/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. February 2012
* $Revision: V1.1.0
*
* Project: CMSIS DSP Library
* Title: arm_cfft_radix4_f32.c
*
* Description: Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function
*
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
* Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @defgroup Radix4_CFFT_CIFFT Radix-4 Complex FFT Functions
*
* \par
* Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).
* Computational complexity of CFFT reduces drastically when compared to DFT.
* \par
* This set of functions implements CFFT/CIFFT
* for Q15, Q31, and floating-point data types. The functions operates on in-place buffer which uses same buffer for input and output.
* Complex input is stored in input buffer in an interleaved fashion.
*
* \par
* The functions operate on blocks of input and output data and each call to the function processes
* 2*fftLen
samples through the transform. pSrc
points to In-place arrays containing 2*fftLen
values.
* \par
* The pSrc
points to the array of in-place buffer of size 2*fftLen
and inputs and outputs are stored in an interleaved fashion as shown below.
*
{real[0], imag[0], real[1], imag[1],..}* * \par Lengths supported by the transform: * \par * Internally, the function utilize a radix-4 decimation in frequency(DIF) algorithm * and the size of the FFT supported are of the lengths [16, 64, 256, 1024]. * * * \par Algorithm: * * Complex Fast Fourier Transform: * \par * 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 ** where N is length of FFT * \par * 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' ** \par * Twiddle factors for radix-4 FFT: *
* Wn = co1 + j * (- si1) * W2n = co2 + j * (- si2) * W3n = co3 + j * (- si3) ** * \par * \image html CFFT.gif "Radix-4 Decimation-in Frequency Complex Fast Fourier Transform" * * \par * Output from Radix-4 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output. * \par * Butterfly CFFT equations: *
* xa' = xa + xb + xc + xd * ya' = ya + yb + yc + yd * xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) * yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) * xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) * yb' = (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) ** * * Complex Inverse Fast Fourier Transform: * \par * CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below. * * \par * Modified Butterfly CIFFT equations: *
* xa' = xa + xb + xc + xd * ya' = ya + yb + yc + yd * xc' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) * yc' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) * xb' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) * yb' = (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) ** * \par Instance Structure * A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused. * There are separate instance structure declarations for each of the 3 supported data types. * * \par Initialization Functions * There is also an associated initialization function for each data type. * The initialization function performs the following operations: * - Sets the values of the internal structure fields. * - Initializes twiddle factor table and bit reversal table pointers * \par * Use of the initialization function is optional. * However, if the initialization function is used, then the instance structure cannot be placed into a const data section. * To place an instance structure into a const data section, the instance structure must be manually initialized. * Manually initialize the instance structure as follows: *
*arm_cfft_radix4_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen}; *arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor}; *arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor}; ** \par * where
fftLen
length of CFFT/CIFFT; ifftFlag
Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);
* bitReverseFlag
Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);
* pTwiddle
points to array of twiddle coefficients; pBitRevTable
points to the array of bit reversal table.
* twidCoefModifier
modifier for twiddle factor table which supports all FFT lengths with same table;
* pBitRevTable
modifier for bit reversal table which supports all FFT lengths with same table.
* onebyfftLen
value of 1/fftLen to calculate CIFFT;
*
* \par Fixed-Point Behavior
* Care must be taken when using the fixed-point versions of the CFFT/CIFFT function.
* Refer to the function specific documentation below for usage guidelines.
*/
/**
* @addtogroup Radix4_CFFT_CIFFT
* @{
*/
/**
* @details
* @brief Processing function for the floating-point Radix-4 CFFT/CIFFT.
* @param[in] *S points to an instance of the floating-point Radix-4 CFFT/CIFFT structure.
* @param[in, out] *pSrc points to the complex data buffer of size 2*fftLen
. Processing occurs in-place.
* @return none.
*/
void arm_cfft_radix4_f32(
const arm_cfft_radix4_instance_f32 * S,
float32_t * pSrc)
{
if(S->ifftFlag == 1u)
{
/* Complex IFFT radix-4 */
arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
S->twidCoefModifier, S->onebyfftLen);
}
else
{
/* Complex FFT radix-4 */
arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
S->twidCoefModifier);
}
if(S->bitReverseFlag == 1u)
{
/* Bit Reversal */
arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
}
}
/**
* @} end of Radix4_CFFT_CIFFT group
*/
/* ----------------------------------------------------------------------
** Internal helper function used by the FFTs
** ------------------------------------------------------------------- */
/*
* @brief Core function for the floating-point CFFT butterfly process.
* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
* @param[in] fftLen length of the FFT.
* @param[in] *pCoef points to the 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_f32(
float32_t * pSrc,
uint16_t fftLen,
float32_t * pCoef,
uint16_t twidCoefModifier)
{
float32_t co1, co2, co3, si1, si2, si3;
uint32_t ia1, ia2, ia3;
uint32_t i0, i1, i2, i3;
uint32_t n1, n2, j, k;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
Ybminusd;
float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
float32_t *ptr1;
/* 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/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
xaIn = pSrc[(2u * i0)];
yaIn = pSrc[(2u * i0) + 1u];
xcIn = pSrc[(2u * i2)];
ycIn = pSrc[(2u * i2) + 1u];
xbIn = pSrc[(2u * i1)];
ybIn = pSrc[(2u * i1) + 1u];
xdIn = pSrc[(2u * i3)];
ydIn = pSrc[(2u * i3) + 1u];
/* xa + xc */
Xaplusc = xaIn + xcIn;
/* xb + xd */
Xbplusd = xbIn + xdIn;
/* ya + yc */
Yaplusc = yaIn + ycIn;
/* yb + yd */
Ybplusd = ybIn + ydIn;
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
/* xa - xc */
Xaminusc = xaIn - xcIn;
/* xb - xd */
Xbminusd = xbIn - xdIn;
/* ya - yc */
Yaminusc = yaIn - ycIn;
/* yb + yd */
Ybminusd = ybIn - ydIn;
/* xa' = xa + xb + xc + xd */
pSrc[(2u * i0)] = Xaplusc + Xbplusd;
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
/* (xa - xc) + (yb - yd) */
Xb12C_out = (Xaminusc + Ybminusd);
/* (ya - yc) + (xb - xd) */
Yb12C_out = (Yaminusc - Xbminusd);
/* (xa + xc) - (xb + xd) */
Xc12C_out = (Xaplusc - Xbplusd);
/* (ya + yc) - (yb + yd) */
Yc12C_out = (Yaplusc - Ybplusd);
/* (xa - xc) - (yb - yd) */
Xd12C_out = (Xaminusc - Ybminusd);
/* (ya - yc) + (xb - xd) */
Yd12C_out = (Xbminusd + Yaminusc);
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
/* index calculation for the coefficients */
ia3 = ia2 + ia1;
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
Xb12_out = Xb12C_out * co1;
Yb12_out = Yb12C_out * co1;
Xc12_out = Xc12C_out * co2;
Yc12_out = Yc12C_out * co2;
Xd12_out = Xd12C_out * co3;
Yd12_out = Yd12C_out * co3;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
Xb12_out += Yb12C_out * si1;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
Yb12_out -= Xb12C_out * si1;
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
Xc12_out += Yc12C_out * si2;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
Yc12_out -= Xc12C_out * si2;
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
Xd12_out += Yd12C_out * si3;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
Yd12_out -= Xd12C_out * si3;
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = Xc12_out;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = Yc12_out;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = Xb12_out;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = Yb12_out;
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = Xd12_out;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = Yd12_out;
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
}
while(--j);
twidCoefModifier <<= 2u;
/* Calculation of second stage to excluding last stage */
for (k = fftLen / 4; 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/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
xaIn = pSrc[(2u * i0)];
yaIn = pSrc[(2u * i0) + 1u];
xbIn = pSrc[(2u * i1)];
ybIn = pSrc[(2u * i1) + 1u];
xcIn = pSrc[(2u * i2)];
ycIn = pSrc[(2u * i2) + 1u];
xdIn = pSrc[(2u * i3)];
ydIn = pSrc[(2u * i3) + 1u];
/* xa - xc */
Xaminusc = xaIn - xcIn;
/* (xb - xd) */
Xbminusd = xbIn - xdIn;
/* ya - yc */
Yaminusc = yaIn - ycIn;
/* (yb - yd) */
Ybminusd = ybIn - ydIn;
/* xa + xc */
Xaplusc = xaIn + xcIn;
/* xb + xd */
Xbplusd = xbIn + xdIn;
/* ya + yc */
Yaplusc = yaIn + ycIn;
/* yb + yd */
Ybplusd = ybIn + ydIn;
/* (xa - xc) + (yb - yd) */
