From: Zhishun Alex Liu Date: Sat, 7 Sep 1985 08:53:04 +0000 (-0800) Subject: date and time created 85/09/06 17:53:04 by zliu X-Git-Tag: BSD-4_3-Snapshot-Development~4684 X-Git-Url: https://git.subgeniuskitty.com/unix-history/.git/commitdiff_plain/9f4a7cc18cb9ce750440a7b59999c6a25f2e7ec4 date and time created 85/09/06 17:53:04 by zliu SCCS-vsn: lib/libm/common_source/pow.c 1.1 --- diff --git a/usr/src/lib/libm/common_source/pow.c b/usr/src/lib/libm/common_source/pow.c new file mode 100644 index 0000000000..e325f0e16d --- /dev/null +++ b/usr/src/lib/libm/common_source/pow.c @@ -0,0 +1,226 @@ +/* + * Copyright (c) 1985 Regents of the University of California. + * + * Use and reproduction of this software are granted in accordance with + * the terms and conditions specified in the Berkeley Software License + * Agreement (in particular, this entails acknowledgement of the programs' + * source, and inclusion of this notice) with the additional understanding + * that all recipients should regard themselves as participants in an + * ongoing research project and hence should feel obligated to report + * their experiences (good or bad) with these elementary function codes, + * using "sendbug 4bsd-bugs@BERKELEY", to the authors. + */ + +#ifndef lint +static char sccsid[] = "@(#)pow.c 1.1 (ELEFUNT) %G%"; +#endif not lint + +/* POW(X,Y) + * RETURN X**Y + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/8/85; + * REVISED BY K.C. NG on 7/10/85. + * + * Required system supported functions: + * scalb(x,n) + * logb(x) + * copysign(x,y) + * finite(x) + * drem(x,y) + * + * Required kernel functions: + * exp__E(a,c) ...return exp(a+c) - 1 - a*a/2 + * log__L(x) ...return (log(1+x) - 2s)/s, s=x/(2+x) + * pow_p(x,y) ...return +(anything)**(finite non zero) + * + * Method + * 1. Compute and return log(x) in three pieces: + * log(x) = n*ln2 + hi + lo, + * where n is an integer. + * 2. Perform y*log(x) by simulating muti-precision arithmetic and + * return the answer in three pieces: + * y*log(x) = m*ln2 + hi + lo, + * where m is an integer. + * 3. Return x**y = exp(y*log(x)) + * = 2^m * ( exp(hi+lo) ). + * + * Special cases: + * (anything) ** 0 is 1 ; + * (anything) ** 1 is itself; + * (anything) ** NaN is NaN; + * NaN ** (anything except 0) is NaN; + * +-(anything > 1) ** +INF is +INF; + * +-(anything > 1) ** -INF is +0; + * +-(anything < 1) ** +INF is +0; + * +-(anything < 1) ** -INF is +INF; + * +-1 ** +-INF is NaN and signal INVALID; + * +0 ** +(anything except 0, NaN) is +0; + * -0 ** +(anything except 0, NaN, odd integer) is +0; + * +0 ** -(anything except 0, NaN) is +INF and signal DIV-BY-ZERO; + * -0 ** -(anything except 0, NaN, odd integer) is +INF with signal; + * -0 ** (odd integer) = -( +0 ** (odd integer) ); + * +INF ** +(anything except 0,NaN) is +INF; + * +INF ** -(anything except 0,NaN) is +0; + * -INF ** (odd integer) = -( +INF ** (odd integer) ); + * -INF ** (even integer) = ( +INF ** (even integer) ); + * -INF ** -(anything except integer,NaN) is NaN with signal; + * -(x=anything) ** (k=integer) is (-1)**k * (x ** k); + * -(anything except 0) ** (non-integer) is NaN with signal; + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX, + * and a Zilog Z8000, + * pow(integer,integer) + * always returns the correct integer provided it is representable. + * In a test run with 100,000 random arguments with 0 < x, y < 20.0 + * on a VAX, the maximum observed error