455b2ccda3
. Disconnect b_exp.c and b_log.c from the build.
* lib/msun/bsdsrc/b_exp.c:
. Replace scalb() usage with C99's ldexp().
. Replace finite(x) usage with C99's isfinite().
. Whitespace changes towards style(9).
. Remove include of "mathimpl.h". It is no longer needed.
. Remove #if 0 ... #endif code, which has been present since svn r93211
(2002-03-26).
. New minimax polynomial coefficients.
. Add comments to explain origins of some constants.
. Use ansi-C prototype. Remove K&R prototype. Add static to prototype.
* lib/msun/bsdsrc/b_log.c:
. Remove include of "mathimpl.h". It is no longer needed.
. Fix comments to actually describe the code.
. Reduce minimax polynomial from degree 4 to degree 3.
This uses newly computed coefficients.
. Use ansi-C prototype. Remove K&R prototype. Add static to prototype.
. Remove volatile in declaration of u1.
. Alphabetize decalaration list.
. Whitespace changes towards style(9).
. In argument reduction of x to g and m, replace use of logb() and
ldexp() with a single call to frexp(). Add code to get 1 <= g < 2.
. Remove #if 0 ... #endif code, which has been present since svn r93211
(2002-03-26).
. The special case m == -1022, replace logb() with ilogb().
* lib/msun/bsdsrc/b_tgamma.c:
. Update comments. Fix comments where needed.
. Add float.h to get LDBL_MANT_DIG for weak reference of tgammal to tgamma.
. Remove include of "mathimpl.h". It is no longer needed.
. Use "math.h" instead of <math.h>.
. Add '#include math_private.h"
. Add struct Double from mathimpl.h and include b_log.c and b_exp.c.
. Remove forward declarations of neg_gam(), small_gam(), smaller_gam,
large_gam() and ratfun_gam() by re-arranging the code to move these
function above their first reference.
. New minimax coefficients for polynomial in large_gam().
. New splitting of a0 into a0hi nd a0lo, which include additional
bits of precision.
. Use ansi-C prototype. Remove K&R prototype.
. Replace the TRUNC() macro with a simple cast of a double entities
to float before assignment (functional changes).
. Replace sin(M_PI*z) with sinpi(z) and cos(M_PI*(0.5-z)) with cospi(0.5-z).
Submitted by: Steve Kargl
Differential Revision: https://reviews.freebsd.org/D33444
Reviewed by: pfg
127 lines
4.2 KiB
C
127 lines
4.2 KiB
C
/*-
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* SPDX-License-Identifier: BSD-3-Clause
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*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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/* @(#)exp.c 8.1 (Berkeley) 6/4/93 */
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/* EXP(X)
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* RETURN THE EXPONENTIAL OF X
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* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
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* CODED IN C BY K.C. NG, 1/19/85;
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* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
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*
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* Required system supported functions:
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* ldexp(x,n)
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* copysign(x,y)
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* isfinite(x)
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*
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* Method:
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* 1. Argument Reduction: given the input x, find r and integer k such
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* that
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* x = k*ln2 + r, |r| <= 0.5*ln2.
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* r will be represented as r := z+c for better accuracy.
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*
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* 2. Compute exp(r) by
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*
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* exp(r) = 1 + r + r*R1/(2-R1),
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* where
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* R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
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*
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* 3. exp(x) = 2^k * exp(r) .
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*
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* Special cases:
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* exp(INF) is INF, exp(NaN) is NaN;
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* exp(-INF)= 0;
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* for finite argument, only exp(0)=1 is exact.
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*
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* Accuracy:
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* exp(x) returns the exponential of x nearly rounded. In a test run
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* with 1,156,000 random arguments on a VAX, the maximum observed
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* error was 0.869 ulps (units in the last place).
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*/
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static const double
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p1 = 1.6666666666666660e-01, /* 0x3fc55555, 0x55555553 */
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p2 = -2.7777777777564776e-03, /* 0xbf66c16c, 0x16c0ac3c */
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p3 = 6.6137564717940088e-05, /* 0x3f11566a, 0xb5c2ba0d */
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p4 = -1.6534060280704225e-06, /* 0xbebbbd53, 0x273e8fb7 */
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p5 = 4.1437773411069054e-08; /* 0x3e663f2a, 0x09c94b6c */
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static const double
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ln2hi = 0x1.62e42fee00000p-1, /* High 32 bits round-down. */
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ln2lo = 0x1.a39ef35793c76p-33; /* Next 53 bits round-to-nearst. */
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static const double
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lnhuge = 0x1.6602b15b7ecf2p9, /* (DBL_MAX_EXP + 9) * log(2.) */
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lntiny = -0x1.77af8ebeae354p9, /* (DBL_MIN_EXP - 53 - 10) * log(2.) */
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invln2 = 0x1.71547652b82fep0; /* 1 / log(2.) */
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/* returns exp(r = x + c) for |c| < |x| with no overlap. */
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static double
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__exp__D(double x, double c)
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{
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double hi, lo, z;
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int k;
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if (x != x) /* x is NaN. */
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return(x);
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if (x <= lnhuge) {
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if (x >= lntiny) {
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/* argument reduction: x --> x - k*ln2 */
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z = invln2 * x;
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k = z + copysign(0.5, x);
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/*
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* Express (x + c) - k * ln2 as hi - lo.
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* Let x = hi - lo rounded.
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*/
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hi = x - k * ln2hi; /* Exact. */
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lo = k * ln2lo - c;
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x = hi - lo;
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/* Return 2^k*[1+x+x*c/(2+c)] */
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z = x * x;
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c = x - z * (p1 + z * (p2 + z * (p3 + z * (p4 +
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z * p5))));
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c = (x * c) / (2 - c);
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return (ldexp(1 + (hi - (lo - c)), k));
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} else {
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/* exp(-INF) is 0. exp(-big) underflows to 0. */
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return (isfinite(x) ? ldexp(1., -5000) : 0);
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}
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} else
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/* exp(INF) is INF, exp(+big#) overflows to INF */
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return (isfinite(x) ? ldexp(1., 5000) : x);
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}
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