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new versions, mostly from Cody and Waite

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ceriel
1989-05-18 15:37:54 +00:00
parent b26f76ed3b
commit e95fbe2d60
10 changed files with 369 additions and 358 deletions
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69
lang/cem/libcc/math/exp.c
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@@ -1,5 +1,5 @@
/*
* (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands.
* (c) copyright 1989 by the Vrije Universiteit, Amsterdam, The Netherlands.
* See the copyright notice in the ACK home directory, in the file "Copyright".
*
* Author: Ceriel J.H. Jacobs
@@ -10,32 +10,33 @@
#include <math.h>
#include <errno.h>
extern int errno;
extern int errno;
extern double ldexp();
double
exp(x)
double x;
double x;
{
/* 2**x = (Q(x*x)+x*P(x*x))/(Q(x*x)-x*P(x*x)) for x in [0,0.5] */
/* Hart & Cheney #1069 */
/* Algorithm and coefficients from:
"Software manual for the elementary functions"
by W.J. Cody and W. Waite, Prentice-Hall, 1980
*/
static double p[3] = {
0.2080384346694663001443843411e+07,
0.3028697169744036299076048876e+05,
0.6061485330061080841615584556e+02
static double p[] = {
0.25000000000000000000e+0,
0.75753180159422776666e-2,
0.31555192765684646356e-4
};
static double q[4] = {
0.6002720360238832528230907598e+07,
0.3277251518082914423057964422e+06,
0.1749287689093076403844945335e+04,
0.1000000000000000000000000000e+01
static double q[] = {
0.50000000000000000000e+0,
0.56817302698551221787e-1,
0.63121894374398503557e-3,
0.75104028399870046114e-6
};
int negative = x < 0;
int ipart, large = 0;
double xsqr, xPxx, Qxx;
extern double floor(), ldexp();
double xn, g;
int n;
int negative = x < 0;
if (x <= M_LN_MIN_D) {
if (x < M_LN_MIN_D) errno = ERANGE;
@@ -46,22 +47,18 @@ exp(x)
return M_MAX_D;
}
if (negative) {
x = -x;
/* ??? avoid underflow ??? */
n = x * M_LOG2E + 0.5; /* 1/ln(2) = log2(e), 0.5 added for rounding */
xn = n;
{
double x1 = (long) x;
double x2 = x - x1;
g = ((x1-xn*0.693359375)+x2) - xn*(-2.1219444005469058277e-4);
}
x /= M_LN2;
ipart = floor(x);
x -= ipart;
if (x > 0.5) {
large = 1;
x -= 0.5;
}
xsqr = x * x;
xPxx = x * POLYNOM2(xsqr, p);
Qxx = POLYNOM3(xsqr, q);
x = (Qxx + xPxx) / (Qxx - xPxx);
if (large) x *= M_SQRT2;
x = ldexp(x, ipart);
if (negative) return 1.0/x;
return x;
xn = g * g;
x = g * POLYNOM2(xn, p);
n += 1;
return (ldexp(0.5 + x/(POLYNOM3(xn, q) - x), n));
}