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libcm/cmMath.c

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8.6 KiB
C
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#include "cmPrefix.h"
#include "cmGlobal.h"
#include "cmFloatTypes.h"
#include "cmMath.h"
#include <sys/types.h> // u_char
// TODO: rewrite to avoid copying
// this code comes via csound source ...
double cmX80ToDouble( 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 cmDoubleToX80(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)(log(val)/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 cmIsPowerOfTwo( unsigned x )
{
return !( (x < 2) || (x & (x-1)) );
}
unsigned cmNextPowerOfTwo( unsigned val )
{
unsigned i;
unsigned mask = 1;
unsigned msb = 0;
unsigned cnt = 0;
// if val is a power of two return it
if( cmIsPowerOfTwo(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 cmNearPowerOfTwo( unsigned i )
{
unsigned vh = cmNextPowerOfTwo(i);
if( vh == 2 )
return vh;
unsigned vl = vh / 2;
if( vh - i < i - vl )
return vh;
return vl;
}
bool cmIsOddU( unsigned v ) { return v % 2 == 1; }
bool cmIsEvenU( unsigned v ) { return !cmIsOddU(v); }
unsigned cmNextOddU( unsigned v ) { return cmIsOddU(v) ? v : v+1; }
unsigned cmPrevOddU( unsigned v ) { return cmIsOddU(v) ? v : v-1; }
unsigned cmNextEvenU( unsigned v ) { return cmIsEvenU(v) ? v : v+1; }
unsigned cmPrevEvenU( unsigned v ) { return cmIsEvenU(v) ? v : v-1; }
// modified bessel function of first kind, order 0
// ref: orfandis appendix B io.m
double cmBessel0( double x )
{
double eps = pow(10.0,-9.0);
double n = 1.0;
double S = 1.0;
double D = 1.0;
while(D > eps*S)
{
double T = x /(2.0*n);
n = n+1;
D = D * pow(T,2.0);
S = S + D;
}
return S;
}
//=================================================================
// The following elliptic-related function approximations come from
// Parks & Burrus, Digital Filter Design, Appendix program 9, pp. 317-326
// which in turn draws directly on other sources
// calculate complete elliptic integral (quarter period) K
// given *complimentary* modulus kc
cmReal_t cmEllipK( cmReal_t kc )
{
cmReal_t a = 1, b = kc, c = 1, tmp;
while( c > cmReal_EPSILON )
{
c = 0.5*(a-b);
tmp = 0.5*(a+b);
b = sqrt(a*b);
a = tmp;
}
return M_PI/(2*a);
}
// calculate elliptic modulus k
// given ratio of complete elliptic integrals r = K/K'
// (solves the "degree equation" for fixed N = K*K1'/K'K1)
cmReal_t cmEllipDeg( cmReal_t r )
{
cmReal_t q,a,b,c,d;
a = b = c = 1;
d = q = exp(-M_PI*r);
while( c > cmReal_EPSILON )
{
a = a + 2*c*d;
c = c*d*d;
b = b + c;
d = d*q;
}
return 4*sqrt(q)*pow(b/a,2);
}
// calculate arc elliptic tangent u (elliptic integral of the 1st kind)
// given argument x = sc(u,k) and *complimentary* modulus kc
cmReal_t cmEllipArcSc( cmReal_t x, cmReal_t kc )
{
cmReal_t a = 1, b = kc, y = 1/x, tmp;
unsigned L = 0;
while( true )
{
tmp = a*b;
a += b;
b = 2*sqrt(tmp);
y -= tmp/y;
if( y == 0 )
y = sqrt(tmp) * 1E-10;
if( fabs(a-b)/a < cmReal_EPSILON )
break;
L *= 2;
if( y < 0 )
L++;
}
if( y < 0 )
L++;
return (atan(a/y) + M_PI*L)/a;
}
// calculate Jacobi elliptic functions sn, cn, and dn
// given argument u and *complimentary* modulus kc
