1*2fe8fb19SBen Gras /* s_expm1f.c -- float version of s_expm1.c.
2*2fe8fb19SBen Gras * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3*2fe8fb19SBen Gras */
4*2fe8fb19SBen Gras
5*2fe8fb19SBen Gras /*
6*2fe8fb19SBen Gras * ====================================================
7*2fe8fb19SBen Gras * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8*2fe8fb19SBen Gras *
9*2fe8fb19SBen Gras * Developed at SunPro, a Sun Microsystems, Inc. business.
10*2fe8fb19SBen Gras * Permission to use, copy, modify, and distribute this
11*2fe8fb19SBen Gras * software is freely granted, provided that this notice
12*2fe8fb19SBen Gras * is preserved.
13*2fe8fb19SBen Gras * ====================================================
14*2fe8fb19SBen Gras */
15*2fe8fb19SBen Gras
16*2fe8fb19SBen Gras #include <sys/cdefs.h>
17*2fe8fb19SBen Gras #if defined(LIBM_SCCS) && !defined(lint)
18*2fe8fb19SBen Gras __RCSID("$NetBSD: s_expm1f.c,v 1.10 2002/05/26 22:01:55 wiz Exp $");
19*2fe8fb19SBen Gras #endif
20*2fe8fb19SBen Gras
21*2fe8fb19SBen Gras #include "math.h"
22*2fe8fb19SBen Gras #include "math_private.h"
23*2fe8fb19SBen Gras
24*2fe8fb19SBen Gras static const float huge = 1.0e+30, tiny = 1.0e-30;
25*2fe8fb19SBen Gras
26*2fe8fb19SBen Gras static const float
27*2fe8fb19SBen Gras one = 1.0,
28*2fe8fb19SBen Gras o_threshold = 8.8721679688e+01,/* 0x42b17180 */
29*2fe8fb19SBen Gras ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
30*2fe8fb19SBen Gras ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
31*2fe8fb19SBen Gras invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
32*2fe8fb19SBen Gras /* scaled coefficients related to expm1 */
33*2fe8fb19SBen Gras Q1 = -3.3333335072e-02, /* 0xbd088889 */
34*2fe8fb19SBen Gras Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
35*2fe8fb19SBen Gras Q3 = -7.9365076090e-05, /* 0xb8a670cd */
36*2fe8fb19SBen Gras Q4 = 4.0082177293e-06, /* 0x36867e54 */
37*2fe8fb19SBen Gras Q5 = -2.0109921195e-07; /* 0xb457edbb */
38*2fe8fb19SBen Gras
39*2fe8fb19SBen Gras float
expm1f(float x)40*2fe8fb19SBen Gras expm1f(float x)
41*2fe8fb19SBen Gras {
42*2fe8fb19SBen Gras float y,hi,lo,c,t,e,hxs,hfx,r1;
43*2fe8fb19SBen Gras int32_t k,xsb;
44*2fe8fb19SBen Gras u_int32_t hx;
45*2fe8fb19SBen Gras
46*2fe8fb19SBen Gras c = 0;
47*2fe8fb19SBen Gras GET_FLOAT_WORD(hx,x);
48*2fe8fb19SBen Gras xsb = hx&0x80000000; /* sign bit of x */
49*2fe8fb19SBen Gras if(xsb==0) y=x; else y= -x; /* y = |x| */
50*2fe8fb19SBen Gras hx &= 0x7fffffff; /* high word of |x| */
51*2fe8fb19SBen Gras
52*2fe8fb19SBen Gras /* filter out huge and non-finite argument */
53*2fe8fb19SBen Gras if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
54*2fe8fb19SBen Gras if(hx >= 0x42b17218) { /* if |x|>=88.721... */
55*2fe8fb19SBen Gras if(hx>0x7f800000)
56*2fe8fb19SBen Gras return x+x; /* NaN */
57*2fe8fb19SBen Gras if(hx==0x7f800000)
58*2fe8fb19SBen Gras return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
59*2fe8fb19SBen Gras if(x > o_threshold) return huge*huge; /* overflow */
60*2fe8fb19SBen Gras }
61*2fe8fb19SBen Gras if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
