| 1 |
39 |
lampret |
/* ef_pow.c -- float version of e_pow.c.
|
| 2 |
|
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
| 3 |
|
|
*/
|
| 4 |
|
|
|
| 5 |
|
|
/*
|
| 6 |
|
|
* ====================================================
|
| 7 |
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
| 8 |
|
|
*
|
| 9 |
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
| 10 |
|
|
* Permission to use, copy, modify, and distribute this
|
| 11 |
|
|
* software is freely granted, provided that this notice
|
| 12 |
|
|
* is preserved.
|
| 13 |
|
|
* ====================================================
|
| 14 |
|
|
*/
|
| 15 |
|
|
|
| 16 |
|
|
#include "fdlibm.h"
|
| 17 |
|
|
|
| 18 |
|
|
#ifdef __v810__
|
| 19 |
|
|
#define const
|
| 20 |
|
|
#endif
|
| 21 |
|
|
|
| 22 |
|
|
#ifdef __STDC__
|
| 23 |
|
|
static const float
|
| 24 |
|
|
#else
|
| 25 |
|
|
static float
|
| 26 |
|
|
#endif
|
| 27 |
|
|
bp[] = {1.0, 1.5,},
|
| 28 |
|
|
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
|
| 29 |
|
|
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
|
| 30 |
|
|
zero = 0.0,
|
| 31 |
|
|
one = 1.0,
|
| 32 |
|
|
two = 2.0,
|
| 33 |
|
|
two24 = 16777216.0, /* 0x4b800000 */
|
| 34 |
|
|
huge = 1.0e30,
|
| 35 |
|
|
tiny = 1.0e-30,
|
| 36 |
|
|
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
| 37 |
|
|
L1 = 6.0000002384e-01, /* 0x3f19999a */
|
| 38 |
|
|
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
|
| 39 |
|
|
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
|
| 40 |
|
|
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
|
| 41 |
|
|
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
|
| 42 |
|
|
L6 = 2.0697501302e-01, /* 0x3e53f142 */
|
| 43 |
|
|
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
|
| 44 |
|
|
P2 = -2.7777778450e-03, /* 0xbb360b61 */
|
| 45 |
|
|
P3 = 6.6137559770e-05, /* 0x388ab355 */
|
| 46 |
|
|
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
|
| 47 |
|
|
P5 = 4.1381369442e-08, /* 0x3331bb4c */
|
| 48 |
|
|
lg2 = 6.9314718246e-01, /* 0x3f317218 */
|
| 49 |
|
|
lg2_h = 6.93145752e-01, /* 0x3f317200 */
|
| 50 |
|
|
lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
|
| 51 |
|
|
ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
|
| 52 |
|
|
cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
|
| 53 |
|
|
cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
|
| 54 |
|
|
cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
|
| 55 |
|
|
ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
|
| 56 |
|
|
ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
|
| 57 |
|
|
ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
|
| 58 |
|
|
|
| 59 |
|
|
#ifdef __STDC__
|
| 60 |
|
|
float __ieee754_powf(float x, float y)
|
| 61 |
|
|
#else
|
| 62 |
|
|
float __ieee754_powf(x,y)
|
| 63 |
|
|
float x, y;
|
| 64 |
|
|
#endif
|
| 65 |
|
|
{
|
| 66 |
|
|
float z,ax,z_h,z_l,p_h,p_l;
|
| 67 |
|
|
float y1,t1,t2,r,s,t,u,v,w;
|
| 68 |
|
|
__int32_t i,j,k,yisint,n;
|
| 69 |
|
|
__int32_t hx,hy,ix,iy,is;
|
| 70 |
|
|
|
| 71 |
|
|
GET_FLOAT_WORD(hx,x);
|
| 72 |
|
|
GET_FLOAT_WORD(hy,y);
|
| 73 |
|
|
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
|
| 74 |
|
|
|
| 75 |
|
|
/* y==zero: x**0 = 1 */
|
| 76 |
|
|
if(iy==0) return one;
|
| 77 |
|
|
|
| 78 |
|
|
/* +-NaN return x+y */
|
| 79 |
|
|
if(ix > 0x7f800000 ||
|
| 80 |
|
|
iy > 0x7f800000)
|
| 81 |
|
|
return x+y;
|
| 82 |
|
|
|
| 83 |
|
|
/* determine if y is an odd int when x < 0
|
| 84 |
|
|
