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