2;
n2 >>= 2U;
ic = 0U;
for (j = 0U; j <= (n2 - 1U); j++)
{
/* index calculation for the coefficients */
C1 = read_q15x2 ((q15_t *) pCoef16 + (2U * ic));
C2 = read_q15x2 ((q15_t *) pCoef16 + (4U * ic));
C3 = read_q15x2 ((q15_t *) pCoef16 + (6U * ic));
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
pSi0 = pSrc16 + 2 * j;
pSi1 = pSi0 + 2 * n2;
pSi2 = pSi1 + 2 * n2;
pSi3 = pSi2 + 2 * n2;
/* Butterfly implementation */
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = read_q15x2 (pSi0);
/* Read yc (real), xc(imag) input */
S = read_q15x2 (pSi2);
/* R = packed( (ya + yc), (xa + xc)) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc)) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = read_q15x2 (pSi1);
/* Read yd (real), xd(imag) input */
U = read_q15x2 (pSi3);
/* T = packed( (yb + yd), (xb + xd)) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
out1 = __SHADD16(R, T);
out1 = __SHADD16(out1, 0);
write_q15x2 (pSi0, out1);
pSi0 += 2 * n1;
/* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
R = __SHSUB16(R, T);
#ifndef ARM_MATH_BIG_ENDIAN
/* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
out1 = __SMUSD(C2, R) >> 16U;
/* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = __SMUADX(C2, R);
#else
/* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out1 = __SMUADX(R, C2) >> 16U;
/* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
out2 = __SMUSD(__QSUB16(0, C2), R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Reading i0+3fftLen/4 */
/* Read yb (real), xb(imag) input */
T = read_q15x2 (pSi1);
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
write_q15x2 (pSi1, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
pSi1 += 2 * n1;
/* Butterfly calculations */
/* Read yd (real), xd(imag) input */
U = read_q15x2 (pSi3);
/* T = packed(yb-yd, xb-xd) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __SHSAX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __SHASX(S, T);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = __SMUSD(C1, S) >> 16U;
out2 = __SMUADX(C1, S);
#else
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __SHASX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __SHSAX(S, T);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = __SMUADX(S, C1) >> 16U;
out2 = __SMUSD(__QSUB16(0, C1), S);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
write_q15x2 (pSi2, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
pSi2 += 2 * n1;
/* Butterfly process for the i0+3fftLen/4 sample */
#ifndef ARM_MATH_BIG_ENDIAN
out1 = __SMUSD(C3, R) >> 16U;
out2 = __SMUADX(C3, R);
#else
out1 = __SMUADX(C3, R) >> 16U;
out2 = __SMUSD(__QSUB16(0, C3), R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
/* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
write_q15x2 (pSi3, ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF));
pSi3 += 2 * n1;
}
}
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2U;
}
/* end of middle stage process */
/* data is in 10.6(q6) format for the 1024 point */
/* data is in 8.8(q8) format for the 256 point */
/* data is in 6.10(q10) format for the 64 point */
/* data is in 4.12(q12) format for the 16 point */
/* Initializations for the last stage */
j = fftLen >> 2;
ptr1 = &pSrc16[0];
/* start of last stage process */
/* Butterfly implementation */
do
{
/* Read xa (real), ya(imag) input */
xaya = read_q15x2_ia ((q15_t **) &ptr1);
/* Read xb (real), yb(imag) input */
xbyb = read_q15x2_ia ((q15_t **) &ptr1);
/* Read xc (real), yc(imag) input */
xcyc = read_q15x2_ia ((q15_t **) &ptr1);
/* Read xd (real), yd(imag) input */
