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 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #if defined(ELFOBJ)
31 #pragma weak powl = __powl
32 #endif
33
34 #include "libm.h"
35 #include "xpg6.h" /* __xpg6 */
36 #define _C99SUSv3_pow _C99SUSv3_pow_treats_Inf_as_an_even_int
37
38 #if defined(__sparc)
39 #define i0 0
40 #define i1 1
41 #define i2 2
42 #define i3 3
43
44 static const long double zero = 0.0L, one = 1.0L, two = 2.0L;
45
46 extern const long double _TBL_logl_hi[], _TBL_logl_lo[];
47
48 static const long double
49 two113 = 10384593717069655257060992658440192.0L,
50 ln2hi = 6.931471805599453094172319547495844850203e-0001L,
51 ln2lo = 1.667085920830552208890449330400379754169e-0025L,
52 A2 = 6.666666666666666666666666666666091393804e-0001L,
53 A3 = 4.000000000000000000000000407167070220671e-0001L,
54 A4 = 2.857142857142857142730077490612903681164e-0001L,
55 A5 = 2.222222222222242577702836920812882605099e-0001L,
56 A6 = 1.818181816435493395985912667105885828356e-0001L,
57 A7 = 1.538537835211839751112067512805496931725e-0001L,
58 B1 = 6.666666666666666666666666666666666667787e-0001L,
59 B2 = 3.999999999999999999999999999999848524411e-0001L,
60 B3 = 2.857142857142857142857142865084581075070e-0001L,
61 B4 = 2.222222222222222222222010781800643808497e-0001L,
62 B5 = 1.818181818181818185051442171337036403674e-0001L,
63 B6 = 1.538461538461508363540720286292008207673e-0001L,
64 B7 = 1.333333333506731842033180638329317108428e-0001L,
65 B8 = 1.176469984587418890634302788283946761670e-0001L,
66 B9 = 1.053794891561452331722969901564862497132e-0001L;
67
68 static long double
69 logl_x(long double x, long double *w) {
70 long double f, f1, v, s, z, qn, h, t;
71 int *px = (int *) &x;
72 int *pz = (int *) &z;
73 int i, j, ix, n;
74
75 n = 0;
76 ix = px[i0];
77 if (ix > 0x3ffef03f && ix < 0x3fff0820) { /* 65/63 > x > 63/65 */
78 f = x - one;
79 z = f * f;
80 if (((ix - 0x3fff0000) | px[i1] | px[i2] | px[i3]) == 0) {
81 *w = zero;
82 return (zero); /* log(1)= +0 */
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 +
90 s * (v * (B1 + v * (B2 + v * (B3 + v * (B4 +
91 v * (B5 + v * (B6 + v * (B7 + v * (B8 + v * B9)))))))));
92 s = (long double) ((double) (h + t));
93 *w = t - (s - h);
94 return (s);
95 }
96 if (ix < 0x00010000) { /* subnormal x */
97 x *= two113;
98 n = -113;
99 ix = px[i0];
100 }
101 /* LARGE_N */
102 n += ((ix + 0x200) >> 16) - 0x3fff;
103 ix = (ix & 0x0000ffff) | 0x3fff0000; /* scale x to [1,2] */
104 px[i0] = ix;
105 i = ix + 0x200;
106 pz[i0] = i & 0xfffffc00;
107 pz[i1] = pz[i2] = pz[i3] = 0;
108 qn = one / (x + z);
109 f = x - z;
110 s = f * qn;
111 f1 = (long double) ((double) f);
112 h = (long double) (2.0 * (double) s);
113 t = qn * ((two * (f - z * h) - h * f1) - h * (f - f1));
114 j = (i >> 10) & 0x3f;
115 v = s * s;
116 qn = (long double) n;
117 t += qn * ln2lo + _TBL_logl_lo[j];
