[444] | 1 | /* ef_pow.c -- float version of e_pow.c. |
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| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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| 3 | */ |
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| 4 | |
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| 5 | /* |
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| 6 | * ==================================================== |
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 8 | * |
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 10 | * Permission to use, copy, modify, and distribute this |
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| 11 | * software is freely granted, provided that this notice |
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| 12 | * is preserved. |
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| 13 | * ==================================================== |
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| 14 | */ |
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| 15 | |
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| 16 | #include "fdlibm.h" |
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| 17 | |
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| 18 | #if __OBSOLETE_MATH |
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| 19 | #ifdef __v810__ |
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| 20 | #define const |
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| 21 | #endif |
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| 22 | |
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| 23 | #ifdef __STDC__ |
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| 24 | static const float |
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| 25 | #else |
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| 26 | static float |
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| 27 | #endif |
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| 28 | bp[] = {1.0, 1.5,}, |
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| 29 | dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ |
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| 30 | dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ |
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| 31 | zero = 0.0, |
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| 32 | one = 1.0, |
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| 33 | two = 2.0, |
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| 34 | two24 = 16777216.0, /* 0x4b800000 */ |
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| 35 | huge = 1.0e30, |
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| 36 | tiny = 1.0e-30, |
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| 37 | /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ |
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| 38 | L1 = 6.0000002384e-01, /* 0x3f19999a */ |
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| 39 | L2 = 4.2857143283e-01, /* 0x3edb6db7 */ |
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| 40 | L3 = 3.3333334327e-01, /* 0x3eaaaaab */ |
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| 41 | L4 = 2.7272811532e-01, /* 0x3e8ba305 */ |
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| 42 | L5 = 2.3066075146e-01, /* 0x3e6c3255 */ |
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| 43 | L6 = 2.0697501302e-01, /* 0x3e53f142 */ |
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| 44 | P1 = 1.6666667163e-01, /* 0x3e2aaaab */ |
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| 45 | P2 = -2.7777778450e-03, /* 0xbb360b61 */ |
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| 46 | P3 = 6.6137559770e-05, /* 0x388ab355 */ |
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| 47 | P4 = -1.6533901999e-06, /* 0xb5ddea0e */ |
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| 48 | P5 = 4.1381369442e-08, /* 0x3331bb4c */ |
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| 49 | lg2 = 6.9314718246e-01, /* 0x3f317218 */ |
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| 50 | lg2_h = 6.93145752e-01, /* 0x3f317200 */ |
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| 51 | lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ |
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| 52 | ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ |
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| 53 | cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ |
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| 54 | cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */ |
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| 55 | cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */ |
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| 56 | ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ |
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| 57 | ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ |
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| 58 | ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ |
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| 59 | |
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| 60 | #ifdef __STDC__ |
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| 61 | float __ieee754_powf(float x, float y) |
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| 62 | #else |
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| 63 | float __ieee754_powf(x,y) |
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| 64 | float x, y; |
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| 65 | #endif |
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| 66 | { |
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| 67 | float z,ax,z_h,z_l,p_h,p_l; |
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| 68 | float y1,t1,t2,r,s,t,u,v,w; |
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| 69 | __int32_t i,j,k,yisint,n; |
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| 70 | __int32_t hx,hy,ix,iy,is; |
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| 71 | |
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| 72 | GET_FLOAT_WORD(hx,x); |
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| 73 | GET_FLOAT_WORD(hy,y); |
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| 74 | ix = hx&0x7fffffff; iy = hy&0x7fffffff; |
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| 75 | |
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| 76 | /* y==zero: x**0 = 1 */ |
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| 77 | if(FLT_UWORD_IS_ZERO(iy)) return one; |
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| 78 | |
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| 79 | /* x|y==NaN return NaN unless x==1 then return 1 */ |
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| 80 | if(FLT_UWORD_IS_NAN(ix) || |
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| 81 | FLT_UWORD_IS_NAN(iy)) { |
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| 82 | if(ix==0x3f800000) return one; |
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| 83 | else return nanf(""); |
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| 84 | } |
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| 85 | |
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| 86 | /* determine if y is an odd int when x < 0 |
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| 87 | * yisint = 0 ... y is not an integer |
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| 88 | * yisint = 1 ... y is an odd int |
