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 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 #pragma weak __powl = powl
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(__sparc)
38 #define i0 0
39 #define i1 1
40 #define i2 2
41 #define i3 3
42
43 static const long double zero = 0.0L, one = 1.0L, two = 2.0L;
44 extern const long double _TBL_logl_hi[], _TBL_logl_lo[];
45 static const long double two113 = 10384593717069655257060992658440192.0L,
46 ln2hi = 6.931471805599453094172319547495844850203e-0001L,
47 ln2lo = 1.667085920830552208890449330400379754169e-0025L,
48 A2 = 6.666666666666666666666666666666091393804e-0001L,
49 A3 = 4.000000000000000000000000407167070220671e-0001L,
50 A4 = 2.857142857142857142730077490612903681164e-0001L,
51 A5 = 2.222222222222242577702836920812882605099e-0001L,
52 A6 = 1.818181816435493395985912667105885828356e-0001L,
53 A7 = 1.538537835211839751112067512805496931725e-0001L,
54 B1 = 6.666666666666666666666666666666666667787e-0001L,
55 B2 = 3.999999999999999999999999999999848524411e-0001L,
56 B3 = 2.857142857142857142857142865084581075070e-0001L,
57 B4 = 2.222222222222222222222010781800643808497e-0001L,
58 B5 = 1.818181818181818185051442171337036403674e-0001L,
59 B6 = 1.538461538461508363540720286292008207673e-0001L,
60 B7 = 1.333333333506731842033180638329317108428e-0001L,
61 B8 = 1.176469984587418890634302788283946761670e-0001L,
62 B9 = 1.053794891561452331722969901564862497132e-0001L;
63
64 static long double
65 logl_x(long double x, long double *w)
66 {
67 long double f, f1, v, s, z, qn, h, t;
68 int *px = (int *)&x;
69 int *pz = (int *)&z;
70 int i, j, ix, n;
71
72 n = 0;
73 ix = px[i0];
74
75 if (ix > 0x3ffef03f && ix < 0x3fff0820) { /* 65/63 > x > 63/65 */
76 f = x - one;
77 z = f * f;
78
79 if (((ix - 0x3fff0000) | px[i1] | px[i2] | px[i3]) == 0) {
80 *w = zero;
81 return (zero); /* log(1)= +0 */
82 }
83
84 qn = one / (two + f);
85 s = f * qn; /* |s|<2**-6 */
86 v = s * s;
87 h = (long double)(2.0 * (double)s);
88 f1 = (long double)((double)f);
89 t = ((two * (f - h) - h * f1) - h * (f - f1)) * qn + s * (v *
90 (B1 + v * (B2 + v * (B3 + v * (B4 + v * (B5 + v * (B6 + v *
91 (B7 + v * (B8 + v * B9)))))))));
92 s = (long double)((double)(h + t));
93 *w = t - (s - h);
94 return (s);
95 }
96
97 if (ix < 0x00010000) { /* subnormal x */
98 x *= two113;
99 n = -113;
100 ix = px[i0];
101 }
102
103 /* LARGE_N */
104 n += ((ix + 0x200) >> 16) - 0x3fff;
105 ix = (ix & 0x0000ffff) | 0x3fff0000; /* scale x to [1,2] */
106 px[i0] = ix;
107 i = ix + 0x200;
108 pz[i0] = i & 0xfffffc00;
109 pz[i1] = pz[i2] = pz[i3] = 0;
110 qn = one / (x + z);
111 f = x - z;
112 s = f * qn;
113 f1 = (long double)((double)f);
114 h = (long double)(2.0 * (double)s);
115 t = qn * ((two * (f - z * h) - h * f1) - h * (f - f1));
116 j = (i >> 10) & 0x3f;
117 v = s * s;
118 qn = (long double)n;
119 t += qn * ln2lo + _TBL_logl_lo[j];