118 t += s * (v * (A2 + v * (A3 + v * (A4 + v * (A5 + v * (A6 +
119 v * A7))))));
120 v = qn * ln2hi + _TBL_logl_hi[j];
121 s = h + v;
122 t += (h - (s - v));
123 z = (long double) ((double) (s + t));
124 *w = t - (z - s);
125 return (z);
126 }
127
128 extern const long double _TBL_expl_hi[], _TBL_expl_lo[];
129 static const long double
130 invln2_32 = 4.616624130844682903551758979206054839765e+1L,
131 ln2_32hi = 2.166084939249829091928849858592451515688e-2L,
132 ln2_32lo = 5.209643502595475652782654157501186731779e-27L,
133 ln2_64 = 1.083042469624914545964425189778400898568e-2L;
134
135 long double
136 powl(long double x, long double y) {
137 long double z, ax;
138 long double y1, y2, w1, w2;
139 int sbx, sby, j, k, yisint, m;
140 int hx, lx, hy, ly, ahx, ahy;
141 int *pz = (int *) &z;
142 int *px = (int *) &x;
143 int *py = (int *) &y;
144
145 hx = px[i0];
146 lx = px[i1] | px[i2] | px[i3];
147 hy = py[i0];
148 ly = py[i1] | py[i2] | py[i3];
149 ahx = hx & ~0x80000000;
150 ahy = hy & ~0x80000000;
151
152 if ((ahy | ly) == 0)
153 return (one); /* x**+-0 = 1 */
154 else if (hx == 0x3fff0000 && lx == 0 &&
155 (__xpg6 & _C99SUSv3_pow) != 0)
156 return (one); /* C99: 1**anything = 1 */
157 else if (ahx > 0x7fff0000 || (ahx == 0x7fff0000 && lx != 0) ||
158 ahy > 0x7fff0000 || (ahy == 0x7fff0000 && ly != 0))
159 return (x + y); /* +-NaN return x+y */
160 /* includes Sun: 1**NaN = NaN */
161 sbx = (unsigned) hx >> 31;
162 sby = (unsigned) hy >> 31;
163 ax = fabsl(x);
164 /*
165 * determine if y is an odd int when x < 0
166 * yisint = 0 ... y is not an integer
167 * yisint = 1 ... y is an odd int
168 * yisint = 2 ... y is an even int
169 */
170 yisint = 0;
171 if (sbx) {
172 if (ahy >= 0x40700000) /* if |y|>=2**113 */
173 yisint = 2; /* even integer y */
174 else if (ahy >= 0x3fff0000) {
175 k = (ahy >> 16) - 0x3fff; /* exponent */
176 if (k > 80) {
177 j = ((unsigned) py[i3]) >> (112 - k);
178 if ((j << (112 - k)) == py[i3])
179 yisint = 2 - (j & 1);
180 } else if (k > 48) {
181 j = ((unsigned) py[i2]) >> (80 - k);
182 if ((j << (80 - k)) == py[i2])
183 yisint = 2 - (j & 1);
184 } else if (k > 16) {
185 j = ((unsigned) py[i1]) >> (48 - k);
186 if ((j << (48 - k)) == py[i1])
187 yisint = 2 - (j & 1);
188 } else if (ly == 0) {
189 j = ahy >> (16 - k);
190 if ((j << (16 - k)) == ahy)
191 yisint = 2 - (j & 1);
192 }
193 }
194 }
195
196 /* special value of y */
197 if (ly == 0) {
198 if (ahy == 0x7fff0000) { /* y is +-inf */
199 if (((ahx - 0x3fff0000) | lx) == 0) {
200 if ((__xpg6 & _C99SUSv3_pow) != 0)
201 return (one);
202 /* C99: (-1)**+-inf = 1 */
203 else
204 return (y - y);
205 /* Sun: (+-1)**+-inf = NaN */
206 } else if (ahx >= 0x3fff0000)
207 /* (|x|>1)**+,-inf = inf,0 */
208 return (sby == 0 ? y : zero);
209 else /* (|x|<1)**-,+inf = inf,0 */
210 return (sby != 0 ? -y : zero);
211 } else if (ahy == 0x3fff0000) { /* y is +-1 */
212 if (sby != 0)
213 return (one / x);
