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 #if defined(LIBM_SCCS) && !defined(lint)
18 __RCSID("$NetBSD: s_expm1f.c,v 1.11 2017/02/09 22:11:09 maya Exp $");
19 #endif
20
21 #include "math.h"
22 #include "math_private.h"
23
24 static const float huge = 1.0e+30, tiny = 1.0e-30;
25
26 static const float
27 one = 1.0,
28 o_threshold = 8.8721679688e+01,/* 0x42b17180 */
29 ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
30 ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
31 invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
32 /* scaled coefficients related to expm1 */
33 Q1 = -3.3333335072e-02, /* 0xbd088889 */
34 Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
35 Q3 = -7.9365076090e-05, /* 0xb8a670cd */
36 Q4 = 4.0082177293e-06, /* 0x36867e54 */
37 Q5 = -2.0109921195e-07; /* 0xb457edbb */
38
39 float
expm1f(float x)40 expm1f(float x)
41 {
42 float y,hi,lo,c,t,e,hxs,hfx,r1;
43 int32_t k,xsb;
44 u_int32_t hx;
45
46 c = 0;
47 GET_FLOAT_WORD(hx,x);
48 xsb = hx&0x80000000; /* sign bit of x */
49 #ifdef DEAD_CODE
50 if(xsb==0) y=x; else y= -x; /* y = |x| */
51 #endif
52 hx &= 0x7fffffff; /* high word of |x| */
53
54 /* filter out huge and non-finite argument */
55 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
56 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
57 if(hx>0x7f800000)
58 return x+x; /* NaN */
59 if(hx==0x7f800000)
60 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
61 if(x > o_threshold) return huge*huge; /* overflow */
62 }
63 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
64 if(x+tiny<(float)0.0) /* raise inexact */
65 return tiny-one; /* return -1 */
66 }
67 }
68
69 /* argument reduction */
70 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
71 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
72 if(xsb==0)
73 {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
74 else
75 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
76 } else {
77 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
78 t = k;
79 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
80 lo = t*ln2_lo;
81 }
82 x = hi - lo;
83 c = (hi-x)-lo;
84 }
85 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
86 t = huge+x; /* return x with inexact flags when x!=0 */
87 return x - (t-(huge+x));
88 }
89 else k = 0;
90
91 /* x is now in primary range */
92 hfx = (float)0.5*x;
93 hxs = x*hfx;
94 r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
95 t = (float)3.0-r1*hfx;
96 e = hxs*((r1-t)/((float)6.0 - x*t));
97 if(k==0) return x - (x*e-hxs); /* c is 0 */
98 else {
99 e = (x*(e-c)-c);
100 e -= hxs;
101 if(k== -1) return (float)0.5*(x-e)-(float)0.5;
102 if(k==1) {
103 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
104 else return one+(float)2.0*(x-e);
105 }
106 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
107 int32_t i;
108 y = one-(e-x);
109 GET_FLOAT_WORD(i,y);
110 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
111 return y-one;
112 }
113 t = one;
114 if(k<23) {
115 int32_t i;
116 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
117 y = t-(e-x);
118 GET_FLOAT_WORD(i,y);
119 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
120 } else {
121 int32_t i;
122 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
123 y = x-(e+t);
124 y += one;
125 GET_FLOAT_WORD(i,y);
126 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
127 }
128 }
129 return y;
130 }
131