1 /*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25
26 /*
27 * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __powf = powf
32
33 #include "libm.h"
34 #include "xpg6.h" /* __xpg6 */
35 #define _C99SUSv3_pow _C99SUSv3_pow_treats_Inf_as_an_even_int
36
37 #if defined(__i386) && !defined(__amd64)
38 extern int __swapRP(int);
39 #endif
40
41 static const double
42 ln2 = 6.93147180559945286227e-01, /* 0x3fe62e42, 0xfefa39ef */
43 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
44 dtwo = 2.0,
45 done = 1.0,
46 dhalf = 0.5,
47 d32 = 32.0,
48 d1_32 = 0.03125,
49 A0 = 1.999999999813723303647511146995966439250e+0000,
50 A1 = 6.666910817935858533770138657139665608610e-0001,
51 t0 = 2.000000000004777489262405315073203746943e+0000,
52 t1 = 1.666663408349926379873111932994250726307e-0001;
53
54 static const double S[] = {
55 1.00000000000000000000e+00, /* 3FF0000000000000 */
56 1.02189714865411662714e+00, /* 3FF059B0D3158574 */
57 1.04427378242741375480e+00, /* 3FF0B5586CF9890F */
58 1.06714040067682369717e+00, /* 3FF11301D0125B51 */
59 1.09050773266525768967e+00, /* 3FF172B83C7D517B */
60 1.11438674259589243221e+00, /* 3FF1D4873168B9AA */
61 1.13878863475669156458e+00, /* 3FF2387A6E756238 */
62 1.16372485877757747552e+00, /* 3FF29E9DF51FDEE1 */
63 1.18920711500272102690e+00, /* 3FF306FE0A31B715 */
64 1.21524735998046895524e+00, /* 3FF371A7373AA9CB */
65 1.24185781207348400201e+00, /* 3FF3DEA64C123422 */
66 1.26905095719173321989e+00, /* 3FF44E086061892D */
67 1.29683955465100964055e+00, /* 3FF4BFDAD5362A27 */
68 1.32523664315974132322e+00, /* 3FF5342B569D4F82 */
69 1.35425554693689265129e+00, /* 3FF5AB07DD485429 */
70 1.38390988196383202258e+00, /* 3FF6247EB03A5585 */
71 1.41421356237309514547e+00, /* 3FF6A09E667F3BCD */
72 1.44518080697704665027e+00, /* 3FF71F75E8EC5F74 */
73 1.47682614593949934623e+00, /* 3FF7A11473EB0187 */
74 1.50916442759342284141e+00, /* 3FF82589994CCE13 */
75 1.54221082540794074411e+00, /* 3FF8ACE5422AA0DB */
76 1.57598084510788649659e+00, /* 3FF93737B0CDC5E5 */
77 1.61049033194925428347e+00, /* 3FF9C49182A3F090 */
78 1.64575547815396494578e+00, /* 3FFA5503B23E255D */
79 1.68179283050742900407e+00, /* 3FFAE89F995AD3AD */
80 1.71861929812247793414e+00, /* 3FFB7F76F2FB5E47 */
81 1.75625216037329945351e+00, /* 3FFC199BDD85529C */
82 1.79470907500310716820e+00, /* 3FFCB720DCEF9069 */
83 1.83400808640934243066e+00, /* 3FFD5818DCFBA487 */
84 1.87416763411029996256e+00, /* 3FFDFC97337B9B5F */
85 1.91520656139714740007e+00, /* 3FFEA4AFA2A490DA */
86 1.95714412417540017941e+00, /* 3FFF50765B6E4540 */
87 };
88
89 static const double TBL[] = {
90 0.00000000000000000e+00, 3.07716586667536873e-02,
91 6.06246218164348399e-02, 8.96121586896871380e-02,
92 1.17783035656383456e-01, 1.45182009844497889e-01,
93 1.71850256926659228e-01, 1.97825743329919868e-01,
94 2.23143551314209765e-01, 2.47836163904581269e-01,
95 2.71933715483641758e-01, 2.95464212893835898e-01,
96 3.18453731118534589e-01, 3.40926586970593193e-01,
97 3.62905493689368475e-01, 3.84411698910332056e-01,
98 4.05465108108164385e-01, 4.26084395310900088e-01,
99 4.46287102628419530e-01, 4.66089729924599239e-01,
100 4.85507815781700824e-01, 5.04556010752395312e-01,
101 5.23248143764547868e-01, 5.41597282432744409e-01,
102 5.59615787935422659e-01, 5.77315365034823613e-01,
103 5.94707107746692776e-01, 6.11801541105992941e-01,
104 6.28608659422374094e-01, 6.45137961373584701e-01,
105 6.61398482245365016e-01, 6.77398823591806143e-01,
106 };
107
108 static const float zero = 0.0F, one = 1.0F, huge = 1.0e25f, tiny = 1.0e-25f;
109
110
111 float
112 powf(float x, float y)
113 {
114 float fx = x, fy = y;
115 float fz;
116 int ix, iy, jx, jy, k, iw, yisint;
117
118 ix = *(int *)&x;
119 iy = *(int *)&y;
120 jx = ix & ~0x80000000;
121 jy = iy & ~0x80000000;
122
123 if (jy == 0)
124 return (one); /* x**+-0 = 1 */
