1 | /* s_expm1f.c -- float version of s_expm1.c. |
2 | */ |
3 | |
4 | /* |
5 | * ==================================================== |
6 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
7 | * |
8 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
9 | * Permission to use, copy, modify, and distribute this |
10 | * software is freely granted, provided that this notice |
11 | * is preserved. |
12 | * ==================================================== |
13 | */ |
14 | |
15 | #include <errno.h> |
16 | #include <float.h> |
17 | #include <math.h> |
18 | #include <math-barriers.h> |
19 | #include <math_private.h> |
20 | #include <math-underflow.h> |
21 | #include <libm-alias-float.h> |
22 | |
23 | static const float huge = 1.0e+30; |
24 | static const float 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 |
40 | __expm1f(float x) |
41 | { |
42 | float y,hi,lo,c,t,e,hxs,hfx,r1; |
43 | int32_t k,xsb; |
44 | uint32_t hx; |
45 | |
46 | GET_FLOAT_WORD(hx,x); |
47 | xsb = hx&0x80000000; /* sign bit of x */ |
48 | if(xsb==0) y=x; else y= -x; /* y = |x| */ |
49 | hx &= 0x7fffffff; /* high word of |x| */ |
50 | |
51 | /* filter out huge and non-finite argument */ |
52 | if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ |
53 | if(hx >= 0x42b17218) { /* if |x|>=88.721... */ |
54 | if(hx>0x7f800000) |
55 | return x+x; /* NaN */ |
56 | if(hx==0x7f800000) |
57 | return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ |
58 | if(x > o_threshold) { |
59 | __set_errno (ERANGE); |
60 | return huge*huge; /* overflow */ |
61 | } |
62 | } |
63 | if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ |
64 | math_force_eval(x+tiny);/* 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 | math_check_force_underflow (x); |
87 | t = huge+x; /* return x with inexact flags when x!=0 */ |
88 | return x - (t-(huge+x)); |
89 | } |
90 | else k = 0; |
91 | |
92 | /* x is now in primary range */ |
93 | hfx = (float)0.5*x; |
94 | hxs = x*hfx; |
95 | r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); |
96 | t = (float)3.0-r1*hfx; |
97 | e = hxs*((r1-t)/((float)6.0 - x*t)); |
98 | if(k==0) return x - (x*e-hxs); /* c is 0 */ |
99 | else { |
100 | e = (x*(e-c)-c); |
101 | e -= hxs; |
102 | if(k== -1) return (float)0.5*(x-e)-(float)0.5; |
103 | if(k==1) { |
104 | if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); |
105 | else return one+(float)2.0*(x-e); |
106 | } |
107 | if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ |
108 | int32_t i; |
109 | y = one-(e-x); |
110 | GET_FLOAT_WORD(i,y); |
111 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
112 | return y-one; |
113 | } |
114 | t = one; |
115 | if(k<23) { |
116 | int32_t i; |
117 | SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ |
118 | y = t-(e-x); |
119 | GET_FLOAT_WORD(i,y); |
120 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
121 | } else { |
122 | int32_t i; |
123 | SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ |
124 | y = x-(e+t); |
125 | y += one; |
126 | GET_FLOAT_WORD(i,y); |
127 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
128 | } |
129 | } |
130 | return y; |
131 | } |
132 | libm_alias_float (__expm1, expm1) |
133 | |