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/* See the import.pl script for potential modifications */
/* s_expm1f.c -- Simple version of s_expm1.c.
* Conversion to Simple 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 1.5f 1995/05/10 20:47:11 jtc Exp $";
#endif
#include "SMath.h"
#include "math_private.h"
static const Simple huge = 1.0e+30f;
static const Simple tiny = 1.0e-30f;
namespace streflop_libm {
#ifdef __STDC__
static const Simple
#else
static Simple
#endif
one = 1.0f,
o_threshold = 8.8721679688e+01f,/* 0x42b17180 */
ln2_hi = 6.9313812256e-01f,/* 0x3f317180 */
ln2_lo = 9.0580006145e-06f,/* 0x3717f7d1 */
invln2 = 1.4426950216e+00f,/* 0x3fb8aa3b */
/* scaled coefficients related to expm1 */
Q1 = -3.3333335072e-02f, /* 0xbd088889 */
Q2 = 1.5873016091e-03f, /* 0x3ad00d01 */
Q3 = -7.9365076090e-05f, /* 0xb8a670cd */
Q4 = 4.0082177293e-06f, /* 0x36867e54 */
Q5 = -2.0109921195e-07f; /* 0xb457edbb */
#ifdef __STDC__
Simple __expm1f(Simple x)
#else
Simple __expm1f(x)
Simple x;
#endif
{
Simple 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|>=88.721f... */
if(hx>0x7f800000)
return x+x; /* NaN */
if(hx==0x7f800000)
return (xsb==0)? x:-Simple(1.0f);/* exp(+-inf)={inf,-1} */
if(x > o_threshold) return huge*huge; /* overflow */
}
if(xsb!=0) { /* x < -27*ln2, return -1.0f with inexact */
if(x+tiny<(Simple)0.0f) /* raise inexact */
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if(hx > 0x3eb17218) { /* if |x| > 0.5f ln2 */
if(hx < 0x3F851592) { /* and |x| < 1.5f 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)?(Simple)0.5f:(Simple)-0.5f);
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 = (Simple)0.5f*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
t = (Simple)3.0f-r1*hfx;
e = hxs*((r1-t)/((Simple)6.0f - 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 (Simple)0.5f*(x-e)-(Simple)0.5f;
if(k==1) {
if(x < (Simple)-0.25f) return -(Simple)2.0f*(e-(x+(Simple)0.5f));
else return one+(Simple)2.0f*(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)
}
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