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Diffstat (limited to 'usr/src/lib/libm/common/Q/expl.c')
-rw-r--r-- | usr/src/lib/libm/common/Q/expl.c | 126 |
1 files changed, 126 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/Q/expl.c b/usr/src/lib/libm/common/Q/expl.c new file mode 100644 index 0000000000..92ace61d75 --- /dev/null +++ b/usr/src/lib/libm/common/Q/expl.c @@ -0,0 +1,126 @@ +/* + * 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. + */ + +/* + * expl(x) + * Table driven method + * Written by K.C. Ng, November 1988. + * Algorithm : + * 1. Argument Reduction: given the input x, find r and integer k + * and j such that + * x = (32k+j)*ln2 + r, |r| <= (1/64)*ln2 . + * + * 2. expl(x) = 2^k * (2^(j/32) + 2^(j/32)*expm1(r)) + * Note: + * a. expm1(r) = (2r)/(2-R), R = r - r^2*(t1 + t2*r^2) + * b. 2^(j/32) is represented as + * _TBL_expl_hi[j]+_TBL_expl_lo[j] + * where + * _TBL_expl_hi[j] = 2^(j/32) rounded + * _TBL_expl_lo[j] = 2^(j/32) - _TBL_expl_hi[j]. + * + * Special cases: + * expl(INF) is INF, expl(NaN) is NaN; + * expl(-INF)= 0; + * for finite argument, only expl(0)=1 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * an ulp (unit in the last place). + * + * Misc. info. + * For 113 bit long double + * if x > 1.135652340629414394949193107797076342845e+4 + * then expl(x) overflow; + * if x < -1.143346274333629787883724384345262150341e+4 + * then expl(x) underflow + * + * Constants: + * Only decimal values are given. We assume that the compiler will convert + * from decimal to binary accurately enough to produce the correct + * hexadecimal values. + */ + +#pragma weak expl = __expl + +#include "libm.h" + +extern const long double _TBL_expl_hi[], _TBL_expl_lo[]; + +static const long double +one = 1.0L, +two = 2.0L, +ln2_64 = 1.083042469624914545964425189778400898568e-2L, +ovflthreshold = 1.135652340629414394949193107797076342845e+4L, +unflthreshold = -1.143346274333629787883724384345262150341e+4L, +invln2_32 = 4.616624130844682903551758979206054839765e+1L, +ln2_32hi = 2.166084939249829091928849858592451515688e-2L, +ln2_32lo = 5.209643502595475652782654157501186731779e-27L; + +/* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */ +static const long double +t1 = 1.666666666666666666666666666660876387437e-1L, +t2 = -2.777777777777777777777707812093173478756e-3L, +t3 = 6.613756613756613482074280932874221202424e-5L, +t4 = -1.653439153392139954169609822742235851120e-6L, +t5 = 4.175314851769539751387852116610973796053e-8L; + +long double +expl(long double x) { + int *px = (int *) &x, ix, j, k, m; + long double t, r; + + ix = px[0]; /* high word of x */ + if (ix >= 0x7fff0000) + return (x + x); /* NaN of +inf */ + if (((unsigned) ix) >= 0xffff0000) + return (-one / x); /* NaN or -inf */ + if ((ix & 0x7fffffff) < 0x3fc30000) { + if ((int) x < 1) + return (one + x); /* |x|<2^-60 */ + } + if (ix > 0) { + if (x > ovflthreshold) + return (scalbnl(x, 20000)); + k = (int) (invln2_32 * (x + ln2_64)); + } else { + if (x < unflthreshold) + return (scalbnl(-x, -40000)); + k = (int) (invln2_32 * (x - ln2_64)); + } + j = k&0x1f; + m = k>>5; + t = (long double) k; + x = (x - t * ln2_32hi) - t * ln2_32lo; + t = x * x; + r = (x - t * (t1 + t * (t2 + t * (t3 + t * (t4 + t * t5))))) - two; + x = _TBL_expl_hi[j] - ((_TBL_expl_hi[j] * (x + x)) / r - + _TBL_expl_lo[j]); + return (scalbnl(x, m)); +} |