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Diffstat (limited to 'usr/src/lib/libm/common/Q/log1pl.c')
| -rw-r--r-- | usr/src/lib/libm/common/Q/log1pl.c | 217 |
1 files changed, 217 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/Q/log1pl.c b/usr/src/lib/libm/common/Q/log1pl.c new file mode 100644 index 0000000000..f00c5eb4ed --- /dev/null +++ b/usr/src/lib/libm/common/Q/log1pl.c @@ -0,0 +1,217 @@ +/* + * 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. + */ + +#ifdef __LITTLE_ENDIAN +#define H0(x) *(3 + (int *) &x) +#define H1(x) *(2 + (int *) &x) +#define H2(x) *(1 + (int *) &x) +#define H3(x) *(int *) &x +#else +#define H0(x) *(int *) &x +#define H1(x) *(1 + (int *) &x) +#define H2(x) *(2 + (int *) &x) +#define H3(x) *(3 + (int *) &x) +#endif + +/* + * log1pl(x) + * Table look-up algorithm by modifying logl.c + * By K.C. Ng, July 6, 1995 + * + * (a). For 1+x in [31/33,33/31], using a special approximation: + * s = x/(2.0+x); ... here |s| <= 0.03125 + * z = s*s; + * return x-s*(x-z*(B1+z*(B2+z*(B3+z*(B4+...+z*B9)...)))); + * (i.e., x is in [-2/33,2/31]) + * + * (b). Otherwise, normalize 1+x = 2^n * 1.f. + * Here we may need a correction term for 1+x rounded. + * Use a 6-bit table look-up: find a 6 bit g that match f to 6.5 bits, + * then + * log(1+x) = n*ln2 + log(1.g) + log(1.f/1.g). + * Here the leading and trailing values of log(1.g) are obtained from + * a size-64 table. + * For log(1.f/1.g), let s = (1.f-1.g)/(1.f+1.g). Note that + * 1.f = 2^-n(1+x) + * + * then + * log(1.f/1.g) = log((1+s)/(1-s)) = 2s + 2/3 s^3 + 2/5 s^5 +... + * Note that |s|<2**-8=0.00390625. We use an odd s-polynomial + * approximation to compute log(1.f/1.g): + * s*(A1+s^2*(A2+s^2*(A3+s^2*(A4+s^2*(A5+s^2*(A6+s^2*A7)))))) + * (Precision is 2**-136.91 bits, absolute error) + * + * CAUTION: + * For x>=1, compute 1+x will lost one bit (OK). + * For x in [-0.5,-1), 1+x is exact. + * For x in (-0.5,-2/33]U[2/31,1), up to 4 last bits of x will be lost + * in 1+x. Therefore, to recover the lost bits, one need to compute + * 1.f-1.g accurately. + * + * Let hx = HI(x), m = (hx>>16)-0x3fff (=ilogbl(x)), note that + * -2/33 = -0.0606...= 2^-5 * 1.939..., + * 2/31 = 0.09375 = 2^-4 * 1.500..., + * so for x in (-0.5,-2/33], -5<=m<=-2, n= -1, 1+f=2*(1+x) + * for x in [2/33,1), -4<=m<=-1, n= 0, f=x + * + * In short: + * if x>0, let g: hg= ((hx + (0x200<<(-m)))>>(10-m))<<(10-m) + * then 1.f-1.g = x-g + * if x<0, let g': hg' =((ix-(0x200)<<(-m-1))>>(9-m))<<(9-m) + * (ix=hx&0x7fffffff) + * then 1.f-1.g = 2*(g'+x), + * + * (c). The final result is computed by + * (n*ln2_hi+_TBL_logl_hi[j]) + + * ( (n*ln2_lo+_TBL_logl_lo[j]) + s*(A1+...) ) + * + * Note. + * For ln2_hi and _TBL_logl_hi[j], we force their last 32 bit to be zero + * so that n*ln2_hi + _TBL_logl_hi[j] is exact. Here + * _TBL_logl_hi[j] + _TBL_logl_lo[j] match log(1+j*2**-6) to 194 bits + * + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#pragma