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 | |
24 | static const float huge = 1.0e+30; |
25 | static const float tiny = 1.0e-30; |
26 | |
27 | static const float |
28 | one = 1.0, |
29 | o_threshold = 8.8721679688e+01,/* 0x42b17180 */ |
30 | ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ |
31 | ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ |
32 | invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ |
33 | /* scaled coefficients related to expm1 */ |
34 | Q1 = -3.3333335072e-02, /* 0xbd088889 */ |
35 | Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ |
36 | Q3 = -7.9365076090e-05, /* 0xb8a670cd */ |
37 | Q4 = 4.0082177293e-06, /* 0x36867e54 */ |
38 | Q5 = -2.0109921195e-07; /* 0xb457edbb */ |
39 | |
40 | float |
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 | } |
133 | libm_alias_float (__expm1, expm1) |
134 | |