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/****************************************************************************
*
* NAME: smbPitchShift.cpp
* VERSION: 1.2
* HOME URL: http://blogs.zynaptiq.com/bernsee
* KNOWN BUGS: none
*
* SYNOPSIS: Routine for doing pitch shifting while maintaining
* duration using the Short Time Fourier Transform.
*
* DESCRIPTION: The routine takes a pitchShift factor value which is between 0.5
* (one octave down) and 2. (one octave up). A value of exactly 1 does not change
* the pitch. numSampsToProcess tells the routine how many samples in indata[0...
* numSampsToProcess-1] should be pitch shifted and moved to outdata[0 ...
* numSampsToProcess-1]. The two buffers can be identical (ie. it can process the
* data in-place). fftFrameSize defines the FFT frame size used for the
* processing. Typical values are 1024, 2048 and 4096. It may be any value <=
* MAX_FRAME_LENGTH but it MUST be a power of 2. osamp is the STFT
* oversampling factor which also determines the overlap between adjacent STFT
* frames. It should at least be 4 for moderate scaling ratios. A value of 32 is
* recommended for best quality. sampleRate takes the sample rate for the signal
* in unit Hz, ie. 44100 for 44.1 kHz audio. The data passed to the routine in
* indata[] should be in the range [-1.0, 1.0), which is also the output range
* for the data, make sure you scale the data accordingly (for 16bit signed integers
* you would have to divide (and multiply) by 32768).
*
* COPYRIGHT 1999-2015 Stephan M. Bernsee <s.bernsee [AT] zynaptiq [DOT] com>
*
* The Wide Open License (WOL)
*
* Permission to use, copy, modify, distribute and sell this software and its
* documentation for any purpose is hereby granted without fee, provided that
* the above copyright notice and this license appear in all source copies.
* THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF
* ANY KIND. See http://www.dspguru.com/wol.htm for more information.
*
*****************************************************************************/
#if defined(SMBPITCHSHIFT_BUILD_DLL)
#define SMTPITCHSHIFT_API __declspec(dllexport)
#elif defined(SMPPITCHSHIFT_USE_DLL)
#define SMTPITCHSHIFT_API __declspec(dllimport)
#else
#define SMTPITCHSHIFT_API
#endif
SMTPITCHSHIFT_API void smbPitchShift(float pitchShift, long numSampsToProcess, long fftFrameSize, long osamp, float sampleRate, float *indata, float *outdata);
#define MAX_FRAME_LENGTH 8192
#include <string.h>
#include <math.h>
#include <stdio.h>
//#define M_PI 3.14159265358979323846f
//#define M_1_PI 0.318309886183790671538f
void smbFft(float *fftBuffer, long fftFrameSize, long sign);
float smbAtan2(float x, float y);
// -----------------------------------------------------------------------------------------------------------------
#define FAST_MATH_TABLE_SIZE 512
const float sinTable_f32[FAST_MATH_TABLE_SIZE + 1] = {
0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f,
0.07356456f, 0.08579731f, 0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f,
0.14673047f, 0.15885814f, 0.17096189f, 0.18303989f, 0.19509032f, 0.20711138f,
0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f,