62*2fe8fb19SBen Gras if(x+tiny<(float)0.0) /* raise inexact */
63*2fe8fb19SBen Gras return tiny-one; /* return -1 */
64*2fe8fb19SBen Gras }
65*2fe8fb19SBen Gras }
66*2fe8fb19SBen Gras
67*2fe8fb19SBen Gras /* argument reduction */
68*2fe8fb19SBen Gras if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
69*2fe8fb19SBen Gras if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
70*2fe8fb19SBen Gras if(xsb==0)
71*2fe8fb19SBen Gras {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
72*2fe8fb19SBen Gras else
73*2fe8fb19SBen Gras {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
74*2fe8fb19SBen Gras } else {
75*2fe8fb19SBen Gras k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
76*2fe8fb19SBen Gras t = k;
77*2fe8fb19SBen Gras hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
78*2fe8fb19SBen Gras lo = t*ln2_lo;
79*2fe8fb19SBen Gras }
80*2fe8fb19SBen Gras x = hi - lo;
81*2fe8fb19SBen Gras c = (hi-x)-lo;
82*2fe8fb19SBen Gras }
83*2fe8fb19SBen Gras else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
84*2fe8fb19SBen Gras t = huge+x; /* return x with inexact flags when x!=0 */
85*2fe8fb19SBen Gras return x - (t-(huge+x));
86*2fe8fb19SBen Gras }
87*2fe8fb19SBen Gras else k = 0;
88*2fe8fb19SBen Gras
89*2fe8fb19SBen Gras /* x is now in primary range */
90*2fe8fb19SBen Gras hfx = (float)0.5*x;
91*2fe8fb19SBen Gras hxs = x*hfx;
92*2fe8fb19SBen Gras r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
93*2fe8fb19SBen Gras t = (float)3.0-r1*hfx;
94*2fe8fb19SBen Gras e = hxs*((r1-t)/((float)6.0 - x*t));
95*2fe8fb19SBen Gras if(k==0) return x - (x*e-hxs); /* c is 0 */
96*2fe8fb19SBen Gras else {
97*2fe8fb19SBen Gras e = (x*(e-c)-c);
98*2fe8fb19SBen Gras e -= hxs;
99*2fe8fb19SBen Gras if(k== -1) return (float)0.5*(x-e)-(float)0.5;
100*2fe8fb19SBen Gras if(k==1) {
101*2fe8fb19SBen Gras if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
102*2fe8fb19SBen Gras else return one+(float)2.0*(x-e);
103*2fe8fb19SBen Gras }
104*2fe8fb19SBen Gras if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
105*2fe8fb19SBen Gras int32_t i;
106*2fe8fb19SBen Gras y = one-(e-x);
107*2fe8fb19SBen Gras GET_FLOAT_WORD(i,y);
108*2fe8fb19SBen Gras SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
109*2fe8fb19SBen Gras return y-one;
110*2fe8fb19SBen Gras }
111*2fe8fb19SBen Gras t = one;
112*2fe8fb19SBen Gras if(k<23) {
113*2fe8fb19SBen Gras int32_t i;
114*2fe8fb19SBen Gras SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
115*2fe8fb19SBen Gras y = t-(e-x);
116*2fe8fb19SBen Gras GET_FLOAT_WORD(i,y);
117*2fe8fb19SBen Gras SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
118*2fe8fb19SBen Gras } else {
119*2fe8fb19SBen Gras int32_t i;
120*2fe8fb19SBen Gras SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
121*2fe8fb19SBen Gras y = x-(e+t);
122*2fe8fb19SBen Gras y += one;
123*2fe8fb19SBen Gras GET_FLOAT_WORD(i,y);
124*2fe8fb19SBen Gras SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
125*2fe8fb19SBen Gras }
126*2fe8fb19SBen Gras }
127*2fe8fb19SBen Gras return y;
128*2fe8fb19SBen Gras }
129