libm/upstream-freebsd/lib/msun/src/e_expf.c

/* e_expf.c -- float version of e_exp.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.
 * ====================================================
 */

#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");

#include <float.h>

#include "math.h"
#include "math_private.h"

static const float
one	= 1.0,
halF[2]	= {0.5,-0.5,},
huge	= 1.0e+30,
o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
ln2HI[2]   ={ 6.9314575195e-01,		/* 0x3f317200 */
	     -6.9314575195e-01,},	/* 0xbf317200 */
ln2LO[2]   ={ 1.4286067653e-06,  	/* 0x35bfbe8e */
	     -1.4286067653e-06,},	/* 0xb5bfbe8e */
invln2 =  1.4426950216e+00, 		/* 0x3fb8aa3b */
/*
 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
 */
P1 =  1.6666625440e-1,		/*  0xaaaa8f.0p-26 */
P2 = -2.7667332906e-3;		/* -0xb55215.0p-32 */

static volatile float twom100 = 7.8886090522e-31;      /* 2**-100=0x0d800000 */

float
__ieee754_expf(float x)
{
	float y,hi=0.0,lo=0.0,c,t,twopk;
	int32_t k=0,xsb;
	u_int32_t hx;

	GET_FLOAT_WORD(hx,x);
	xsb = (hx>>31)&1;		/* sign bit of x */
	hx &= 0x7fffffff;		/* high word of |x| */

    /* filter out non-finite argument */
	if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
	    if(hx>0x7f800000)
		 return x+x;	 		/* NaN */
            if(hx==0x7f800000)
		return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
	    if(x > o_threshold) return huge*huge; /* overflow */
	    if(x < u_threshold) return twom100*twom100; /* underflow */
	}

    /* argument reduction */
	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
	    } else {
		k  = invln2*x+halF[xsb];
		t  = k;
		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
		lo = t*ln2LO[0];
	    }
	    STRICT_ASSIGN(float, x, hi - lo);
	}
	else if(hx < 0x39000000)  {	/* when |x|<2**-14 */
	    if(huge+x>one) return one+x;/* trigger inexact */
	}
	else k = 0;

    /* x is now in primary range */
	t  = x*x;
	if(k >= -125)
	    SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));
	else
	    SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23));
	c  = x - t*(P1+t*P2);
	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x);
	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);
	if(k >= -125) {
	    if(k==128) return y*2.0F*0x1p127F;
	    return y*twopk;
	} else {
	    return y*twopk*twom100;
	}
}