0.29028468f, 0.30200595f, 0.31368174f, 0.32531029f, 0.33688985f, 0.34841868f,
0.35989504f, 0.37131719f, 0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f,
0.42755509f, 0.43861624f, 0.44961133f, 0.46053871f, 0.47139674f, 0.48218377f,
0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f,
0.55557023f, 0.56573181f, 0.57580819f, 0.58579786f, 0.59569930f, 0.60551104f,
0.61523159f, 0.62485949f, 0.63439328f, 0.64383154f, 0.65317284f, 0.66241578f,
0.67155895f, 0.68060100f, 0.68954054f, 0.69837625f, 0.70710678f, 0.71573083f,
0.72424708f, 0.73265427f, 0.74095113f, 0.74913639f, 0.75720885f, 0.76516727f,
0.77301045f, 0.78073723f, 0.78834643f, 0.79583690f, 0.80320753f, 0.81045720f,
0.81758481f, 0.82458930f, 0.83146961f, 0.83822471f, 0.84485357f, 0.85135519f,
0.85772861f, 0.86397286f, 0.87008699f, 0.87607009f, 0.88192126f, 0.88763962f,
0.89322430f, 0.89867447f, 0.90398929f, 0.90916798f, 0.91420976f, 0.91911385f,
0.92387953f, 0.92850608f, 0.93299280f, 0.93733901f, 0.94154407f, 0.94560733f,
0.94952818f, 0.95330604f, 0.95694034f, 0.96043052f, 0.96377607f, 0.96697647f,
0.97003125f, 0.97293995f, 0.97570213f, 0.97831737f, 0.98078528f, 0.98310549f,
0.98527764f, 0.98730142f, 0.98917651f, 0.99090264f, 0.99247953f, 0.99390697f,
0.99518473f, 0.99631261f, 0.99729046f, 0.99811811f, 0.99879546f, 0.99932238f,
0.99969882f, 0.99992470f, 1.00000000f, 0.99992470f, 0.99969882f, 0.99932238f,
0.99879546f, 0.99811811f, 0.99729046f, 0.99631261f, 0.99518473f, 0.99390697f,
0.99247953f, 0.99090264f, 0.98917651f, 0.98730142f, 0.98527764f, 0.98310549f,
0.98078528f, 0.97831737f, 0.97570213f, 0.97293995f, 0.97003125f, 0.96697647f,
0.96377607f, 0.96043052f, 0.95694034f, 0.95330604f, 0.94952818f, 0.94560733f,
0.94154407f, 0.93733901f, 0.93299280f, 0.92850608f, 0.92387953f, 0.91911385f,
0.91420976f, 0.90916798f, 0.90398929f, 0.89867447f, 0.89322430f, 0.88763962f,
0.88192126f, 0.87607009f, 0.87008699f, 0.86397286f, 0.85772861f, 0.85135519f,
0.84485357f, 0.83822471f, 0.83146961f, 0.82458930f, 0.81758481f, 0.81045720f,
0.80320753f, 0.79583690f, 0.78834643f, 0.78073723f, 0.77301045f, 0.76516727f,
0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f,
0.70710678f, 0.69837625f, 0.68954054f, 0.68060100f, 0.67155895f, 0.66241578f,
0.65317284f, 0.64383154f, 0.63439328f, 0.62485949f, 0.61523159f, 0.60551104f,
0.59569930f, 0.58579786f, 0.57580819f, 0.56573181f, 0.55557023f, 0.54532499f,
0.53499762f, 0.52458968f, 0.51410274f, 0.50353838f, 0.49289819f, 0.48218377f,
0.47139674f, 0.46053871f, 0.44961133f, 0.43861624f, 0.42755509f, 0.41642956f,
0.40524131f, 0.39399204f, 0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f,
0.33688985f, 0.32531029f, 0.31368174f, 0.30200595f, 0.29028468f, 0.27851969f,
0.26671276f, 0.25486566f, 0.24298018f, 0.23105811f, 0.21910124f, 0.20711138f,
0.19509032f, 0.18303989f, 0.17096189f, 0.15885814f, 0.14673047f, 0.13458071f,
0.12241068f, 0.11022221f, 0.09801714f, 0.08579731f, 0.07356456f, 0.06132074f,
0.04906767f, 0.03680722f, 0.02454123f, 0.01227154f, 0.00000000f, -0.01227154f,
-0.02454123f, -0.03680722f, -0.04906767f, -0.06132074f, -0.07356456f,
-0.08579731f, -0.09801714f, -0.11022221f, -0.12241068f, -0.13458071f,