Xb12C_out = (Xaminusc + Ybminusd);
/* (ya - yc) - (xb - xd) */
Yb12C_out = (Yaminusc - Xbminusd);
/* xa + xc -(xb + xd) */
Xc12C_out = (Xaplusc - Xbplusd);
/* (ya + yc) - (yb + yd) */
Yc12C_out = (Yaplusc - Ybplusd);
/* (xa - xc) - (yb - yd) */
Xd12C_out = (Xaminusc - Ybminusd);
/* (ya - yc) + (xb - xd) */
Yd12C_out = (Xbminusd + Yaminusc);
pSrc[(2u * i0)] = Xaplusc + Xbplusd;
pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
Xb12_out = Xb12C_out * co1;
Yb12_out = Yb12C_out * co1;
Xc12_out = Xc12C_out * co2;
Yc12_out = Yc12C_out * co2;
Xd12_out = Xd12C_out * co3;
Yd12_out = Yd12C_out * co3;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
Xb12_out += Yb12C_out * si1;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
Yb12_out -= Xb12C_out * si1;
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
Xc12_out += Yc12C_out * si2;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
Yc12_out -= Xc12C_out * si2;
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
Xd12_out += Yd12C_out * si3;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
Yd12_out -= Xd12C_out * si3;
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = Xc12_out;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = Yc12_out;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = Xb12_out;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = Yb12_out;
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = Xd12_out;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = Yd12_out;
}
}
twidCoefModifier <<= 2u;
}
j = fftLen >> 2;
ptr1 = &pSrc[0];
/* Calculations of last stage */
do
{
xaIn = ptr1[0];
xcIn = ptr1[4];
yaIn = ptr1[1];
ycIn = ptr1[5];
/* xa + xc */
Xaplusc = xaIn + xcIn;
xbIn = ptr1[2];
/* xa - xc */
Xaminusc = xaIn - xcIn;
xdIn = ptr1[6];
/* ya + yc */
Yaplusc = yaIn + ycIn;
ybIn = ptr1[3];
/* ya - yc */
Yaminusc = yaIn - ycIn;
ydIn = ptr1[7];
/* xb + xd */
Xbplusd = xbIn + xdIn;
/* yb + yd */
Ybplusd = ybIn + ydIn;
/* xa' = xa + xb + xc + xd */
ptr1[0] = (Xaplusc + Xbplusd);
/* (xb-xd) */
Xbminusd = xbIn - xdIn;
/* ya' = ya + yb + yc + yd */
ptr1[1] = (Yaplusc + Ybplusd);
/* (yb-yd) */
Ybminusd = ybIn - ydIn;
/* xc' = (xa-xb+xc-xd) */
ptr1[2] = (Xaplusc - Xbplusd);
/* yc' = (ya-yb+yc-yd) */
ptr1[3] = (Yaplusc - Ybplusd);
/* xb' = (xa+yb-xc-yd) */
ptr1[4] = (Xaminusc + Ybminusd);
/* yb' = (ya-xb-yc+xd) */
ptr1[5] = (Yaminusc - Xbminusd);
/* xd' = (xa-yb-xc+yd)) */
ptr1[6] = (Xaminusc - Ybminusd);
/* yd' = (ya+xb-yc-xd) */
ptr1[7] = (Xbminusd + Yaminusc);
/* increment pointer by 8 */
ptr1 = ptr1 + 8u;
} while(--j);
#else
float32_t t1, t2, r1, r2, s1, s2;
/* Run the below code for Cortex-M0 */
/* Initializations for the fft calculation */
n2 = fftLen;
n1 = n2;
for (k = fftLen; k > 1u; k >>= 2u)
{
/* Initializations for the fft calculation */
n1 = n2;
n2 >>= 2u;
ia1 = 0u;
/* FFT Calculation */
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/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* 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;
/* 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;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb - xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
/* (xa - xc) + (yb - yd) */
r1 = r2 + t1;
/* (xa - xc) - (yb - yd) */
r2 = r2 - t1;
/* (ya - yc) - (xb - xd) */
s1 = s2 - t2;
/* (ya - yc) + (xb - xd) */
s2 = s2 + t2;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
}
}
twidCoefModifier <<= 2u;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/*
* @brief Core function for the floating-point CIFFT butterfly process.
* @param[in, out] *pSrc points to the in-place buffer of floating-point 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.
* @param[in] onebyfftLen value of 1/fftLen.
* @return none.
