3 * fast mathematics routines.
7 * A Fast, Compact Approximation of the Exponential Function
9 * IDSIA, Lugano, Switzerland
10 * http://www.inf.ethz.ch/~schraudo/pubs/exp.pdf
12 * Fast log() Function, by Laurent de Soras:
13 * http://www.flipcode.com/cgi-bin/msg.cgi?showThread=Tip-Fastlogfunction&forum=totd&id=-1
22 #define _SG_FMATH_HXX 1
25 # error This library requires C++
31 double fast_exp(double val);
32 double fast_exp2(const double val);
34 float fast_pow(const float val1, const float val2);
35 float fast_log2(const float cal);
36 float fast_root(const float f, const int n);
38 float _fast_pow2(const float cal);
39 float _fast_log2(const float val);
41 float fast_sin(const float val);
42 float fast_cos(const float val);
43 float fast_tan(const float val);
44 float fast_asin(const float val);
45 float fast_acos(const float val);
46 float fast_atan(const float val);
48 void fast_BSL(float &x, register unsigned long shiftAmount);
49 void fast_BSR(float &x, register unsigned long shiftAmount);
52 inline float fast_log2 (float val)
59 const int log_2 = ((v.i >> 23) & 255) - 128;
63 v.f = ((-1.0f/3) * v.f + 2) * v.f - 2.0f/3; // (1)
70 * This function is about 3 times faster than the system log() function
71 * and has an error of about 0.01%
73 inline float fast_log (const float &val)
75 return (fast_log2 (val) * 0.69314718f);
78 inline float fast_log10 (const float &val)
80 return (fast_log2(val) / 3.321928095f);
85 * This function is about twice as fast as the system pow(x,y) function
87 inline float fast_pow(const float val1, const float val2)
89 return _fast_pow2(val2 * _fast_log2(val1));
94 * Haven't seen this elsewhere, probably because it is too obvious?
95 * Anyway, these functions are intended for 32-bit floating point numbers
96 * only and should work a bit faster than the regular ones.
98 inline float fast_abs(float f)
100 int i=((*(int*)&f)&0x7fffffff);
101 return (*(float*)&i);
104 inline float fast_neg(float f)
106 int i=((*(int*)&f)^0x80000000);
107 return (*(float*)&i);
110 inline int fast_sgn(float f)
112 return 1+(((*(int*)&f)>>31)<<1);
115 #endif // !_SG_FMATH_HXX