it appears that the "code markup" that SE has is unfriendly with angle characters (you know ">" or "<"), so you'll probably have to hit "edit" to see all of itfile: __functions.h
//
// FILE: __functions.h
//
// fast and approximate transcendental functions
//
// copyright (c) 2004 Robert Bristow-Johnson
//
// [email protected]
//
#ifndef __FUNCTIONS_H
#define __FUNCTIONS_H
#define TINY 1.0e-8
#define HUGE 1.0e8
#define PI (3.1415926535897932384626433832795028841972) /* pi */
#define ONE_OVER_PI (0.3183098861837906661338147750939)
#define TWOPI (6.2831853071795864769252867665590057683943) /* 2*pi */
#define ONE_OVER_TWOPI (0.15915494309189535682609381638)
#define PI_2 (1.5707963267948966192313216916397514420986) /* pi/2 */
#define TWO_OVER_PI (0.636619772367581332267629550188)
#define LN2 (0.6931471805599453094172321214581765680755) /* ln(2) */
#define ONE_OVER_LN2 (1.44269504088896333066907387547)
#define LN10 (2.3025850929940456840179914546843642076011) /* ln(10) */
#define ONE_OVER_LN10 (0.43429448190325177635683940025)
#define ROOT2 (1.4142135623730950488016887242096980785697) /* sqrt(2) */
#define ONE_OVER_ROOT2 (0.707106781186547438494264988549)
#define DB_LOG2_ENERGY (3.01029995663981154631945610163) /* dB = DB_LOG2_ENERGY*__log2(energy) */
#define DB_LOG2_AMPL (6.02059991327962309263891220326) /* dB = DB_LOG2_AMPL*__log2(amplitude) */
#define ONE_OVER_DB_LOG2_AMPL (0.16609640474436811218256075335) /* amplitude = __exp2(ONE_OVER_DB_LOG2_AMPL*dB) */
#define LONG_OFFSET 4096L
#define FLOAT_OFFSET 4096.0
float __sqrt(float x);
float __log2(float x);
float __exp2(float x);
float __log(float x);
float __exp(float x);
float __pow(float x, float y);
float __sin_pi(float x);
float __cos_pi(float x);
float __sin(float x);
float __cos(float x);
float __tan(float x);
float __atan(float x);
float __asin(float x);
float __acos(float x);
float __arg(float Imag, float Real);
float __poly(float *a, int order, float x);
float __map(float *f, float scaler, float x);
float __discreteMap(float *f, float scaler, float x);
unsigned long __random();
#endif
file: __functions.c
//
// FILE: __functions.c
//
// fast and approximate transcendental functions
//
// copyright (c) 2004 Robert Bristow-Johnson
//
// [email protected]
//
#define STD_MATH_LIB 0
#include "__functions.h"
#if STD_MATH_LIB
#include "math.h" // angle brackets don't work with SE markup
#endif
float __sqrt(register float x)
{
#if STD_MATH_LIB
return (float) sqrt((double)x);
#else
if (x > 5.877471754e-39)
{
register float accumulator, xPower;
register long intPart;
register union {float f; long i;} xBits;
xBits.f = x;
intPart = ((xBits.i)>>23); /* get biased exponent */
intPart -= 127; /* unbias it */
x = (float)(xBits.i & 0x007FFFFF); /* mask off exponent leaving 0x800000*(mantissa - 1) */
x *= 1.192092895507812e-07; /* divide by 0x800000 */
accumulator = 1.0 + 0.49959804148061*x;
xPower = x*x;
accumulator += -0.12047308243453*xPower;
xPower *= x;
accumulator += 0.04585425015501*xPower;
xPower *= x;
accumulator += -0.01076564682800*xPower;
if (intPart & 0x00000001)
{
