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author | bde <bde@FreeBSD.org> | 2002-03-21 11:33:50 +0000 |
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committer | bde <bde@FreeBSD.org> | 2002-03-21 11:33:50 +0000 |
commit | 25e5396e19b0f82eb681edcb4148bf508e13ef7b (patch) | |
tree | f857447bc7f96c3eb151e18553b45266f7a5de9b /lib/libm/common_source/gamma.c | |
parent | 0b5ce40729be23e49728c3a57975f177afc5d27d (diff) | |
download | FreeBSD-src-25e5396e19b0f82eb681edcb4148bf508e13ef7b.zip FreeBSD-src-25e5396e19b0f82eb681edcb4148bf508e13ef7b.tar.gz |
Removed the last vestiges of libm. These have been repo-copied to
msun/bsdsrc. Everything except true gamma() and its support functions
was superseded by msun long ago, at least on IEEE machines.
Diffstat (limited to 'lib/libm/common_source/gamma.c')
-rw-r--r-- | lib/libm/common_source/gamma.c | 339 |
1 files changed, 0 insertions, 339 deletions
diff --git a/lib/libm/common_source/gamma.c b/lib/libm/common_source/gamma.c deleted file mode 100644 index 084d8bb..0000000 --- a/lib/libm/common_source/gamma.c +++ /dev/null @@ -1,339 +0,0 @@ -/*- - * Copyright (c) 1992, 1993 - * The Regents of the University of California. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * 3. All advertising materials mentioning features or use of this software - * must display the following acknowledgement: - * This product includes software developed by the University of - * California, Berkeley and its contributors. - * 4. Neither the name of the University nor the names of its contributors - * may be used to endorse or promote products derived from this software - * without specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - */ - -#include <sys/cdefs.h> -__FBSDID("$FreeBSD$"); - -#ifndef lint -static char sccsid[] = "@(#)gamma.c 8.1 (Berkeley) 6/4/93"; -#endif /* not lint */ - -/* - * This code by P. McIlroy, Oct 1992; - * - * The financial support of UUNET Communications Services is greatfully - * acknowledged. - */ - -#include <math.h> -#include "mathimpl.h" -#include <errno.h> - -/* METHOD: - * x < 0: Use reflection formula, G(x) = pi/(sin(pi*x)*x*G(x)) - * At negative integers, return +Inf, and set errno. - * - * x < 6.5: - * Use argument reduction G(x+1) = xG(x) to reach the - * range [1.066124,2.066124]. Use a rational - * approximation centered at the minimum (x0+1) to - * ensure monotonicity. - * - * x >= 6.5: Use the asymptotic approximation (Stirling's formula) - * adjusted for equal-ripples: - * - * log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + 1/x*P(1/(x*x)) - * - * Keep extra precision in multiplying (x-.5)(log(x)-1), to - * avoid premature round-off. - * - * Special values: - * non-positive integer: Set overflow trap; return +Inf; - * x > 171.63: Set overflow trap; return +Inf; - * NaN: Set invalid trap; return NaN - * - * Accuracy: Gamma(x) is accurate to within - * x > 0: error provably < 0.9ulp. - * Maximum observed in 1,000,000 trials was .87ulp. - * x < 0: - * Maximum observed error < 4ulp in 1,000,000 trials. - */ - -static double neg_gam __P((double)); -static double small_gam __P((double)); -static double smaller_gam __P((double)); -static struct Double large_gam __P((double)); -static struct Double ratfun_gam __P((double, double)); - -/* - * Rational approximation, A0 + x*x*P(x)/Q(x), on the interval - * [1.066.., 2.066..] accurate to 4.25e-19. - */ -#define LEFT -.3955078125 /* left boundary for rat. approx */ -#define x0 .461632144968362356785 /* xmin - 1 */ - -#define a0_hi 0.88560319441088874992 -#define a0_lo -.00000000000000004996427036469019695 -#define P0 6.21389571821820863029017800727e-01 -#define P1 2.65757198651533466104979197553e-01 -#define P2 5.53859446429917461063308081748e-03 -#define P3 1.38456698304096573887145282811e-03 -#define P4 2.40659950032711365819348969808e-03 -#define Q0 1.45019531250000000000000000000e+00 -#define Q1 1.06258521948016171343454061571e+00 -#define Q2 -2.07474561943859936441469926649e-01 -#define Q3 -1.46734131782005422506287573015e-01 -#define Q4 3.07878176156175520361557573779e-02 -#define Q5 5.12449347980666221336054633184e-03 -#define Q6 -1.76012741431666995019222898833e-03 -#define Q7 9.35021023573788935372153030556e-05 -#define Q8 6.13275507472443958924745652239e-06 -/* - * Constants for large x approximation (x in [6, Inf]) - * (Accurate to 2.8*10^-19 absolute) - */ -#define lns2pi_hi 0.418945312500000 -#define lns2pi_lo -.000006779295327258219670263595 -#define Pa0 8.33333333333333148296162562474e-02 -#define Pa1 -2.77777777774548123579378966497e-03 -#define Pa2 7.93650778754435631476282786423e-04 -#define Pa3 -5.95235082566672847950717262222e-04 -#define Pa4 8.41428560346653702135821806252e-04 -#define Pa5 -1.89773526463879200348872089421e-03 -#define Pa6 5.69394463439411649408050664078e-03 -#define Pa7 -1.44705562421428915453880392761e-02 - -static const double zero = 0., one = 1.0, tiny = 1e-300; -static int endian; -/* - * TRUNC sets trailing bits in a floating-point number to zero. - * is a temporary variable. - */ -#if defined(vax) || defined(tahoe) -#define _IEEE 0 -#define TRUNC(x) x = (double) (float) (x) -#else -#define _IEEE 1 -#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000 -#define infnan(x) 0.0 -#endif - -double -gamma(x) - double x; -{ - struct Double u; - endian = (*(int *) &one) ? 1 : 0; - - if (x >= 6) { - if(x > 171.63) - return(one/zero); - u = large_gam(x); - return(__exp__D(u.a, u.b)); - } else if (x >= 1.0 + LEFT + x0) - return (small_gam(x)); - else if (x > 1.e-17) - return (smaller_gam(x)); - else if (x > -1.e-17) { - if (x == 0.0) - if (!_IEEE) return (infnan(ERANGE)); - else return (one/x); - one+1e-20; /* Raise inexact flag. */ - return (one/x); - } else if (!finite(x)) { - if (_IEEE) /* x = NaN, -Inf */ - return (x*x); - else - return (infnan(EDOM)); - } else - return (neg_gam(x)); -} -/* - * Accurate to max(ulp(1/128) absolute, 2^-66 relative) error. - */ -static struct Double -large_gam(x) - double x; -{ - double z, p; - int i; - struct Double t, u, v; - - z = one/(x*x); - p = Pa0+z*(Pa1+z*(Pa2+z*(Pa3+z*(Pa4+z*(Pa5+z*(Pa6+z*Pa7)))))); - p = p/x; - - u = __log__D(x); - u.a -= one; - v.a = (x -= .5); - TRUNC(v.a); - v.b = x - v.a; - t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */ - t.b = v.b*u.a + x*u.b; - /* return