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)