accumulator *= ROOT2; /* an odd input exponent means an extra sqrt(2) in the output */
}
xBits.i = intPart >> 1; /* divide exponent by 2, lose LSB */
xBits.i += 127; /* rebias exponent */
xBits.i <<= 23; /* move biased exponent into exponent bits */
return accumulator * xBits.f;
}
else
{
return 0.0;
}
#endif
}
float __log2(register float x)
{
#if STD_MATH_LIB
return (float) (ONE_OVER_LN2*log((double)x));
#else
if (x > 5.877471754e-39)
{
register float accumulator, xPower;
register long intPart;
register union {float f; long i;} xBits;
xBits.f = x;
intPart = ((xBits.i)>>23); /* get biased exponent */
intPart -= 127; /* unbias it */
x = (float)(xBits.i & 0x007FFFFF); /* mask off exponent leaving 0x800000*(mantissa - 1) */
x *= 1.192092895507812e-07; /* divide by 0x800000 */
accumulator = 1.44254494359510*x;
xPower = x*x;
accumulator += -0.71814525675041*xPower;
xPower *= x;
accumulator += 0.45754919692582*xPower;
xPower *= x;
accumulator += -0.27790534462866*xPower;
xPower *= x;
accumulator += 0.12179791068782*xPower;
xPower *= x;
accumulator += -0.02584144982967*xPower;
return accumulator + (float)intPart;
}
else
{
return -HUGE;
}
#endif
}
float __exp2(register float x)
{
#if STD_MATH_LIB
return (float) exp(LN2*(double)x);
#else
if (x >= -127.0)
{
register float accumulator, xPower;
register union {float f; long i;} xBits;
xBits.i = (long)(x + FLOAT_OFFSET) - LONG_OFFSET; /* integer part */
x -= (float)(xBits.i); /* fractional part */
accumulator = 1.0 + 0.69303212081966*x;
xPower = x*x;
accumulator += 0.24137976293709*xPower;
xPower *= x;
accumulator += 0.05203236900844*xPower;
xPower *= x;
accumulator += 0.01355574723481*xPower;
xBits.i += 127; /* bias integer part */
xBits.i <<= 23; /* move biased int part into exponent bits */
return accumulator * xBits.f;
}
else
{
return 0.0;
}
#endif
}
float __log(register float x)
{
#if STD_MATH_LIB
return (float) log((double)x);
#else
return LN2*__log2(x);
#endif
}
float __exp(register float x)
{
#if STD_MATH_LIB
return (float) exp((double)x);
#else
return __exp2(ONE_OVER_LN2*x);
#endif
}
float __pow(float x, float y)
{
#if STD_MATH_LIB
return (float) pow((double)x, (double)y);
#else
return __exp2(y*__log2(x));
#endif
}
float __sin_pi(register float x)
{
#if STD_MATH_LIB
return (float) sin(PI*(double)x);
#else
register float accumulator, xPower, xSquared;
register long evenIntPart = ((long)(0.5*x + 1024.5) - 1024)<<1;
x -= (float)evenIntPart;
xSquared = x*x;
accumulator = 3.14159265358979*x;
xPower = xSquared*x;
accumulator += -5.16731953364340*xPower;
xPower *= xSquared;
accumulator += 2.54620566822659*xPower;
xPower *= xSquared;
accumulator += -0.586027023087261*xPower;
xPower *= xSquared;
accumulator += 0.06554823491427*xPower;
return accumulator;
#endif
}
float __cos_pi(register float x)
{
#if STD_MATH_LIB
return (float) cos(PI*(double)x);
#else
register float accumulator, xPower, xSquared;
register long evenIntPart = ((long)(0.5*x + 1024.5) - 1024)<<1;
x -= (float)evenIntPart;
xSquared = x*x;
accumulator = 1.57079632679490*x; /* series for sin(PI/2*x) */
xPower = xSquared*x;
accumulator += -0.64596406188166*xPower;
