path: root/backend/src/libocl/tmpl/ocl_math_common.tmpl.cl

/*
 * Copyright © 2012 - 2014 Intel Corporation
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library. If not, see <http://www.gnu.org/licenses/>.
 *
 */
#include "ocl_math_common.h"
#include "ocl_float.h"
#include "ocl_relational.h"
#include "ocl_common.h"
#include "ocl_integer.h"
#include "ocl_convert.h"

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
INLINE int  __HI(double x){
    long x64 = as_long(x);
    int high = convert_int((x64 >> 32) & 0xFFFFFFFF);
    return high;
};

INLINE int  __LO(double x){
    long x64 = as_long(x);
    int low = convert_int(x64  & 0xFFFFFFFFUL);
    return low;
};

INLINE void  __setHigh(double *x, int val){
    long x64 = as_long(*x);
    long high = x64  & 0x00000000FFFFFFFF;
    high |= ((long)val << 32);
    *x = as_double(high);
};

INLINE void  __setLow(double *x, unsigned int val){
    long x64 = as_long(*x);
    long low = x64  & 0xFFFFFFFF00000000;
    low |= (long)val;
    *x = as_double(low);
};

OVERLOADABLE double acos(double x)
{
    double one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
    pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
    pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
    pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
    pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
    pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
    pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
    pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
    pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
    pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
    qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
    qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
    qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
    qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */

    double z,p,q,r,w,s,c,df;
    int hx,ix;
    hx = __HI(x);
    ix = hx&0x7fffffff;
    if(ix>=0x3ff00000) {    /* |x| >= 1 */
        if(((ix-0x3ff00000)|__LO(x))==0) {  /* |x|==1 */
        if(hx>0) return 0.0;        /* acos(1) = 0  */
        else return pi+2.0*pio2_lo; /* acos(-1)= pi */
        }
        return (x-x)/(x-x);     /* acos(|x|>1) is NaN */
    }
    if(ix<0x3fe00000) { /* |x| < 0.5 */
        if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
        z = x*x;
        p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
        q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
        r = p/q;
        return pio2_hi - (x - (pio2_lo-x*r));
    } else  if (hx<0) {     /* x < -0.5 */
        z = (one+x)*0.5;
        p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
        q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
        s = sqrt(z);
        r = p/q;
        w = r*s-pio2_lo;
        return pi - 2.0*(s+w);
    } else {            /* x > 0.5 */
        z = (one-x)*0.5;
        s = sqrt(z);
        df = s;
        __setLow(&df, 0);
        c  = (z-df*df)/(s+df);
        p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
        q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
        r = p/q;
        w = r*s+c;
        return 2.0*(df+w);
    }
}

OVERLOADABLE double acospi(double x)
{
	return acos(x)/M_PI;
}

OVERLOADABLE double acosh(double x)
{
	double one = 1.0,
	ln2 = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */

	double t;
	int hx;
	hx = __HI(x);
	if(hx<0x3ff00000) {		/* x < 1 */
		return (x-x)/(x-x);
	} else if(hx >=0x41b00000) {	/* x > 2**28 */
		if(hx >=0x7ff00000) {	/* x is inf of NaN */
			return x+x;
		} else
		return log(x)+ln2;	/* acosh(huge)=log(2x) */
	} else if(((hx-0x3ff00000)|__LO(x))==0) {
		return 0.0;			/* acosh(1) = 0 */
	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
		t=x*x;
		return log(2.0*x-one/(x+sqrt(t-one)));
	} else {			/* 1<x<2 */
		t = x-one;
		return log1p(t+sqrt(2.0*t+t*t));
	}
}

OVERLOADABLE double asin(double x)
{
    double one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
    huge =  1.000e+300,
    pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
    pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
    pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
        /* coefficient for R(x^2) */
    pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
    pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
    pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
    pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
    pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
    pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
    qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
    qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
    qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
    qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */

    double t,w,p,q,c,r,s;
    int hx,ix;
    hx = __HI(x);
    ix = hx&0x7fffffff;
    if(ix>= 0x3ff00000) {       /* |x|>= 1 */
        if(((ix-0x3ff00000)|__LO(x))==0)
            /* asin(1)=+-pi/2 with inexact */
        return x*pio2_hi+x*pio2_lo;
        return (x-x)/(x-x);     /* asin(|x|>1) is NaN */
    } else if (ix<0x3fe00000) { /* |x|<0.5 */
        if(ix<0x3e400000) {     /* if |x| < 2**-27 */
        if(huge+x>one) return x;/* return x with inexact if x!=0*/
        } else
        t = x*x;
        p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
        q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
        w = p/q;
        return x+x*w;
    }
    /* 1> |x|>= 0.5 */
    w = one-fabs(x);
    t = w*0.5;
    p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
    q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
    s = sqrt(t);
    if(ix>=0x3FEF3333) {    /* if |x| > 0.975 */
        w = p/q;
        t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
    } else {
        w  = s;
        __setLow(&w, 0);
        c  = (t-w*w)/(s+w);
        r  = p/q;
        p  = 2.0*s*r-(pio2_lo-2.0*c);
        q  = pio4_hi-2.0*w;
        t  = pio4_hi-(p-q);
    }
    if(hx>0) return t; else return -t;
}

