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/* ----------------------------------------------------------------------
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date: 31. July 2014
* $Revision: V1.4.4
*
* Project: CMSIS DSP Library
* Title: arm_cfft_radix8_f32.c
*
* Description: Radix-8 Decimation in Frequency CFFT & CIFFT Floating point processing function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* - Neither the name of ARM LIMITED nor the names of its contributors
* may be used to endorse or promote products derived from this
* software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @defgroup Radix8_CFFT_CIFFT Radix-8 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 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-8 decimation in frequency(DIF) algorithm
* and the size of the FFT supported are of the lengths [ 64, 512, 4096].
*
*
* \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-8 FFT:
* <pre>
* Wn = co1 + j * (- si1)
* W2n = co2 + j * (- si2)
* W3n = co3 + j * (- si3)
* </pre>
*
* \par
* \image html CFFT.gif "Radix-8 Decimation-in Frequency Complex Fast Fourier Transform"
*
* \par
* Output from Radix-8 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>
*
* \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.
*/
/*
* @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_radix8_butterfly_f32(
float32_t * pSrc,
uint16_t fftLen,
const float32_t * pCoef,
uint16_t twidCoefModifier)
{
uint32_t ia1, ia2, ia3, ia4, ia5, ia6, ia7;
uint32_t i1, i2, i3, i4, i5, i6, i7, i8;
uint32_t id;
uint32_t n1, n2, j;
float32_t r1, r2, r3, r4, r5, r6, r7, r8;
float32_t t1, t2;
float32_t s1, s2, s3, s4, s5, s6, s7, s8;
float32_t p1, p2, p3, p4;
float32_t co2, co3, co4, co5, co6, co7, co8;
float32_t si2, si3, si4, si5, si6, si7, si8;
const float32_t C81 = 0.70710678118f;
n2 = fftLen;
do
{
n1 = n2;
n2 = n2 >> 3;
i1 = 0;
do
{
i2 = i1 + n2;
i3 = i2 + n2;
i4 = i3 + n2;
i5 = i4 + n2;
i6 = i5 + n2;
i7 = i6 + n2;
i8 = i7 + n2;
r1 = pSrc[2 * i1] + pSrc[2 * i5];
r5 = pSrc[2 * i1] - pSrc[2 * i5];
r2 = pSrc[2 * i2] + pSrc[2 * i6];
r6 = pSrc[2 * i2] - pSrc[2 * i6];
r3 = pSrc[2 * i3] + pSrc[2 * i7];
r7 = pSrc[2 * i3] - pSrc[2 * i7];
r4 = pSrc[2 * i4] + pSrc[2 * i8];
r8 = pSrc[2 * i4] - pSrc[2 * i8];
t1 = r1 - r3;
r1 = r1 + r3;
r3 = r2 - r4;
r2 = r2 + r4;
pSrc[2 * i1] = r1 + r2;
pSrc[2 * i5] = r1 - r2;
r1 = pSrc[2 * i1 + 1] + pSrc[2 * i5 + 1];
s5 = pSrc[2 * i1 + 1] - pSrc[2 * i5 + 1];
r2 = pSrc[2 * i2 + 1] + pSrc[2 * i6 + 1];
s6 = pSrc[2 * i2 + 1] - pSrc[2 * i6 + 1];
s3 = pSrc[2 * i3 + 1] + pSrc[2 * i7 + 1];
s7 = pSrc[2 * i3 + 1] - pSrc[2 * i7 + 1];
r4 = pSrc[2 * i4 + 1] + pSrc[2 * i8 + 1];
s8 = pSrc[2 * i4 + 1] - pSrc[2 * i8 + 1];
t2 = r1 - s3;
r1 = r1 + s3;
s3 = r2 - r4;
r2 = r2 + r4;
pSrc[2 * i1 + 1] = r1 + r2;
pSrc[2 * i5 + 1] = r1 - r2;
pSrc[2 * i3] = t1 + s3;
pSrc[2 * i7] = t1 - s3;
pSrc[2 * i3 + 1] = t2 - r3;
pSrc[2 * i7 + 1] = t2 + r3;
r1 = (r6 - r8) * C81;
r6 = (r6 + r8) * C81;
r2 = (s6 - s8) * C81;
s6 = (s6 + s8) * C81;
t1 = r5 - r1;
r5 = r5 + r1;
r8 = r7 - r6;
r7 = r7 + r6;
t2 = s5 - r2;
