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 <errno.h>
17#include <float.h>
18#include <math.h>
19#include <math-barriers.h>
20#include <math_private.h>
21#include <math-underflow.h>
22#include <libm-alias-float.h>
23
24static const float huge = 1.0e+30;
25static const float tiny = 1.0e-30;
26
27static const float
28one = 1.0,
29o_threshold = 8.8721679688e+01,/* 0x42b17180 */
30ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
31ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
32invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
33 /* scaled coefficients related to expm1 */
34Q1 = -3.3333335072e-02, /* 0xbd088889 */
35Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
36Q3 = -7.9365076090e-05, /* 0xb8a670cd */
37Q4 = 4.0082177293e-06, /* 0x36867e54 */
38Q5 = -2.0109921195e-07; /* 0xb457edbb */
39
40float
41__expm1f(float x)
42{
43 float y,hi,lo,c,t,e,hxs,hfx,r1;
44 int32_t k,xsb;
45 uint32_t hx;
46
47 GET_FLOAT_WORD(hx,x);
48 xsb = hx&0x80000000; /* sign bit of x */
49 if(xsb==0) y=x; else y= -x; /* y = |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) {
60 __set_errno (ERANGE);
61 return huge*huge; /* overflow */
62 }
63 }
64 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
65 math_force_eval(x+tiny);/* raise inexact */
66 return tiny-one; /* return -1 */
67 }
68 }
69
70 /* argument reduction */
71 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
72 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
73 if(xsb==0)
74 {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
75 else
76 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
77 } else {
78 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
79 t = k;
80 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
81 lo = t*ln2_lo;
82 }
83 x = hi - lo;
84 c = (hi-x)-lo;
85 }
86 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
87 math_check_force_underflow (x);
88 t = huge+x; /* return x with inexact flags when x!=0 */
89 return x - (t-(huge+x));
90 }
91 else k = 0;
92
93 /* x is now in primary range */
94 hfx = (float)0.5*x;
95 hxs = x*hfx;
96 r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
97 t = (float)3.0-r1*hfx;
98 e = hxs*((r1-t)/((float)6.0 - x*t));
99 if(k==0) return x - (x*e-hxs); /* c is 0 */
100 else {
101 e = (x*(e-c)-c);
102 e -= hxs;
103 if(k== -1) return (float)0.5*(x-e)-(float)0.5;
104 if(k==1) {
105 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
106 else return one+(float)2.0*(x-e);
107 }
108 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
109 int32_t i;
110 y = one-(e-x);
111 GET_FLOAT_WORD(i,y);
112 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
113 return y-one;
114 }
115 t = one;
116 if(k<23) {
117 int32_t i;
118 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
119 y = t-(e-x);
120 GET_FLOAT_WORD(i,y);
121 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
122 } else {
123 int32_t i;
124 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
125 y = x-(e+t);
126 y += one;
127 GET_FLOAT_WORD(i,y);
128 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
129 }
130 }
131 return y;
132}
133libm_alias_float (__expm1, expm1)
134