-0.14673047f, -0.15885814f, -0.17096189f, -0.18303989f, -0.19509032f,
-0.20711138f, -0.21910124f, -0.23105811f, -0.24298018f, -0.25486566f,
-0.26671276f, -0.27851969f, -0.29028468f, -0.30200595f, -0.31368174f,
-0.32531029f, -0.33688985f, -0.34841868f, -0.35989504f, -0.37131719f,
-0.38268343f, -0.39399204f, -0.40524131f, -0.41642956f, -0.42755509f,
-0.43861624f, -0.44961133f, -0.46053871f, -0.47139674f, -0.48218377f,
-0.49289819f, -0.50353838f, -0.51410274f, -0.52458968f, -0.53499762f,
-0.54532499f, -0.55557023f, -0.56573181f, -0.57580819f, -0.58579786f,
-0.59569930f, -0.60551104f, -0.61523159f, -0.62485949f, -0.63439328f,
-0.64383154f, -0.65317284f, -0.66241578f, -0.67155895f, -0.68060100f,
-0.68954054f, -0.69837625f, -0.70710678f, -0.71573083f, -0.72424708f,
-0.73265427f, -0.74095113f, -0.74913639f, -0.75720885f, -0.76516727f,
-0.77301045f, -0.78073723f, -0.78834643f, -0.79583690f, -0.80320753f,
-0.81045720f, -0.81758481f, -0.82458930f, -0.83146961f, -0.83822471f,
-0.84485357f, -0.85135519f, -0.85772861f, -0.86397286f, -0.87008699f,
-0.87607009f, -0.88192126f, -0.88763962f, -0.89322430f, -0.89867447f,
-0.90398929f, -0.90916798f, -0.91420976f, -0.91911385f, -0.92387953f,
-0.92850608f, -0.93299280f, -0.93733901f, -0.94154407f, -0.94560733f,
-0.94952818f, -0.95330604f, -0.95694034f, -0.96043052f, -0.96377607f,
-0.96697647f, -0.97003125f, -0.97293995f, -0.97570213f, -0.97831737f,
-0.98078528f, -0.98310549f, -0.98527764f, -0.98730142f, -0.98917651f,
-0.99090264f, -0.99247953f, -0.99390697f, -0.99518473f, -0.99631261f,
-0.99729046f, -0.99811811f, -0.99879546f, -0.99932238f, -0.99969882f,
-0.99992470f, -1.00000000f, -0.99992470f, -0.99969882f, -0.99932238f,
-0.99879546f, -0.99811811f, -0.99729046f, -0.99631261f, -0.99518473f,
-0.99390697f, -0.99247953f, -0.99090264f, -0.98917651f, -0.98730142f,
-0.98527764f, -0.98310549f, -0.98078528f, -0.97831737f, -0.97570213f,
-0.97293995f, -0.97003125f, -0.96697647f, -0.96377607f, -0.96043052f,
-0.95694034f, -0.95330604f, -0.94952818f, -0.94560733f, -0.94154407f,
-0.93733901f, -0.93299280f, -0.92850608f, -0.92387953f, -0.91911385f,
-0.91420976f, -0.90916798f, -0.90398929f, -0.89867447f, -0.89322430f,
-0.88763962f, -0.88192126f, -0.87607009f, -0.87008699f, -0.86397286f,
-0.85772861f, -0.85135519f, -0.84485357f, -0.83822471f, -0.83146961f,
-0.82458930f, -0.81758481f, -0.81045720f, -0.80320753f, -0.79583690f,
-0.78834643f, -0.78073723f, -0.77301045f, -0.76516727f, -0.75720885f,
-0.74913639f, -0.74095113f, -0.73265427f, -0.72424708f, -0.71573083f,
-0.70710678f, -0.69837625f, -0.68954054f, -0.68060100f, -0.67155895f,
-0.66241578f, -0.65317284f, -0.64383154f, -0.63439328f, -0.62485949f,
-0.61523159f, -0.60551104f, -0.59569930f, -0.58579786f, -0.57580819f,
-0.56573181f, -0.55557023f, -0.54532499f, -0.53499762f, -0.52458968f,
-0.51410274f, -0.50353838f, -0.49289819f, -0.48218377f, -0.47139674f,
-0.46053871f, -0.44961133f, -0.43861624f, -0.42755509f, -0.41642956f,
-0.40524131f, -0.39399204f, -0.38268343f, -0.37131719f, -0.35989504f,
-0.34841868f, -0.33688985f, -0.32531029f, -0.31368174f, -0.30200595f,
-0.29028468f, -0.27851969f, -0.26671276f, -0.25486566f, -0.24298018f,
-0.23105811f, -0.21910124f, -0.20711138f, -0.19509032f, -0.18303989f,
