/* s_expm1f.c -- float version of s_expm1.c.

 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.

 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunPro, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

#include <errno.h>

#include <float.h>

#include <math.h>

#include <math-barriers.h>

#include <math_private.h>

#include <math-underflow.h>

#include <libm-alias-float.h>

static const float huge = 1.0e+30;

static const float tiny = 1.0e-30;

static const float

one		= 1.0,

o_threshold	= 8.8721679688e+01,/* 0x42b17180 */

ln2_hi		= 6.9313812256e-01,/* 0x3f317180 */

ln2_lo		= 9.0580006145e-06,/* 0x3717f7d1 */

invln2		= 1.4426950216e+00,/* 0x3fb8aa3b */

	/* scaled coefficients related to expm1 */

Q1  =  -3.3333335072e-02, /* 0xbd088889 */

Q2  =   1.5873016091e-03, /* 0x3ad00d01 */

Q3  =  -7.9365076090e-05, /* 0xb8a670cd */

Q4  =   4.0082177293e-06, /* 0x36867e54 */

Q5  =  -2.0109921195e-07; /* 0xb457edbb */

float

__expm1f(float x)

{

	float y,hi,lo,c,t,e,hxs,hfx,r1;

	int32_t k,xsb;

	uint32_t hx;

	GET_FLOAT_WORD(hx,x);

	xsb = hx&0x80000000;		/* sign bit of x */

	if(xsb==0) y=x; else y= -x;	/* y = |x| */

	hx &= 0x7fffffff;		/* high word of |x| */

    /* filter out huge and non-finite argument */

	if(hx >= 0x4195b844) {			/* if |x|>=27*ln2 */

	    if(hx >= 0x42b17218) {		/* if |x|>=88.721... */

		if(hx>0x7f800000)

		    return x+x;		 /* NaN */

		if(hx==0x7f800000)

		    return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */

		if(x > o_threshold) {

		  __set_errno (ERANGE);

		  return huge*huge; /* overflow */

		}

	    }

	    if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */

		math_force_eval(x+tiny);/* raise inexact */

		return tiny-one;	/* return -1 */

	    }

	}

    /* argument reduction */

	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */

	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */

		if(xsb==0)

		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}

		else

		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}

	    } else {

		k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);

		t  = k;

		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */

		lo = t*ln2_lo;

	    }

	    x  = hi - lo;

	    c  = (hi-x)-lo;

	}

	else if(hx < 0x33000000) {	/* when |x|<2**-25, return x */

	    math_check_force_underflow (x);

	    t = huge+x;	/* return x with inexact flags when x!=0 */

	    return x - (t-(huge+x));

	}

	else k = 0;

    /* x is now in primary range */

	hfx = (float)0.5*x;

	hxs = x*hfx;

	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));

	t  = (float)3.0-r1*hfx;

	e  = hxs*((r1-t)/((float)6.0 - x*t));

	if(k==0) return x - (x*e-hxs);		/* c is 0 */

	else {

	    e  = (x*(e-c)-c);

	    e -= hxs;

	    if(k== -1) return (float)0.5*(x-e)-(float)0.5;

	    if(k==1) {

		if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));

		else	      return  one+(float)2.0*(x-e);

	    }

	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */

		int32_t i;

		y = one-(e-x);

		GET_FLOAT_WORD(i,y);

		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */

		return y-one;

	    }

	    t = one;

	    if(k<23) {

		int32_t i;

		SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */

		y = t-(e-x);

		GET_FLOAT_WORD(i,y);

		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */

	   } else {

		int32_t i;

		SET_FLOAT_WORD(t,((0x7f-k)<<23));	/* 2^-k */

		y = x-(e+t);

		y += one;

		GET_FLOAT_WORD(i,y);

		SET_FLOAT_WORD(y,i+(k<<23));	/* add k to y's exponent */

	    }

	}

	return y;

}

libm_alias_float (__expm1, expm1)