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authorbde <bde@FreeBSD.org>2002-03-21 11:33:50 +0000
committerbde <bde@FreeBSD.org>2002-03-21 11:33:50 +0000
commit25e5396e19b0f82eb681edcb4148bf508e13ef7b (patch)
treef857447bc7f96c3eb151e18553b45266f7a5de9b /lib/libm
parent0b5ce40729be23e49728c3a57975f177afc5d27d (diff)
downloadFreeBSD-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 Everything except true gamma() and its support functions was superseded by msun long ago, at least on IEEE machines.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')
-rw-r--r--lib/libm/README-FREEBSD7
-rw-r--r--lib/libm/common_source/exp.c206
-rw-r--r--lib/libm/common_source/gamma.c339
-rw-r--r--lib/libm/common_source/log.c489
-rw-r--r--lib/libm/common_source/mathimpl.h98
5 files changed, 0 insertions, 1139 deletions
diff --git a/lib/libm/README-FREEBSD b/lib/libm/README-FREEBSD
deleted file mode 100644
index d7ad931..0000000
--- a/lib/libm/README-FREEBSD
+++ /dev/null
@@ -1,7 +0,0 @@
-$FreeBSD$
-
-The libm library has been superceded by the msun library. The
-source has not been delegated to the attic yet because there are
-still bits that need to be merged into msun.
-
-(end)
diff --git a/lib/libm/common_source/exp.c b/lib/libm/common_source/exp.c
deleted file mode 100644
index 7cdda2f..0000000
--- a/lib/libm/common_source/exp.c
+++ /dev/null
@@ -1,206 +0,0 @@
-/*
- * Copyright (c) 1985, 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[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93";
-#endif /* not lint */
-
-/* EXP(X)
- * RETURN THE EXPONENTIAL OF X
- * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
- * CODED IN C BY K.C. NG, 1/19/85;
- * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
- *
- * Required system supported functions:
- * scalb(x,n)
- * copysign(x,y)
- * finite(x)
- *
- * Method:
- * 1. Argument Reduction: given the input x, find r and integer k such
- * that
- * x = k*ln2 + r, |r| <= 0.5*ln2 .
- * r will be represented as r := z+c for better accuracy.
- *
- * 2. Compute exp(r) by
- *
- * exp(r) = 1 + r + r*R1/(2-R1),
- * where
- * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
- *
- * 3. exp(x) = 2^k * exp(r) .
- *
- * Special cases:
- * exp(INF) is INF, exp(NaN) is NaN;
- * exp(-INF)= 0;
- * for finite argument, only exp(0)=1 is exact.
- *
- * Accuracy:
- * exp(x) returns the exponential of x nearly rounded. In a test run
- * with 1,156,000 random arguments on a VAX, the maximum observed
- * error was 0.869 ulps (units in the last place).
- *
- * 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.
- */
-
-#include "mathimpl.h"
-
-vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
-vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
-vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010)
-vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF)
-vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
-vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1)
-vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94)
-vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
-vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
-vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683)
-
-#ifdef vccast
-#define ln2hi vccast(ln2hi)
-#define ln2lo vccast(ln2lo)
-#define lnhuge vccast(lnhuge)
-#define lntiny vccast(lntiny)
-#define invln2 vccast(invln2)
-#define p1 vccast(p1)
-#define p2 vccast(p2)
-#define p3 vccast(p3)
-#define p4 vccast(p4)
-#define p5 vccast(p5)
-#endif
-
-ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E)
-ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93)
-ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C)
-ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
-ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0)
-ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
-ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
-ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
-ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354)
-ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
-
-double exp(x)
-double x;
-{
- double z,hi,lo,c;
- int k;
-
-#if !defined(vax)&&!defined(tahoe)
- if(x!=x) return(x); /* x is NaN */