-0.17096189f, -0.15885814f, -0.14673047f, -0.13458071f, -0.12241068f,
-0.11022221f, -0.09801714f, -0.08579731f, -0.07356456f, -0.06132074f,
-0.04906767f, -0.03680722f, -0.02454123f, -0.01227154f, -0.00000000f
};
inline float fastsin(
float x)
{
float sinVal, fract, in; /* Temporary variables for input, output */
unsigned short index; /* Index variable */
float a, b; /* Two nearest output values */
int n;
float findex;
/* input x is in radians */
/* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
in = x * 0.159154943092f;
/* Calculation of floor value of input */
n = (int)in;
/* Make negative values towards -infinity */
if (x < 0.0f)
{
n--;
}
/* Map input value to [0 1] */
in = in - (float)n;
/* Calculation of index of the table */
findex = (float)FAST_MATH_TABLE_SIZE * in;
if (findex >= 512.0f) {
findex -= 512.0f;
}
index = ((unsigned short)findex) & 0x1ff;
/* fractional value calculation */
fract = findex - (float)index;
/* Read two nearest values of input value from the sin table */
a = sinTable_f32[index];
b = sinTable_f32[index + 1];
/* Linear interpolation process */
sinVal = (1.0f - fract)*a + fract*b;
/* Return the output value */
return (sinVal);
}
inline float fastcos(
float x)
{
float cosVal, fract, in; /* Temporary variables for input, output */
unsigned short index; /* Index variable */
float a, b; /* Two nearest output values */
int n;
float findex;
/* input x is in radians */
/* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi, add 0.25 (pi/2) to read sine table */
in = x * 0.159154943092f + 0.25f;
/* Calculation of floor value of input */
n = (int)in;
/* Make negative values towards -infinity */
if (in < 0.0f)
{
n--;
}
/* Map input value to [0 1] */
in = in - (float)n;
/* Calculation of index of the table */
findex = (float)FAST_MATH_TABLE_SIZE * in;
index = ((unsigned short)findex) & 0x1ff;
/* fractional value calculation */
fract = findex - (float)index;
/* Read two nearest values of input value from the cos table */
a = sinTable_f32[index];
b = sinTable_f32[index + 1];
/* Linear interpolation process */
cosVal = (1.0f - fract)*a + fract*b;
/* Return the output value */
return (cosVal);
}
float fastAtan2(float y, float x) {
//float coeff_1 = PI/4.0f;
float coeff_1 = 0.785398163f;
float coeff_2 = 3.0f * coeff_1;
float abs_y = abs(y) + 0.00000001f; // kludge to prevent 0/0 condition;
float angle;
if (x >= 0.0f) {
float r = (x - abs_y) / (x + abs_y);
angle = coeff_1 - coeff_1 * r;
}
else {
float r = (x + abs_y) / (abs_y - x);
angle = coeff_2 - coeff_1 * r;
}
return y < 0.0f ? -angle : angle;
}
float fastSqrt(float v)
{
int i;
float x2, y;
const float threehalfs = 1.5F;
x2 = v * 0.5F;
y = v;
i = *(int *)&y;
i = 0x5f375a86 - (i >> 1);
y = *(float *)&i;
y = y * (threehalfs - (x2 * y * y));
y = y * (threehalfs - (x2 * y * y));
y = y * (threehalfs - (x2 * y * y));
return v*y;
}
void smbPitchShift(float pitchShift, long numSampsToProcess, long fftFrameSize, long osamp, float sampleRate, float *indata, float *outdata)
/*
Routine smbPitchShift(). See top of file for explanation
Purpose: doing pitch shifting while maintaining duration using the Short
Time Fourier Transform.