xdyd = read_q15x2_ia ((q15_t **) &ptr1);
/* R = packed((ya + yc), (xa + xc)) */
R = __QADD16(xaya, xcyc);
/* T = packed((yb + yd), (xb + xd)) */
T = __QADD16(xbyb, xdyd);
/* pointer updation for writing */
ptr1 = ptr1 - 8U;
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
write_q15x2_ia (&ptr1, __SHADD16(R, T));
/* T = packed((yb + yd), (xb + xd)) */
T = __QADD16(xbyb, xdyd);
/* xc' = (xa-xb+xc-xd) */
/* yc' = (ya-yb+yc-yd) */
write_q15x2_ia (&ptr1, __SHSUB16(R, T));
/* S = packed((ya - yc), (xa - xc)) */
S = __QSUB16(xaya, xcyc);
/* Read yd (real), xd(imag) input */
/* T = packed( (yb - yd), (xb - xd)) */
U = __QSUB16(xbyb, xdyd);
#ifndef ARM_MATH_BIG_ENDIAN
/* xb' = (xa+yb-xc-yd) */
/* yb' = (ya-xb-yc+xd) */
write_q15x2_ia (&ptr1, __SHASX(S, U));
/* xd' = (xa-yb-xc+yd) */
/* yd' = (ya+xb-yc-xd) */
write_q15x2_ia (&ptr1, __SHSAX(S, U));
#else
/* xb' = (xa+yb-xc-yd) */
/* yb' = (ya-xb-yc+xd) */
write_q15x2_ia (&ptr1, __SHSAX(S, U));
/* xd' = (xa-yb-xc+yd) */
/* yd' = (ya+xb-yc-xd) */
write_q15x2_ia (&ptr1, __SHASX(S, U));
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
} while (--j);
/* end of last stage process */
/* output is in 11.5(q5) format for the 1024 point */
/* output is in 9.7(q7) format for the 256 point */
/* output is in 7.9(q9) format for the 64 point */
/* output is in 5.11(q11) format for the 16 point */
#else /* arm_radix4_butterfly_inverse_q15 */
q15_t R0, R1, S0, S1, T0, T1, U0, U1;
q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2;
uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2U;
/* Index for twiddle coefficient */
ic = 0U;
/* Index for input read and output write */
i0 = 0U;
j = n2;
/* Input is in 1.15(q15) format */
/* Start of first stage process */
do
{
/* Butterfly implementation */
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* input is down scale by 4 to avoid overflow */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2U] >> 2U;
T1 = pSrc16[(i0 * 2U) + 1U] >> 2U;
/* input is down scale by 4 to avoid overflow */
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2U] >> 2U;
S1 = pSrc16[(i2 * 2U) + 1U] >> 2U;
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16U);
R1 = __SSAT(T1 + S1, 16U);
/* S0 = (ya - yc), S1 = (xa - xc) */
S0 = __SSAT(T0 - S0, 16U);
S1 = __SSAT(T1 - S1, 16U);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* input is down scale by 4 to avoid overflow */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U] >> 2U;
T1 = pSrc16[(i1 * 2U) + 1U] >> 2U;
/* Read yd (real), xd(imag) input */
/* input is down scale by 4 to avoid overflow */
U0 = pSrc16[i3 * 2U] >> 2U;
U1 = pSrc16[(i3 * 2U) + 1U] >> 2U;
/* T0 = (yb + yd), T1 = (xb + xd) */
T0 = __SSAT(T0 + U0, 16U);
T1 = __SSAT(T1 + U1, 16U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U);
pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U);
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc)- (xb + xd) */
R0 = __SSAT(R0 - T0, 16U);
R1 = __SSAT(R1 - T1, 16U);
/* co2 & si2 are read from Coefficient pointer */
Co2 = pCoef16[2U * ic * 2U];
Si2 = pCoef16[(2U * ic * 2U) + 1U];
/* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
out1 = (q15_t) ((Co2 * R0 - Si2 * R1) >> 16U);
/* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
out2 = (q15_t) ((Si2 * R0 + Co2 * R1) >> 16U);
/* Reading i0+fftLen/4 */
/* input is down scale by 4 to avoid overflow */
/* T0 = yb, T1 = xb */
T0 = pSrc16[i1 * 2U] >> 2U;
T1 = pSrc16[(i1 * 2U) + 1U] >> 2U;
/* writing the butterfly processed i0 + fftLen/4 sample */
/* writing output(xc', yc') in little endian format */
