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#if defined(LIBM_SCCS) && !defined(lint)
18__RCSID("$NetBSD: s_expm1f.c,v 1.11 2017/02/09 22:11:09 maya Exp $");
19#endif
20
21#include "math.h"
22#include "math_private.h"
23
24static const float huge = 1.0e+30, tiny = 1.0e-30;
25
26static const float
27one		= 1.0,
28o_threshold	= 8.8721679688e+01,/* 0x42b17180 */
29ln2_hi		= 6.9313812256e-01,/* 0x3f317180 */
30ln2_lo		= 9.0580006145e-06,/* 0x3717f7d1 */
31invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */
32	/* scaled coefficients related to expm1 */
33Q1  =  -3.3333335072e-02, /* 0xbd088889 */
34Q2  =   1.5873016091e-03, /* 0x3ad00d01 */
35Q3  =  -7.9365076090e-05, /* 0xb8a670cd */
36Q4  =   4.0082177293e-06, /* 0x36867e54 */
37Q5  =  -2.0109921195e-07; /* 0xb457edbb */
38
39float
40expm1f(float x)
41{
42	float y,hi,lo,c,t,e,hxs,hfx,r1;
43	int32_t k,xsb;
44	u_int32_t hx;
45
46	c = 0;
47	GET_FLOAT_WORD(hx,x);
48	xsb = hx&0x80000000;		/* sign bit of x */
49#ifdef DEAD_CODE
50	if(xsb==0) y=x; else y= -x;	/* y = |x| */
51#endif
52	hx &= 0x7fffffff;		/* high word of |x| */
53
54    /* filter out huge and non-finite argument */
55	if(hx >= 0x4195b844) {			/* if |x|>=27*ln2 */
56	    if(hx >= 0x42b17218) {		/* if |x|>=88.721... */
57                if(hx>0x7f800000)
58		    return x+x; 	 /* NaN */
59		if(hx==0x7f800000)
60		    return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
61	        if(x > o_threshold) return huge*huge; /* overflow */
62	    }
63	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
64		if(x+tiny<(float)0.0)	/* 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	    t = huge+x;	/* return x with inexact flags when x!=0 */
87	    return x - (t-(huge+x));
88	}
89	else k = 0;
90
91    /* x is now in primary range */
92	hfx = (float)0.5*x;
93	hxs = x*hfx;
94	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
95	t  = (float)3.0-r1*hfx;
96	e  = hxs*((r1-t)/((float)6.0 - x*t));
97	if(k==0) return x - (x*e-hxs);		/* c is 0 */
98	else {
99	    e  = (x*(e-c)-c);
100	    e -= hxs;
101	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;
102	    if(k==1)  {
103	       	if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
104	       	else 	      return  one+(float)2.0*(x-e);
105	    }
106	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
107	        int32_t i;
108	        y = one-(e-x);
109		GET_FLOAT_WORD(i,y);
110		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
111	        return y-one;
112	    }
113	    t = one;
114	    if(k<23) {
115	        int32_t i;
116	        SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
117	       	y = t-(e-x);
118		GET_FLOAT_WORD(i,y);
119		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
120	   } else {
121	        int32_t i;
122		SET_FLOAT_WORD(t,((0x7f-k)<<23));	/* 2^-k */
123	       	y = x-(e+t);
124	       	y += one;
125		GET_FLOAT_WORD(i,y);
126		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
127	    }
128	}
129	return y;
130}
131