OVERLOADABLE double asinpi(double x)
{
	return asin(x)/M_PI;
}

OVERLOADABLE double asinh(double x)
{
	double one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
	ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
	huge=  1.00000000000000000000e+300;
	double t,w;

	int hx,ix;
	hx = __HI(x);
	ix = hx&0x7fffffff;
	if(ix>=0x7ff00000) return x+x;	/* x is inf or NaN */
	if(ix< 0x3e300000) {	/* |x|<2**-28 */
		if(huge+x>one) return x;	/* return x inexact except 0 */
	}
	if(ix>0x41b00000) {	/* |x| > 2**28 */
		w = log(fabs(x))+ln2;
	} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */
		t = fabs(x);
		w = log(2.0*t+one/(sqrt(x*x+one)+t));
	} else {		/* 2.0 > |x| > 2**-28 */
		t = x*x;
		w =log1p(fabs(x)+t/(one+sqrt(one+t)));
	}
	if(hx>0) return w; else return -w;
}

OVERLOADABLE double atan(double x)
{
	double atanhi[] = {
	  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
	  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
	  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
	  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
	};

	double atanlo[] = {
	  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
	  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
	  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
	  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
	};

	double aT[] = {
	  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
	 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
	  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
	 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
	  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
	 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
	  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
	 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
	  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
	 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
	  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
	};

	double one   = 1.0,
	huge   = 1.0e300;
	double w,s1,s2,z;
	int ix,hx,id;

	hx = __HI(x);
	ix = hx&0x7fffffff;
	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
		if(ix>0x7ff00000 ||(ix==0x7ff00000 && (__LO(x)!=0)))
		return x+x;		/* NaN */
		if(hx>0) return  atanhi[3]+atanlo[3];
		else	 return -atanhi[3]-atanlo[3];
	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
		if (ix < 0x3e200000) {	/* |x| < 2^-29 */
		if(huge+x>one) return x;	/* raise inexact */
		}
		id = -1;
	} else {
	x = fabs(x);
	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
		if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
		id = 0; x = (2.0*x-one)/(2.0+x);
		} else {			/* 11/16<=|x|< 19/16 */
		id = 1; x  = (x-one)/(x+one);
		}
	} else {
		if (ix < 0x40038000) {	/* |x| < 2.4375 */
		id = 2; x  = (x-1.5)/(one+1.5*x);
		} else {			/* 2.4375 <= |x| < 2^66 */
		id = 3; x  = -1.0/x;
		}
	}}
	/* end of argument reduction */
	z = x*x;
	w = z*z;
	/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
	if (id<0) return x - x*(s1+s2);
	else {
		z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
		return (hx<0)? -z:z;
	}
}

OVERLOADABLE double atan2(double x, double y)
{
	double tiny  = 1.0e-300,
	zero  = 0.0,
	pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
	pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
	pi	  = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
	pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */

	double z;
	int k,m,hx,hy,ix,iy;
	unsigned lx,ly;

	hx = __HI(x); ix = hx&0x7fffffff;
	lx = __LO(x);
	hy = __HI(y); iy = hy&0x7fffffff;
	ly = __LO(y);
	if(((ix|((lx|-lx)>>31))>0x7ff00000)||
	   ((iy|((ly|-ly)>>31))>0x7ff00000))	/* x or y is NaN */
	   return x+y;

	if((hx-0x3ff00000|lx)==0)
		{
			if(iy>=0x44100000) {	/* if |x| >= 2^66 */
			if(iy>0x7ff00000 ||(iy==0x7ff00000 && (__LO(y)!=0)))
			return y+y;		/* NaN */
			if(hy >0)
					return  pi_o_2;
			else
					return pi;
			}
				return atan(y);   /* x=1.0 */
		}
	m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */

	/* when y = 0 */
	if((iy|ly)==0) {
		switch(m) {
		case 0:
		case 1: return y;   /* atan(+-0,+anything)=+-0 */
		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
		}
	}
	/* when x = 0 */
	if((ix|lx)==0) return (hx<0)?  -pi-tiny: pi+tiny;

	/* when x is INF */
	if(ix==0x7ff00000) {
		if(iy==0x7ff00000) {
		switch(m) {
			case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
			case 1: return 3.0*pi_o_4-tiny;/* atan(-INF,+INF) */
			case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
			case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
		}
		}
			else {
		switch(m) {
			case 0: return  zero  ; /* atan(+...,+INF) */
			case 1: return pi_o_2; /* atan(-...,+INF) */
			case 2: return  pi_o_2+tiny  ;  /* atan(+...,-INF) */
			case 3: return -pi_o_2-tiny  ;  /* atan(-...,-INF) */
		}
		}
	}
	/* when y is INF */
	if(iy==0x7ff00000) return (hx<0)? -pi-tiny: pi+tiny;