-#endif /* !defined(vax)&&!defined(tahoe) */
- if( x <= lnhuge ) {
- if( x >= lntiny ) {
-
- /* argument reduction : x --> x - k*ln2 */
-
- k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
-
- /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
-
- hi=x-k*ln2hi;
- x=hi-(lo=k*ln2lo);
-
- /* return 2^k*[1+x+x*c/(2+c)] */
- z=x*x;
- c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
- return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
-
- }
- /* end of x > lntiny */
-
- else
- /* exp(-big#) underflows to zero */
- if(finite(x)) return(scalb(1.0,-5000));
-
- /* exp(-INF) is zero */
- else return(0.0);
- }
- /* end of x < lnhuge */
-
- else
- /* exp(INF) is INF, exp(+big#) overflows to INF */
- return( finite(x) ? scalb(1.0,5000) : x);
-}
-
-/* returns exp(r = x + c) for |c| < |x| with no overlap. */
-
-double __exp__D(x, c)
-double x, c;
-{
- double z,hi,lo, t;
- int k;
-
-#if !defined(vax)&&!defined(tahoe)
- if (x!=x) return(x); /* x is NaN */
-#endif /* !defined(vax)&&!defined(tahoe) */
- if ( x <= lnhuge ) {
- if ( x >= lntiny ) {
-
- /* argument reduction : x --> x - k*ln2 */
- z = invln2*x;
- k = z + copysign(.5, x);
-
- /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */
-
- hi=(x-k*ln2hi); /* Exact. */
- x= hi - (lo = k*ln2lo-c);
- /* return 2^k*[1+x+x*c/(2+c)] */
- z=x*x;
- c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
- c = (x*c)/(2.0-c);
-
- return scalb(1.+(hi-(lo - c)), k);
- }
- /* end of x > lntiny */
-
- else
- /* exp(-big#) underflows to zero */
- if(finite(x)) return(scalb(1.0,-5000));
-
- /* exp(-INF) is zero */
- else return(0.0);
- }
- /* end of x < lnhuge */
-
- else
- /* exp(INF) is INF, exp(+big#) overflows to INF */
- return( finite(x) ? scalb(1.0,5000) : x);
-}
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));
-}
diff --git a/lib/libm/common_source/log.c b/lib/libm/common_source/log.c
deleted file mode 100644
index fb873c6..0000000
--- a/lib/libm/common_source/log.c
+++ /dev/null
@@ -1,489 +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[] = "@(#)log.c 8.2 (Berkeley) 11/30/93";
-#endif /* not lint */
-
-#include <math.h>
-#include <errno.h>
-
-#include "mathimpl.h"
-
-/* Table-driven natural logarithm.
- *
- * This code was derived, with minor modifications, from:
- * Peter Tang, "Table-Driven Implementation of the
- * Logarithm in IEEE Floating-Point arithmetic." ACM Trans.
- * Math Software, vol 16. no 4, pp 378-400, Dec 1990).
- *
- * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256,
- * where F = j/128 for j an integer in [0, 128].
- *
- * log(2^m) = log2_hi*m + log2_tail*m
- * since m is an integer, the dominant term is exact.
- * m has at most 10 digits (for subnormal numbers),
- * and log2_hi has 11 trailing zero bits.
- *
- * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h
- * logF_hi[] + 512 is exact.
- *
- * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ...
- * the leading term is calculated to extra precision in two
- * parts, the larger of which adds exactly to the dominant
- * m and F terms.
- * There are two cases:
- * 1. when m, j are non-zero (m | j), use absolute
- * precision for the leading term.
- * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1).
- * In this case, use a relative precision of 24 bits.
- * (This is done differently in the original paper)
- *
- * Special cases:
- * 0 return signalling -Inf
- * neg return signalling NaN
- * +Inf return +Inf
-*/
-
-#if defined(vax) || defined(tahoe)
-#define _IEEE 0
-#define TRUNC(x) x = (double) (float) (x)
-#else
-#define _IEEE 1
-#define endian (((*(int *) &one)) ? 1 : 0)
-#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000
-#define infnan(x) 0.0
-#endif
-
-#define N 128
-
-/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128.
- * Used for generation of extend precision logarithms.
- * The constant 35184372088832 is 2^45, so the divide is exact.
- * It ensures correct reading of logF_head, even for inaccurate
- * decimal-to-binary conversion routines. (Everybody gets the
- * right answer for integers less than 2^53.)
- * Values for log(F) were generated using error < 10^-57 absolute
- * with the bc -l package.