214 else
215 return (x);
216 } else if (hy == 0x40000000) /* y is 2 */
217 return (x * x);
218 else if (hy == 0x3ffe0000) { /* y is 0.5 */
219 if (!((ahx | lx) == 0 || ((ahx - 0x7fff0000) | lx) ==
220 0))
221 return (sqrtl(x));
222 }
223 }
224
225 /* special value of x */
226 if (lx == 0) {
227 if (ahx == 0x7fff0000 || ahx == 0 || ahx == 0x3fff0000) {
228 /* x is +-0,+-inf,+-1 */
229 z = ax;
230 if (sby == 1)
231 z = one / z; /* z = 1/|x| if y is negative */
232 if (sbx == 1) {
233 if (ahx == 0x3fff0000 && yisint == 0)
234 z = zero / zero;
235 /* (-1)**non-int is NaN */
236 else if (yisint == 1)
237 z = -z; /* (x<0)**odd = -(|x|**odd) */
238 }
239 return (z);
240 }
241 }
242
243 /* (x<0)**(non-int) is NaN */
244 if (sbx == 1 && yisint == 0)
245 return (zero / zero); /* should be volatile */
246
247 /* Now ax is finite, y is finite */
248 /* first compute log(ax) = w1+w2, with 53 bits w1 */
249 w1 = logl_x(ax, &w2);
250
251 /* split up y into y1+y2 and compute (y1+y2)*(w1+w2) */
252 if (ly == 0 || ahy >= 0x43fe0000) {
253 y1 = y * w1;
254 y2 = y * w2;
255 } else {
256 y1 = (long double) ((double) y);
257 y2 = (y - y1) * w1 + y * w2;
258 y1 *= w1;
259 }
260 z = y1 + y2;
261 j = pz[i0];
262 if ((unsigned) j >= 0xffff0000) { /* NaN or -inf */
263 if (sbx == 1 && yisint == 1)
264 return (one / z);
265 else
266 return (-one / z);
267 } else if ((j & ~0x80000000) < 0x3fc30000) { /* |x|<2^-60 */
268 if (sbx == 1 && yisint == 1)
269 return (-one - z);
270 else
271 return (one + z);
272 } else if (j > 0) {
273 if (j > 0x400d0000) {
274 if (sbx == 1 && yisint == 1)
275 return (scalbnl(-one, 20000));
276 else
277 return (scalbnl(one, 20000));
278 }
279 k = (int) (invln2_32 * (z + ln2_64));
280 } else {
281 if ((unsigned) j > 0xc00d0000) {
282 if (sbx == 1 && yisint == 1)
283 return (scalbnl(-one, -20000));
284 else
285 return (scalbnl(one, -20000));
286 }
287 k = (int) (invln2_32 * (z - ln2_64));
288 }
289 j = k & 0x1f;
290 m = k >> 5;
291 {
292 /* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */
293 long double
294 t1 = 1.666666666666666666666666666660876387437e-1L,
295 t2 = -2.777777777777777777777707812093173478756e-3L,
296 t3 = 6.613756613756613482074280932874221202424e-5L,
297 t4 = -1.653439153392139954169609822742235851120e-6L,
298 t5 = 4.175314851769539751387852116610973796053e-8L;
299 long double t = (long double) k;
300
301 w1 = (y2 - (t * ln2_32hi - y1)) - t * ln2_32lo;
302 t = w1 * w1;
303 w2 = (w1 - t * (t1 + t * (t2 + t * (t3 + t * (t4 + t * t5))))) -
304 two;
305 z = _TBL_expl_hi[j] - ((_TBL_expl_hi[j] * (w1 + w1)) / w2 -
306 _TBL_expl_lo[j]);
307 }
308 j = m + (pz[i0] >> 16);
309 if (j && (unsigned) j < 0x7fff)
310 pz[i0] += m << 16;
311 else
312 z = scalbnl(z, m);
313
314 if (sbx == 1 && yisint == 1)
315 z = -z; /* (-ve)**(odd int) */
316 return (z);
317 }
318 #else
319 #error Unsupported Architecture
320 #endif /* defined(__sparc) */