	/* compute y/x */
	k = (iy-ix)>>20;
	if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
	else if(hx<0&&k<-60) z=0.0;	 /* |y|/x < -2**60 */
	else z=atan(fabs(y/x));	 /* safe to do y/x */
	switch (m) {
		case 0: return	   z  ;   /* atan(+,+) */
		case 2: __setHigh(&z, __HI(z) ^ 0x80000000);
			return	   pi_o_2 - z  ;   /* atan(-,+) */
		case 1: return  pi_o_2 + (z-pi_lo);/* atan(+,-) */
		default: /* case 3 */
			__setHigh(&z, __HI(z) ^ 0x80000000);
				return  (z-pi_lo)-pi_o_2;/* atan(-,-) */
	}
}

OVERLOADABLE double atanpi(double x)
{
	return atan(x)/M_PI;
}

OVERLOADABLE double atan2pi(double x, double y)
{
	return atan2(x, y)/M_PI;
}

OVERLOADABLE double atanh(double x)
{
		double one = 1.0, huge = 1e300;

	double t, zero = 0;
	int hx,ix;
	unsigned lx;
	hx = __HI(x);		/* high word */
	lx = __LO(x);		/* low word */
	ix = hx&0x7fffffff;
	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
		return (x-x)/(x-x);
	if(ix==0x3ff00000)
		return x/zero;
	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
	__setHigh(&x, ix);		/* x <- |x| */
	if(ix<0x3fe00000) {		/* x < 0.5 */
		t = x+x;
		t = 0.5*log1p(t+t*x/(one-x));
	} else
		t = 0.5*log1p((x+x)/(one-x));
	if(hx>=0) return t; else return -t;

		return 0.0;
}

OVERLOADABLE double exp(double x)
{
	double one	= 1.0,
	halF[2]	= {0.5,-0.5,},
	huge	= 1.0e+300,
	twom1000= 9.33263618503218878990e-302,	 /* 2**-1000=0x01700000,0*/
	o_threshold=  7.09782712893383973096e+02,  /* 0x40862E42, 0xFEFA39EF */
	u_threshold= -7.45133219101941108420e+02,  /* 0xc0874910, 0xD52D3051 */
	ln2HI[2]   ={ 6.93147180369123816490e-01,  /* 0x3fe62e42, 0xfee00000 */
			 -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
	ln2LO[2]   ={ 1.90821492927058770002e-10,  /* 0x3dea39ef, 0x35793c76 */
			 -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
	invln2 =  1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
	P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
	P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
	P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
	P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
	P5   =  4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */

	double y,hi,lo,c,t;
	int k,xsb;
	unsigned hx;

	hx	= __HI(x);	/* high word of x */
	xsb = (hx>>31)&1;		/* sign bit of x */
	hx &= 0x7fffffff;		/* high word of |x| */

	/* filter out non-finite argument */
	if(hx >= 0x40862E42) {			/* if |x|>=709.78... */
			if(hx>=0x7ff00000) {
		if(((hx&0xfffff)|__LO(x))!=0)
			 return x+x;		/* NaN */
		else return (xsb==0)? x:0.0;	/* exp(+-inf)={inf,0} */
		}
		if(x > o_threshold) return huge*huge; /* overflow */
		if(x < u_threshold) return twom1000*twom1000; /* underflow */
	}

	/* argument reduction */
	if(hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */
		if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */
		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
		} else {
		k  = (int)(invln2*x+halF[xsb]);
		t  = k;
		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
		lo = t*ln2LO[0];
		}
		x  = hi - lo;
	}
	else if(hx < 0x3e300000)  { /* when |x|<2**-28 */
		if(huge+x>one) return one+x;/* trigger inexact */
	}
	else k = 0;

	/* x is now in primary range */
	t  = x*x;
	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
	if(k==0)	return one-((x*c)/(c-2.0)-x);
	else		y = one-((lo-(x*c)/(2.0-c))-hi);
	if(k >= -1021) {
		__setHigh(&y, __HI(y) + (k<<20)); /* add k to y's exponent */
		return y;
	} else {
		__setHigh(&y, __HI(y) + ((k+1000)<<20));/* add k to y's exponent */
		return y*twom1000;
	}

