mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-23 13:30:06 +00:00
137 lines
3.8 KiB
C
137 lines
3.8 KiB
C
/* s_expm1f.c -- float version of s_expm1.c.
|
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
#if defined(LIBM_SCCS) && !defined(lint)
|
|
static char rcsid[] = "$NetBSD: s_expm1f.c,v 1.5 1995/05/10 20:47:11 jtc Exp $";
|
|
#endif
|
|
|
|
#include "math.h"
|
|
#include "math_private.h"
|
|
|
|
static const volatile float huge = 1.0e+30;
|
|
static const volatile float tiny = 1.0e-30;
|
|
|
|
#ifdef __STDC__
|
|
static const float
|
|
#else
|
|
static float
|
|
#endif
|
|
one = 1.0,
|
|
o_threshold = 8.8721679688e+01,/* 0x42b17180 */
|
|
ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
|
|
ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
|
|
invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
|
|
/* scaled coefficients related to expm1 */
|
|
Q1 = -3.3333335072e-02, /* 0xbd088889 */
|
|
Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
|
|
Q3 = -7.9365076090e-05, /* 0xb8a670cd */
|
|
Q4 = 4.0082177293e-06, /* 0x36867e54 */
|
|
Q5 = -2.0109921195e-07; /* 0xb457edbb */
|
|
|
|
#ifdef __STDC__
|
|
float __expm1f(float x)
|
|
#else
|
|
float __expm1f(x)
|
|
float x;
|
|
#endif
|
|
{
|
|
float y,hi,lo,c,t,e,hxs,hfx,r1;
|
|
int32_t k,xsb;
|
|
u_int32_t hx;
|
|
|
|
GET_FLOAT_WORD(hx,x);
|
|
xsb = hx&0x80000000; /* sign bit of x */
|
|
if(xsb==0) y=x; else y= -x; /* y = |x| */
|
|
hx &= 0x7fffffff; /* high word of |x| */
|
|
|
|
/* filter out huge and non-finite argument */
|
|
if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
|
|
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
|
|
if(hx>0x7f800000)
|
|
return x+x; /* NaN */
|
|
if(hx==0x7f800000)
|
|
return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
|
|
if(x > o_threshold) return huge*huge; /* overflow */
|
|
}
|
|
if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
|
|
if(x+tiny<(float)0.0) /* raise inexact */
|
|
return tiny-one; /* return -1 */
|
|
}
|
|
}
|
|
|
|
/* argument reduction */
|
|
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
|
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
|
|
if(xsb==0)
|
|
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
|
|
else
|
|
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
|
|
} else {
|
|
k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
|
|
t = k;
|
|
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
|
|
lo = t*ln2_lo;
|
|
}
|
|
x = hi - lo;
|
|
c = (hi-x)-lo;
|
|
}
|
|
else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
|
|
t = huge+x; /* return x with inexact flags when x!=0 */
|
|
return x - (t-(huge+x));
|
|
}
|
|
else k = 0;
|
|
|
|
/* x is now in primary range */
|
|
hfx = (float)0.5*x;
|
|
hxs = x*hfx;
|
|
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
|
|
t = (float)3.0-r1*hfx;
|
|
e = hxs*((r1-t)/((float)6.0 - x*t));
|
|
if(k==0) return x - (x*e-hxs); /* c is 0 */
|
|
else {
|
|
e = (x*(e-c)-c);
|
|
e -= hxs;
|
|
if(k== -1) return (float)0.5*(x-e)-(float)0.5;
|
|
if(k==1) {
|
|
if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
|
|
else return one+(float)2.0*(x-e);
|
|
}
|
|
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
|
|
int32_t i;
|
|
y = one-(e-x);
|
|
GET_FLOAT_WORD(i,y);
|
|
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
|
return y-one;
|
|
}
|
|
t = one;
|
|
if(k<23) {
|
|
int32_t i;
|
|
SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
|
|
y = t-(e-x);
|
|
GET_FLOAT_WORD(i,y);
|
|
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
|
} else {
|
|
int32_t i;
|
|
SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
|
|
y = x-(e+t);
|
|
y += one;
|
|
GET_FLOAT_WORD(i,y);
|
|
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
|
|
}
|
|
}
|
|
return y;
|
|
}
|
|
weak_alias (__expm1f, expm1f)
|