s5 = s5 + r2;
s8 = s7 - s6;
s7 = s7 + s6;
pSrc[2 * i2] = r5 + s7;
pSrc[2 * i8] = r5 - s7;
pSrc[2 * i6] = t1 + s8;
pSrc[2 * i4] = t1 - s8;
pSrc[2 * i2 + 1] = s5 - r7;
pSrc[2 * i8 + 1] = s5 + r7;
pSrc[2 * i6 + 1] = t2 - r8;
pSrc[2 * i4 + 1] = t2 + r8;
i1 += n1;
} while(i1 < fftLen);
if(n2 < 8)
break;
ia1 = 0;
j = 1;
do
{
/* index calculation for the coefficients */
id = ia1 + twidCoefModifier;
ia1 = id;
ia2 = ia1 + id;
ia3 = ia2 + id;
ia4 = ia3 + id;
ia5 = ia4 + id;
ia6 = ia5 + id;
ia7 = ia6 + id;
co2 = pCoef[2 * ia1];
co3 = pCoef[2 * ia2];
co4 = pCoef[2 * ia3];
co5 = pCoef[2 * ia4];
co6 = pCoef[2 * ia5];
co7 = pCoef[2 * ia6];
co8 = pCoef[2 * ia7];
si2 = pCoef[2 * ia1 + 1];
si3 = pCoef[2 * ia2 + 1];
si4 = pCoef[2 * ia3 + 1];
si5 = pCoef[2 * ia4 + 1];
si6 = pCoef[2 * ia5 + 1];
si7 = pCoef[2 * ia6 + 1];
si8 = pCoef[2 * ia7 + 1];
i1 = j;
do
{
/* index calculation for the input */
i2 = i1 + n2;
i3 = i2 + n2;
i4 = i3 + n2;
i5 = i4 + n2;
i6 = i5 + n2;
i7 = i6 + n2;
i8 = i7 + n2;
r1 = pSrc[2 * i1] + pSrc[2 * i5];
r5 = pSrc[2 * i1] - pSrc[2 * i5];
r2 = pSrc[2 * i2] + pSrc[2 * i6];
r6 = pSrc[2 * i2] - pSrc[2 * i6];
r3 = pSrc[2 * i3] + pSrc[2 * i7];
r7 = pSrc[2 * i3] - pSrc[2 * i7];
r4 = pSrc[2 * i4] + pSrc[2 * i8];
r8 = pSrc[2 * i4] - pSrc[2 * i8];
t1 = r1 - r3;
r1 = r1 + r3;
r3 = r2 - r4;
r2 = r2 + r4;
pSrc[2 * i1] = r1 + r2;
r2 = r1 - r2;
s1 = pSrc[2 * i1 + 1] + pSrc[2 * i5 + 1];
s5 = pSrc[2 * i1 + 1] - pSrc[2 * i5 + 1];
s2 = pSrc[2 * i2 + 1] + pSrc[2 * i6 + 1];
s6 = pSrc[2 * i2 + 1] - pSrc[2 * i6 + 1];
s3 = pSrc[2 * i3 + 1] + pSrc[2 * i7 + 1];
s7 = pSrc[2 * i3 + 1] - pSrc[2 * i7 + 1];
s4 = pSrc[2 * i4 + 1] + pSrc[2 * i8 + 1];
s8 = pSrc[2 * i4 + 1] - pSrc[2 * i8 + 1];
t2 = s1 - s3;
s1 = s1 + s3;
s3 = s2 - s4;
s2 = s2 + s4;
r1 = t1 + s3;
t1 = t1 - s3;
pSrc[2 * i1 + 1] = s1 + s2;
s2 = s1 - s2;
s1 = t2 - r3;
t2 = t2 + r3;
p1 = co5 * r2;
p2 = si5 * s2;
p3 = co5 * s2;
p4 = si5 * r2;
pSrc[2 * i5] = p1 + p2;
pSrc[2 * i5 + 1] = p3 - p4;
p1 = co3 * r1;
p2 = si3 * s1;
p3 = co3 * s1;
p4 = si3 * r1;
pSrc[2 * i3] = p1 + p2;
pSrc[2 * i3 + 1] = p3 - p4;
p1 = co7 * t1;
p2 = si7 * t2;
p3 = co7 * t2;
p4 = si7 * t1;
pSrc[2 * i7] = p1 + p2;
pSrc[2 * i7 + 1] = p3 - p4;
r1 = (r6 - r8) * C81;
r6 = (r6 + r8) * C81;
s1 = (s6 - s8) * C81;
s6 = (s6 + s8) * C81;
t1 = r5 - r1;
r5 = r5 + r1;
r8 = r7 - r6;
r7 = r7 + r6;
t2 = s5 - s1;
s5 = s5 + s1;
s8 = s7 - s6;
s7 = s7 + s6;
r1 = r5 + s7;
r5 = r5 - s7;
r6 = t1 + s8;
t1 = t1 - s8;
s1 = s5 - r7;
s5 = s5 + r7;
s6 = t2 - r8;
t2 = t2 + r8;
p1 = co2 * r1;
p2 = si2 * s1;
p3 = co2 * s1;
p4 = si2 * r1;
pSrc[2 * i2] = p1 + p2;
pSrc[2 * i2 + 1] = p3 - p4;
p1 = co8 * r5;
p2 = si8 * s5;
p3 = co8 * s5;
p4 = si8 * r5;
pSrc[2 * i8] = p1 + p2;
pSrc[2 * i8 + 1] = p3 - p4;
p1 = co6 * r6;
p2 = si6 * s6;
p3 = co6 * s6;
p4 = si6 * r6;
pSrc[2 * i6] = p1 + p2;
pSrc[2 * i6 + 1] = p3 - p4;
p1 = co4 * t1;
p2 = si4 * t2;
p3 = co4 * t2;
p4 = si4 * t1;
pSrc[2 * i4] = p1 + p2;
pSrc[2 * i4 + 1] = p3 - p4;
i1 += n1;
} while(i1 < fftLen);
j++;
} while(j < n2);
twidCoefModifier <<= 3;
} while(n2 > 7);
}
/**
* @} end of Radix8_CFFT_CIFFT group
*/
|