}

OVERLOADABLE double expm1(double x)
{
	double one	= 1.0,
	huge		= 1.0e+300,
	tiny		= 1.0e-300,
	o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
	ln2_hi		= 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
	ln2_lo		= 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
	invln2		= 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
		/* scaled coefficients related to expm1 */
	Q1	=  -3.33333333333331316428e-02, /* BFA11111 111110F4 */
	Q2	=	1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
	Q3	=  -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
	Q4	=	4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
	Q5	=  -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */

	double y,hi,lo,c,t,e,hxs,hfx,r1;
	int k,xsb;
	unsigned hx;

	hx	= __HI(x);	/* high word of 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 >= 0x4043687A) {			/* if |x|>=56*ln2 */
		if(hx >= 0x40862E42) {		/* if |x|>=709.78... */
				if(hx>=0x7ff00000) {
			if(((hx&0xfffff)|__LO(x))!=0)
				 return x+x;	 /* NaN */
			else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
			}
			if(x > o_threshold) return huge*huge; /* overflow */
		}
		if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
		if(x+tiny<0.0)		/* raise inexact */
		return tiny-one;	/* return -1 */
		}
	}

	/* argument reduction */
	if(hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */
		if(hx < 0x3FF0A2B2) {	/* 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)?0.5:-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 < 0x3c900000) {		/* when |x|<2**-54, return 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 = 0.5*x;
	hxs = x*hfx;
	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
	t  = 3.0-r1*hfx;
	e  = hxs*((r1-t)/(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 0.5*(x-e)-0.5;
		if(k==1)
	{
			if(x < -0.25)
			return -2.0*(e-(x+0.5));
			else
			return	one+2.0*(x-e);
		}

		if (k <= -2 || k>56) {	 /* suffice to return exp(x)-1 */
			y = one-(e-x);
			__setHigh(&y, __HI(y) + (k<<20));;	/* add k to y's exponent */
			return y-one;
		}
		t = one;
		if(k<20) {
			__setHigh(&t, 0x3ff00000 - (0x200000>>k));	/* t=1-2^-k */
			y = t-(e-x);
			__setHigh(&y, __HI(y) + (k<<20));	/* add k to y's exponent */
	   } else {
			__setHigh(&t, ((0x3ff-k)<<20)); /* 2^-k */
			y = x-(e+t);
			y += one;
			__setHigh(&y, __HI(y) + (k<<20));	/* add k to y's exponent */
		}
	}
	return y;
}

OVERLOADABLE double ceil(double x)
{
    double ret;
    ulong lval = as_ulong(x);
    int exp = ((lval >> 52) & 0x7FF) - 1023;
    int sign = (lval >> 63) & 0x1;

    long i = (1L << (52 - exp));
    long mask = 0x10000000000000 - i;
    unsigned long uv = 0xFFF0000000000000 + mask;
    ulong vv = lval & uv;
    double	dp = as_double(vv);
    ret = ((vv != lval) && !sign) ? dp +1.0:dp;

    ret = ((exp < 0) && sign) ? 0:ret;
    double tmp = (lval & DF_ABS_MASK) ? 1.0:0.0;
    ret = ((exp < 0) && !sign) ? tmp:ret;
    ret = (exp >= 52) ? x:ret;

     return ret;
}

OVERLOADABLE double copysign(double x, double y)
{
	ulong uy = as_ulong(y);
	ulong sign = uy & DF_SIGN_MASK;
	ulong ux = as_ulong(x);
	ux = (ux & DF_ABS_MASK) | sign;
	return as_double(ux);
}

double __scalbn (double x, int n)
{
	double two54   =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
	twom54  =  5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
	huge   = 1.0e+300,
	tiny   = 1.0e-300;

	int  k,hx,lx;
	hx = __HI(x);
	lx = __LO(x);
		k = (hx&0x7ff00000)>>20;		/* extract exponent */
		if (k==0) {				/* 0 or subnormal x */
			if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
		x *= two54;
		hx = __HI(x);
		k = ((hx&0x7ff00000)>>20) - 54;
			if (n< -50000) return tiny*x; 	/*underflow*/
		}
		if (k==0x7ff) return x+x;		/* NaN or Inf */
		k = k+n;
		if (k >  0x7fe) return huge*copysign(huge,x); /* overflow  */
		if (k > 0) 				/* normal result */
		{__setHigh(&x, (hx&0x800fffff)|(k<<20)); return x;}
		if (k <= -54)
			{
			if (n > 50000) 	/* in case integer overflow in n+k */
		return huge*copysign(huge,x);	/*overflow*/
		else return tiny*copysign(tiny,x); 	/*underflow*/
		}
		k += 54;				/* subnormal result */
		__setHigh(&x, (hx&0x800fffff)|(k<<20));
		return x*twom54;
}

int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
{
	double zero   = 0.0,
	one	= 1.0,
	two24   =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
	twon24  =  5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */

	double PIo2[] = {
	  1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
	  7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
	  5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
	  3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
	  1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
	  1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
	  2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
	  2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
	};

	const int init_jk[] = {2,3,4,6}; /* initial value for jk */

	int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
	double z,fw,f[20],fq[20],q[20];

