1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
|
/* e_powf.c -- float version of e_pow.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/* Copyright (C) 2017 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <math.h>
#include <math_private.h>
static const float huge = 1.0e+30, tiny = 1.0e-30;
static const float
bp[] = {1.0, 1.5,},
zero = 0.0,
one = 1.0,
two = 2.0,
two24 = 16777216.0, /* 0x4b800000 */
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 6.0000002384e-01, /* 0x3f19999a */
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
L6 = 2.0697501302e-01, /* 0x3e53f142 */
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
P2 = -2.7777778450e-03, /* 0xbb360b61 */
P3 = 6.6137559770e-05, /* 0x388ab355 */
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
P5 = 4.1381369442e-08, /* 0x3331bb4c */
ovt = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */
static const double
dp[] = { 0.0, 0x1.2b803473f7ad1p-1, }, /* log2(1.5) */
lg2 = M_LN2,
cp = 2.0/3.0/M_LN2,
invln2 = 1.0/M_LN2;
float
__ieee754_powf(float x, float y)
{
float z, ax, s;
double d1, d2;
int32_t i,j,k,yisint,n;
int32_t hx,hy,ix,iy;
GET_FLOAT_WORD(hy,y);
iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 */
if(iy==0 && !issignaling (x)) return one;
/* x==+-1 */
if(x == 1.0 && !issignaling (y)) return one;
if(x == -1.0 && isinf(y)) return one;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
/* +-NaN return x+y */
if(__builtin_expect(ix > 0x7f800000 ||
iy > 0x7f800000, 0))
return x+y;
/* special value of y */
if (__builtin_expect(iy==0x7f800000, 0)) { /* y is +-inf */
if (ix==0x3f800000)
return y - y; /* inf**+-1 is NaN */
else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3f800000) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3f000000) { /* y is 0.5 */
if(__builtin_expect(hx>=0, 1)) /* x >= +0 */
return __ieee754_sqrtf(x);
}
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if(hx<0) {
if(iy>=0x4b800000) yisint = 2; /* even integer y */
else if(iy>=0x3f800000) {
k = (iy>>23)-0x7f; /* exponent */
j = iy>>(23-k);
if((j<<(23-k))==iy) yisint = 2-(j&1);
}
}
ax = fabsf(x);
/* special value of x */
if(__builtin_expect(ix==0x7f800000||ix==0||ix==0x3f800000, 0)){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3f800000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if(yisint==1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
/* (x<0)**(non-int) is NaN */
if(__builtin_expect(((((u_int32_t)hx>>31)-1)|yisint)==0, 0))
return (x-x)/(x-x);
/* |y| is huge */
if(__builtin_expect(iy>0x4d000000, 0)) { /* if |y| > 2**27 */
/* over/underflow if x is not close to one */
if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
d2 = ax-1; /* d2 has 20 trailing zeros. */
d2 = d2 * invln2 -
(d2 * d2) * (0.5 - d2 * (0.333333333333 - d2 * 0.25)) * invln2;
} else {
/* Avoid internal underflow for tiny y. The exact value
of y does not matter if |y| <= 2**-32. */
if (iy < 0x2f800000)
SET_FLOAT_WORD (y, (hy & 0x80000000) | 0x2f800000);
n = 0;
/* take care subnormal number */
if(ix<0x00800000)
{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
n += ((ix)>>23)-0x7f;
j = ix&0x007fffff;
/* determine interval */
ix = j|0x3f800000; /* normalize ix */
if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00800000;}
SET_FLOAT_WORD(ax,ix);
/* compute d1 = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
d1 = (ax-(double)bp[k])/(ax+(double)bp[k]);
/* compute d2 = log(ax) */
d2 = d1 * d1;
d2 = 3.0 + d2 + d2*d2*(L1+d2*(L2+d2*(L3+d2*(L4+d2*(L5+d2*L6)))));
/* 2/(3log2)*(d2+...) */
d2 = d1*d2*cp;
/* log2(ax) = (d2+..)*2/(3*log2) */
d2 = d2+dp[k]+(double)n;
}
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
s = -one; /* (-ve)**(odd int) */
/* compute y * d2 */
d1 = y * d2;
z = d1;
GET_FLOAT_WORD(j,z);
if (__builtin_expect(j>0x43000000, 0)) /* if z > 128 */
return s*huge*huge; /* overflow */
else if (__builtin_expect(j==0x43000000, 0)) { /* if z == 128 */
if(ovt>(z-d1)) return s*huge*huge; /* overflow */
}
else if (__builtin_expect((j&0x7fffffff)>0x43160000, 0))/* z <= -150 */
return s*tiny*tiny; /* underflow */
else if (__builtin_expect((u_int32_t) j==0xc3160000, 0)){/* z == -150*/
if(0.0<=(z-d1)) return s*tiny*tiny; /* underflow */
}
/*
* compute 2**d1
*/
i = j&0x7fffffff;
k = (i>>23)-0x7f;
n = 0;
if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x00800000>>(k+1));
k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
SET_FLOAT_WORD(z,n&~(0x007fffff>>k));
n = ((n&0x007fffff)|0x00800000)>>(23-k);
if(j<0) n = -n;
d1 -= z;
}
d1 = d1 * lg2;
d2 = d1*d1;
d2 = d1 - d2*(P1+d2*(P2+d2*(P3+d2*(P4+d2*P5))));
d2 = (d1*d2)/(d2-two);
z = one - (d2-d1);
GET_FLOAT_WORD(j,z);
j += (n<<23);
if((j>>23)<=0) /* subnormal output */
{
z = __scalbnf (z, n);
float force_underflow = z * z;
math_force_eval (force_underflow);
}
else SET_FLOAT_WORD(z,j);
return s*z;
}
strong_alias (__ieee754_powf, __powf_finite)
|