120 t += s * (v * (A2 + v * (A3 + v * (A4 + v * (A5 + v * (A6 + v *
121 A7))))));
122 v = qn * ln2hi + _TBL_logl_hi[j];
123 s = h + v;
124 t += (h - (s - v));
125 z = (long double)((double)(s + t));
126 *w = t - (z - s);
127 return (z);
128 }
129
130 extern const long double _TBL_expl_hi[], _TBL_expl_lo[];
131 static const long double
132 invln2_32 = 4.616624130844682903551758979206054839765e+1L,
133 ln2_32hi = 2.166084939249829091928849858592451515688e-2L,
134 ln2_32lo = 5.209643502595475652782654157501186731779e-27L,
135 ln2_64 = 1.083042469624914545964425189778400898568e-2L;
136
137 long double
138 powl(long double x, long double y)
139 {
140 long double z, ax;
141 long double y1, y2, w1, w2;
142 int sbx, sby, j, k, yisint, m;
143 int hx, lx, hy, ly, ahx, ahy;
144 int *pz = (int *)&z;
145 int *px = (int *)&x;
146 int *py = (int *)&y;
147
148 hx = px[i0];
149 lx = px[i1] | px[i2] | px[i3];
150 hy = py[i0];
151 ly = py[i1] | py[i2] | py[i3];
152 ahx = hx & ~0x80000000;
153 ahy = hy & ~0x80000000;
154
155 if ((ahy | ly) == 0)
156 return (one); /* x**+-0 = 1 */
157 else if (hx == 0x3fff0000 && lx == 0 && (__xpg6 & _C99SUSv3_pow) != 0)
158 return (one); /* C99: 1**anything = 1 */
159 else if (ahx > 0x7fff0000 || (ahx == 0x7fff0000 && lx != 0) || ahy >
160 0x7fff0000 || (ahy == 0x7fff0000 && ly != 0))
161 return (x + y); /* +-NaN return x+y */
162
163 /* includes Sun: 1**NaN = NaN */
164 sbx = (unsigned)hx >> 31;
165 sby = (unsigned)hy >> 31;
166 ax = fabsl(x);
167
168 /*
169 * determine if y is an odd int when x < 0
170 * yisint = 0 ... y is not an integer
171 * yisint = 1 ... y is an odd int
172 * yisint = 2 ... y is an even int
173 */
174 yisint = 0;
175
176 if (sbx) {
177 if (ahy >= 0x40700000) { /* if |y|>=2**113 */
178 yisint = 2; /* even integer y */
179 } else if (ahy >= 0x3fff0000) {
180 k = (ahy >> 16) - 0x3fff; /* exponent */
181
182 if (k > 80) {
183 j = ((unsigned)py[i3]) >> (112 - k);
184
185 if ((j << (112 - k)) == py[i3])
186 yisint = 2 - (j & 1);
187 } else if (k > 48) {
188 j = ((unsigned)py[i2]) >> (80 - k);
189
190 if ((j << (80 - k)) == py[i2])
191 yisint = 2 - (j & 1);
192 } else if (k > 16) {
193 j = ((unsigned)py[i1]) >> (48 - k);
194
195 if ((j << (48 - k)) == py[i1])
196 yisint = 2 - (j & 1);
197 } else if (ly == 0) {
198 j = ahy >> (16 - k);
199
200 if ((j << (16 - k)) == ahy)
201 yisint = 2 - (j & 1);
202 }
203 }
204 }
205
206 /* special value of y */
207 if (ly == 0) {
208 if (ahy == 0x7fff0000) { /* y is +-inf */
209 if (((ahx - 0x3fff0000) | lx) == 0) {
210 if ((__xpg6 & _C99SUSv3_pow) != 0)
211 return (one);
212 /* C99: (-1)**+-inf = 1 */
213 else
214 return (y - y);
215
216 /* Sun: (+-1)**+-inf = NaN */
217 } else if (ahx >= 0x3fff0000) {
218 /* (|x|>1)**+,-inf = inf,0 */
219 return (sby == 0 ? y : zero);
220 } else { /* (|x|<1)**-,+inf = inf,0 */
221 return (sby != 0 ? -y : zero);
222 }
223 } else if (ahy == 0x3fff0000) { /* y is +-1 */
224 if (sby != 0)
225 return (one / x);
