Google Git
Sign in
android / platform / external / arduino-ide / f876b2abdebd02acfa4ba21e607327be4f9668d4 / . / hardware / arduino / sam / system / CMSIS / CMSIS / DSP_Lib / Source / TransformFunctions / arm_cfft_radix4_f32.c
blob: 7dfe4c349d7f23c76a1bf137778508908665a8ec [file] [log] [blame]
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* 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 1.0.10 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 CFFT_CIFFT 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
* <code>2*fftLen</code> samples through the transform. <code>pSrc</code> points to In-place arrays containing <code>2*fftLen</code> values.
* \par
* The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below.
* <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
*
* \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:
*
* <b>Complex Fast Fourier Transform:</b>
* \par
* Input real and imaginary data:
* <pre>
* 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
* </pre>
* where N is length of FFT
* \par
* Output real and imaginary data:
* <pre>
* X(4r) = xa'+ j * ya'
* X(4r+1) = xb'+ j * yb'
* X(4r+2) = xc'+ j * yc'
* X(4r+3) = xd'+ j * yd'
* </pre>
* \par
* Twiddle factors for radix-4 FFT:
* <pre>
* Wn = co1 + j * (- si1)
* W2n = co2 + j * (- si2)
* W3n = co3 + j * (- si3)
* </pre>
*
* \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
* <b> Butterfly CFFT equations:</b>
* <pre>
* 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)
* </pre>
*
*
* <b>Complex Inverse Fast Fourier Transform:</b>
* \par
* CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.
*
* \par
* <b> Modified Butterfly CIFFT equations:</b>
* <pre>
* 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)
* </pre>
*
* \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:
* <pre>
*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};
* </pre>
* \par
* where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);
* <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);
* <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table.
* <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;
* <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.
* <code>onebyfftLen</code> 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 CFFT_CIFFT
* @{
*/
/**
* @details
* @brief Processing function for the floating-point CFFT/CIFFT.
* @param[in] *S points to an instance of the floating-point 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.
*/
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 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;
float32_t t1, t2, r1, r2, s1, s2;
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 */
/* 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 */
/* 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];
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
/* 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;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
/* 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);
/* index calculation for the coefficients */
ia3 = ia2 + ia1;
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* 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);
/* 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;
/* 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 + xb */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xb */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xc + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = r1 + t1;
/* (xa + xb) - (xc + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = s1 + t2;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb-yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb-xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = r1;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = s1;
/* (xa+yb-xc-yd) */
r1 = r2 + t1;
/* (xa-yb-xc+yd) */
r2 = r2 - t1;
/* (ya-xb-yc+xd) */
s1 = s2 - t2;
/* (ya+xb-yc-xd) */
s2 = s2 + t2;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = r1;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = s1;
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = r2;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = s2;
}
#else
/* 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;
float32_t t1, t2, r1, r2, s1, s2;
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 */
/* 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 */
/* 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];
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
/* 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;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
/* 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);
/* index calculation for the coefficients */
ia3 = ia2 + ia1;
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* 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);
/* 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;
/* 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;
}
#else
/* 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 */
}
/*
* @brief In-place bit reversal function.
* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
* @param[in] fftSize length of the FFT.
* @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table.
* @param[in] *pBitRevTab points to the bit reversal table.
* @return none.
*/
void arm_bitreversal_f32(
float32_t * pSrc,
uint16_t fftSize,
uint16_t bitRevFactor,
uint16_t * pBitRevTab)
{
uint16_t fftLenBy2, fftLenBy2p1;
uint16_t i, j;
float32_t in;
/* Initializations */
j = 0u;
fftLenBy2 = fftSize >> 1u;
fftLenBy2p1 = (fftSize >> 1u) + 1u;
/* Bit Reversal Implementation */
for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
{
if(i < j)
{
/* pSrc[i] <-> pSrc[j]; */
in = pSrc[2u * i];
pSrc[2u * i] = pSrc[2u * j];
pSrc[2u * j] = in;
/* pSrc[i+1u] <-> pSrc[j+1u] */
in = pSrc[(2u * i) + 1u];
pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u];
pSrc[(2u * j) + 1u] = in;
/* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */
in = pSrc[2u * (i + fftLenBy2p1)];
pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)];
pSrc[2u * (j + fftLenBy2p1)] = in;
/* pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */
in = pSrc[(2u * (i + fftLenBy2p1)) + 1u];
pSrc[(2u * (i + fftLenBy2p1)) + 1u] =
pSrc[(2u * (j + fftLenBy2p1)) + 1u];
pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in;
}
/* pSrc[i+1u] <-> pSrc[j+1u] */
in = pSrc[2u * (i + 1u)];
pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)];
pSrc[2u * (j + fftLenBy2)] = in;
/* pSrc[i+2u] <-> pSrc[j+2u] */
in = pSrc[(2u * (i + 1u)) + 1u];
pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u];
pSrc[(2u * (j + fftLenBy2)) + 1u] = in;
/* Reading the index for the bit reversal */
j = *pBitRevTab;
/* Updating the bit reversal index depending on the fft length */
pBitRevTab += bitRevFactor;
}
}