t.a + t.b + lns2pi_hi + lns2pi_lo + p */ - t.b += lns2pi_lo; t.b += p; - u.a = lns2pi_hi + t.b; u.a += t.a; - u.b = t.a - u.a; - u.b += lns2pi_hi; u.b += t.b; - return (u); -} -/* - * Good to < 1 ulp. (provably .90 ulp; .87 ulp on 1,000,000 runs.) - * It also has correct monotonicity. - */ -static double -small_gam(x) - double x; -{ - double y, ym1, t, x1; - struct Double yy, r; - y = x - one; - ym1 = y - one; - if (y <= 1.0 + (LEFT + x0)) { - yy = ratfun_gam(y - x0, 0); - return (yy.a + yy.b); - } - r.a = y; - TRUNC(r.a); - yy.a = r.a - one; - y = ym1; - yy.b = r.b = y - yy.a; - /* Argument reduction: G(x+1) = x*G(x) */ - for (ym1 = y-one; ym1 > LEFT + x0; y = ym1--, yy.a--) { - t = r.a*yy.a; - r.b = r.a*yy.b + y*r.b; - r.a = t; - TRUNC(r.a); - r.b += (t - r.a); - } - /* Return r*gamma(y). */ - yy = ratfun_gam(y - x0, 0); - y = r.b*(yy.a + yy.b) + r.a*yy.b; - y += yy.a*r.a; - return (y); -} -/* - * Good on (0, 1+x0+LEFT]. Accurate to 1ulp. - */ -static double -smaller_gam(x) - double x; -{ - double t, d; - struct Double r, xx; - if (x < x0 + LEFT) { - t = x, TRUNC(t); - d = (t+x)*(x-t); - t *= t; - xx.a = (t + x), TRUNC(xx.a); - xx.b = x - xx.a; xx.b += t; xx.b += d; - t = (one-x0); t += x; - d = (one-x0); d -= t; d += x; - x = xx.a + xx.b; - } else { - xx.a = x, TRUNC(xx.a); - xx.b = x - xx.a; - t = x - x0; - d = (-x0 -t); d += x; - } - r = ratfun_gam(t, d); - d = r.a/x, TRUNC(d); - r.a -= d*xx.a; r.a -= d*xx.b; r.a += r.b; - return (d + r.a/x); -} -/* - * returns (z+c)^2 * P(z)/Q(z) + a0 - */ -static struct Double -ratfun_gam(z, c) - double z, c; -{ - int i; - double p, q; - struct Double r, t; - - q = Q0 +z*(Q1+z*(Q2+z*(Q3+z*(Q4+z*(Q5+z*(Q6+z*(Q7+z*Q8))))))); - p = P0 + z*(P1 + z*(P2 + z*(P3 + z*P4))); - - /* return r.a + r.b = a0 + (z+c)^2*p/q, with r.a truncated to 26 bits. */ - p = p/q; - t.a = z, TRUNC(t.a); /* t ~= z + c */ - t.b = (z - t.a) + c; - t.b *= (t.a + z); - q = (t.a *= t.a); /* t = (z+c)^2 */ - TRUNC(t.a); - t.b += (q - t.a); - r.a = p, TRUNC(r.a); /* r = P/Q */ - r.b = p - r.a; - t.b = t.b*p + t.a*r.b + a0_lo; - t.a *= r.a; /* t = (z+c)^2*(P/Q) */ - r.a = t.a + a0_hi, TRUNC(r.a); - r.b = ((a0_hi-r.a) + t.a) + t.b; - return (r); /* r = a0 + t */ -} - -static double -neg_gam(x) - double x; -{ - int sgn = 1; - struct Double lg, lsine; - double y, z; - - y = floor(x + .5); - if (y == x) /* Negative integer. */ - if(!_IEEE) - return (infnan(ERANGE)); - else - return (one/zero); - z = fabs(x - y); - y = .5*ceil(x); - if (y == ceil(y)) - sgn = -1; - if (z < .25) - z = sin(M_PI*z); - else - z = cos(M_PI*(0.5-z)); - /* Special case: G(1-x) = Inf; G(x) may be nonzero. */ - if (x < -170) { - if (x < -190) - return ((double)sgn*tiny*tiny); - y = one - x; /* exact: 128 < |x| < 255 */ - lg = large_gam(y); - lsine = __log__D(M_PI/z); /* = TRUNC(log(u)) + small */ - lg.a -= lsine.a; /* exact (opposite signs) */ - lg.b -= lsine.b; - y = -(lg.a + lg.b); - z = (y + lg.a) + lg.b; - y = __exp__D(y, z); - if (sgn < 0) y = -y; - return (y); - } - y = one-x; - if (one-y == x) - y = gamma(y); - else /* 1-x is inexact */ - y = -x*gamma(-x); - if (sgn < 0) y = -y; - return (M_PI / (y*z)); -} |