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