Author: (c)1999-2015 Stephan M. Bernsee <s.bernsee [AT] zynaptiq [DOT] com>
*/
{
static float gInFIFO[MAX_FRAME_LENGTH];
static float gOutFIFO[MAX_FRAME_LENGTH];
static float gFFTworksp[2 * MAX_FRAME_LENGTH];
static float gLastPhase[MAX_FRAME_LENGTH / 2 + 1];
static float gSumPhase[MAX_FRAME_LENGTH / 2 + 1];
static float gOutputAccum[2 * MAX_FRAME_LENGTH];
static float gAnaFreq[MAX_FRAME_LENGTH];
static float gAnaMagn[MAX_FRAME_LENGTH];
static float gSynFreq[MAX_FRAME_LENGTH];
static float gSynMagn[MAX_FRAME_LENGTH];
static long gRover = false, gInit = false;
float phase, tmp, real, imag;
long i, k, qpd, index;
float M_2PI = 2.0f*M_PI;
float W_2PI = M_2PI / fftFrameSize;
/* set up some handy variables */
long fftFrameSize2 = fftFrameSize / 2;
long stepSize = fftFrameSize / osamp;
float freqPerBin = sampleRate / (float)fftFrameSize;
float expct = W_2PI*(float)stepSize;
float pi_osamp = (M_2PI / osamp);
float pi_osamp_expct = pi_osamp + expct;
float pi_osamp_freqPerBin = pi_osamp / freqPerBin;
float osamp_freqPerBin = osamp* freqPerBin / M_2PI;
float fft_osamp = 1.0f / (fftFrameSize2*osamp);
long inFifoLatency = fftFrameSize - stepSize;
if (gRover == false)
gRover = inFifoLatency;
/* initialize our static arrays */
if (gInit == false) {
memset(gInFIFO, 0, MAX_FRAME_LENGTH*sizeof(float));
memset(gOutFIFO, 0, MAX_FRAME_LENGTH*sizeof(float));
memset(gFFTworksp, 0, 2 * MAX_FRAME_LENGTH*sizeof(float));
memset(gLastPhase, 0, (MAX_FRAME_LENGTH / 2 + 1)*sizeof(float));
memset(gSumPhase, 0, (MAX_FRAME_LENGTH / 2 + 1)*sizeof(float));
memset(gOutputAccum, 0, 2 * MAX_FRAME_LENGTH*sizeof(float));
memset(gAnaFreq, 0, MAX_FRAME_LENGTH*sizeof(float));
memset(gAnaMagn, 0, MAX_FRAME_LENGTH*sizeof(float));
gInit = true;
}
/* main processing loop */
for (i = 0; i < numSampsToProcess; i++){
/* As long as we have not yet collected enough data just read in */
gInFIFO[gRover] = indata[i];
outdata[i] = gOutFIFO[gRover - inFifoLatency];
gRover++;
/* now we have enough data for processing */
if (gRover >= fftFrameSize) {
gRover = inFifoLatency;
/* do windowing and re,im interleave */
float * sFFTworksp = gFFTworksp;
for (k = 0; k < fftFrameSize; k++) {
sFFTworksp[0] = gInFIFO[k] * (-0.5f*fastcos(W_2PI*k) + 0.5f);
sFFTworksp[1] = 0.0f;
sFFTworksp += 2;
}
/* ***************** ANALYSIS ******************* */
/* do transform */
smbFft(gFFTworksp, fftFrameSize, -1);
/* this is the analysis step */
float *pFFTworksp = gFFTworksp;
for (k = 0; k <= fftFrameSize2; k++) {
/* de-interlace FFT buffer */
real = pFFTworksp[0];
imag = pFFTworksp[1];
/* compute magnitude and phase */
gAnaMagn[k] = 2.0f*fastSqrt(real*real + imag*imag);
phase = fastAtan2(imag, real);
/* compute phase difference */
/* subtract expected phase difference */
tmp = (phase - gLastPhase[k]) - (float)k*expct;
gLastPhase[k] = phase;
/* map delta phase into +/- Pi interval */
qpd = tmp * M_1_PI;
if (qpd >= 0)
qpd += qpd & 1;
else
qpd -= qpd & 1;
/* get deviation from bin frequency from the +/- Pi interval */
/* compute the k-th partials' true frequency */
/* store magnitude and true frequency in analysis arrays */
gAnaFreq[k] = (k + (tmp - M_PI*qpd) * osamp_freqPerBin);
pFFTworksp += 2;
}
/* ***************** PROCESSING ******************* */
/* this does the actual pitch shifting */
memset(gSynMagn, 0, fftFrameSize*sizeof(float));
memset(gSynFreq, 0, fftFrameSize*sizeof(float));
for (k = 0; k <= fftFrameSize2; k++) {
index = k*pitchShift;
if (index <= fftFrameSize2) {
gSynMagn[index] += gAnaMagn[k];
gSynFreq[index] = gAnaFreq[k] * pitchShift;
}
}
/* ***************** SYNTHESIS ******************* */
/* this is the synthesis step */
float *tFFTworksp = gFFTworksp;
