musl/src/math/s_expm1f.c

/* s_expm1f.c -- float version of s_expm1.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
 */

/*
 * ====================================================
 * 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 float
one             = 1.0,
huge            = 1.0e+30,
tiny            = 1.0e-30,
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=0.0,t,e,hxs,hfx,r1;
        int32_t k,xsb;
        uint32_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;
}