	/* initialize jk*/
	jk = init_jk[prec];
	jp = jk;

	/* determine jx,jv,q0, note that 3>q0 */
	jx =  nx-1;
	jv = (e0-3)/24; if(jv<0) jv=0;
	q0 =  e0-24*(jv+1);

	/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
	j = jv-jx; m = jx+jk;
	for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];

	/* compute q[0],q[1],...q[jk] */
	for (i=0;i<=jk;i++) {
		for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
	}

	jz = jk;
recompute:
	/* distill q[] into iq[] reversingly */
	for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
		fw	=  (double)((int)(twon24* z));
		iq[i] =  (int)(z-two24*fw);
		z	 =  q[j-1]+fw;
	}

	/* compute n */
	z  = __scalbn(z,q0);		/* actual value of z */
	z -= 8.0*floor(z*0.125);		/* trim off integer >= 8 */
	n  = (int) z;
	z -= (double)n;
	ih = 0;
	if(q0>0) {	/* need iq[jz-1] to determine n */
		i  = (iq[jz-1]>>(24-q0)); n += i;
		iq[jz-1] -= i<<(24-q0);
		ih = iq[jz-1]>>(23-q0);
	}
	else if(q0==0) ih = iq[jz-1]>>23;
	else if(z>=0.5) ih=2;

	if(ih>0) {	/* q > 0.5 */
		n += 1; carry = 0;
		for(i=0;i<jz ;i++) {	/* compute 1-q */
		j = iq[i];
		if(carry==0) {
			if(j!=0) {
			carry = 1; iq[i] = 0x1000000- j;
			}
		} else  iq[i] = 0xffffff - j;
		}
		if(q0>0) {		/* rare case: chance is 1 in 12 */
			switch(q0) {
			case 1:
			   iq[jz-1] &= 0x7fffff; break;
			case 2:
			   iq[jz-1] &= 0x3fffff; break;
			}
		}
		if(ih==2) {
		z = one - z;
		if(carry!=0) z -= __scalbn(one,q0);
		}
	}

	/* check if recomputation is needed */
	if(z==zero) {
		j = 0;
		for (i=jz-1;i>=jk;i--) j |= iq[i];
		if(j==0) { /* need recomputation */
		for(k=1;iq[jk-k]==0;k++);   /* k = no. of terms needed */

		for(i=jz+1;i<=jz+k;i++) {   /* add q[jz+1] to q[jz+k] */
			f[jx+i] = (double) ipio2[jv+i];
			for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
			q[i] = fw;
		}
		jz += k;
		goto recompute;
		}
	}

	/* chop off zero terms */
	if(z==0.0) {
		jz -= 1; q0 -= 24;
		while(iq[jz]==0) { jz--; q0-=24;}
	} else { /* break z into 24-bit if necessary */
		z = __scalbn(z,-q0);
		if(z>=two24) {
		fw = (double)((int)(twon24*z));
		iq[jz] = (int)(z-two24*fw);
		jz += 1; q0 += 24;
		iq[jz] = (int) fw;
		} else iq[jz] = (int) z ;
	}

	/* convert integer "bit" chunk to floating-point value */
	fw = __scalbn(one,q0);
	for(i=jz;i>=0;i--) {
		q[i] = fw*(double)iq[i]; fw*=twon24;
	}

	/* compute PIo2[0,...,jp]*q[jz,...,0] */
	for(i=jz;i>=0;i--) {
		for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
		fq[jz-i] = fw;
	}

	/* compress fq[] into y[] */
	switch(prec) {
		case 0:
		fw = 0.0;
		for (i=jz;i>=0;i--) fw += fq[i];
		y[0] = (ih==0)? fw: -fw;
		break;
		case 1:
		case 2:
		fw = 0.0;
		for (i=jz;i>=0;i--) fw += fq[i];
		y[0] = (ih==0)? fw: -fw;
		fw = fq[0]-fw;
		for (i=1;i<=jz;i++) fw += fq[i];
		y[1] = (ih==0)? fw: -fw;
		break;
		case 3:	/* painful */
		for (i=jz;i>0;i--) {
			fw	  = fq[i-1]+fq[i];
			fq[i]  += fq[i-1]-fw;
			fq[i-1] = fw;
		}
		for (i=jz;i>1;i--) {
			fw	  = fq[i-1]+fq[i];
			fq[i]  += fq[i-1]-fw;
			fq[i-1] = fw;
		}
		for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
		if(ih==0) {
			y[0] =  fq[0]; y[1] =  fq[1]; y[2] =  fw;
		} else {
			y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
		}
	}
	return n&7;
}

int __ieee754_rem_pio2(double x, double *y)
{
	int two_over_pi[] = {
	0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
	0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
	0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
	0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
	0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
	0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
	0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
	0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
	0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
	0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
	0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
	};

