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+/*
+ * CDDL HEADER START
+ *
+ * The contents of this file are subject to the terms of the
+ * Common Development and Distribution License (the "License").
+ * You may not use this file except in compliance with the License.
+ *
+ * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
+ * or http://www.opensolaris.org/os/licensing.
+ * See the License for the specific language governing permissions
+ * and limitations under the License.
+ *
+ * When distributing Covered Code, include this CDDL HEADER in each
+ * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
+ * If applicable, add the following below this CDDL HEADER, with the
+ * fields enclosed by brackets "[]" replaced with your own identifying
+ * information: Portions Copyright [yyyy] [name of copyright owner]
+ *
+ * CDDL HEADER END
+ */
+
+/*
+ * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
+ */
+/*
+ * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#if defined(ELFOBJ)
+#pragma weak pow = __pow
+#endif
+
+/*
+ * pow(x,y) return x**y
+ * n
+ * Method: Let x = 2 * (1+f)
+ * 1. Compute and return log2(x) in two pieces:
+ * log2(x) = w1 + w2,
+ * where w1 has 24 bits trailing zero.
+ * 2. Perform y*log2(x) by simulating muti-precision arithmetic
+ * 3. Return x**y = exp2(y*log(x))
+ *
+ * Special cases:
+ * 1. (anything) ** +-0 is 1
+ * 1'. 1 ** (anything) is 1 (C99; 1 ** +-INF/NAN used to be NAN)
+ * 2. (anything) ** 1 is itself
+ * 3. (anything except 1) ** NAN is NAN ("except 1" is C99)
+ * 4. NAN ** (anything except 0) is NAN
+ * 5. +-(|x| > 1) ** +INF is +INF
+ * 6. +-(|x| > 1) ** -INF is +0
+ * 7. +-(|x| < 1) ** +INF is +0
+ * 8. +-(|x| < 1) ** -INF is +INF
+ * 9. -1 ** +-INF is 1 (C99; -1 ** +-INF used to be NAN)
+ * 10. +0 ** (+anything except 0, NAN) is +0
+ * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
+ * 12. +0 ** (-anything except 0, NAN) is +INF
+ * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
+ * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
+ * 15. +INF ** (+anything except 0,NAN) is +INF
+ * 16. +INF ** (-anything except 0,NAN) is +0
+ * 17. -INF ** (anything) = -0 ** (-anything)
+ * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+ * 19. (-anything except 0 and inf) ** (non-integer) is NAN
+ *
+ * Accuracy:
+ * pow(x,y) returns x**y nearly rounded. In particular
+ * pow(integer,integer)
+ * always returns the correct integer provided it is representable.
+ */
+
+#include "libm.h"
+#include "xpg6.h" /* __xpg6 */
+#define _C99SUSv3_pow _C99SUSv3_pow_treats_Inf_as_an_even_int
+
+static const double zero = 0.0, one = 1.0, two = 2.0;
+
+extern const double _TBL_log2_hi[], _TBL_log2_lo[];
+static const double
+ two53 = 9007199254740992.0,
+ A1_hi = 2.8853900432586669921875,
+ A1_lo = 3.8519259825035041963606002e-8,
+ A1 = 2.885390081777926817222541963606002026086e+0000,
+ A2 = 9.617966939207270828380543979852286255862e-0001,
+ A3 = 5.770807680887875964868853124873696201995e-0001,
+ B0_hi = 2.8853900432586669921875,
+ B0_lo = 3.8519259822532793056374320585e-8,
+ B0 = 2.885390081777926814720293056374320585689e+0000,
+ B1 = 9.617966939259755138949202350396200257632e-0001,
+ B2 = 5.770780163585687000782112776448797953382e-0001,
+ B3 = 4.121985488948771523290174512461778354953e-0001,
+ B4 = 3.207590534812432970433641789022666850193e-0001;
+
+static double