-*/
-static double A1 = .08333333333333178827;
-static double A2 = .01250000000377174923;
-static double A3 = .002232139987919447809;
-static double A4 = .0004348877777076145742;
-
-static double logF_head[N+1] = {
- 0.,
- .007782140442060381246,
- .015504186535963526694,
- .023167059281547608406,
- .030771658666765233647,
- .038318864302141264488,
- .045809536031242714670,
- .053244514518837604555,
- .060624621816486978786,
- .067950661908525944454,
- .075223421237524235039,
- .082443669210988446138,
- .089612158689760690322,
- .096729626458454731618,
- .103796793681567578460,
- .110814366340264314203,
- .117783035656430001836,
- .124703478501032805070,
- .131576357788617315236,
- .138402322859292326029,
- .145182009844575077295,
- .151916042025732167530,
- .158605030176659056451,
- .165249572895390883786,
- .171850256926518341060,
- .178407657472689606947,
- .184922338493834104156,
- .191394852999565046047,
- .197825743329758552135,
- .204215541428766300668,
- .210564769107350002741,
- .216873938300523150246,
- .223143551314024080056,
- .229374101064877322642,
- .235566071312860003672,
- .241719936886966024758,
- .247836163904594286577,
- .253915209980732470285,
- .259957524436686071567,
- .265963548496984003577,
- .271933715484010463114,
- .277868451003087102435,
- .283768173130738432519,
- .289633292582948342896,
- .295464212893421063199,
- .301261330578199704177,
- .307025035294827830512,
- .312755710004239517729,
- .318453731118097493890,
- .324119468654316733591,
- .329753286372579168528,
- .335355541920762334484,
- .340926586970454081892,
- .346466767346100823488,
- .351976423156884266063,
- .357455888922231679316,
- .362905493689140712376,
- .368325561158599157352,
- .373716409793814818840,
- .379078352934811846353,
- .384411698910298582632,
- .389716751140440464951,
- .394993808240542421117,
- .400243164127459749579,
- .405465108107819105498,
- .410659924985338875558,
- .415827895143593195825,
- .420969294644237379543,
- .426084395310681429691,
- .431173464818130014464,
- .436236766774527495726,
- .441274560805140936281,
- .446287102628048160113,
- .451274644139630254358,
- .456237433481874177232,
- .461175715122408291790,
- .466089729924533457960,
- .470979715219073113985,
- .475845904869856894947,
- .480688529345570714212,
- .485507815781602403149,
- .490303988045525329653,
- .495077266798034543171,
- .499827869556611403822,
- .504556010751912253908,
- .509261901790523552335,
- .513945751101346104405,
- .518607764208354637958,
- .523248143765158602036,
- .527867089620485785417,
- .532464798869114019908,
- .537041465897345915436,
- .541597282432121573947,
- .546132437597407260909,
- .550647117952394182793,
- .555141507540611200965,
- .559615787935399566777,
- .564070138285387656651,
- .568504735352689749561,
- .572919753562018740922,
- .577315365035246941260,
- .581691739635061821900,
- .586049045003164792433,
- .590387446602107957005,
- .594707107746216934174,
- .599008189645246602594,
- .603290851438941899687,
- .607555250224322662688,
- .611801541106615331955,
- .616029877215623855590,
- .620240409751204424537,
- .624433288012369303032,
- .628608659422752680256,
- .632766669570628437213,
- .636907462236194987781,
- .641031179420679109171,
- .645137961373620782978,
- .649227946625615004450,
- .653301272011958644725,
- .657358072709030238911,
- .661398482245203922502,
- .665422632544505177065,
- .669430653942981734871,
- .673422675212350441142,
- .677398823590920073911,
- .681359224807238206267,
- .685304003098281100392,
- .689233281238557538017,
- .693147180560117703862
-};
-
-static double logF_tail[N+1] = {
- 0.,
- -.00000000000000543229938420049,
- .00000000000000172745674997061,
- -.00000000000001323017818229233,
- -.00000000000001154527628289872,
- -.00000000000000466529469958300,
- .00000000000005148849572685810,
- -.00000000000002532168943117445,
- -.00000000000005213620639136504,
- -.00000000000001819506003016881,
- .00000000000006329065958724544,
- .00000000000008614512936087814,
- -.00000000000007355770219435028,
- .00000000000009638067658552277,
- .00000000000007598636597194141,
- .00000000000002579999128306990,
- -.00000000000004654729747598444,
- -.00000000000007556920687451336,
- .00000000000010195735223708472,
- -.00000000000017319034406422306,
- -.00000000000007718001336828098,
- .00000000000010980754099855238,
- -.00000000000002047235780046195,
- -.00000000000008372091099235912,
- .00000000000014088127937111135,
- .00000000000012869017157588257,
- .00000000000017788850778198106,
- .00000000000006440856150696891,
- .00000000000016132822667240822,
- -.00000000000007540916511956188,
- -.00000000000000036507188831790,
- .00000000000009120937249914984,