was 1.79 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. + */ + +#ifdef VAX /* VAX D format */ +#include +extern double infnan(); + +/* double static */ +/* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */ +/* ln2lo = 1.6465949582897081279E-12 , Hex 2^-39 * .E7BCD5E4F1D9CC */ +/* invln2 = 1.4426950408889634148E0 , Hex 2^ 1 * .B8AA3B295C17F1 */ +/* sqrt2 = 1.4142135623730950622E0 ; Hex 2^ 1 * .B504F333F9DE65 */ +static long ln2hix[] = { 0x72174031, 0x0000f7d0}; +static long ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1}; +static long invln2x[] = { 0xaa3b40b8, 0x17f1295c}; +static long sqrt2x[] = { 0x04f340b5, 0xde6533f9}; +#define ln2hi (*(double*)ln2hix) +#define ln2lo (*(double*)ln2lox) +#define invln2 (*(double*)invln2x) +#define sqrt2 (*(double*)sqrt2x) +#else /* IEEE double */ +double static +ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */ +ln2lo = 1.9082149292705877000E-10 , /*Hex 2^-33 * 1.A39EF35793C76 */ +invln2 = 1.4426950408889633870E0 , /*Hex 2^ 0 * 1.71547652B82FE */ +sqrt2 = 1.4142135623730951455E0 ; /*Hex 2^ 0 * 1.6A09E667F3BCD */ +#endif + +double static zero=0.0, half=1.0/2.0, one=1.0, two=2.0, negone= -1.0; + +double pow(x,y) +double x,y; +{ + double drem(),pow_p(),copysign(),t; + int finite(); + + if (y==zero) return(one); + else if(y==one +#ifndef VAX + ||x!=x +#endif + ) return( x ); /* if x is NaN or y=1 */ +#ifndef VAX + else if(y!=y) return( y ); /* if y is NaN */ +#endif + else if(!finite(y)) /* if y is INF */ + if((t=copysign(x,one))==one) return(zero/zero); + else if(t>one) return((y>zero)?y:zero); + else return((yzero)?-x:one/(-x)); + else { /* return NaN */ +#ifdef VAX + return (infnan(EDOM)); /* NaN */ +#else /* IEEE double */ + return(zero/zero); +#endif + } +} + +/* pow_p(x,y) return x**y for x with sign=1 and finite y */ +static double pow_p(x,y) +double x,y; +{ + double logb(),scalb(),copysign(),log__L(),exp__E(); + double c,s,t,z,tx,ty; + float sx,sy; + long k=0; + int n,m; + + if(x==zero||!finite(x)) { /* if x is +INF or +0 */ +#ifdef VAX + return((y>zero)?x:infnan(ERANGE)); /* if yzero)?x:one/x); +#endif + } + if(x==1.0) return(x); /* if x=1.0, return 1 since y is finite */ + + /* reduce x to z in [sqrt(1/2)-1, sqrt(2)-1] */ + z=scalb(x,-(n=logb(x))); +#ifndef VAX /* IEEE double */ /* subnormal number */ + if(n <= -1022) {n += (m=logb(z)); z=scalb(z,-m);} +#endif + if(z >= sqrt2 ) {n += 1; z *= half;} z -= one ; + + /* log(x) = nlog2+log(1+z) ~ nlog2 + t + tx */ + s=z/(two+z); c=z*z*half; tx=s*(c+log__L(s*s)); + t= z-(c-tx); tx += (z-t)-c; + + /* if y*log(x) is neither too big nor too small */ + if((s=logb(y)+logb(n+t)) < 12.0) + if(s>-60.0) { + + /* compute y*log(x) ~ mlog2 + t + c */ + s=y*(n+invln2*t); + m=s+copysign(half,s); /* m := nint(y*log(x)) */ + k=y; + if((double)k==y) { /* if y is an integer */ + k = m-k*n; + sx=t; tx+=(t-sx); } + else { /* if y is not an integer */ + k =m; + tx+=n*ln2lo; + sx=(c=n*ln2hi)+t; tx+=(c-sx)+t; } + /* end of checking whether k==y */ + + sy=y; ty=y-sy; /* y ~ sy + ty */ + s=(double)sx*sy-k*ln2hi; /* (sy+ty)*(sx+tx)-kln2 */ + z=(tx*ty-k*ln2lo); + tx=tx*sy; ty=sx*ty; + t=ty+z; t+=tx; t+=s; + c= -((((t-s)-tx)-ty)-z); + + /* return exp(y*log(x)) */ + t += exp__E(t,c); return(scalb(one+t,m)); + } + /* end of if log(y*log(x)) > -60.0 */ + + else + /* exp(+- tiny) = 1 with inexact flag */ + {ln2hi+ln2lo; return(one);} + else if(copysign(one,y)*(n+invln2*t)