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libcw/cwMath.cpp

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C++
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#include "cwCommon.h"
#include "cwLog.h"
#include "cwCommonImpl.h"
#include "cwMath.h"
#include "cwMem.h"
#include <algorithm>
// TODO: rewrite to avoid copying
// this code comes via csound source ...
double cw::math::x80ToDouble( unsigned char rate[10] )
{
char sign;
short exp = 0;
unsigned long mant1 = 0;
unsigned long mant0 = 0;
double val;
unsigned char* p = (unsigned char*)rate;
exp = *p++;
exp <<= 8;
exp |= *p++;
sign = (exp & 0x8000) ? 1 : 0;
exp &= 0x7FFF;
mant1 = *p++;
mant1 <<= 8;
mant1 |= *p++;
mant1 <<= 8;
mant1 |= *p++;
mant1 <<= 8;
mant1 |= *p++;
mant0 = *p++;
mant0 <<= 8;
mant0 |= *p++;
mant0 <<= 8;
mant0 |= *p++;
mant0 <<= 8;
mant0 |= *p++;
/* special test for all bits zero meaning zero
- else pow(2,-16383) bombs */
if (mant1 == 0 && mant0 == 0 && exp == 0 && sign == 0)
return 0.0;
else {
val = ((double)mant0) * pow(2.0,-63.0);
val += ((double)mant1) * pow(2.0,-31.0);
val *= pow(2.0,((double) exp) - 16383.0);
return sign ? -val : val;
}
}
// TODO: rewrite to avoid copying
/*
* Convert double to IEEE 80 bit floating point
* Should be portable to all C compilers.
* 19aug91 aldel/dpwe covered for MSB bug in Ultrix 'cc'
*/
void cw::math::doubleToX80(double val, unsigned char rate[10])
{
char sign = 0;
short exp = 0;
unsigned long mant1 = 0;
unsigned long mant0 = 0;
unsigned char* p = (unsigned char*)rate;
if (val < 0.0) { sign = 1; val = -val; }
if (val != 0.0) /* val identically zero -> all elements zero */
{
exp = (short)(std::log(val)/std::log(2.0) + 16383.0);
val *= pow(2.0, 31.0+16383.0-(double)exp);
mant1 =((unsigned)val);
val -= ((double)mant1);
val *= pow(2.0, 32.0);
mant0 =((double)val);
}
*p++ = ((sign<<7)|(exp>>8));
*p++ = (u_char)(0xFF & exp);
*p++ = (u_char)(0xFF & (mant1>>24));
*p++ = (u_char)(0xFF & (mant1>>16));
*p++ = (u_char)(0xFF & (mant1>> 8));
*p++ = (u_char)(0xFF & (mant1));
*p++ = (u_char)(0xFF & (mant0>>24));
*p++ = (u_char)(0xFF & (mant0>>16));
*p++ = (u_char)(0xFF & (mant0>> 8));
*p++ = (u_char)(0xFF & (mant0));
}
bool cw::math::isPowerOfTwo( unsigned x )
{
return x==1 || (!( (x < 2) || (x & (x-1)) ));
}
unsigned cw::math::nextPowerOfTwo( unsigned val )
{
unsigned i;
unsigned mask = 1;
unsigned msb = 0;
unsigned cnt = 0;
// if val is a power of two return it
if( isPowerOfTwo(val) )
return val;
// next pow of zero is 2
if( val == 0 )
return 2;
// if the next power of two can't be represented in 32 bits
if( val > 0x80000000)
{
assert(0);
return 0;
}
// find most sig. bit that is set - the number with only the next msb set is next pow 2
for(i=0; i<31; i++,mask<<=1)
if( mask & val )
{
msb = i;
cnt++;
}
return 1 << (msb + 1);
}
unsigned cw::math::nearPowerOfTwo( unsigned i )
{
unsigned vh = nextPowerOfTwo(i);
if( vh == 2 )
return vh;
unsigned vl = vh / 2;
if( vh - i < i - vl )
return vh;
return vl;
}
bool cw::math::isOddU( unsigned v ) { return v % 2 == 1; }
bool cw::math::isEvenU( unsigned v ) { return !isOddU(v); }
unsigned cw::math::nextOddU( unsigned v ) { return isOddU(v) ? v : v+1; }
unsigned cw::math::prevOddU( unsigned v ) { return isOddU(v) ? v : v-1; }
unsigned cw::math::nextEvenU( unsigned v ) { return isEvenU(v) ? v : v+1; }
unsigned cw::math::prevEvenU( unsigned v ) { return isEvenU(v) ? v : v-1; }
unsigned cw::math::modIncr(int idx, int delta, int maxN )
{
int sum = idx + delta;
if( sum >= maxN )
return sum - maxN;
if( sum < 0 )
return maxN + sum;
return sum;
}
unsigned cw::math::hzToMidi( double hz )
{
float midi = 12.0 * std::log2(hz/13.75) + 9;
if( midi < 0 )
midi = 0;
if( midi > 127 )
midi = 127;
return (unsigned)lround(midi);
}
float cw::math::midiToHz( unsigned midi )
{
double m = midi <= 127 ? midi : 127;
return (float)( 13.75 * pow(2.0,(m - 9.0)/12.0));
}
//=================================================================
// Random numbers
int cw::math::randInt( int min, int max )
{
assert( min <= max );
int range = max - min;
return min + std::max(0,std::min(range,(int)round(range * (double)rand() / RAND_MAX)));
