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 <sys/cdefs.h>
17__FBSDID("$FreeBSD$");
18
19#include <float.h>
20
21#include "math.h"
22#include "math_private.h"
23
24static const float
25one		= 1.0,
26tiny		= 1.0e-30,
27o_threshold	= 8.8721679688e+01,/* 0x42b17180 */
28ln2_hi		= 6.9313812256e-01,/* 0x3f317180 */
29ln2_lo		= 9.0580006145e-06,/* 0x3717f7d1 */
30invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */
31/*
32 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
33 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
34 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
35 */
36Q1 = -3.3333212137e-2,		/* -0x888868.0p-28 */
37Q2 =  1.5807170421e-3;		/*  0xcf3010.0p-33 */
38
39static volatile float huge = 1.0e+30;
40
41float
42expm1f(float x)
43{
44	float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
45	int32_t k,xsb;
46	u_int32_t hx;
47
48	GET_FLOAT_WORD(hx,x);
49	xsb = hx&0x80000000;		/* sign bit of 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) return huge*huge; /* overflow */
60	    }
61	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
62		if(x+tiny<(float)0.0)	/* raise inexact */
63		return tiny-one;	/* return -1 */
64	    }
65	}
66
67    /* argument reduction */
68	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
69	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
70		if(xsb==0)
71		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
72		else
73		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
74	    } else {
75		k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
76		t  = k;
77		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */
78		lo = t*ln2_lo;
79	    }
80	    STRICT_ASSIGN(float, x, hi - lo);
81	    c  = (hi-x)-lo;
82	}
83	else if(hx < 0x33000000) {  	/* when |x|<2**-25, return x */
84	    t = huge+x;	/* return x with inexact flags when x!=0 */
85	    return x - (t-(huge+x));
86	}
87	else k = 0;
88
89    /* x is now in primary range */
90	hfx = (float)0.5*x;
91	hxs = x*hfx;
92	r1 = one+hxs*(Q1+hxs*Q2);
93	t  = (float)3.0-r1*hfx;
94	e  = hxs*((r1-t)/((float)6.0 - x*t));
95	if(k==0) return x - (x*e-hxs);		/* c is 0 */
96	else {
97	    SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));	/* 2^k */
98	    e  = (x*(e-c)-c);
99	    e -= hxs;
100	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;
101	    if(k==1) {
102	       	if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
103	       	else 	      return  one+(float)2.0*(x-e);
104	    }
105	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
106	        y = one-(e-x);
107		if (k == 128) y = y*2.0F*0x1p127F;
108		else y = y*twopk;
109	        return y-one;
110	    }
111	    t = one;
112	    if(k<23) {
113	        SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
114	       	y = t-(e-x);
115		y = y*twopk;
116	   } else {
117		SET_FLOAT_WORD(t,((0x7f-k)<<23));	/* 2^-k */
118	       	y = x-(e+t);
119	       	y += one;
120		y = y*twopk;
121	    }
122	}
123	return y;
124}
125