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| 89 | * yisint = 2 ... y is an even int |
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| 90 | */ |
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| 91 | yisint = 0; |
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| 92 | if(hx<0) { |
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| 93 | if(iy>=0x4b800000) yisint = 2; /* even integer y */ |
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| 94 | else if(iy>=0x3f800000) { |
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| 95 | k = (iy>>23)-0x7f; /* exponent */ |
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| 96 | j = iy>>(23-k); |
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| 97 | if((j<<(23-k))==iy) yisint = 2-(j&1); |
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| 98 | } |
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| 99 | } |
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| 100 | |
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| 101 | /* special value of y */ |
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| 102 | if (FLT_UWORD_IS_INFINITE(iy)) { /* y is +-inf */ |
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| 103 | if (ix==0x3f800000) |
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| 104 | return one; /* +-1**+-inf = 1 */ |
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| 105 | else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ |
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| 106 | return (hy>=0)? y: zero; |
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| 107 | else /* (|x|<1)**-,+inf = inf,0 */ |
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| 108 | return (hy<0)?-y: zero; |
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| 109 | } |
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| 110 | if(iy==0x3f800000) { /* y is +-1 */ |
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| 111 | if(hy<0) return one/x; else return x; |
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| 112 | } |
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| 113 | if(hy==0x40000000) return x*x; /* y is 2 */ |
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| 114 | if(hy==0x3f000000) { /* y is 0.5 */ |
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| 115 | if(hx>=0) /* x >= +0 */ |
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| 116 | return __ieee754_sqrtf(x); |
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| 117 | } |
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| 118 | |
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| 119 | ax = fabsf(x); |
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| 120 | /* special value of x */ |
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| 121 | if(FLT_UWORD_IS_INFINITE(ix)||FLT_UWORD_IS_ZERO(ix)||ix==0x3f800000){ |
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| 122 | z = ax; /*x is +-0,+-inf,+-1*/ |
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| 123 | if(hy<0) z = one/z; /* z = (1/|x|) */ |
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| 124 | if(hx<0) { |
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| 125 | if(((ix-0x3f800000)|yisint)==0) { |
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| 126 | z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
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| 127 | } else if(yisint==1) |
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| 128 | z = -z; /* (x<0)**odd = -(|x|**odd) */ |
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| 129 | } |
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| 130 | return z; |
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| 131 | } |
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| 132 | |
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| 133 | /* (x<0)**(non-int) is NaN */ |
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| 134 | if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); |
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| 135 | |
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| 136 | /* |y| is huge */ |
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| 137 | if(iy>0x4d000000) { /* if |y| > 2**27 */ |
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| 138 | /* over/underflow if x is not close to one */ |
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| 139 | if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; |
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| 140 | if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny; |
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| 141 | /* now |1-x| is tiny <= 2**-20, suffice to compute |
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| 142 | log(x) by x-x^2/2+x^3/3-x^4/4 */ |
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| 143 | t = ax-1; /* t has 20 trailing zeros */ |
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| 144 | w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); |
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| 145 | u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ |
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| 146 | v = t*ivln2_l-w*ivln2; |
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| 147 | t1 = u+v; |
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| 148 | GET_FLOAT_WORD(is,t1); |
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| 149 | SET_FLOAT_WORD(t1,is&0xfffff000); |
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| 150 | t2 = v-(t1-u); |
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| 151 | } else { |
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| 152 | float s2,s_h,s_l,t_h,t_l; |
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| 153 | n = 0; |
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| 154 | /* take care subnormal number */ |
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| 155 | if(FLT_UWORD_IS_SUBNORMAL(ix)) |
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| 156 | {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } |
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| 157 | n += ((ix)>>23)-0x7f; |
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| 158 | j = ix&0x007fffff; |
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| 159 | /* determine interval */ |
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| 160 | ix = j|0x3f800000; /* normalize ix */ |
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| 161 | if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */ |
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| 162 | else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ |
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| 163 | else {k=0;n+=1;ix -= 0x00800000;} |
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| 164 | SET_FLOAT_WORD(ax,ix); |
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| 165 | |
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| 166 | /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ |
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| 167 | u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ |
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| 168 | v = one/(ax+bp[k]); |
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| 169 | s = u*v; |
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| 170 | s_h = s; |
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| 171 | GET_FLOAT_WORD(is,s_h); |
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| 172 | SET_FLOAT_WORD(s_h,is&0xfffff000); |
