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("$FreeBSD$");
18
19 #include <float.h>
20
21 #include "math.h"
22 #include "math_private.h"
23
24 static const float
25 one = 1.0,
26 tiny = 1.0e-30,
27 o_threshold = 8.8721679688e+01,/* 0x42b17180 */
28 ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
29 ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
30 invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
31 /*
32 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
33 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
34 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
35 */
36 Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
37 Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
38
39 static volatile float huge = 1.0e+30;
40
41 float
expm1f(float x)42 expm1f(float x)
43 {
44 float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
45 int32_t k,xsb;
46 u_int32_t hx;
47
48 GET_FLOAT_WORD(hx,x);
49 xsb = hx&0x80000000; /* sign bit of x */
50 hx &= 0x7fffffff; /* high word of |x| */
51
52 /* filter out huge and non-finite argument */
53 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
54 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
55 if(hx>0x7f800000)
56 return x+x; /* NaN */
57 if(hx==0x7f800000)
58 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
59 if(x > o_threshold) return huge*huge; /* overflow */
60 }
61 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
62 if(x+tiny<(float)0.0) /* raise inexact */
63 return tiny-one; /* return -1 */
64 }
65 }
66
67 /* argument reduction */
68 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
69 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
70 if(xsb==0)
71 {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
72 else
73 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
74 } else {
75 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
76 t = k;
77 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
78 lo = t*ln2_lo;
79 }
80 STRICT_ASSIGN(float, x, hi - lo);
81 c = (hi-x)-lo;
82 }
83 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
84 t = huge+x; /* return x with inexact flags when x!=0 */
85 return x - (t-(huge+x));
86 }
87 else k = 0;
88
89 /* x is now in primary range */
90 hfx = (float)0.5*x;
91 hxs = x*hfx;
92 r1 = one+hxs*(Q1+hxs*Q2);
93 t = (float)3.0-r1*hfx;
94 e = hxs*((r1-t)/((float)6.0 - x*t));
95 if(k==0) return x - (x*e-hxs); /* c is 0 */
96 else {
97 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */
98 e = (x*(e-c)-c);
99 e -= hxs;
100 if(k== -1) return (float)0.5*(x-e)-(float)0.5;
101 if(k==1) {
102 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
103 else return one+(float)2.0*(x-e);
104 }
105 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
106 y = one-(e-x);
107 if (k == 128) y = y*2.0F*0x1p127F;
108 else y = y*twopk;
109 return y-one;
110 }
111 t = one;
112 if(k<23) {
113 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
114 y = t-(e-x);
115 y = y*twopk;
116 } else {
117 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
118 y = x-(e+t);
119 y += one;
120 y = y*twopk;
121 }
122 }
123 return y;
124 }
125