*/
void arm_radix4_butterfly_inverse_f32(
float32_t * pSrc,
uint16_t fftLen,
float32_t * pCoef,
uint16_t twidCoefModifier,
float32_t onebyfftLen)
{
float32_t co1, co2, co3, si1, si2, si3;
uint32_t ia1, ia2, ia3;
uint32_t i0, i1, i2, i3;
uint32_t n1, n2, j, k;
#ifndef ARM_MATH_CM0
float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
Ybminusd;
float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
float32_t *ptr1;
/* 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/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
xaIn = pSrc[(2u * i0)];
yaIn = pSrc[(2u * i0) + 1u];
xcIn = pSrc[(2u * i2)];
ycIn = pSrc[(2u * i2) + 1u];
xbIn = pSrc[(2u * i1)];
ybIn = pSrc[(2u * i1) + 1u];
xdIn = pSrc[(2u * i3)];
ydIn = pSrc[(2u * i3) + 1u];
/* xa + xc */
Xaplusc = xaIn + xcIn;
/* xb + xd */
Xbplusd = xbIn + xdIn;
/* ya + yc */
Yaplusc = yaIn + ycIn;
/* yb + yd */
Ybplusd = ybIn + ydIn;
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
/* xa - xc */
Xaminusc = xaIn - xcIn;
/* xb - xd */
Xbminusd = xbIn - xdIn;
/* ya - yc */
Yaminusc = yaIn - ycIn;
/* yb - yd */
Ybminusd = ybIn - ydIn;
/* xa' = xa + xb + xc + xd */
pSrc[(2u * i0)] = Xaplusc + Xbplusd;
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
/* (xa - xc) - (yb - yd) */
Xb12C_out = (Xaminusc - Ybminusd);
/* (ya - yc) + (xb - xd) */
Yb12C_out = (Yaminusc + Xbminusd);
/* (xa + xc) - (xb + xd) */
Xc12C_out = (Xaplusc - Xbplusd);
/* (ya + yc) - (yb + yd) */
Yc12C_out = (Yaplusc - Ybplusd);
/* (xa - xc) + (yb - yd) */
Xd12C_out = (Xaminusc + Ybminusd);
/* (ya - yc) - (xb - xd) */
Yd12C_out = (Yaminusc - Xbminusd);
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
/* index calculation for the coefficients */
ia3 = ia2 + ia1;
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
Xb12_out = Xb12C_out * co1;
Yb12_out = Yb12C_out * co1;
Xc12_out = Xc12C_out * co2;
Yc12_out = Yc12C_out * co2;
Xd12_out = Xd12C_out * co3;
Yd12_out = Yd12C_out * co3;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
Xb12_out -= Yb12C_out * si1;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
Yb12_out += Xb12C_out * si1;
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
Xc12_out -= Yc12C_out * si2;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
Yc12_out += Xc12C_out * si2;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
Xd12_out -= Yd12C_out * si3;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
Yd12_out += Xd12C_out * si3;
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = Xc12_out;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = Yc12_out;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = Xb12_out;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = Yb12_out;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = Xd12_out;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = Yd12_out;
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
} while(--j);
twidCoefModifier <<= 2u;
/* Calculation of second stage to excluding last stage */
for (k = fftLen / 4; 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/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
xaIn = pSrc[(2u * i0)];
yaIn = pSrc[(2u * i0) + 1u];
xbIn = pSrc[(2u * i1)];
ybIn = pSrc[(2u * i1) + 1u];
xcIn = pSrc[(2u * i2)];
ycIn = pSrc[(2u * i2) + 1u];
xdIn = pSrc[(2u * i3)];
ydIn = pSrc[(2u * i3) + 1u];
/* xa - xc */
Xaminusc = xaIn - xcIn;
/* (xb - xd) */
Xbminusd = xbIn - xdIn;
/* ya - yc */
Yaminusc = yaIn - ycIn;
/* (yb - yd) */
Ybminusd = ybIn - ydIn;
/* xa + xc */
Xaplusc = xaIn + xcIn;
/* xb + xd */
Xbplusd = xbIn + xdIn;
/* ya + yc */
Yaplusc = yaIn + ycIn;
/* yb + yd */
Ybplusd = ybIn + ydIn;
/* (xa - xc) - (yb - yd) */
Xb12C_out = (Xaminusc - Ybminusd);
/* (ya - yc) + (xb - xd) */
Yb12C_out = (Yaminusc + Xbminusd);
/* xa + xc -(xb + xd) */
Xc12C_out = (Xaplusc - Xbplusd);
/* (ya + yc) - (yb + yd) */
Yc12C_out = (Yaplusc - Ybplusd);
/* (xa - xc) + (yb - yd) */
Xd12C_out = (Xaminusc + Ybminusd);
/* (ya - yc) - (xb - xd) */
Yd12C_out = (Yaminusc - Xbminusd);
pSrc[(2u * i0)] = Xaplusc + Xbplusd;
pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;
Xb12_out = Xb12C_out * co1;
Yb12_out = Yb12C_out * co1;
