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      1 /* s_expm1f.c -- float version of s_expm1.c.
      2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 #ifndef lint
     17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_expm1f.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
     18 #endif
     19 
     20 #include "math.h"
     21 #include "math_private.h"
     22 
     23 static const float
     24 one		= 1.0,
     25 huge		= 1.0e+30,
     26 tiny		= 1.0e-30,
     27 o_threshold	= 8.8721679688e+01,/* 0x42b17180 */
     28 ln2_hi		= 6.9313812256e-01,/* 0x3f317180 */
     29 ln2_lo		= 9.0580006145e-06,/* 0x3717f7d1 */
     30 invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */
     31 	/* scaled coefficients related to expm1 */
     32 Q1  =  -3.3333335072e-02, /* 0xbd088889 */
     33 Q2  =   1.5873016091e-03, /* 0x3ad00d01 */
     34 Q3  =  -7.9365076090e-05, /* 0xb8a670cd */
     35 Q4  =   4.0082177293e-06, /* 0x36867e54 */
     36 Q5  =  -2.0109921195e-07; /* 0xb457edbb */
     37 
     38 float
     39 expm1f(float x)
     40 {
     41 	float y,hi,lo,c,t,e,hxs,hfx,r1;
     42 	int32_t k,xsb;
     43 	u_int32_t hx;
     44 
     45 	GET_FLOAT_WORD(hx,x);
     46 	xsb = hx&0x80000000;		/* sign bit of x */
     47 	if(xsb==0) y=x; else y= -x;	/* y = |x| */
     48 	hx &= 0x7fffffff;		/* high word of |x| */
     49 
     50     /* filter out huge and non-finite argument */
     51 	if(hx >= 0x4195b844) {			/* if |x|>=27*ln2 */
     52 	    if(hx >= 0x42b17218) {		/* if |x|>=88.721... */
     53                 if(hx>0x7f800000)
     54 		    return x+x; 	 /* NaN */
     55 		if(hx==0x7f800000)
     56 		    return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
     57 	        if(x > o_threshold) return huge*huge; /* overflow */
     58 	    }
     59 	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
     60 		if(x+tiny<(float)0.0)	/* raise inexact */
     61 		return tiny-one;	/* return -1 */
     62 	    }
     63 	}
     64 
     65     /* argument reduction */
     66 	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
     67 	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
     68 		if(xsb==0)
     69 		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
     70 		else
     71 		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
     72 	    } else {
     73 		k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
     74 		t  = k;
     75 		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */
     76 		lo = t*ln2_lo;
     77 	    }
     78 	    x  = hi - lo;
     79 	    c  = (hi-x)-lo;
     80 	}
     81 	else if(hx < 0x33000000) {  	/* when |x|<2**-25, return x */
     82 	    t = huge+x;	/* return x with inexact flags when x!=0 */
     83 	    return x - (t-(huge+x));
     84 	}
     85 	else k = 0;
     86 
     87     /* x is now in primary range */
     88 	hfx = (float)0.5*x;
     89 	hxs = x*hfx;
     90 	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
     91 	t  = (float)3.0-r1*hfx;
     92 	e  = hxs*((r1-t)/((float)6.0 - x*t));
     93 	if(k==0) return x - (x*e-hxs);		/* c is 0 */
     94 	else {
     95 	    e  = (x*(e-c)-c);
     96 	    e -= hxs;
     97 	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;
     98 	    if(k==1)
     99 	       	if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
    100 	       	else 	      return  one+(float)2.0*(x-e);
    101 	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
    102 	        int32_t i;
    103 	        y = one-(e-x);
    104 		GET_FLOAT_WORD(i,y);
    105 		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
    106 	        return y-one;
    107 	    }
    108 	    t = one;
    109 	    if(k<23) {
    110 	        int32_t i;
    111 	        SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
    112 	       	y = t-(e-x);
    113 		GET_FLOAT_WORD(i,y);
    114 		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
    115 	   } else {
    116 	        int32_t i;
    117 		SET_FLOAT_WORD(t,((0x7f-k)<<23));	/* 2^-k */
    118 	       	y = x-(e+t);
    119 	       	y += one;
    120 		GET_FLOAT_WORD(i,y);
    121 		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */
    122 	    }
    123 	}
    124 	return y;
    125 }
    126