1 /* s_expm1f.c -- float version of s_expm1.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
13 * ====================================================
16 #include <sys/cdefs.h>
17 __FBSDID("$FreeBSD$");
20 #include "math_private.h"
26 o_threshold = 8.8721679688e+01,/* 0x42b17180 */
27 ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
28 ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
29 invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
31 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
32 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
33 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
35 Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
36 Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
41 float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
46 xsb = hx&0x80000000; /* sign bit of x */
47 if(xsb==0) y=x; else y= -x; /* y = |x| */
48 hx &= 0x7fffffff; /* high word of |x| */
50 /* filter out huge and non-finite argument */
51 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
52 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
56 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
57 if(x > o_threshold) return huge*huge; /* overflow */
59 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
60 if(x+tiny<(float)0.0) /* raise inexact */
61 return tiny-one; /* return -1 */
65 /* argument reduction */
66 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
67 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
69 {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
71 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
73 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
75 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
81 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
82 t = huge+x; /* return x with inexact flags when x!=0 */
83 return x - (t-(huge+x));
87 /* x is now in primary range */
90 r1 = one+hxs*(Q1+hxs*Q2);
91 t = (float)3.0-r1*hfx;
92 e = hxs*((r1-t)/((float)6.0 - x*t));
93 if(k==0) return x - (x*e-hxs); /* c is 0 */
95 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */
98 if(k== -1) return (float)0.5*(x-e)-(float)0.5;
100 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
101 else return one+(float)2.0*(x-e);
103 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
105 if (k == 128) y = y*2.0F*0x1p127F;
111 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
115 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */