source: azure_iot_hub/trunk/musl-1.1.18/src/math/powf.c@ 389

Last change on this file since 389 was 389, checked in by coas-nagasima, 5 years ago

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1/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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 "libm.h"
17
18static const float
19bp[] = {1.0, 1.5,},
20dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
21dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
22two24 = 16777216.0, /* 0x4b800000 */
23huge = 1.0e30,
24tiny = 1.0e-30,
25/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
26L1 = 6.0000002384e-01, /* 0x3f19999a */
27L2 = 4.2857143283e-01, /* 0x3edb6db7 */
28L3 = 3.3333334327e-01, /* 0x3eaaaaab */
29L4 = 2.7272811532e-01, /* 0x3e8ba305 */
30L5 = 2.3066075146e-01, /* 0x3e6c3255 */
31L6 = 2.0697501302e-01, /* 0x3e53f142 */
32P1 = 1.6666667163e-01, /* 0x3e2aaaab */
33P2 = -2.7777778450e-03, /* 0xbb360b61 */
34P3 = 6.6137559770e-05, /* 0x388ab355 */
35P4 = -1.6533901999e-06, /* 0xb5ddea0e */
36P5 = 4.1381369442e-08, /* 0x3331bb4c */
37lg2 = 6.9314718246e-01, /* 0x3f317218 */
38lg2_h = 6.93145752e-01, /* 0x3f317200 */
39lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
40ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
41cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
42cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */
43cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */
44ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
45ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
46ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
47
48float powf(float x, float y)
49{
50 float z,ax,z_h,z_l,p_h,p_l;
51 float y1,t1,t2,r,s,sn,t,u,v,w;
52 int32_t i,j,k,yisint,n;
53 int32_t hx,hy,ix,iy,is;
54
55 GET_FLOAT_WORD(hx, x);
56 GET_FLOAT_WORD(hy, y);
57 ix = hx & 0x7fffffff;
58 iy = hy & 0x7fffffff;
59
60 /* x**0 = 1, even if x is NaN */
61 if (iy == 0)
62 return 1.0f;
63 /* 1**y = 1, even if y is NaN */
64 if (hx == 0x3f800000)
65 return 1.0f;
66 /* NaN if either arg is NaN */
67 if (ix > 0x7f800000 || iy > 0x7f800000)
68 return x + y;
69
70 /* determine if y is an odd int when x < 0
71 * yisint = 0 ... y is not an integer
72 * yisint = 1 ... y is an odd int
73 * yisint = 2 ... y is an even int
74 */
75 yisint = 0;
76 if (hx < 0) {
77 if (iy >= 0x4b800000)
78 yisint = 2; /* even integer y */
79 else if (iy >= 0x3f800000) {
80 k = (iy>>23) - 0x7f; /* exponent */
81 j = iy>>(23-k);
82 if ((j<<(23-k)) == iy)
83 yisint = 2 - (j & 1);
84 }
85 }
86
87 /* special value of y */
88 if (iy == 0x7f800000) { /* y is +-inf */
89 if (ix == 0x3f800000) /* (-1)**+-inf is 1 */
90 return 1.0f;
91 else if (ix > 0x3f800000) /* (|x|>1)**+-inf = inf,0 */
92 return hy >= 0 ? y : 0.0f;
93 else /* (|x|<1)**+-inf = 0,inf */
94 return hy >= 0 ? 0.0f: -y;
95 }
96 if (iy == 0x3f800000) /* y is +-1 */
97 return hy >= 0 ? x : 1.0f/x;
98 if (hy == 0x40000000) /* y is 2 */
99 return x*x;
100 if (hy == 0x3f000000) { /* y is 0.5 */
101 if (hx >= 0) /* x >= +0 */
102 return sqrtf(x);
103 }
104
105 ax = fabsf(x);
106 /* special value of x */
107 if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
108 z = ax;
109 if (hy < 0) /* z = (1/|x|) */
110 z = 1.0f/z;
111 if (hx < 0) {
112 if (((ix-0x3f800000)|yisint) == 0) {
113 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
114 } else if (yisint == 1)
115 z = -z; /* (x<0)**odd = -(|x|**odd) */
116 }
117 return z;
118 }
119
120 sn = 1.0f; /* sign of result */
121 if (hx < 0) {
122 if (yisint == 0) /* (x<0)**(non-int) is NaN */
123 return (x-x)/(x-x);
124 if (yisint == 1) /* (x<0)**(odd int) */
125 sn = -1.0f;
126 }
127
128 /* |y| is huge */
129 if (iy > 0x4d000000) { /* if |y| > 2**27 */
130 /* over/underflow if x is not close to one */
131 if (ix < 0x3f7ffff8)
132 return hy < 0 ? sn*huge*huge : sn*tiny*tiny;
