1/* s_expm1f.c -- float version of s_expm1.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
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
12 * is preserved.
13 * ====================================================
14 */
15
16#include <sys/cdefs.h>
17__FBSDID("$FreeBSD: head/lib/msun/src/s_expm1f.c 226596 2011-10-21 06:26:38Z das $");
18
19#include <float.h>
20
21#include "math.h"
22#include "math_private.h"
23
24static const float
25one = 1.0,
26huge = 1.0e+30,
27tiny = 1.0e-30,
28o_threshold = 8.8721679688e+01,/* 0x42b17180 */
29ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
30ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
31invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
32/*
33 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
34 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
35 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
36 */
37Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
38Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
39
40float
41expm1f(float x)
42{
43 float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
44 int32_t k,xsb;
45 u_int32_t hx;
46
47 GET_FLOAT_WORD(hx,x);
48 xsb = hx&0x80000000; /* sign bit of x */
49 hx &= 0x7fffffff; /* high word of |x| */
50
51 /* filter out huge and non-finite argument */
52 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
53 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
54 if(hx>0x7f800000)
55 return x+x; /* NaN */
56 if(hx==0x7f800000)
57 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
58 if(x > o_threshold) return huge*huge; /* overflow */
59 }
60 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
61 if(x+tiny<(float)0.0) /* raise inexact */
62 return tiny-one; /* return -1 */
63 }
64 }
65
66 /* argument reduction */
67 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
68 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
69 if(xsb==0)
70 {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
71 else
72 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
73 } else {
74 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
75 t = k;
76 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
77 lo = t*ln2_lo;
78 }
79 STRICT_ASSIGN(float, x, hi - lo);
80 c = (hi-x)-lo;
81 }
82 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
83 t = huge+x; /* return x with inexact flags when x!=0 */
84 return x - (t-(huge+x));
85 }
86 else k = 0;
87
88 /* x is now in primary range */
89 hfx = (float)0.5*x;
90 hxs = x*hfx;
91 r1 = one+hxs*(Q1+hxs*Q2);
92 t = (float)3.0-r1*hfx;
93 e = hxs*((r1-t)/((float)6.0 - x*t));
94 if(k==0) return x - (x*e-hxs); /* c is 0 */
95 else {
96 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */
97 e = (x*(e-c)-c);
98 e -= hxs;
99 if(k== -1) return (float)0.5*(x-e)-(float)0.5;
100 if(k==1) {
101 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
102 else return one+(float)2.0*(x-e);
103 }
104 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
105 y = one-(e-x);
106 if (k == 128) y = y*2.0F*0x1p127F;
107 else y = y*twopk;
108 return y-one;
109 }
110 t = one;
111 if(k<23) {
112 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
113 y = t-(e-x);
114 y = y*twopk;
115 } else {
116 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
117 y = x-(e+t);
118 y += one;
119 y = y*twopk;
120 }
121 }
122 return y;
123}