xPower *= xSquared;
accumulator += 0.07969158490912*xPower;
xPower *= xSquared;
accumulator += -0.00467687997706*xPower;
xPower *= xSquared;
accumulator += 0.00015303015470*xPower;
return 1.0 - 2.0*accumulator*accumulator; /* cos(w) = 1 - 2*(sin(w/2))^2 */
#endif
}
float __sin(register float x)
{
#if STD_MATH_LIB
return (float) sin((double)x);
#else
x *= ONE_OVER_PI;
return __sin_pi(x);
#endif
}
float __cos(register float x)
{
#if STD_MATH_LIB
return (float) cos((double)x);
#else
x *= ONE_OVER_PI;
return __cos_pi(x);
#endif
}
float __tan(register float x)
{
#if STD_MATH_LIB
return (float) tan((double)x);
#else
x *= ONE_OVER_PI;
return __sin_pi(x)/__cos_pi(x);
#endif
}
float __atan(register float x)
{
#if STD_MATH_LIB
return (float) atan((double)x);
#else
register float accumulator, xPower, xSquared, offset;
offset = 0.0;
if (x < -1.0)
{
offset = -PI_2;
x = -1.0/x;
}
else if (x > 1.0)
{
offset = PI_2;
x = -1.0/x;
}
xSquared = x*x;
accumulator = 1.0;
xPower = xSquared;
accumulator += 0.33288950512027*xPower;
xPower *= xSquared;
accumulator += -0.08467922817644*xPower;
xPower *= xSquared;
accumulator += 0.03252232640125*xPower;
xPower *= xSquared;
accumulator += -0.00749305860992*xPower;
return offset + x/accumulator;
#endif
}
float __asin(register float x)
{
#if STD_MATH_LIB
return (float) asin((double)x);
#else
return __atan(x/__sqrt(1.0 - x*x));
#endif
}
float __acos(register float x)
{
#if STD_MATH_LIB
return (float) acos((double)x);
#else
return __atan(__sqrt(1.0 - x*x)/x);
#endif
}
float __arg(float Imag, float Real)
{
#if STD_MATH_LIB
return (float) atan2((double)Imag, (double)Real);
#else
register float accumulator, xPower, xSquared, offset, x;
if (Imag > 0.0)
{
if (Imag <= -Real)
{
offset = PI;
x = Imag/Real;
}
else if (Imag > Real)
{
offset = PI_2;
x = -Real/Imag;
}
else
{
offset = 0.0;
x = Imag/Real;
}
}
else
{
if (Imag >= Real)
{
offset = -PI;
x = Imag/Real;
}
else if (Imag < -Real)
{
offset = -PI_2;
x = -Real/Imag;
}
else
{
offset = 0.0;
x = Imag/Real;
}
}
xSquared = x*x;
accumulator = 1.0;
xPower = xSquared;
accumulator += 0.33288950512027*xPower;
xPower *= xSquared;
accumulator += -0.08467922817644*xPower;
xPower *= xSquared;
accumulator += 0.03252232640125*xPower;
xPower *= xSquared;
accumulator += -0.00749305860992*xPower;
return offset + x/accumulator;
#endif
}
float __poly(float *a, int order, float x)
{
register float accumulator = 0.0, xPower;
register int n;
accumulator = a[0];
xPower = x;
for (n=1; n<=order; n++)
{
accumulator += a[n]*xPower;
xPower *= x;
}
return accumulator;
}
float __map(float *f, float scaler, float x)
{
register long i;
x *= scaler;
i = (long)(x + FLOAT_OFFSET) - LONG_OFFSET; /* round down without floor() */
return f[i] + (f[i+1] - f[i])*(x - (float)i); /* linear interpolate between points */
}
float __discreteMap(float *f, float scaler, float x)
{
register long i;
x *= scaler;
i = (long)(x + (FLOAT_OFFSET+0.5)) - LONG_OFFSET; /* round to nearest */
return f[i];
}
unsigned long __random()
{
static unsigned long seed0 = 0x5B7A2775, seed1 = 0x80C7169F;
seed0 += seed1;
seed1 += seed0;
return seed1;
}