pSrc16[i1 * 2U] = out1;
pSrc16[(i1 * 2U) + 1U] = out2;
/* Butterfly calculations */
/* input is down scale by 4 to avoid overflow */
/* U0 = yd, U1 = xd) */
U0 = pSrc16[i3 * 2U] >> 2U;
U1 = pSrc16[(i3 * 2U) + 1U] >> 2U;
/* T0 = yb-yd, T1 = xb-xd) */
T0 = __SSAT(T0 - U0, 16U);
T1 = __SSAT(T1 - U1, 16U);
/* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */
R0 = (q15_t) __SSAT((q31_t) (S0 + T1), 16);
R1 = (q15_t) __SSAT((q31_t) (S1 - T0), 16);
/* S = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */
S0 = (q15_t) __SSAT((q31_t) (S0 - T1), 16);
S1 = (q15_t) __SSAT((q31_t) (S1 + T0), 16);
/* co1 & si1 are read from Coefficient pointer */
Co1 = pCoef16[ic * 2U];
Si1 = pCoef16[(ic * 2U) + 1U];
/* Butterfly process for the i0+fftLen/2 sample */
/* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
out1 = (q15_t) ((Co1 * S0 - Si1 * S1) >> 16U);
/* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
out2 = (q15_t) ((Si1 * S0 + Co1 * S1) >> 16U);
/* writing output(xb', yb') in little endian format */
pSrc16[i2 * 2U] = out1;
pSrc16[(i2 * 2U) + 1U] = out2;
/* Co3 & si3 are read from Coefficient pointer */
Co3 = pCoef16[3U * ic * 2U];
Si3 = pCoef16[(3U * ic * 2U) + 1U];
/* Butterfly process for the i0+3fftLen/4 sample */
/* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */
out1 = (q15_t) ((Co3 * R0 - Si3 * R1) >> 16U);
/* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */
out2 = (q15_t) ((Si3 * R0 + Co3 * R1) >> 16U);
/* writing output(xd', yd') in little endian format */
pSrc16[i3 * 2U] = out1;
pSrc16[(i3 * 2U) + 1U] = out2;
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1U;
} while (--j);
/* End of first stage process */
/* data is in 4.11(q11) format */
/* Start of Middle stage process */
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2U;
/* Calculation of Middle stage */
for (k = fftLen / 4U; k > 4U; k >>= 2U)
{
/* Initializations for the middle stage */
n1 = n2;
n2 >>= 2U;
ic = 0U;
for (j = 0U; j <= (n2 - 1U); j++)
{
/* index calculation for the coefficients */
Co1 = pCoef16[ic * 2U];
Si1 = pCoef16[(ic * 2U) + 1U];
Co2 = pCoef16[2U * ic * 2U];
Si2 = pCoef16[2U * ic * 2U + 1U];
Co3 = pCoef16[3U * ic * 2U];
Si3 = pCoef16[(3U * ic * 2U) + 1U];
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Butterfly implementation */
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2U];
T1 = pSrc16[(i0 * 2U) + 1U];
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2U];
S1 = pSrc16[(i2 * 2U) + 1U];
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16U);
R1 = __SSAT(T1 + S1, 16U);
/* S0 = (ya - yc), S1 = (xa - xc) */
S0 = __SSAT(T0 - S0, 16U);
S1 = __SSAT(T1 - S1, 16U);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U];
T1 = pSrc16[(i1 * 2U) + 1U];
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U];
U1 = pSrc16[(i3 * 2U) + 1U];
/* T0 = (yb + yd), T1 = (xb + xd) */
T0 = __SSAT(T0 + U0, 16U);
T1 = __SSAT(T1 + U1, 16U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc16[i0 * 2U] = ((R0 >> 1U) + (T0 >> 1U)) >> 1U;
pSrc16[(i0 * 2U) + 1U] = ((R1 >> 1U) + (T1 >> 1U)) >> 1U;
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
R0 = (R0 >> 1U) - (T0 >> 1U);
R1 = (R1 >> 1U) - (T1 >> 1U);
/* (ya-yb+yc-yd)* (si2) - (xa-xb+xc-xd)* co2 */
out1 = (q15_t) ((Co2 * R0 - Si2 * R1) >> 16);
/* (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
out2 = (q15_t) ((Si2 * R0 + Co2 * R1) >> 16);
/* Reading i0+3fftLen/4 */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U];
T1 = pSrc16[(i1 * 2U) + 1U];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
/* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
pSrc16[i1 * 2U] = out1;
pSrc16[(i1 * 2U) + 1U] = out2;
/* Butterfly calculations */
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U];
U1 = pSrc16[(i3 * 2U) + 1U];
/* T0 = yb-yd, T1 = xb-xd) */
T0 = __SSAT(T0 - U0, 16U);
T1 = __SSAT(T1 - U1, 16U);
/* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */
R0 = (S0 >> 1U) + (T1 >> 1U);
R1 = (S1 >> 1U) - (T0 >> 1U);
/* S1 = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */
S0 = (S0 >> 1U) - (T1 >> 1U);
S1 = (S1 >> 1U) + (T0 >> 1U);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = (q15_t) ((Co1 * S0 - Si1 * S1) >> 16U);
out2 = (q15_t) ((Si1 * S0 + Co1 * S1) >> 16U);
/* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
/* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
pSrc16[i2 * 2U] = out1;
pSrc16[(i2 * 2U) + 1U] = out2;
/* Butterfly process for the i0+3fftLen/4 sample */
out1 = (q15_t) ((Co3 * R0 - Si3 * R1) >> 16U);
out2 = (q15_t) ((Si3 * R0 + Co3 * R1) >> 16U);
/* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */
/* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */
pSrc16[i3 * 2U] = out1;
pSrc16[(i3 * 2U) + 1U] = out2;
}
}
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2U;
}
/* End of Middle stages process */
/* data is in 10.6(q6) format for the 1024 point */
/* data is in 8.8(q8) format for the 256 point */
/* data is in 6.10(q10) format for the 64 point */
/* data is in 4.12(q12) format for the 16 point */
/* start of last stage process */
/* Initializations for the last stage */
n1 = n2;
n2 >>= 2U;
/* Butterfly implementation */
for (i0 = 0U; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2U];
T1 = pSrc16[(i0 * 2U) + 1U];
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2U];
S1 = pSrc16[(i2 * 2U) + 1U];
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16U);
R1 = __SSAT(T1 + S1, 16U);
/* S0 = (ya - yc), S1 = (xa - xc) */
S0 = __SSAT(T0 - S0, 16U);
S1 = __SSAT(T1 - S1, 16U);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U];
T1 = pSrc16[(i1 * 2U) + 1U];
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U];
U1 = pSrc16[(i3 * 2U) + 1U];
/* T0 = (yb + yd), T1 = (xb + xd) */
T0 = __SSAT(T0 + U0, 16U);
T1 = __SSAT(T1 + U1, 16U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc16[i0 * 2U] = (R0 >> 1U) + (T0 >> 1U);
pSrc16[(i0 * 2U) + 1U] = (R1 >> 1U) + (T1 >> 1U);
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
R0 = (R0 >> 1U) - (T0 >> 1U);
R1 = (R1 >> 1U) - (T1 >> 1U);
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2U];
T1 = pSrc16[(i1 * 2U) + 1U];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd) */
/* yc' = (ya-yb+yc-yd) */
pSrc16[i1 * 2U] = R0;
pSrc16[(i1 * 2U) + 1U] = R1;
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2U];
U1 = pSrc16[(i3 * 2U) + 1U];
/* T0 = (yb - yd), T1 = (xb - xd) */
T0 = __SSAT(T0 - U0, 16U);
T1 = __SSAT(T1 - U1, 16U);
/* writing the butterfly processed i0 + fftLen/2 sample */
/* xb' = (xa-yb-xc+yd) */
/* yb' = (ya+xb-yc-xd) */
pSrc16[i2 * 2U] = (S0 >> 1U) - (T1 >> 1U);
pSrc16[(i2 * 2U) + 1U] = (S1 >> 1U) + (T0 >> 1U);
/* writing the butterfly processed i0 + 3fftLen/4 sample */
/* xd' = (xa+yb-xc-yd) */
/* yd' = (ya-xb-yc+xd) */
pSrc16[i3 * 2U] = (S0 >> 1U) + (T1 >> 1U);
pSrc16[(i3 * 2U) + 1U] = (S1 >> 1U) - (T0 >> 1U);
}
/* end of last stage process */
/* output is in 11.5(q5) format for the 1024 point */
/* output is in 9.7(q7) format for the 256 point */
/* output is in 7.9(q9) format for the 64 point */
/* output is in 5.11(q11) format for the 16 point */
#endif /* #if defined (ARM_MATH_DSP) */
}