* yisint = 0 ... y is not an integer
|
| 85 |
|
|
* yisint = 1 ... y is an odd int
|
| 86 |
|
|
* yisint = 2 ... y is an even int
|
| 87 |
|
|
*/
|
| 88 |
|
|
yisint = 0;
|
| 89 |
|
|
if(hx<0) {
|
| 90 |
|
|
if(iy>=0x4b800000) yisint = 2; /* even integer y */
|
| 91 |
|
|
else if(iy>=0x3f800000) {
|
| 92 |
|
|
k = (iy>>23)-0x7f; /* exponent */
|
| 93 |
|
|
j = iy>>(23-k);
|
| 94 |
|
|
if((j<<(23-k))==iy) yisint = 2-(j&1);
|
| 95 |
|
|
}
|
| 96 |
|
|
}
|
| 97 |
|
|
|
| 98 |
|
|
/* special value of y */
|
| 99 |
|
|
if (iy==0x7f800000) { /* y is +-inf */
|
| 100 |
|
|
if (ix==0x3f800000)
|
| 101 |
|
|
return y - y; /* inf**+-1 is NaN */
|
| 102 |
|
|
else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
|
| 103 |
|
|
return (hy>=0)? y: zero;
|
| 104 |
|
|
else /* (|x|<1)**-,+inf = inf,0 */
|
| 105 |
|
|
return (hy<0)?-y: zero;
|
| 106 |
|
|
}
|
| 107 |
|
|
if(iy==0x3f800000) { /* y is +-1 */
|
| 108 |
|
|
if(hy<0) return one/x; else return x;
|
| 109 |
|
|
}
|
| 110 |
|
|
if(hy==0x40000000) return x*x; /* y is 2 */
|
| 111 |
|
|
if(hy==0x3f000000) { /* y is 0.5 */
|
| 112 |
|
|
if(hx>=0) /* x >= +0 */
|
| 113 |
|
|
return __ieee754_sqrtf(x);
|
| 114 |
|
|
}
|
| 115 |
|
|
|
| 116 |
|
|
ax = fabsf(x);
|
| 117 |
|
|
/* special value of x */
|
| 118 |
|
|
if(ix==0x7f800000||ix==0||ix==0x3f800000){
|
| 119 |
|
|
z = ax; /*x is +-0,+-inf,+-1*/
|
| 120 |
|
|
if(hy<0) z = one/z; /* z = (1/|x|) */
|
| 121 |
|
|
if(hx<0) {
|
| 122 |
|
|
if(((ix-0x3f800000)|yisint)==0) {
|
| 123 |
|
|
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
|
| 124 |
|
|
} else if(yisint==1)
|
| 125 |
|
|
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
| 126 |
|
|
}
|
| 127 |
|
|
return z;
|
| 128 |
|
|
}
|
| 129 |
|
|
|
| 130 |
|
|
/* (x<0)**(non-int) is NaN */
|
| 131 |
|
|
if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
|
| 132 |
|
|
|
| 133 |
|
|
/* |y| is huge */
|
| 134 |
|
|
if(iy>0x4d000000) { /* if |y| > 2**27 */
|
| 135 |
|
|
/* over/underflow if x is not close to one */
|
| 136 |
|
|
if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
|
| 137 |
|
|
if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
|
| 138 |
|
|
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
| 139 |
|
|
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
| 140 |
|
|
t = x-1; /* t has 20 trailing zeros */
|
| 141 |
|
|
w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
|
| 142 |
|
|
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
|
| 143 |
|
|
v = t*ivln2_l-w*ivln2;
|
| 144 |
|
|
t1 = u+v;
|
| 145 |
|
|
GET_FLOAT_WORD(is,t1);
|
| 146 |
|
|
SET_FLOAT_WORD(t1,is&0xfffff000);
|
| 147 |
|
|
t2 = v-(t1-u);
|
| 148 |
|
|
} else {
|
| 149 |
|
|
float s2,s_h,s_l,t_h,t_l;
|
| 150 |
|
|
n = 0;
|
| 151 |
|
|
/* take care subnormal number */
|
| 152 |
|
|
if(ix<0x00800000)
|
| 153 |
|
|
{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
|
| 154 |
|
|
n += ((ix)>>23)-0x7f;
|
| 155 |
|
|
j = ix&0x007fffff;
|
| 156 |
|
|
/* determine interval */
|
| 157 |
|
|
ix = j|0x3f800000; /* normalize ix */
|
| 158 |
|
|
if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
|
| 159 |
|
|
else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
|
| 160 |
|
|
else {k=0;n+=1;ix -= 0x00800000;}
|
| 161 |
|
|
SET_FLOAT_WORD(ax,ix);
|
| 162 |
|
|
|
| 163 |
|
|
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
| 164 |
|
|
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
| 165 |
|
|
v = one/(ax+bp[k]);
|
| 166 |
|
|
s = u*v;
|
| 167 |
|
|
