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  • Committer: Package Import Robot
  • Author(s): Kevin Bortis
  • Date: 2013-09-20 20:54:14 UTC
  • Revision ID: package-import@ubuntu.com-20130920205414-5b61trtmma18w58o
Tags: upstream-0.9.13
Import upstream version 0.9.13

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src/math/expm1f.c
 
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/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
 
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/*
 
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 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 
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 */
 
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/*
 
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 * ====================================================
 
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 
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 *
 
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
 
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 * Permission to use, copy, modify, and distribute this
 
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 * software is freely granted, provided that this notice
 
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 * is preserved.
 
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 * ====================================================
 
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 */
 
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#include "libm.h"
 
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static const float
 
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huge        = 1.0e+30,
 
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tiny        = 1.0e-30,
 
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o_threshold = 8.8721679688e+01, /* 0x42b17180 */
 
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ln2_hi      = 6.9313812256e-01, /* 0x3f317180 */
 
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ln2_lo      = 9.0580006145e-06, /* 0x3717f7d1 */
 
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invln2      = 1.4426950216e+00, /* 0x3fb8aa3b */
 
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/*
 
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 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
 
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 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
 
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 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
 
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 */
 
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Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
 
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Q2 =  1.5807170421e-3; /*  0xcf3010.0p-33 */
 
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float expm1f(float x)
 
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{
 
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        float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
 
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        int32_t k,xsb;
 
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        uint32_t hx;
 
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        GET_FLOAT_WORD(hx, x);
 
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        xsb = hx&0x80000000;  /* sign bit of x */
 
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        hx &= 0x7fffffff;     /* high word of |x| */
 
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        /* filter out huge and non-finite argument */
 
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        if (hx >= 0x4195b844) {  /* if |x|>=27*ln2 */
 
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                if (hx >= 0x42b17218) {  /* if |x|>=88.721... */
 
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                        if (hx > 0x7f800000)  /* NaN */
 
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                                return x+x;
 
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                        if (hx == 0x7f800000) /* exp(+-inf)={inf,-1} */
 
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                                return xsb==0 ? x : -1.0;
 
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                        if (x > o_threshold)
 
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                                return huge*huge; /* overflow */
 
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                }
 
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                if (xsb != 0) {  /* x < -27*ln2 */
 
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                        /* raise inexact */
 
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                        if (x+tiny < 0.0f)
 
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                                return tiny-1.0f;  /* return -1 */
 
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                }
 
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        }
 
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        /* argument reduction */
 
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        if (hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
 
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                if (hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
 
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                        if (xsb == 0) {
 
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                                hi = x - ln2_hi;
 
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                                lo = ln2_lo;
 
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                                k =  1;
 
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                        } else {
 
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                                hi = x + ln2_hi;
 
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                                lo = -ln2_lo;
 
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                                k = -1;
 
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                        }
 
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                } else {
 
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                        k  = invln2*x + (xsb==0 ? 0.5f : -0.5f);
 
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                        t  = k;
 
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                        hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
 
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                        lo = t*ln2_lo;
 
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                }
 
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                STRICT_ASSIGN(float, x, hi - lo);
 
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                c = (hi-x)-lo;
 
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        } else if (hx < 0x33000000) {  /* when |x|<2**-25, return x */
 
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                t = huge+x; /* return x with inexact flags when x!=0 */
 
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                return x - (t-(huge+x));
 
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        } else
 
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                k = 0;
 
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        /* x is now in primary range */
 
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        hfx = 0.5f*x;
 
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        hxs = x*hfx;
 
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        r1 = 1.0f+hxs*(Q1+hxs*Q2);
 
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        t  = 3.0f - r1*hfx;
 
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        e  = hxs*((r1-t)/(6.0f - x*t));
 
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        if (k == 0)  /* c is 0 */
 
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                return x - (x*e-hxs);
 
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        SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));   /* 2^k */
 
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        e  = x*(e-c) - c;
 
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        e -= hxs;
 
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        if (k == -1)
 
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                return 0.5f*(x-e) - 0.5f;
 
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        if (k == 1) {
 
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                if (x < -0.25f)
 
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                        return -2.0f*(e-(x+0.5f));
 
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                return 1.0f + 2.0f*(x-e);
 
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        }
 
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        if (k <= -2 || k > 56) {   /* suffice to return exp(x)-1 */
 
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                y = 1.0f - (e - x);
 
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                if (k == 128)
 
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                        y = y*2.0f*0x1p127f;
 
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                else
 
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                        y = y*twopk;
 
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                return y - 1.0f;
 
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        }
 
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        t = 1.0f;
 
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        if (k < 23) {
 
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                SET_FLOAT_WORD(t, 0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
 
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                y = t - (e - x);
 
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                y = y*twopk;
 
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        } else {
 
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                SET_FLOAT_WORD(t, (0x7f-k)<<23);  /* 2^-k */
 
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                y = x - (e + t);
 
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                y += 1.0f;
 
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                y = y*twopk;
 
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        }
 
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        return y;
 
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}