	int npio2_hw[] = {
	0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
	0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
	0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
	0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
	0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
	0x404858EB, 0x404921FB,
	};

	double zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
	halfD =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
	two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
	invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
	pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
	pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
	pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
	pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
	pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
	pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */

	double z,w,t,r,fn;
	double tx[3];
	int e0,i,j,nx,n,ix,hx;

	hx = __HI(x);		/* high word of x */
	ix = hx&0x7fffffff;
	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
		{y[0] = x; y[1] = 0; return 0;}
	if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
		if(hx>0) {
		z = x - pio2_1;
		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
			y[0] = z - pio2_1t;
			y[1] = (z-y[0])-pio2_1t;
		} else {		/* near pi/2, use 33+33+53 bit pi */
			z -= pio2_2;
			y[0] = z - pio2_2t;
			y[1] = (z-y[0])-pio2_2t;
		}
		return 1;
		} else {	/* negative x */
		z = x + pio2_1;
		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
			y[0] = z + pio2_1t;
			y[1] = (z-y[0])+pio2_1t;
		} else {		/* near pi/2, use 33+33+53 bit pi */
			z += pio2_2;
			y[0] = z + pio2_2t;
			y[1] = (z-y[0])+pio2_2t;
		}
		return -1;
		}
	}
	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
		t  = fabs(x);
		n  = (int) (t*invpio2+halfD);
		fn = (double)n;
		r  = t-fn*pio2_1;
		w  = fn*pio2_1t;	/* 1st round good to 85 bit */
		if(n<32&&ix!=npio2_hw[n-1]) {
		y[0] = r-w;	/* quick check no cancellation */
		} else {
			j  = ix>>20;
			y[0] = r-w;
			i = j-(((__HI(y[0]))>>20)&0x7ff);
			if(i>16) {  /* 2nd iteration needed, good to 118 */
			t  = r;
			w  = fn*pio2_2;
			r  = t-w;
			w  = fn*pio2_2t-((t-r)-w);
			y[0] = r-w;
			i = j-(((__HI(y[0]))>>20)&0x7ff);
			if(i>49)  {	/* 3rd iteration need, 151 bits acc */
				t  = r;	/* will cover all possible cases */
				w  = fn*pio2_3;
				r  = t-w;
				w  = fn*pio2_3t-((t-r)-w);
				y[0] = r-w;
			}
		}
		}
		y[1] = (r-y[0])-w;
		if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
		else	 return n;
	}
	/*
	 * all other (large) arguments
	 */
	if(ix>=0x7ff00000) {		/* x is inf or NaN */
		y[0]=y[1]=x-x; return 0;
	}
	/* set z = scalbn(|x|,ilogb(x)-23) */
	__setLow(&z,  __LO(x));
	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
	__setHigh(&z, ix - (e0<<20));
	for(i=0;i<2;i++) {
		tx[i] = (double)((int)(z));
		z	 = (z-tx[i])*two24;
	}
	tx[2] = z;
	nx = 3;
	while(tx[nx-1]==zero) nx--;	/* skip zero term */
	n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
	return n;
}

double __kernel_cos(double x, double y)
{
	double one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
	C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
	C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
	C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
	C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
	C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
	C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */

	double a,hz,z,r,qx;
	int ix;
	ix = __HI(x)&0x7fffffff;	/* ix = |x|'s high word*/
	if(ix<0x3e400000) {			/* if x < 2**27 */
		if(((int)x)==0) return one;		/* generate inexact */
	}
	z  = x*x;
	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
	if(ix < 0x3FD33333) 			/* if |x| < 0.3 */
		return one - (0.5*z - (z*r - x*y));
	else {
		if(ix > 0x3fe90000) {		/* x > 0.78125 */
		qx = 0.28125;
		} else {
			__setHigh(&qx,  ix-0x00200000);	/* x/4 */
			__setLow(&qx, 0);
		}
		hz = 0.5*z-qx;
		a  = one-qx;
		return a - (hz - (z*r-x*y));
	}
}

double __kernel_sin(double x, double y, int iy)
{
	double halfD =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
	S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
	S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
	S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
	S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
	S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
	S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */

	double z,r,v;
	int ix;
	ix = __HI(x)&0x7fffffff;	/* high word of x */
	if(ix<0x3e400000)			/* |x| < 2**-27 */
	   {if((int)x==0) return x;}		/* generate inexact */
	z	=  x*x;
	v	=  z*x;
	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
	if(iy==0) return x+v*(S1+z*r);
	else	  return x-((z*(halfD*y-v*r)-y)-v*S1);
}

OVERLOADABLE double cos(double x)
{
	double y[2],z=0.0;
	int n, ix;

	/* High word of x. */
	ix = __HI(x);

	/* |x| ~< pi/4 */
	ix &= 0x7fffffff;
	if(ix <= 0x3fe921fb) return __kernel_cos(x,z);