s_h = s;
|
| 168 |
|
|
GET_FLOAT_WORD(is,s_h);
|
| 169 |
|
|
SET_FLOAT_WORD(s_h,is&0xfffff000);
|
| 170 |
|
|
/* t_h=ax+bp[k] High */
|
| 171 |
|
|
SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
|
| 172 |
|
|
t_l = ax - (t_h-bp[k]);
|
| 173 |
|
|
s_l = v*((u-s_h*t_h)-s_h*t_l);
|
| 174 |
|
|
/* compute log(ax) */
|
| 175 |
|
|
s2 = s*s;
|
| 176 |
|
|
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
|
| 177 |
|
|
r += s_l*(s_h+s);
|
| 178 |
|
|
s2 = s_h*s_h;
|
| 179 |
|
|
t_h = (float)3.0+s2+r;
|
| 180 |
|
|
GET_FLOAT_WORD(is,t_h);
|
| 181 |
|
|
SET_FLOAT_WORD(t_h,is&0xfffff000);
|
| 182 |
|
|
t_l = r-((t_h-(float)3.0)-s2);
|
| 183 |
|
|
/* u+v = s*(1+...) */
|
| 184 |
|
|
u = s_h*t_h;
|
| 185 |
|
|
v = s_l*t_h+t_l*s;
|
| 186 |
|
|
/* 2/(3log2)*(s+...) */
|
| 187 |
|
|
p_h = u+v;
|
| 188 |
|
|
GET_FLOAT_WORD(is,p_h);
|
| 189 |
|
|
SET_FLOAT_WORD(p_h,is&0xfffff000);
|
| 190 |
|
|
p_l = v-(p_h-u);
|
| 191 |
|
|
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
|
| 192 |
|
|
z_l = cp_l*p_h+p_l*cp+dp_l[k];
|
| 193 |
|
|
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
| 194 |
|
|
t = (float)n;
|
| 195 |
|
|
t1 = (((z_h+z_l)+dp_h[k])+t);
|
| 196 |
|
|
GET_FLOAT_WORD(is,t1);
|
| 197 |
|
|
SET_FLOAT_WORD(t1,is&0xfffff000);
|
| 198 |
|
|
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
|
| 199 |
|
|
}
|
| 200 |
|
|
|
| 201 |
|
|
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
| 202 |
|
|
if(((((__uint32_t)hx>>31)-1)|(yisint-1))==0)
|
| 203 |
|
|
s = -one; /* (-ve)**(odd int) */
|
| 204 |
|
|
|
| 205 |
|
|
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
| 206 |
|
|
GET_FLOAT_WORD(is,y);
|
| 207 |
|
|
SET_FLOAT_WORD(y1,is&0xfffff000);
|
| 208 |
|
|
p_l = (y-y1)*t1+y*t2;
|
| 209 |
|
|
p_h = y1*t1;
|
| 210 |
|
|
z = p_l+p_h;
|
| 211 |
|
|
GET_FLOAT_WORD(j,z);
|
| 212 |
|
|
if (j>0x43000000) /* if z > 128 */
|
| 213 |
|
|
return s*huge*huge; /* overflow */
|
| 214 |
|
|
else if (j==0x43000000) { /* if z == 128 */
|
| 215 |
|
|
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
|
| 216 |
|
|
}
|
| 217 |
|
|
else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
|
| 218 |
|
|
return s*tiny*tiny; /* underflow */
|
| 219 |
|
|
else if (j==0xc3160000){ /* z == -150 */
|
| 220 |
|
|
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
|
| 221 |
|
|
}
|
| 222 |
|
|
/*
|
| 223 |
|
|
* compute 2**(p_h+p_l)
|
| 224 |
|
|
*/
|
| 225 |
|
|
i = j&0x7fffffff;
|
| 226 |
|
|
k = (i>>23)-0x7f;
|
| 227 |
|
|
n = 0;
|
| 228 |
|
|
if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
|
| 229 |
|
|
n = j+(0x00800000>>(k+1));
|
| 230 |
|
|
k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
|
| 231 |
|
|
SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
|
| 232 |
|
|
n = ((n&0x007fffff)|0x00800000)>>(23-k);
|
| 233 |
|
|
if(j<0) n = -n;
|
| 234 |
|
|
p_h -= t;
|
| 235 |
|
|
}
|
| 236 |
|
|
t = p_l+p_h;
|
| 237 |
|
|
GET_FLOAT_WORD(is,t);
|
| 238 |
|
|
SET_FLOAT_WORD(t,is&0xfffff000);
|
| 239 |
|
|
u = t*lg2_h;
|
| 240 |
|
|
v = (p_l-(t-p_h))*lg2+t*lg2_l;
|
| 241 |
|
|
z = u+v;
|
| 242 |
|
|
w = v-(z-u);
|
| 243 |
|
|
t = z*z;
|
| 244 |
|
|
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
| 245 |
|
|
r = (z*t1)/(t1-two)-(w+z*w);
|
| 246 |
|
|
z = one-(r-z);
|
| 247 |
|
|
GET_FLOAT_WORD(j,z);
|
| 248 |
|
|
j += (n<<23);
|
| 249 |
|
|
if((j>>23)<=0) z = scalbnf(z,(int)n); /* subnormal output */
|
| 250 |
|
|
else SET_FLOAT_WORD(z,j);
|
| 251 |
|
|
return s*z;
|
| 252 |
|
|
}
|