weak log1pl = __log1pl + +#include "libm.h" + +extern const long double _TBL_logl_hi[], _TBL_logl_lo[]; + +static const long double +zero = 0.0L, +one = 1.0L, +two = 2.0L, +ln2hi = 6.931471805599453094172319547495844850203e-0001L, +ln2lo = 1.667085920830552208890449330400379754169e-0025L, +A1 = 2.000000000000000000000000000000000000024e+0000L, +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 = 6.666666666666666666666666666666961498329e-0001L, +B2 = 3.999999999999999999999999990037655042358e-0001L, +B3 = 2.857142857142857142857273426428347457918e-0001L, +B4 = 2.222222222222222221353229049747910109566e-0001L, +B5 = 1.818181818181821503532559306309070138046e-0001L, +B6 = 1.538461538453809210486356084587356788556e-0001L, +B7 = 1.333333344463358756121456892645178795480e-0001L, +B8 = 1.176460904783899064854645174603360383792e-0001L, +B9 = 1.057293869956598995326368602518056990746e-0001L; + +long double +log1pl(long double x) { + long double f, s, z, qn, h, t, y, g; + int i, j, ix, iy, n, hx, m; + + hx = H0(x); + ix = hx & 0x7fffffff; + if (ix < 0x3ffaf07c) { /* |x|<2/33 */ + if (ix <= 0x3f8d0000) { /* x <= 2**-114, return x */ + if ((int) x == 0) + return (x); + } + s = x / (two + x); /* |s|<2**-8 */ + z = s * s; + return (x - s * (x - z * (B1 + z * (B2 + z * (B3 + z * (B4 + + z * (B5 + z * (B6 + z * (B7 + z * (B8 + z * B9)))))))))); + } + if (ix >= 0x7fff0000) { /* x is +inf or NaN */ + return (x + fabsl(x)); + } + if (hx < 0 && ix >= 0x3fff0000) { + if (ix > 0x3fff0000 || (H1(x) | H2(x) | H3(x)) != 0) + x = zero; + return (x / zero); /* log1p(x) is NaN if x<-1 */ + /* log1p(-1) is -inf */ + } + if (ix >= 0x7ffeffff) + y = x; /* avoid spurious overflow */ + else + y = one + x; + iy = H0(y); + n = ((iy + 0x200) >> 16) - 0x3fff; + iy = (iy & 0x0000ffff) | 0x3fff0000; /* scale 1+x to [1,2] */ + H0(y) = iy; + z = zero; + m = (ix >> 16) - 0x3fff; + /* HI(1+x) = (((hx&0xffff)|0x10000)>>(-m))|0x3fff0000 */ + if (n == 0) { /* x in [2/33,1) */ + g = zero; + H0(g) = ((hx + (0x200 << (-m))) >> (10 - m)) << (10 - m); + t = x - g; + i = (((((hx & 0xffff) | 0x10000) >> (-m)) | 0x3fff0000) + + 0x200) >> 10; + H0(z) = i << 10; + + } else if ((1 + n) == 0 && (ix < 0x3ffe0000)) { /* x in (-0.5,-2/33] */ + g = zero; + H0(g) = ((ix + (0x200 << (-m - 1))) >> (9 - m)) << (9 - m); + t = g + x; + t = t + t; + /* + * HI(2*(1+x)) = + * ((0x10000-(((hx&0xffff)|0x10000)>>(-m)))<<1)|0x3fff0000 + */ + /* + * i = + * ((((0x10000-(((hx&0xffff)|0x10000)>>(-m)))<<1)|0x3fff0000)+ + * 0x200)>>10; H0(z)=i<<10; + */ + z = two * (one - g); + i = H0(z) >> 10; + } else { + i = (iy + 0x200) >> 10; + H0(z) = i << 10; + t = y - z; + } + + s = t / (y + z); + j = i & 0x3f; + z = s * s; + qn = (long double) n; + t = qn * ln2lo + _TBL_logl_lo[j]; + h = qn * ln2hi + _TBL_logl_hi[j]; + f = t + s * (A1 + z * (A2 + z * (A3 + z * (A4 + z * (A5 + z * (A6 + + z * A7)))))); + return (h + f); +} |