diff --git a/lib/libm/README-FREEBSD b/lib/libm/README-FREEBSD deleted file mode 100644 index d7ad931ca1b6..000000000000 --- a/lib/libm/README-FREEBSD +++ /dev/null @@ -1,7 +0,0 @@ -$FreeBSD$ - -The libm library has been superceded by the msun library.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 7cdda2f4be36..000000000000 --- 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 -__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 084d8bbe5759..000000000000 --- 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 -__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 -#include "mathimpl.h" -#include - -/* 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 fb873c62133e..000000000000 --- 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 -__FBSDID("$FreeBSD$"); - -#ifndef lint -static char sccsid[] = "@(#)log.c 8.2 (Berkeley) 11/30/93"; -#endif /* not lint */ - -#include -#include - -#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 6a2a37d9f811..000000000000 --- 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 -#include - -#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));