226 else
227 return (x);
228 } else if (hy == 0x40000000) { /* y is 2 */
229 return (x * x);
230 } else if (hy == 0x3ffe0000) { /* y is 0.5 */
231 if (!((ahx | lx) == 0 || ((ahx - 0x7fff0000) | lx) ==
232 0))
233 return (sqrtl(x));
234 }
235 }
236
237 /* special value of x */
238 if (lx == 0) {
239 if (ahx == 0x7fff0000 || ahx == 0 || ahx == 0x3fff0000) {
240 /* x is +-0,+-inf,+-1 */
241 z = ax;
242
243 if (sby == 1)
244 z = one / z; /* z = 1/|x| if y is negative */
245
246 if (sbx == 1) {
247 if (ahx == 0x3fff0000 && yisint == 0)
248 z = zero / zero;
249 /* (-1)**non-int is NaN */
250 else if (yisint == 1)
251 z = -z; /* (x<0)**odd = -(|x|**odd) */
252 }
253
254 return (z);
255 }
256 }
257
258 /* (x<0)**(non-int) is NaN */
259 if (sbx == 1 && yisint == 0)
260 return (zero / zero); /* should be volatile */
261
262 /*
263 * Now ax is finite, y is finite
264 * first compute log(ax) = w1+w2, with 53 bits w1
265 */
266 w1 = logl_x(ax, &w2);
267
268 /* split up y into y1+y2 and compute (y1+y2)*(w1+w2) */
269 if (ly == 0 || ahy >= 0x43fe0000) {
270 y1 = y * w1;
271 y2 = y * w2;
272 } else {
273 y1 = (long double)((double)y);
274 y2 = (y - y1) * w1 + y * w2;
275 y1 *= w1;
276 }
277
278 z = y1 + y2;
279 j = pz[i0];
280
281 if ((unsigned)j >= 0xffff0000) { /* NaN or -inf */
282 if (sbx == 1 && yisint == 1)
283 return (one / z);
284 else
285 return (-one / z);
286 } else if ((j & ~0x80000000) < 0x3fc30000) { /* |x|<2^-60 */
287 if (sbx == 1 && yisint == 1)
288 return (-one - z);
289 else
290 return (one + z);
291 } else if (j > 0) {
292 if (j > 0x400d0000) {
293 if (sbx == 1 && yisint == 1)
294 return (scalbnl(-one, 20000));
295 else
296 return (scalbnl(one, 20000));
297 }
298
299 k = (int)(invln2_32 * (z + ln2_64));
300 } else {
301 if ((unsigned)j > 0xc00d0000) {
302 if (sbx == 1 && yisint == 1)
303 return (scalbnl(-one, -20000));
304 else
305 return (scalbnl(one, -20000));
306 }
307
308 k = (int)(invln2_32 * (z - ln2_64));
309 }
310
311 j = k & 0x1f;
312 m = k >> 5;
313 {
314 /* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */
315 long double t1 = 1.666666666666666666666666666660876387437e-1L,
316 t2 = -2.777777777777777777777707812093173478756e-3L,
317 t3 = 6.613756613756613482074280932874221202424e-5L,
318 t4 = -1.653439153392139954169609822742235851120e-6L,
319 t5 = 4.175314851769539751387852116610973796053e-8L;
320 long double t = (long double)k;
321
322 w1 = (y2 - (t * ln2_32hi - y1)) - t * ln2_32lo;
323 t = w1 * w1;
324 w2 = (w1 - t * (t1 + t * (t2 + t * (t3 + t * (t4 + t * t5))))) -
325 two;
326 z = _TBL_expl_hi[j] - ((_TBL_expl_hi[j] * (w1 + w1)) / w2 -
327 _TBL_expl_lo[j]);
328 }
329 j = m + (pz[i0] >> 16);
330
331 if (j && (unsigned)j < 0x7fff)
332 pz[i0] += m << 16;
333 else
334 z = scalbnl(z, m);
335
336 if (sbx == 1 && yisint == 1)
337 z = -z; /* (-ve)**(odd int) */
338
339 return (z);
340 }
341 #else
342 #error Unsupported Architecture
343 #endif /* defined(__sparc) */