125 else if (ix == 0x3f800000 && (__xpg6 & _C99SUSv3_pow) != 0)
126 return (one); /* C99: 1**anything = 1 */
127 else if (((0x7f800000 - jx) | (0x7f800000 - jy)) < 0)
128 return (fx * fy); /* at least one of x or y is NaN */
129
130 /*
131 * includes Sun: 1**NaN = NaN
132 */
133
134 /*
135 * determine if y is an odd int
136 * yisint = 0 ... y is not an integer
137 * yisint = 1 ... y is an odd int
138 * yisint = 2 ... y is an even int
139 */
140 yisint = 0;
141
142 if (ix < 0) {
143 if (jy >= 0x4b800000) {
144 yisint = 2; /* |y|>=2**24: y must be even */
145 } else if (jy >= 0x3f800000) {
146 k = (jy >> 23) - 0x7f; /* exponent */
147 iw = jy >> (23 - k);
148
149 if ((iw << (23 - k)) == jy)
150 yisint = 2 - (iw & 1);
151 }
152 }
153
154 /* special value of y */
155 if ((jy & ~0x7f800000) == 0) {
156 if (jy == 0x7f800000) { /* y is +-inf */
157 if (jx == 0x3f800000) {
158 if ((__xpg6 & _C99SUSv3_pow) != 0)
159 fz = one;
160 /* C99: (-1)**+-inf is 1 */
161 else
162 fz = fy - fy;
163
164 /* Sun: (+-1)**+-inf = NaN */
165 } else if (jx > 0x3f800000) {
166 /* (|x|>1)**+,-inf = inf,0 */
167 if (iy > 0)
168 fz = fy;
169 else
170 fz = zero;
171 } else { /* (|x|<1)**-,+inf = inf,0 */
172 if (iy < 0)
173 fz = -fy;
174 else
175 fz = zero;
176 }
177
178 return (fz);
179 } else if (jy == 0x3f800000) { /* y is +-1 */
180 if (iy < 0)
181 fx = one / fx; /* y is -1 */
182
183 return (fx);
184 } else if (iy == 0x40000000) { /* y is 2 */
185 return (fx * fx);
186 } else if (iy == 0x3f000000) { /* y is 0.5 */
187 if (jx != 0 && jx != 0x7f800000)
188 return (sqrtf(x));
189 }
190 }
191
192 /* special value of x */
193 if ((jx & ~0x7f800000) == 0) {
194 if (jx == 0x7f800000 || jx == 0 || jx == 0x3f800000) {
195 /* x is +-0,+-inf,-1; set fz = |x|**y */
196 *(int *)&fz = jx;
197
198 if (iy < 0)
199 fz = one / fz;
200
201 if (ix < 0) {
202 if (jx == 0x3f800000 && yisint == 0) {
203 /* (-1)**non-int is NaN */
204 fz = zero;
205 fz /= fz;
206 } else if (yisint == 1) {
207 /* (x<0)**odd = -(|x|**odd) */
208 fz = -fz;
209 }
210 }
211
212 return (fz);
213 }
214 }
215
216 /* (x<0)**(non-int) is NaN */
217 if (ix < 0 && yisint == 0) {
218 fz = zero;
219 return (fz / fz);
220 }
221
222 /*
223 * compute exp(y*log(|x|))
224 * fx = *(float *) &jx;
225 * fz = (float) exp(((double) fy) * log((double) fx));
226 */
227 {
228 double dx, dy, dz, ds;
229 int *px = (int *)&dx, *pz = (int *)&dz, i, n, m;
230
231 #if defined(__i386) && !defined(__amd64)
232 int rp = __swapRP(fp_extended);
233 #endif
234
235 fx = *(float *)&jx;
236 dx = (double)fx;
237
238 /* compute log(x)/ln2 */
239 i = px[HIWORD] + 0x4000;
240 n = (i >> 20) - 0x3ff;
241 pz[HIWORD] = i & 0xffff8000;
242 pz[LOWORD] = 0;
243 ds = (dx - dz) / (dx + dz);
244 i = (i >> 15) & 0x1f;
245 dz = ds * ds;
246 dy = invln2 * (TBL[i] + ds * (A0 + dz * A1));
247
248 if (n == 0)
249 dz = (double)fy * dy;
250 else
251 dz = (double)fy * (dy + (double)n);
252
253 /* compute exp2(dz=y*ln(x)) */
254 i = pz[HIWORD];
255
256 if ((i & ~0x80000000) >= 0x40640000) { /* |z| >= 160.0 */
257 fz = (i > 0) ? huge : tiny;
258
259 if (ix < 0 && yisint == 1)
260 fz *= -fz; /* (-ve)**(odd int) */
261 else
262 fz *= fz;
263
264 #if defined(__i386) && !defined(__amd64)
265 if (rp != fp_extended)
266 (void) __swapRP(rp);
267 #endif
268 return (fz);
269 }
270
271 n = (int)(d32 * dz + (i > 0 ? dhalf : -dhalf));
272 i = n & 0x1f;
273 m = n >> 5;
274 dy = ln2 * (dz - d1_32 * (double)n);
275 dx = S[i] * (done - (dtwo * dy) / (dy * (done - dy * t1) - t0));
276
277 if (m != 0)
278 px[HIWORD] += m << 20;
279
280 fz = (float)dx;
281 #if defined(__i386) && !defined(__amd64)
282 if (rp != fp_extended)
283 (void) __swapRP(rp);
284 #endif
285 }
286
287 /* end of computing exp(y*log(x)) */
288 if (ix < 0 && yisint == 1)
289 fz = -fz; /* (-ve)**(odd int) */
290
291 return (fz);
292 }