+log2_x(double x, double *w) {
+ double f, s, z, qn, h, t;
+ int *px = (int *) &x;
+ int *pz = (int *) &z;
+ int i, j, ix, n;
+
+ n = 0;
+ ix = px[HIWORD];
+ if (ix >= 0x3fef03f1 && ix < 0x3ff08208) { /* 65/63 > x > 63/65 */
+ double f1, v;
+ f = x - one;
+ if (((ix - 0x3ff00000) | px[LOWORD]) == 0) {
+ *w = zero;
+ return (zero); /* log2(1)= +0 */
+ }
+ qn = one / (two + f);
+ s = f * qn; /* |s|<2**-6 */
+ v = s * s;
+ h = (double) ((float) s);
+ f1 = (double) ((float) f);
+ t = qn * (((f - two * h) - h * f1) - h * (f - f1));
+ /* s = h+t */
+ f1 = h * B0_lo + s * (v * (B1 + v * (B2 + v * (B3 + v * B4))));
+ t = f1 + t * B0;
+ h *= B0_hi;
+ s = (double) ((float) (h + t));
+ *w = t - (s - h);
+ return (s);
+ }
+ if (ix < 0x00100000) { /* subnormal x */
+ x *= two53;
+ n = -53;
+ ix = px[HIWORD];
+ }
+ /* LARGE N */
+ n += ((ix + 0x1000) >> 20) - 0x3ff;
+ ix = (ix & 0x000fffff) | 0x3ff00000; /* scale x to [1,2] */
+ px[HIWORD] = ix;
+ i = ix + 0x1000;
+ pz[HIWORD] = i & 0xffffe000;
+ pz[LOWORD] = 0;
+ qn = one / (x + z);
+ f = x - z;
+ s = f * qn;
+ h = (double) ((float) s);
+ t = qn * ((f - (h + h) * z) - h * f);
+ j = (i >> 13) & 0x7f;
+ f = s * s;
+ t = t * A1 + h * A1_lo;
+ t += (s * f) * (A2 + f * A3);
+ qn = h * A1_hi;
+ s = n + _TBL_log2_hi[j];
+ h = qn + s;
+ t += _TBL_log2_lo[j] - ((h - s) - qn);
+ f = (double) ((float) (h + t));
+ *w = t - (f - h);
+ return (f);
+}
+
+extern const double _TBL_exp2_hi[], _TBL_exp2_lo[];
+static const double /* poly app of 2^x-1 on [-1e-10,2^-7+1e-10] */
+ E1 = 6.931471805599453100674958533810346197328e-0001,
+ E2 = 2.402265069587779347846769151717493815979e-0001,
+ E3 = 5.550410866475410512631124892773937864699e-0002,
+ E4 = 9.618143209991026824853712740162451423355e-0003,
+ E5 = 1.333357676549940345096774122231849082991e-0003;
+
+double
+pow(double x, double y) {
+ double z, ax;
+ double y1, y2, w1, w2;
+ int sbx, sby, j, k, yisint;
+ int hx, hy, ahx, ahy;
+ unsigned lx, ly;
+ int *pz = (int *) &z;
+
+ hx = ((int *) &x)[HIWORD];
+ lx = ((unsigned *) &x)[LOWORD];
+ hy = ((int *) &y)[HIWORD];
+ ly = ((unsigned *) &y)[LOWORD];
+ ahx = hx & ~0x80000000;
+ ahy = hy & ~0x80000000;
+ if ((ahy | ly) == 0) { /* y==zero */
+ if ((ahx | lx) == 0)
+ z = _SVID_libm_err(x, y, 20); /* +-0**+-0 */
+ else if ((ahx | (((lx | -lx) >> 31) & 1)) > 0x7ff00000)
+ z = _SVID_libm_err(x, y, 42); /* NaN**+-0 */
+ else
+ z = one; /* x**+-0 = 1 */
+ return (z);
+ } else if (hx == 0x3ff00000 && lx == 0 &&
+ (__xpg6 & _C99SUSv3_pow) != 0)
+ return (one); /* C99: 1**anything = 1 */
+ else if (ahx > 0x7ff00000 || (ahx == 0x7ff00000 && lx != 0) ||
+ ahy > 0x7ff00000 || (ahy == 0x7ff00000 && ly != 0))
+ return (x * y); /* +-NaN return x*y; + -> * for Cheetah */
+ /* includes Sun: 1**NaN = NaN */
+ sbx = (unsigned) hx >> 31;
+ sby = (unsigned) hy >> 31;
+ ax = fabs(x);
+
+ /*
+ * determine if y is an odd int when x < 0
+ * yisint = 0 ... y is not an integer
+ * yisint = 1 ... y is an odd int
+ * yisint = 2 ... y is an even int
+ */
+ yisint = 0;
+ if (sbx) {
+ if (ahy >= 0x43400000)
+ yisint = 2; /* even integer y */
+ else if (ahy >= 0x3ff00000) {
+ k = (ahy >> 20) - 0x3ff; /* exponent */
+ if (k > 20) {
+ j = ly >> (52 - k);
+ if ((j << (52 - k)) == ly)
+ yisint = 2 - (j & 1);
+ } else if (ly == 0) {
+ j = ahy >> (20 - k);
+ if ((j << (20 - k)) == ahy)
+ yisint = 2 - (j & 1);
+ }
+ }
+ }
+ /* special value of y */