133 if (ix > 0x3f800007)
134 return hy > 0 ? sn*huge*huge : sn*tiny*tiny;
135 /* now |1-x| is tiny <= 2**-20, suffice to compute
136 log(x) by x-x^2/2+x^3/3-x^4/4 */
137 t = ax - 1; /* t has 20 trailing zeros */
138 w = (t*t)*(0.5f - t*(0.333333333333f - t*0.25f));
139 u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
140 v = t*ivln2_l - w*ivln2;
141 t1 = u + v;
142 GET_FLOAT_WORD(is, t1);
143 SET_FLOAT_WORD(t1, is & 0xfffff000);
144 t2 = v - (t1-u);
145 } else {
146 float s2,s_h,s_l,t_h,t_l;
147 n = 0;
148 /* take care subnormal number */
149 if (ix < 0x00800000) {
150 ax *= two24;
151 n -= 24;
152 GET_FLOAT_WORD(ix, ax);
153 }
154 n += ((ix)>>23) - 0x7f;
155 j = ix & 0x007fffff;
156 /* determine interval */
157 ix = j | 0x3f800000; /* normalize ix */
158 if (j <= 0x1cc471) /* |x|<sqrt(3/2) */
159 k = 0;
160 else if (j < 0x5db3d7) /* |x|<sqrt(3) */
161 k = 1;
162 else {
163 k = 0;
164 n += 1;
165 ix -= 0x00800000;
166 }
167 SET_FLOAT_WORD(ax, ix);
168
169 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
170 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
171 v = 1.0f/(ax+bp[k]);
172 s = u*v;
173 s_h = s;
174 GET_FLOAT_WORD(is, s_h);
175 SET_FLOAT_WORD(s_h, is & 0xfffff000);
176 /* t_h=ax+bp[k] High */
177 is = ((ix>>1) & 0xfffff000) | 0x20000000;
178 SET_FLOAT_WORD(t_h, is + 0x00400000 + (k<<21));
179 t_l = ax - (t_h - bp[k]);
180 s_l = v*((u - s_h*t_h) - s_h*t_l);
181 /* compute log(ax) */
182 s2 = s*s;
183 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
184 r += s_l*(s_h+s);
185 s2 = s_h*s_h;
186 t_h = 3.0f + s2 + r;
187 GET_FLOAT_WORD(is, t_h);
188 SET_FLOAT_WORD(t_h, is & 0xfffff000);
189 t_l = r - ((t_h - 3.0f) - s2);
190 /* u+v = s*(1+...) */
191 u = s_h*t_h;
192 v = s_l*t_h + t_l*s;
193 /* 2/(3log2)*(s+...) */
194 p_h = u + v;
195 GET_FLOAT_WORD(is, p_h);
196 SET_FLOAT_WORD(p_h, is & 0xfffff000);
197 p_l = v - (p_h - u);
198 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
199 z_l = cp_l*p_h + p_l*cp+dp_l[k];
200 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
201 t = (float)n;
202 t1 = (((z_h + z_l) + dp_h[k]) + t);
203 GET_FLOAT_WORD(is, t1);
204 SET_FLOAT_WORD(t1, is & 0xfffff000);
205 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
206 }
207
208 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
209 GET_FLOAT_WORD(is, y);
210 SET_FLOAT_WORD(y1, is & 0xfffff000);
211 p_l = (y-y1)*t1 + y*t2;
212 p_h = y1*t1;
213 z = p_l + p_h;
214 GET_FLOAT_WORD(j, z);
215 if (j > 0x43000000) /* if z > 128 */
216 return sn*huge*huge; /* overflow */
217 else if (j == 0x43000000) { /* if z == 128 */
218 if (p_l + ovt > z - p_h)
219 return sn*huge*huge; /* overflow */
220 } else if ((j&0x7fffffff) > 0x43160000) /* z < -150 */ // FIXME: check should be (uint32_t)j > 0xc3160000
221 return sn*tiny*tiny; /* underflow */
222 else if (j == 0xc3160000) { /* z == -150 */
223 if (p_l <= z-p_h)
224 return sn*tiny*tiny; /* underflow */
225 }
226 /*
227 * compute 2**(p_h+p_l)
228 */
229 i = j & 0x7fffffff;
230 k = (i>>23) - 0x7f;
231 n = 0;
232 if (i > 0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
233 n = j + (0x00800000>>(k+1));
234 k = ((n&0x7fffffff)>>23) - 0x7f; /* new k for n */
235 SET_FLOAT_WORD(t, n & ~(0x007fffff>>k));
236 n = ((n&0x007fffff)|0x00800000)>>(23-k);
237 if (j < 0)
238 n = -n;
239 p_h -= t;
240 }
241 t = p_l + p_h;
242 GET_FLOAT_WORD(is, t);
243 SET_FLOAT_WORD(t, is & 0xffff8000);
244 u = t*lg2_h;
245 v = (p_l-(t-p_h))*lg2 + t*lg2_l;
246 z = u + v;
247 w = v - (z - u);
248 t = z*z;
249 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
250 r = (z*t1)/(t1-2.0f) - (w+z*w);
251 z = 1.0f - (r - z);
252 GET_FLOAT_WORD(j, z);
253 j += n<<23;
254 if ((j>>23) <= 0) /* subnormal output */
255 z = scalbnf(z, n);
256 else
257 SET_FLOAT_WORD(z, j);
258 return sn*z;
259}
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