cmRC_t cmEllipJ( cmReal_t u, cmReal_t kc, cmReal_t* sn, cmReal_t* cn, cmReal_t* dn )
{
assert( sn != NULL || cn != NULL || dn != NULL );
if( u == 0 )
{
if( sn != NULL ) *sn = 0;
if( cn != NULL ) *cn = 1;
if( dn != NULL ) *dn = 1;
return cmOkRC;
}
int i;
cmReal_t a,b,c,d,e,tmp,_sn,_cn,_dn;
cmReal_t aa[16], bb[16];
a = 1;
b = kc;
for( i = 0; i < 16; i++ )
{
aa[i] = a;
bb[i] = b;
tmp = (a+b)/2;
b = sqrt(a*b);
a = tmp;
if( (a-b)/a < cmReal_EPSILON )
break;
}
c = a/tan(u*a);
d = 1;
for( ; i >= 0; i-- )
{
e = c*c/a;
c = c*d;
a = aa[i];
d = (e + bb[i]) / (e+a);
}
_sn = 1/sqrt(1+c*c);
_cn = _sn*c;
_dn = d;
if( sn != NULL ) *sn = _sn;
if( cn != NULL ) *cn = _cn;
if( dn != NULL ) *dn = _dn;
return cmOkRC;
}
//=================================================================
// bilinear transform
// z = (2*sr + s)/(2*sr - s)
cmRC_t cmBlt( unsigned n, cmReal_t sr, cmReal_t* rp, cmReal_t* ip )
{
unsigned i;
cmReal_t a = 2*sr,
tr, ti, td;
for( i = 0; i < n; i++ )
{
tr = rp[i];
ti = ip[i];
td = pow(a-tr, 2) + ti*ti;
rp[i] = (a*a - tr*tr - ti*ti)/td;
ip[i] = 2*a*ti/td;
if( tr < -1E15 )
rp[i] = 0;
if( fabs(ti) > 1E15 )
ip[i] = 0;
}
return cmOkRC;
}
unsigned cmHzToMidi( double hz )
{
float midi = 12.0 * log2(hz/13.75) + 9;
if( midi < 0 )
midi = 0;
if( midi > 127 )
midi = 127;
return (unsigned)lround(midi);
}
float cmMidiToHz( unsigned midi )
{
double m = midi <= 127 ? midi : 127;
return (float)( 13.75 * pow(2.0,(m - 9.0)/12.0));
}
//=================================================================
// Floating point byte swapping
// Unions used to type-pun the swapping functions and thereby
// avoid strict aliasing problems with -O2. Using unions for
// this purpose is apparently legal under C99 but not C++.
typedef union
{
unsigned u;
float f;
} _cmMathU_t;
typedef union
{
unsigned long long u;
double f;
} _cmMathUL_t;
unsigned cmFfSwapFloatToUInt( float v )
{
assert( sizeof(float) == sizeof(unsigned));
_cmMathU_t u;
u.f=v;
return cmSwap32(u.u);
}
float cmFfSwapUIntToFloat( unsigned v )
{
assert( sizeof(float) == sizeof(unsigned));
_cmMathU_t u;
u.u = cmSwap32(v);
return u.f;
}
unsigned long long cmFfSwapDoubleToULLong( double v )
{
assert( sizeof(double) == sizeof(unsigned long long));
_cmMathUL_t u;
u.f = v;
return cmSwap64(u.u);
}
double cmFfSwapULLongToDouble( unsigned long long v )
{
assert( sizeof(double) == sizeof(unsigned long long));
_cmMathUL_t u;
u.u = cmSwap64(v);
return u.f;
}
int cmRandInt( int min, int max )
{
assert( min <= max );
int offs = max - min;
return min + cmMax(0,cmMin(offs,(int)round(offs * (double)rand() / RAND_MAX)));
}
unsigned cmRandUInt( unsigned min, unsigned max )
{
assert( min <= max );
unsigned offs = max - min;
return min + cmMax(0,cmMin(offs,(unsigned)round(offs * (double)rand() / RAND_MAX)));
}
float cmRandFloat( float min, float max )
{
assert( min <= max );
float offs = max - min;
return min + cmMax(0,cmMin(offs,(float)(offs * (double)rand() / RAND_MAX)));
}
double cmRandDouble( double min, double max )
{
assert( min <= max );
double offs = max - min;
return min + cmMax(0,cmMin(offs,(offs * (double)rand() / RAND_MAX)));
}
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