	/* cos(Inf or NaN) is NaN */
	else if (ix>=0x7ff00000) return x-x;

	/* argument reduction needed */
	else {
		n = __ieee754_rem_pio2(x,y);
		switch(n&3) {
		case 0: return  __kernel_cos(y[0],y[1]);
		case 1: return -__kernel_sin(y[0],y[1],1);
		case 2: return -__kernel_cos(y[0],y[1]);
		default:
				return  __kernel_sin(y[0],y[1],1);
		}
	}
}

OVERLOADABLE double cosh(double x)
{
	double one = 1.0, dHalf=0.5, huge = 1.0e300;

	double t,w;
	int ix;
	unsigned lx;

	/* High word of |x|. */
	ix = __HI(x);
	ix &= 0x7fffffff;

	/* x is INF or NaN */
	if(ix>=0x7ff00000) return x*x;

	/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
	if(ix<0x3fd62e43) {
		t = expm1(fabs(x));
		w = one+t;
		if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
		return one+(t*t)/(w+w);
	}

	/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
	if (ix < 0x40360000) {
		t = exp(fabs(x));
		return dHalf*t+dHalf/t;
	}

	/* |x| in [22, log(maxdouble)] return half*exp(|x|) */
	if (ix < 0x40862E42)  return dHalf*exp(fabs(x));

	/* |x| in [log(maxdouble), overflowthresold] */
	lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
	if (ix<0x408633CE ||
		  ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
		w = exp(dHalf*fabs(x));
		t = dHalf*w;
		return t*w;
	}

	/* |x| > overflowthresold, cosh(x) overflow */
	return huge*huge;

}

OVERLOADABLE double fabs(double x)
{
    long  qw = as_ulong(x);
    qw &= 0x7FFFFFFFFFFFFFFF;
    return as_double(qw);
}

OVERLOADABLE double fdim(double x, double y)
{
	if(isnan(x))
		return x;
	if(isnan(y))
		return y;
	return x > y ? (x - y) : +0.f;
}

OVERLOADABLE double floor(double x)
{
    ulong lval = as_ulong(x);
    int exp = ((lval >> 52) & 0x7FF) - 1023;
    int sign = (lval >> 63) & 0x1;
    if(exp < 0)
    {
        if(sign)
	{
		if(lval & DF_ABS_MASK)
			return -1L;
		else
			return 0.0;
	}
        else return 0.0;
    }
    else
    {
        if(exp >= 52)
            return x;
         long i = (1L << (52 - exp));
         i = 0x10000000000000 - i;
         unsigned long uv = 0xFFF0000000000000 + i;
         ulong vv = lval & uv;
         double  dp = as_double(vv);
         if(vv != lval)
            dp -= sign;

         return dp;
    }
}

OVERLOADABLE double log(double x)
{
	double ln2_hi	=  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
	ln2_lo	=  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
	two54	=  1.80143985094819840000e+16,	/* 43500000 00000000 */
	Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
	Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
	Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
	Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
	Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
	Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
	Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

	double zero = 0;
	double hfsq,f,s,z,R,w,t1,t2,dk;
	int k,hx,i,j;
	unsigned lx;

	hx = __HI(x);		/* high word of x */
	lx = __LO(x);		/* low  word of x */

	k=0;
	if (hx < 0x00100000)
	{			/* x < 2**-1022  */
		if (((hx&0x7fffffff)|lx)==0)
		return -two54/zero;		/* log(+-0)=-inf */
		if (hx<0)
			return (x-x)/zero;	/* log(-#) = NaN */
		k -= 54; x *= two54; /* subnormal number, scale up x */
		hx = __HI(x);		/* high word of x */
	}
	if (hx >= 0x7ff00000) return x+x;
	k += (hx>>20)-1023;
	hx &= 0x000fffff;
	i = (hx+0x95f64)&0x100000;
	__setHigh(&x, (hx|(i^0x3ff00000)));	/* normalize x or x/2 */
	k += (i>>20);
	f = x-1.0;
	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
		if(f==zero)
		{
			if(k==0) return zero;
			else
			{
				dk=(double)k;
				return dk*ln2_hi+dk*ln2_lo;
			}
		}

		R = f*f*(0.5-0.33333333333333333*f);
		if(k==0)
			return f-R;
		else {dk=(double)k;
			return dk*ln2_hi-((R-dk*ln2_lo)-f);}
	}
	s = f/(2.0+f);
	dk = (double)k;
	z = s*s;
	i = hx-0x6147a;
	w = z*z;
	j = 0x6b851-hx;
	t1= w*(Lg2+w*(Lg4+w*Lg6));
	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
	i |= j;
	R = t2+t1;
	if(i>0) {
	hfsq=0.5*f*f;
	if(k==0)
		return f-(hfsq-s*(hfsq+R));
	else
		return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
	}
	else
	{
		if(k==0)
			return f-s*(f-R);
		else
			return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
	}