}
unsigned cw::math::randUInt( unsigned min, unsigned max )
{
assert( min <= max );
unsigned range = max - min;
unsigned val = (unsigned)round(range * (double)rand() / RAND_MAX);
return min + std::max((unsigned)0,std::min(range,val));
}
float cw::math::randFloat( float min, float max )
{
assert( min <= max );
float range = max - min;
float val = (float)(range * (double)rand() / RAND_MAX);
return min + std::max(0.0f,std::min(range,val));
}
double cw::math::randDouble( double min, double max )
{
assert( min <= max );
double range = max - min;
double val = range * (double)rand() / RAND_MAX;
return min + std::max(0.0,std::min(range,val));
}
//=================================================================
// Base on: http://stackoverflow.com/questions/3874627/floating-point-comparison-functions-for-c-sharp
bool cw::math::isCloseD( double x0, double x1, double eps )
{
double d = fabs(x0-x1);
if( x0 == x1 )
return true;
if( x0==0 || x1==0 || d<DBL_MIN )
return d < (eps * DBL_MIN);
return (d / std::min( fabs(x0) + fabs(x1), DBL_MAX)) < eps;
}
bool cw::math::isCloseF( float x0, float x1, double eps_d )
{
float eps = (float)eps_d;
float d = fabsf(x0-x1);
if( x0 == x1 )
return true;
if( x0==0 || x1==0 || d<FLT_MIN )
return d < (eps * FLT_MIN);
return (d / std::min( fabsf(x0) + fabsf(x1), FLT_MAX)) < eps;
}
bool cw::math::isCloseI( int x0, int x1, double eps )
{
if( x0 == x1 )
return true;
return abs(x0-x1)/(abs(x0)+abs(x1)) < eps;
}
bool cw::math::isCloseU( unsigned x0, unsigned x1, double eps )
{
if( x0 == x1 )
return true;
if( x0 > x1 )
return (x0-x1)/(x0+x1) < eps;
else
return (x1-x0)/(x0+x1) < eps;
}
//=================================================================
// lFSR() implementation based on note at bottom of:
// http://www.ece.u.edu/~koopman/lfsr/index.html
void cw::math::lFSR( unsigned lfsrN, unsigned tapMask, unsigned seed, unsigned* yV, unsigned yN )
{
assert( 0 < lfsrN && lfsrN < 32 );
unsigned i;
for(i=0; i<yN; ++i)
{
if( (yV[i] = seed & 1)==1 )
seed = (seed >> 1) ^ tapMask;
else
seed = (seed >> 1);
}
}
namespace cw
{
namespace math
{
bool mLS_IsBalanced( const unsigned* xV, int xN)
{
int a = 0;
int i;
for(i=0; i<xN; ++i)
if( xV[i] == 1 )
++a;
return abs(a - (xN-a)) == 1;
}
}
unsigned _genGoldCopy( int* y, unsigned yi, unsigned yN, unsigned* x, unsigned xN)
{
unsigned i;
for(i=0; i<xN; ++i,++yi)
y[yi] = x[i]==1 ? -1 : 1;
assert(yi <= yN);
return yi;
}
}
bool cw::math::genGoldCodes( unsigned lfsrN, unsigned poly_coeff0, unsigned poly_coeff1, unsigned goldN, int* yM, unsigned mlsN )
{
bool retFl = true;
unsigned yi = 0;
unsigned yN = goldN * mlsN;
unsigned* mls0V = mem::allocZ<unsigned>(mlsN);
unsigned* mls1V = mem::allocZ<unsigned>(mlsN);
unsigned* xorV = mem::allocZ<unsigned>(mlsN);
unsigned i,j;
lFSR(lfsrN, poly_coeff0, 1 << (lfsrN-1), mls0V, mlsN);
lFSR(lfsrN, poly_coeff1, 1 << (lfsrN-1), mls1V, mlsN);
if( mLS_IsBalanced(mls0V,mlsN) )
yi = _genGoldCopy(yM, yi, yN, mls0V, mlsN);
if( yi<yN && mLS_IsBalanced(mls1V,mlsN) )
yi = _genGoldCopy(yM, yi, yN, mls1V, mlsN);
for(i=0; yi < yN && i<mlsN-1; ++i )
{
for(j=0; j<mlsN; ++j)
xorV[j] = (mls0V[j] + mls1V[ (i+j) % mlsN ]) % 2;
if( mLS_IsBalanced(xorV,mlsN) )
yi = _genGoldCopy(yM,yi,yN,xorV,mlsN);
}
if(yi < yN )
{
//rc = errMsg(err,kOpFailAtRC,"Gold code generation failed. Insuffient balanced pairs.");
retFl = false;
}
mem::release(mls0V);
mem::release(mls1V);
mem::release(xorV);
return retFl;
}
bool cw::math::lFSR_Test()
{
// lfsrN = 5; % 5 6 7;
// poly_coeff0 = 0x12; % 0x12 0x21 0x41;
// poly_coeff1 = 0x1e; % 0x1e 0x36 0x72;
unsigned lfsrN = 7;
unsigned pc0 = 0x41;
unsigned pc1 = 0x72;
unsigned mlsN = (1 << lfsrN)-1;
unsigned yN = mlsN*2;
unsigned yV[ yN ];
unsigned i;
lFSR( lfsrN, pc0, 1 << (lfsrN-1), yV, yN );
for(i=0; i<mlsN; ++i)
if( yV[i] != yV[i+mlsN] )
return false;
//atVOU_PrintL(NULL,"0x12",yV,mlsN,2);
lFSR( lfsrN, pc1, 1 << (lfsrN-1), yV, yN );
//atVOU_PrintL(NULL,"0x17",yV,mlsN,2);
for(i=0; i<mlsN; ++i)
if( yV[i] != yV[i+mlsN] )
return false;
return true;
}
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