124 lines
3.5 KiB
C
124 lines
3.5 KiB
C
/* s_expm1f.c -- float version of s_expm1.c.
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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 "cdefs-compat.h"
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//__FBSDID("$FreeBSD: src/lib/msun/src/s_expm1f.c,v 1.12 2011/10/21 06:26:38 das Exp $");
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#include <float.h>
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#include <openlibm_math.h>
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#include "math_private.h"
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static const float
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one = 1.0,
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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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OLM_DLLEXPORT float
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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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u_int32_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)
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return x+x; /* NaN */
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if(hx==0x7f800000)
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return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
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if(x > o_threshold) return huge*huge; /* overflow */
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}
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if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
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if(x+tiny<(float)0.0) /* raise inexact */
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return tiny-one; /* 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; lo = ln2_lo; k = 1;}
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else
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{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
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} else {
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k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
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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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}
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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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}
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else k = 0;
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/* x is now in primary range */
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hfx = (float)0.5*x;
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hxs = x*hfx;
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r1 = one+hxs*(Q1+hxs*Q2);
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t = (float)3.0-r1*hfx;
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e = hxs*((r1-t)/((float)6.0 - x*t));
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if(k==0) return x - (x*e-hxs); /* c is 0 */
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else {
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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) return (float)0.5*(x-e)-(float)0.5;
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if(k==1) {
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if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
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else return one+(float)2.0*(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 = one-(e-x);
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if (k == 128) y = y*2.0F*0x1p127F;
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else y = y*twopk;
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return y-one;
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}
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t = one;
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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 += one;
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y = y*twopk;
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}
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}
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return y;
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}
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