Xc12_out = Xc12C_out * co2;
Yc12_out = Yc12C_out * co2;
Xd12_out = Xd12C_out * co3;
Yd12_out = Yd12C_out * co3;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
Xb12_out -= Yb12C_out * si1;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
Yb12_out += Xb12C_out * si1;
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
Xc12_out -= Yc12C_out * si2;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
Yc12_out += Xc12C_out * si2;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
Xd12_out -= Yd12C_out * si3;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
Yd12_out += Xd12C_out * si3;
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = Xc12_out;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = Yc12_out;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = Xb12_out;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = Yb12_out;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = Xd12_out;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = Yd12_out;
}
}
twidCoefModifier <<= 2u;
}
/* Initializations of last stage */
j = fftLen >> 2;
ptr1 = &pSrc[0];
/* Calculations of last stage */
do
{
xaIn = ptr1[0];
xcIn = ptr1[4];
yaIn = ptr1[1];
ycIn = ptr1[5];
/* Butterfly implementation */
/* xa + xc */
Xaplusc = xaIn + xcIn;
xbIn = ptr1[2];
/* xa - xc */
Xaminusc = xaIn - xcIn;
xdIn = ptr1[6];
/* ya + yc */
Yaplusc = yaIn + ycIn;
ybIn = ptr1[3];
/* ya - yc */
Yaminusc = yaIn - ycIn;
ydIn = ptr1[7];
/* xc + xd */
Xbplusd = xbIn + xdIn;
/* yb + yd */
Ybplusd = ybIn + ydIn;
/* xa' = xa + xb + xc + xd */
ptr1[0] = (Xaplusc + Xbplusd) * onebyfftLen;
/* (xb-xd) */
Xbminusd = xbIn - xdIn;
/* ya' = ya + yb + yc + yd */
ptr1[1] = (Yaplusc + Ybplusd) * onebyfftLen;
/* (yb-yd) */
Ybminusd = ybIn - ydIn;
/* xc' = (xa-xb+xc-xd) * onebyfftLen */
ptr1[2] = (Xaplusc - Xbplusd) * onebyfftLen;
/* yc' = (ya-yb+yc-yd) * onebyfftLen */
ptr1[3] = (Yaplusc - Ybplusd) * onebyfftLen;
/* xb' = (xa-yb-xc+yd) * onebyfftLen */
ptr1[4] = (Xaminusc - Ybminusd) * onebyfftLen;
/* yb' = (ya+xb-yc-xd) * onebyfftLen */
ptr1[5] = (Yaminusc + Xbminusd) * onebyfftLen;
/* xd' = (xa-yb-xc+yd) * onebyfftLen */
ptr1[6] = (Xaminusc + Ybminusd) * onebyfftLen;
/* yd' = (ya-xb-yc+xd) * onebyfftLen */
ptr1[7] = (Yaminusc - Xbminusd) * onebyfftLen;
/* increment source pointer by 8 for next calculations */
ptr1 = ptr1 + 8u;
} while(--j);
#else
float32_t t1, t2, r1, r2, s1, s2;
/* Run the below code for Cortex-M0 */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* Calculation of first stage */
for (k = fftLen; 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/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* 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;
/* 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;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb - xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
/* (xa - xc) - (yb - yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb - yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb - xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb - xd) */
s2 = s2 - t2;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
}
}
twidCoefModifier <<= 2u;
}
/* Initializations of last stage */
n1 = n2;
n2 >>= 2u;
/* Calculations of last stage */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xc */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xc + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1) * onebyfftLen;
/* (xa + xb) - (xc + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb-yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb-xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = r1 * onebyfftLen;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;
/* (xa - xc) - (yb-yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb-yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb-xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb-xd) */
s2 = s2 - t2;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = r1 * onebyfftLen;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = r2 * onebyfftLen;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
}
#endif /* #ifndef ARM_MATH_CM0 */
}