/* * 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. */ #pragma weak __powl = powl #include "libm.h" #include "xpg6.h" /* __xpg6 */ #define _C99SUSv3_pow _C99SUSv3_pow_treats_Inf_as_an_even_int #if defined(__sparc) #define i0 0 #define i1 1 #define i2 2 #define i3 3 static const long double zero = 0.0L, one = 1.0L, two = 2.0L; extern const long double _TBL_logl_hi[], _TBL_logl_lo[]; static const long double two113 = 10384593717069655257060992658440192.0L, ln2hi = 6.931471805599453094172319547495844850203e-0001L, ln2lo = 1.667085920830552208890449330400379754169e-0025L, A2 = 6.666666666666666666666666666666091393804e-0001L, A3 = 4.000000000000000000000000407167070220671e-0001L, A4 = 2.857142857142857142730077490612903681164e-0001L, A5 = 2.222222222222242577702836920812882605099e-0001L, A6 = 1.818181816435493395985912667105885828356e-0001L, A7 = 1.538537835211839751112067512805496931725e-0001L, B1 = 6.666666666666666666666666666666666667787e-0001L, B2 = 3.999999999999999999999999999999848524411e-0001L, B3 = 2.857142857142857142857142865084581075070e-0001L, B4 = 2.222222222222222222222010781800643808497e-0001L, B5 = 1.818181818181818185051442171337036403674e-0001L, B6 = 1.538461538461508363540720286292008207673e-0001L, B7 = 1.333333333506731842033180638329317108428e-0001L, B8 = 1.176469984587418890634302788283946761670e-0001L, B9 = 1.053794891561452331722969901564862497132e-0001L; static long double logl_x(long double x, long double *w) { long double f, f1, v, s, z, qn, h, t; int *px = (int *) &x; int *pz = (int *) &z; int i, j, ix, n; n = 0; ix = px[i0]; if (ix > 0x3ffef03f && ix < 0x3fff0820) { /* 65/63 > x > 63/65 */ f = x - one; z = f * f; if (((ix - 0x3fff0000) | px[i1] | px[i2] | px[i3]) == 0) { *w = zero; return (zero); /* log(1)= +0 */ } qn = one / (two + f); s = f * qn; /* |s|<2**-6 */ v = s * s; h = (long double) (2.0 * (double) s); f1 = (long double) ((double) f); t = ((two * (f - h) - h * f1) - h * (f - f1)) * qn + s * (v * (B1 + v * (B2 + v * (B3 + v * (B4 + v * (B5 + v * (B6 + v * (B7 + v * (B8 + v * B9))))))))); s = (long double) ((double) (h + t)); *w = t - (s - h); return (s); } if (ix < 0x00010000) { /* subnormal x */ x *= two113; n = -113; ix = px[i0]; } /* LARGE_N */ n += ((ix + 0x200) >> 16) - 0x3fff; ix = (ix & 0x0000ffff) | 0x3fff0000; /* scale x to [1,2] */ px[i0] = ix; i = ix + 0x200; pz[i0] = i & 0xfffffc00; pz[i1] = pz[i2] = pz[i3] = 0; qn = one / (x + z); f = x - z; s = f * qn; f1 = (long double) ((double) f); h = (long double) (2.0 * (double) s); t = qn * ((two * (f - z * h) - h * f1) - h * (f - f1)); j = (i >> 10) & 0x3f; v = s * s; qn = (long double) n; t += qn * ln2lo + _TBL_logl_lo[j]; t += s * (v * (A2 + v * (A3 + v * (A4 + v * (A5 + v * (A6 + v * A7)))))); v = qn * ln2hi + _TBL_logl_hi[j]; s = h + v; t += (h - (s - v)); z = (long double) ((double) (s + t)); *w = t - (z - s); return (z); } extern const long double _TBL_expl_hi[], _TBL_expl_lo[]; static const long double invln2_32 = 4.616624130844682903551758979206054839765e+1L, ln2_32hi = 2.166084939249829091928849858592451515688e-2L, ln2_32lo = 5.209643502595475652782654157501186731779e-27L, ln2_64 = 1.083042469624914545964425189778400898568e-2L; long double powl(long double x, long double y) { long double z, ax; long double y1, y2, w1, w2; int sbx, sby, j, k, yisint, m; int hx, lx, hy, ly, ahx, ahy; int *pz = (int *) &z; int *px = (int *) &x; int *py = (int *) &y; hx = px[i0]; lx = px[i1] | px[i2] | px[i3]; hy = py[i0]; ly = py[i1] | py[i2] | py[i3]; ahx = hx & ~0x80000000; ahy = hy & ~0x80000000; if ((ahy | ly) == 0) return (one); /* x**+-0 = 1 */ else if (hx == 0x3fff0000 && lx == 0 && (__xpg6 & _C99SUSv3_pow) != 0) return (one); /* C99: 1**anything = 1 */ else if (ahx > 0x7fff0000 || (ahx == 0x7fff0000 && lx != 0) || ahy > 0x7fff0000 || (ahy == 0x7fff0000 && ly != 0)) return (x + y); /* +-NaN return x+y */ /* includes Sun: 1**NaN = NaN */ sbx = (unsigned) hx >> 31; sby = (unsigned) hy >> 31; ax = fabsl(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 >= 0x40700000) /* if |y|>=2**113 */ yisint = 2; /* even integer y */ else if (ahy >= 0x3fff0000) { k = (ahy >> 16) - 0x3fff; /* exponent */ if (k > 80) { j = ((unsigned) py[i3]) >> (112 - k); if ((j << (112 - k)) == py[i3]) yisint = 2 - (j & 1); } else if (k > 48) { j = ((unsigned) py[i2]) >> (80 - k); if ((j << (80 - k)) == py[i2]) yisint = 2 - (j & 1); } else if (k > 16) { j = ((unsigned) py[i1]) >> (48 - k); if ((j << (48 - k)) == py[i1]) yisint = 2 - (j & 1); } else if (ly == 0) { j = ahy >> (16 - k); if ((j << (16 - k)) == ahy) yisint = 2 - (j & 1); } } } /* special value of y */ if (ly == 0) { if (ahy == 0x7fff0000) { /* y is +-inf */ if (((ahx - 0x3fff0000) | lx) == 0) { if ((__xpg6 & _C99SUSv3_pow) != 0) return (one); /* C99: (-1)**+-inf = 1 */ else return (y - y); /* Sun: (+-1)**+-inf = NaN */ } else if (ahx >= 0x3fff0000) /* (|x|>1)**+,-inf = inf,0 */ return (sby == 0 ? y : zero); else /* (|x|<1)**-,+inf = inf,0 */ return (sby != 0 ? -y : zero); } else if (ahy == 0x3fff0000) { /* y is +-1 */ if (sby != 0) return (one / x); else return (x); } else if (hy == 0x40000000) /* y is 2 */ return (x * x); else if (hy == 0x3ffe0000) { /* y is 0.5 */ if (!((ahx | lx) == 0 || ((ahx - 0x7fff0000) | lx) == 0)) return (sqrtl(x)); } } /* special value of x */ if (lx == 0) { if (ahx == 0x7fff0000 || ahx == 0 || ahx == 0x3fff0000) { /* x is +-0,+-inf,+-1 */ z = ax; if (sby == 1) z = one / z; /* z = 1/|x| if y is negative */ if (sbx == 1) { if (ahx == 0x3fff0000 && yisint == 0) z = zero / zero; /* (-1)**non-int is NaN */ 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 (zero / zero); /* should be volatile */ /* Now ax is finite, y is finite */ /* first compute log(ax) = w1+w2, with 53 bits w1 */ w1 = logl_x(ax, &w2); /* split up y into y1+y2 and compute (y1+y2)*(w1+w2) */ if (ly == 0 || ahy >= 0x43fe0000) { y1 = y * w1; y2 = y * w2; } else { y1 = (long double) ((double) y); y2 = (y - y1) * w1 + y * w2; y1 *= w1; } z = y1 + y2; j = pz[i0]; if ((unsigned) j >= 0xffff0000) { /* NaN or -inf */ if (sbx == 1 && yisint == 1) return (one / z); else return (-one / z); } else if ((j & ~0x80000000) < 0x3fc30000) { /* |x|<2^-60 */ if (sbx == 1 && yisint == 1) return (-one - z); else return (one + z); } else if (j > 0) { if (j > 0x400d0000) { if (sbx == 1 && yisint == 1) return (scalbnl(-one, 20000)); else return (scalbnl(one, 20000)); } k = (int) (invln2_32 * (z + ln2_64)); } else { if ((unsigned) j > 0xc00d0000) { if (sbx == 1 && yisint == 1) return (scalbnl(-one, -20000)); else return (scalbnl(one, -20000)); } k = (int) (invln2_32 * (z - ln2_64)); } j = k & 0x1f; m = k >> 5; { /* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */ long double t1 = 1.666666666666666666666666666660876387437e-1L, t2 = -2.777777777777777777777707812093173478756e-3L, t3 = 6.613756613756613482074280932874221202424e-5L, t4 = -1.653439153392139954169609822742235851120e-6L, t5 = 4.175314851769539751387852116610973796053e-8L; long double t = (long double) k; w1 = (y2 - (t * ln2_32hi - y1)) - t * ln2_32lo; t = w1 * w1; w2 = (w1 - t * (t1 + t * (t2 + t * (t3 + t * (t4 + t * t5))))) - two; z = _TBL_expl_hi[j] - ((_TBL_expl_hi[j] * (w1 + w1)) / w2 - _TBL_expl_lo[j]); } j = m + (pz[i0] >> 16); if (j && (unsigned) j < 0x7fff) pz[i0] += m << 16; else z = scalbnl(z, m); if (sbx == 1 && yisint == 1) z = -z; /* (-ve)**(odd int) */ return (z); } #else #error Unsupported Architecture #endif /* defined(__sparc) */