s_expm1f.c - vx32 - Local 9vx git repository for patches.
(HTM) git clone git://r-36.net/vx32
(DIR) Log
(DIR) Files
(DIR) Refs
---
s_expm1f.c (3677B)
---
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 #ifndef lint
17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_expm1f.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
18 #endif
19
20 #include "math.h"
21 #include "math_private.h"
22
23 static const float
24 one = 1.0,
25 huge = 1.0e+30,
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 /* scaled coefficients related to expm1 */
32 Q1 = -3.3333335072e-02, /* 0xbd088889 */
33 Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
34 Q3 = -7.9365076090e-05, /* 0xb8a670cd */
35 Q4 = 4.0082177293e-06, /* 0x36867e54 */
36 Q5 = -2.0109921195e-07; /* 0xb457edbb */
37
38 float
39 expm1f(float x)
40 {
41 float y,hi,lo,c,t,e,hxs,hfx,r1;
42 int32_t k,xsb;
43 u_int32_t hx;
44
45 GET_FLOAT_WORD(hx,x);
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| */
49
50 /* filter out huge and non-finite argument */
51 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
52 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
53 if(hx>0x7f800000)
54 return x+x; /* NaN */
55 if(hx==0x7f800000)
56 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
57 if(x > o_threshold) return huge*huge; /* overflow */
58 }
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 */
62 }
63 }
64
65 /* argument reduction */
66 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
67 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
68 if(xsb==0)
69 {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
70 else
71 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
72 } else {
73 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
74 t = k;
75 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
76 lo = t*ln2_lo;
77 }
78 x = hi - lo;
79 c = (hi-x)-lo;
80 }
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));
84 }
85 else k = 0;
86
87 /* x is now in primary range */
88 hfx = (float)0.5*x;
89 hxs = x*hfx;
90 r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
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 */
94 else {
95 e = (x*(e-c)-c);
96 e -= hxs;
97 if(k== -1) return (float)0.5*(x-e)-(float)0.5;
98 if(k==1)
99 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
100 else return one+(float)2.0*(x-e);
101 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
102 int32_t i;
103 y = one-(e-x);
104 GET_FLOAT_WORD(i,y);
105 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
106 return y-one;
107 }
108 t = one;
109 if(k<23) {
110 int32_t i;
111 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
112 y = t-(e-x);
113 GET_FLOAT_WORD(i,y);
114 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
115 } else {
116 int32_t i;
117 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
118 y = x-(e+t);
119 y += one;
120 GET_FLOAT_WORD(i,y);
121 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
122 }
123 }
124 return y;
125 }