+ if (ly == 0) {
+ if (ahy == 0x7ff00000) { /* y is +-inf */
+ if (((ahx - 0x3ff00000) | lx) == 0) {
+ if ((__xpg6 & _C99SUSv3_pow) != 0)
+ return (one);
+ /* C99: (-1)**+-inf = 1 */
+ else
+ return (y - y);
+ /* Sun: (+-1)**+-inf = NaN */
+ } else if (ahx >= 0x3ff00000)
+ /* (|x|>1)**+,-inf = inf,0 */
+ return (sby == 0 ? y : zero);
+ else /* (|x|<1)**-,+inf = inf,0 */
+ return (sby != 0 ? -y : zero);
+ }
+ if (ahy == 0x3ff00000) { /* y is +-1 */
+ if (sby != 0) { /* y is -1 */
+ if (x == zero) /* divided by zero */
+ return (_SVID_libm_err(x, y, 23));
+ else if (ahx < 0x40000 || ((ahx - 0x40000) |
+ lx) == 0) /* overflow */
+ return (_SVID_libm_err(x, y, 21));
+ else
+ return (one / x);
+ } else
+ return (x);
+ }
+ if (hy == 0x40000000) { /* y is 2 */
+ if (ahx >= 0x5ff00000 && ahx < 0x7ff00000)
+ return (_SVID_libm_err(x, y, 21));
+ /* x*x overflow */
+ else if ((ahx < 0x1e56a09e && (ahx | lx) != 0) ||
+ (ahx == 0x1e56a09e && lx < 0x667f3bcd))
+ return (_SVID_libm_err(x, y, 22));
+ /* x*x underflow */
+ else
+ return (x * x);
+ }
+ if (hy == 0x3fe00000) {
+ if (!((ahx | lx) == 0 || ((ahx - 0x7ff00000) | lx) ==
+ 0 || sbx == 1))
+ return (sqrt(x)); /* y is 0.5 and x > 0 */
+ }
+ }
+ /* special value of x */
+ if (lx == 0) {
+ if (ahx == 0x7ff00000 || ahx == 0 || ahx == 0x3ff00000) {
+ /* x is +-0,+-inf,-1 */
+ z = ax;
+ if (sby == 1) {
+ z = one / z; /* z = |x|**y */
+ if (ahx == 0)
+ return (_SVID_libm_err(x, y, 23));
+ }
+ if (sbx == 1) {
+ if (ahx == 0x3ff00000 && yisint == 0)
+ z = _SVID_libm_err(x, y, 24);
+ /* neg**non-integral is NaN + invalid */
+ else if (yisint == 1)
+ z = -z; /* (x<0)**odd = -(|x|**odd) */
+ }
+ return (z);
+ }
+ }
+ /* (x<0)**(non-int) is NaN */
+ if (sbx == 1 && yisint == 0)
+ return (_SVID_libm_err(x, y, 24));
+ /* Now ax is finite, y is finite */
+ /* first compute log2(ax) = w1+w2, with 24 bits w1 */
+ w1 = log2_x(ax, &w2);
+
+ /* split up y into y1+y2 and compute (y1+y2)*(w1+w2) */
+ if (((ly & 0x07ffffff) == 0) || ahy >= 0x47e00000 ||
+ ahy <= 0x38100000) {
+ /* no need to split if y is short or too large or too small */
+ y1 = y * w1;
+ y2 = y * w2;
+ } else {
+ y1 = (double) ((float) y);
+ y2 = (y - y1) * w1 + y * w2;
+ y1 *= w1;
+ }
+ z = y1 + y2;
+ j = pz[HIWORD];
+ if (j >= 0x40900000) { /* z >= 1024 */
+ if (!(j == 0x40900000 && pz[LOWORD] == 0)) /* z > 1024 */
+ return (_SVID_libm_err(x, y, 21)); /* overflow */
+ else {
+ w2 = y1 - z;
+ w2 += y2;
+ /* rounded to inf */
+ if (w2 >= -8.008566259537296567160e-17)
+ return (_SVID_libm_err(x, y, 21));
+ /* overflow */
+ }
+ } else if ((j & ~0x80000000) >= 0x4090cc00) { /* z <= -1075 */
+ if (!(j == 0xc090cc00 && pz[LOWORD] == 0)) /* z < -1075 */
+ return (_SVID_libm_err(x, y, 22)); /* underflow */
+ else {
+ w2 = y1 - z;
+ w2 += y2;
+ if (w2 <= zero) /* underflow */
+ return (_SVID_libm_err(x, y, 22));
+ }
+ }
+ /*
+ * compute 2**(k+f[j]+g)
+ */
+ k = (int) (z * 64.0 + (((hy ^ (ahx - 0x3ff00000)) > 0) ? 0.5 : -0.5));
+ j = k & 63;
+ w1 = y2 - ((double) k * 0.015625 - y1);
+ w2 = _TBL_exp2_hi[j];
+ z = _TBL_exp2_lo[j] + (w2 * w1) * (E1 + w1 * (E2 + w1 * (E3 + w1 *
+ (E4 + w1 * E5))));
+ z += w2;
+ k >>= 6;
+ if (k < -1021)
+ z = scalbn(z, k);
+ else /* subnormal output */
+ pz[HIWORD] += k << 20;
+ if (sbx == 1 && yisint == 1)
+ z = -z; /* (-ve)**(odd int) */
+ return (z);
+}
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