- .00000000000018567570959796010,
- -.00000000000003149265065191483,
- -.00000000000009309459495196889,
- .00000000000017914338601329117,
- -.00000000000001302979717330866,
- .00000000000023097385217586939,
- .00000000000023999540484211737,
- .00000000000015393776174455408,
- -.00000000000036870428315837678,
- .00000000000036920375082080089,
- -.00000000000009383417223663699,
- .00000000000009433398189512690,
- .00000000000041481318704258568,
- -.00000000000003792316480209314,
- .00000000000008403156304792424,
- -.00000000000034262934348285429,
- .00000000000043712191957429145,
- -.00000000000010475750058776541,
- -.00000000000011118671389559323,
- .00000000000037549577257259853,
- .00000000000013912841212197565,
- .00000000000010775743037572640,
- .00000000000029391859187648000,
- -.00000000000042790509060060774,
- .00000000000022774076114039555,
- .00000000000010849569622967912,
- -.00000000000023073801945705758,
- .00000000000015761203773969435,
- .00000000000003345710269544082,
- -.00000000000041525158063436123,
- .00000000000032655698896907146,
- -.00000000000044704265010452446,
- .00000000000034527647952039772,
- -.00000000000007048962392109746,
- .00000000000011776978751369214,
- -.00000000000010774341461609578,
- .00000000000021863343293215910,
- .00000000000024132639491333131,
- .00000000000039057462209830700,
- -.00000000000026570679203560751,
- .00000000000037135141919592021,
- -.00000000000017166921336082431,
- -.00000000000028658285157914353,
- -.00000000000023812542263446809,
- .00000000000006576659768580062,
- -.00000000000028210143846181267,
- .00000000000010701931762114254,
- .00000000000018119346366441110,
- .00000000000009840465278232627,
- -.00000000000033149150282752542,
- -.00000000000018302857356041668,
- -.00000000000016207400156744949,
- .00000000000048303314949553201,
- -.00000000000071560553172382115,
- .00000000000088821239518571855,
- -.00000000000030900580513238244,
- -.00000000000061076551972851496,
- .00000000000035659969663347830,
- .00000000000035782396591276383,
- -.00000000000046226087001544578,
- .00000000000062279762917225156,
- .00000000000072838947272065741,
- .00000000000026809646615211673,
- -.00000000000010960825046059278,
- .00000000000002311949383800537,
- -.00000000000058469058005299247,
- -.00000000000002103748251144494,
- -.00000000000023323182945587408,
- -.00000000000042333694288141916,
- -.00000000000043933937969737844,
- .00000000000041341647073835565,
- .00000000000006841763641591466,
- .00000000000047585534004430641,
- .00000000000083679678674757695,
- -.00000000000085763734646658640,
- .00000000000021913281229340092,
- -.00000000000062242842536431148,
- -.00000000000010983594325438430,
- .00000000000065310431377633651,
- -.00000000000047580199021710769,
- -.00000000000037854251265457040,
- .00000000000040939233218678664,
- .00000000000087424383914858291,
- .00000000000025218188456842882,
- -.00000000000003608131360422557,
- -.00000000000050518555924280902,
- .00000000000078699403323355317,
- -.00000000000067020876961949060,
- .00000000000016108575753932458,
- .00000000000058527188436251509,
- -.00000000000035246757297904791,
- -.00000000000018372084495629058,
- .00000000000088606689813494916,
- .00000000000066486268071468700,
- .00000000000063831615170646519,
- .00000000000025144230728376072,
- -.00000000000017239444525614834
-};
-
-double
-#ifdef _ANSI_SOURCE
-log(double x)
-#else
-log(x) double x;
-#endif
-{
- int m, j;
- double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0;
- volatile double u1;
-
- /* Catch special cases */
- if (x <= 0)
- if (_IEEE && x == zero) /* log(0) = -Inf */
- return (-one/zero);
- else if (_IEEE) /* log(neg) = NaN */
- return (zero/zero);
- else if (x == zero) /* NOT REACHED IF _IEEE */
- return (infnan(-ERANGE));
- else
- return (infnan(EDOM));
- else if (!finite(x))
- if (_IEEE) /* x = NaN, Inf */
- return (x+x);
- else
- return (infnan(ERANGE));
-
- /* Argument reduction: 1 <= g < 2; x/2^m = g; */
- /* y = F*(1 + f/F) for |f| <= 2^-8 */
-
- m = logb(x);
- g = ldexp(x, -m);
- if (_IEEE && m == -1022) {
- j = logb(g), m += j;
- g = ldexp(g, -j);
- }
- j = N*(g-1) + .5;
- F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */
- f = g - F;
-
- /* Approximate expansion for log(1+f/F) ~= u + q */
- g = 1/(2*F+f);
- u = 2*f*g;
- v = u*u;
- q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
-
- /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8,
- * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits.
- * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750
- */
- if (m | j)
- u1 = u + 513, u1 -= 513;
-
- /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero;
- * u1 = u to 24 bits.