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| 173 | /* t_h=ax+bp[k] High */ |
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| 174 | SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21)); |
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| 175 | t_l = ax - (t_h-bp[k]); |
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| 176 | s_l = v*((u-s_h*t_h)-s_h*t_l); |
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| 177 | /* compute log(ax) */ |
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| 178 | s2 = s*s; |
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| 179 | r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); |
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| 180 | r += s_l*(s_h+s); |
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| 181 | s2 = s_h*s_h; |
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| 182 | t_h = (float)3.0+s2+r; |
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| 183 | GET_FLOAT_WORD(is,t_h); |
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| 184 | SET_FLOAT_WORD(t_h,is&0xfffff000); |
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| 185 | t_l = r-((t_h-(float)3.0)-s2); |
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| 186 | /* u+v = s*(1+...) */ |
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| 187 | u = s_h*t_h; |
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| 188 | v = s_l*t_h+t_l*s; |
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| 189 | /* 2/(3log2)*(s+...) */ |
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| 190 | p_h = u+v; |
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| 191 | GET_FLOAT_WORD(is,p_h); |
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| 192 | SET_FLOAT_WORD(p_h,is&0xfffff000); |
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| 193 | p_l = v-(p_h-u); |
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| 194 | z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ |
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| 195 | z_l = cp_l*p_h+p_l*cp+dp_l[k]; |
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| 196 | /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ |
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| 197 | t = (float)n; |
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| 198 | t1 = (((z_h+z_l)+dp_h[k])+t); |
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| 199 | GET_FLOAT_WORD(is,t1); |
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| 200 | SET_FLOAT_WORD(t1,is&0xfffff000); |
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| 201 | t2 = z_l-(((t1-t)-dp_h[k])-z_h); |
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| 202 | } |
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| 203 | |
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| 204 | s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ |
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| 205 | if(((((__uint32_t)hx>>31)-1)|(yisint-1))==0) |
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| 206 | s = -one; /* (-ve)**(odd int) */ |
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| 207 | |
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| 208 | /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ |
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| 209 | GET_FLOAT_WORD(is,y); |
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| 210 | SET_FLOAT_WORD(y1,is&0xfffff000); |
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| 211 | p_l = (y-y1)*t1+y*t2; |
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| 212 | p_h = y1*t1; |
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| 213 | z = p_l+p_h; |
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| 214 | GET_FLOAT_WORD(j,z); |
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| 215 | i = j&0x7fffffff; |
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| 216 | if (j>0) { |
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| 217 | if (i>FLT_UWORD_EXP_MAX) |
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| 218 | return s*huge*huge; /* overflow */ |
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| 219 | else if (i==FLT_UWORD_EXP_MAX) |
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| 220 | if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ |
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| 221 | } else { |
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| 222 | if (i>FLT_UWORD_EXP_MIN) |
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| 223 | return s*tiny*tiny; /* underflow */ |
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| 224 | else if (i==FLT_UWORD_EXP_MIN) |
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| 225 | if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ |
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| 226 | } |
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| 227 | /* |
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| 228 | * compute 2**(p_h+p_l) |
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| 229 | */ |
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| 230 | k = (i>>23)-0x7f; |
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| 231 | n = 0; |
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| 232 | if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ |
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| 233 | n = j+(0x00800000>>(k+1)); |
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| 234 | k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ |
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| 235 | SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); |
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| 236 | n = ((n&0x007fffff)|0x00800000)>>(23-k); |
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| 237 | if(j<0) n = -n; |
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| 238 | p_h -= t; |
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| 239 | } |
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| 240 | t = p_l+p_h; |
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| 241 | GET_FLOAT_WORD(is,t); |
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| 242 | SET_FLOAT_WORD(t,is&0xfffff000); |
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| 243 | u = t*lg2_h; |
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| 244 | v = (p_l-(t-p_h))*lg2+t*lg2_l; |
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| 245 | z = u+v; |
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| 246 | w = v-(z-u); |
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| 247 | t = z*z; |
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| 248 | t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); |
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| 249 | r = (z*t1)/(t1-two)-(w+z*w); |
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| 250 | z = one-(r-z); |
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| 251 | GET_FLOAT_WORD(j,z); |
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| 252 | j += (n<<23); |
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| 253 | if((j>>23)<=0) z = scalbnf(z,(int)n); /* subnormal output */ |
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| 254 | else SET_FLOAT_WORD(z,j); |
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| 255 | return s*z; |
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| 256 | } |
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| 257 | #endif /* __OBSOLETE_MATH */ |
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