1 /* s_log1pf.c -- float version of s_log1p.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 <float.h>
16 #include <math.h>
17 #include <math-barriers.h>
18 #include <math_private.h>
19 #include <math-underflow.h>
20 #include <libc-diag.h>
21
22 static const float
23 ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
24 ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
25 two25 = 3.355443200e+07, /* 0x4c000000 */
26 Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
27 Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
28 Lp3 = 2.8571429849e-01, /* 3E924925 */
29 Lp4 = 2.2222198546e-01, /* 3E638E29 */
30 Lp5 = 1.8183572590e-01, /* 3E3A3325 */
31 Lp6 = 1.5313838422e-01, /* 3E1CD04F */
32 Lp7 = 1.4798198640e-01; /* 3E178897 */
33
34 static const float zero = 0.0;
35
36 float
__log1pf(float x)37 __log1pf(float x)
38 {
39 float hfsq,f,c,s,z,R,u;
40 int32_t k,hx,hu,ax;
41
42 GET_FLOAT_WORD(hx,x);
43 ax = hx&0x7fffffff;
44
45 k = 1;
46 if (hx < 0x3ed413d7) { /* x < 0.41422 */
47 if(ax>=0x3f800000) { /* x <= -1.0 */
48 if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=-inf */
49 else return (x-x)/(x-x); /* log1p(x<-1)=NaN */
50 }
51 if(ax<0x31000000) { /* |x| < 2**-29 */
52 math_force_eval(two25+x); /* raise inexact */
53 if (ax<0x24800000) /* |x| < 2**-54 */
54 {
55 math_check_force_underflow (x);
56 return x;
57 }
58 else
59 return x - x*x*(float)0.5;
60 }
61 if(hx>0||hx<=((int32_t)0xbe95f61f)) {
62 k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
63 }
64 if (hx >= 0x7f800000) return x+x;
65 if(k!=0) {
66 if(hx<0x5a000000) {
67 u = (float)1.0+x;
68 GET_FLOAT_WORD(hu,u);
69 k = (hu>>23)-127;
70 /* correction term */
71 c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
72 c /= u;
73 } else {
74 u = x;
75 GET_FLOAT_WORD(hu,u);
76 k = (hu>>23)-127;
77 c = 0;
78 }
79 hu &= 0x007fffff;
80 if(hu<0x3504f7) {
81 SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
82 } else {
83 k += 1;
84 SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
85 hu = (0x00800000-hu)>>2;
86 }
87 f = u-(float)1.0;
88 }
89 hfsq=(float)0.5*f*f;
90 if(hu==0) { /* |f| < 2**-20 */
91 if(f==zero) {
92 if(k==0) return zero;
93 else {c += k*ln2_lo; return k*ln2_hi+c;}
94 }
95 R = hfsq*(1.0f-0.66666666666666666f*f);
96 if(k==0) return f-R; else
97 return k*ln2_hi-((R-(k*ln2_lo+c))-f);
98 }
99 s = f/((float)2.0+f);
100 z = s*s;
101 R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
102 if (k == 0)
103 return f - (hfsq - s * (hfsq + R));
104 else
105 {
106 /* With GCC 7 when compiling with -Os the compiler warns
107 that c might be used uninitialized. This can't be true
108 because k must be 0 for c to be uninitialized and we
109 handled that computation earlier without using c. */
110 DIAG_PUSH_NEEDS_COMMENT;
111 DIAG_IGNORE_Os_NEEDS_COMMENT (7, "-Wmaybe-uninitialized");
112 return k * ln2_hi - ((hfsq - (s * (hfsq + R)
113 + (k * ln2_lo + c))) - f);
114 DIAG_POP_NEEDS_COMMENT;
115 }
116 }
117