for (k = 0; k <= fftFrameSize2; k++) {
gSumPhase[k] += pi_osamp_freqPerBin * gSynFreq[k] - pi_osamp_expct*k;
tFFTworksp[0] = gSynMagn[k] * fastcos(gSumPhase[k]);
tFFTworksp[1] = gSynMagn[k] * fastsin(gSumPhase[k]);
tFFTworksp += 2;
}
/* zero negative frequencies */
memset(gFFTworksp + (fftFrameSize + 2), 0, sizeof(float) * 2 * fftFrameSize);
/* do inverse transform */
smbFft(gFFTworksp, fftFrameSize, 1);
/* do windowing and add to output accumulator */
float *ppFFTworksp = gFFTworksp;
for (k = 0; k < fftFrameSize; k++) {
gOutputAccum[k] += (-fastcos(W_2PI*k) *ppFFTworksp[0] * fft_osamp) + ppFFTworksp[0] * fft_osamp;
ppFFTworksp += 2;
}
memcpy(gOutFIFO, gOutputAccum, stepSize*sizeof(float));
/* shift accumulator */
memmove(gOutputAccum, gOutputAccum + stepSize, fftFrameSize*sizeof(float));
/* move input FIFO */
memcpy(gInFIFO, gInFIFO + stepSize, sizeof(float)*inFifoLatency);
}
}
}
// -----------------------------------------------------------------------------------------------------------------
void smbFft(float *fftBuffer, long fftFrameSize, long sign)
/*
FFT routine, (C)1996 S.M.Bernsee. Sign = -1 is FFT, 1 is iFFT (inverse)
Fills fftBuffer[0...2*fftFrameSize-1] with the Fourier transform of the
time domain data in fftBuffer[0...2*fftFrameSize-1]. The FFT array takes
and returns the cosine and sine parts in an interleaved manner, ie.
fftBuffer[0] = cosPart[0], fftBuffer[1] = sinPart[0], asf. fftFrameSize
must be a power of 2. It expects a complex input signal (see footnote 2),
ie. when working with 'common' audio signals our input signal has to be
passed as {in[0],0.,in[1],0.,in[2],0.,...} asf. In that case, the transform
of the frequencies of interest is in fftBuffer[0...fftFrameSize].
*/
{
float wr, wi, arg, *p1, *p2, temp;
float tr, ti, ur, ui, *p1r, *p1i, *p2r, *p2i;
long i, bitm, j, le, le2, k;
for (i = 2; i < 2 * fftFrameSize - 2; i += 2) {
for (bitm = 2, j = 0; bitm < 2 * fftFrameSize; bitm <<= 1) {
if (i & bitm) j++;
j <<= 1;
}
if (i < j) {
p1 = fftBuffer + i; p2 = fftBuffer + j;
temp = *p1; *(p1++) = *p2;
*(p2++) = temp; temp = *p1;
*p1 = *p2; *p2 = temp;
}
}
long k_size = (long)(log((float)fftFrameSize) / log(2.0f) + 0.5f);
for (k = 0, le = 2; k < k_size; k++) {
le <<= 1;
le2 = le >> 1;
ur = 1.0f;
ui = 0.0f;
arg = M_PI / (le2 >> 1);
wr = fastcos(arg);
wi = sign*fastsin(arg);
for (j = 0; j < le2; j += 2) {
p1r = fftBuffer + j; p1i = p1r + 1;
p2r = p1r + le2; p2i = p2r + 1;
for (i = j; i < 2 * fftFrameSize; i += le) {
tr = *p2r * ur - *p2i * ui;
ti = *p2r * ui + *p2i * ur;
*p2r = *p1r - tr; *p2i = *p1i - ti;
*p1r += tr; *p1i += ti;
p1r += le; p1i += le;
p2r += le; p2i += le;
}
tr = ur*wr - ui*wi;
ui = ur*wi + ui*wr;
ur = tr;
}
}
}
// -----------------------------------------------------------------------------------------------------------------
/*
12/12/02, smb
PLEASE NOTE:
There have been some reports on domain errors when the atan2() function was used
as in the above code. Usually, a domain error should not interrupt the program flow
(maybe except in Debug mode) but rather be handled "silently" and a global variable
should be set according to this error. However, on some occasions people ran into
this kind of scenario, so a replacement atan2() function is provided here.
If you are experiencing domain errors and your program stops, simply replace all
instances of atan2() with calls to the smbAtan2() function below.
*/
float smbAtan2(float x, float y)
{
float signx;
if (x > 0.0f) signx = 1.0f;
else signx = -1.0f;
if (x == 0.0f) return 0.0f;
if (y == 0.0f) return signx * M_PI / 2.0f;
return fastAtan2(x, y);
}
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