- */
- else
- u1 = u, TRUNC(u1);
- u2 = (2.0*(f - F*u1) - u1*f) * g;
- /* u1 + u2 = 2f/(2F+f) to extra precision. */
-
- /* log(x) = log(2^m*F*(1+f/F)) = */
- /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */
- /* (exact) + (tiny) */
-
- u1 += m*logF_head[N] + logF_head[j]; /* exact */
- u2 = (u2 + logF_tail[j]) + q; /* tiny */
- u2 += logF_tail[N]*m;
- return (u1 + u2);
-}
-
-/*
- * Extra precision variant, returning struct {double a, b;};
- * log(x) = a+b to 63 bits, with a is rounded to 26 bits.
- */
-struct Double
-#ifdef _ANSI_SOURCE
-__log__D(double x)
-#else
-__log__D(x) double x;
-#endif
-{
- int m, j;
- double F, f, g, q, u, v, u2, one = 1.0;
- volatile double u1;
- struct Double r;
-
- /* Argument reduction: 1 <= g < 2; x/2^m = g; */
- /* y = F*(1 + f/F) for |f| <= 2^-8 */
-
- m = logb(x);
- g = ldexp(x, -m);
- if (_IEEE && m == -1022) {
- j = logb(g), m += j;
- g = ldexp(g, -j);
- }
- j = N*(g-1) + .5;
- F = (1.0/N) * j + 1;
- f = g - F;
-
- g = 1/(2*F+f);
- u = 2*f*g;
- v = u*u;
- q = u*v*(A1 + v*(A2 + v*(A3 + v*A4)));
- if (m | j)
- u1 = u + 513, u1 -= 513;
- else
- u1 = u, TRUNC(u1);
- u2 = (2.0*(f - F*u1) - u1*f) * g;
-
- u1 += m*logF_head[N] + logF_head[j];
-
- u2 += logF_tail[j]; u2 += q;
- u2 += logF_tail[N]*m;
- r.a = u1 + u2; /* Only difference is here */
- TRUNC(r.a);
- r.b = (u1 - r.a) + u2;
- return (r);
-}
diff --git a/lib/libm/common_source/mathimpl.h b/lib/libm/common_source/mathimpl.h
deleted file mode 100644
index 6a2a37d..0000000
--- a/lib/libm/common_source/mathimpl.h
+++ /dev/null
@@ -1,98 +0,0 @@
-/*
- * Copyright (c) 1988, 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.
- *
- * @(#)mathimpl.h 8.1 (Berkeley) 6/4/93
- */
-
-#include <sys/cdefs.h>
-#include <math.h>
-
-#if defined(vax)||defined(tahoe)
-
-/* Deal with different ways to concatenate in cpp */
-# ifdef __STDC__
-# define cat3(a,b,c) a ## b ## c
-# else
-# define cat3(a,b,c) a/**/b/**/c
-# endif
-
-/* Deal with vax/tahoe byte order issues */
-# ifdef vax
-# define cat3t(a,b,c) cat3(a,b,c)
-# else
-# define cat3t(a,b,c) cat3(a,c,b)
-# endif
-
-# define vccast(name) (*(const double *)(cat3(name,,x)))
-
- /*
- * Define a constant to high precision on a Vax or Tahoe.
- *
- * Args are the name to define, the decimal floating point value,
- * four 16-bit chunks of the float value in hex
- * (because the vax and tahoe differ in float format!), the power
- * of 2 of the hex-float exponent, and the hex-float mantissa.
- * Most of these arguments are not used at compile time; they are
- * used in a post-check to make sure the constants were compiled
- * correctly.
- *
- * People who want to use the constant will have to do their own
- * #define foo vccast(foo)
- * since CPP cannot do this for them from inside another macro (sigh).
- * We define "vccast" if this needs doing.
- */
-# define vc(name, value, x1,x2,x3,x4, bexp, xval) \
- const static long cat3(name,,x)[] = {cat3t(0x,x1,x2), cat3t(0x,x3,x4)};
-
-# define ic(name, value, bexp, xval) ;
-
-#else /* vax or tahoe */
-
- /* Hooray, we have an IEEE machine */
-# undef vccast
-# define vc(name, value, x1,x2,x3,x4, bexp, xval) ;
-
-# define ic(name, value, bexp, xval) \
- const static double name = value;
-
-#endif /* defined(vax)||defined(tahoe) */
-
-
-/*
- * Functions internal to the math package, yet not static.
- */
-extern double __exp__E();
-extern double __log__L();
-
-struct Double {double a, b;};
-double __exp__D __P((double, double));
-struct Double __log__D __P((double));
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