s_expm1f.c

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/* 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.
 * ====================================================
 */

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

static const volatile float huge = 1.0e+30, tiny = 1.0e-30;

static const float
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 */

float
expm1f(float x)
{
    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;
}