}

OVERLOADABLE double log2(double x)
{
	double ln2 = 0.69314718055994530942,
	zero = 0,
	two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
	Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
	Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
	Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
	Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
	Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
	Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
	Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

	double hfsq,f,s,z,R,w,t1,t2,dk;
	int k,hx,i,j;
	uint lx;

	hx = __HI(x);
	lx = __LO(x);

	k=0;
	if (hx < 0x00100000)
	{			/* x < 2**-1022  */
		if (((hx&0x7fffffff)|lx)==0)
			return -two54/(x-x);		/* log(+-0)=-inf */

		if (hx<0) return (x-x)/(x-x);	/* log(-#) = NaN */

		k -= 54; x *= two54; /* subnormal number, scale up x */
		hx = __HI(x);
	}

	if (hx >= 0x7ff00000) return x+x;
	k += (hx>>20)-1023;
	hx &= 0x000fffff;
	i = (hx+0x95f64)&0x100000;
	__setHigh(&x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
	k += (i>>20);
	dk = (double) k;
	f = x-1.0;

	if((0x000fffff&(2+hx))<3)
	{	/* |f| < 2**-20 */
		if(f==zero) return dk;
		R = f*f*(0.5-0.33333333333333333*f);
		return dk-(R-f)/ln2;
	}

	s = f/(2.0+f);
	z = s*s;
	i = hx-0x6147a;
	w = z*z;
	j = 0x6b851-hx;
	t1= w*(Lg2+w*(Lg4+w*Lg6));
	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
	i |= j;
	R = t2+t1;
	if(i>0)
	{
		hfsq=0.5*f*f;
		return dk-((hfsq-(s*(hfsq+R)))-f)/ln2;
	}
	else
	{
		return dk-((s*(f-R))-f)/ln2;
	}
}

OVERLOADABLE double log10(double x)
{
	double zero = 0.0,
	two54	   =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
	ivln10	   =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
	log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
	log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */

	double y,z;
	int i,k,hx;
	unsigned lx;

	hx = __HI(x);	/* high word of x */
	lx = __LO(x);	/* low word of x */

	k=0;
	if (hx < 0x00100000)
	{  /* x < 2**-1022  */
		if (((hx&0x7fffffff)|lx)==0)
			return -two54/zero; /* log(+-0)=-inf */

		if (hx<0)
			return (x-x)/zero;/* log(-#) = NaN */

		k -= 54; x *= two54; /* subnormal number, scale up x */
		hx = __HI(x);/* high word of x */
	}

	if (hx >= 0x7ff00000) return x+x;
	k += (hx>>20)-1023;
	i  = ((unsigned)k&0x80000000)>>31;
	hx = (hx&0x000fffff)|((0x3ff-i)<<20);
	y  = (double)(k+i);
	__setHigh(&x, hx);
	z  = y*log10_2lo + ivln10*log(x);
	return  z+y*log10_2hi;
}

OVERLOADABLE double log1p(double x)
{
	double ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
	ln2_lo	=  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
	two54	=  1.80143985094819840000e+16,	/* 43500000 00000000 */
	Lp1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
	Lp2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
	Lp3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
	Lp4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
	Lp5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
	Lp6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
	Lp7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

	double hfsq,f,c,s,z,R,u,zero = 0;
	int k,hx,hu,ax;

	hx = __HI(x);		/* high word of x */
	ax = hx&0x7fffffff;

	k = 1;
	if (hx < 0x3FDA827A) {			/* x < 0.41422	*/
		if(ax>=0x3ff00000) {		/* x <= -1.0 */
		if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */
		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
		}
		if(ax<0x3e200000) { 		/* |x| < 2**-29 */
		if(two54+x>zero 		/* raise inexact */
				&&ax<0x3c900000)		/* |x| < 2**-54 */
			return x;
		else
			return x - x*x*0.5;
		}
		if(hx>0||hx<=((int)0xbfd2bec3)) {
		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
	}
	if (hx >= 0x7ff00000) return x+x;
	if(k!=0) {
		if(hx<0x43400000) {
		u  = 1.0+x;
			hu = __HI(u);		/* high word of u */
			k  = (hu>>20)-1023;
			c  = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
		c /= u;
		} else {
		u  = x;
			hu = __HI(u);		/* high word of u */
			k  = (hu>>20)-1023;
		c  = 0;
		}
		hu &= 0x000fffff;
		if(hu<0x6a09e) {
			__setHigh(&u, hu|0x3ff00000);	/* normalize u */
		} else {
			k += 1;
			__setHigh(&u, hu|0x3fe00000);	/* normalize u/2 */
			hu = (0x00100000-hu)>>2;
		}
		f = u-1.0;
	}
	hfsq=0.5*f*f;
	if(hu==0) { /* |f| < 2**-20 */
		if(f==zero)
		{
			if(k==0) return zero;
			else {c += k*ln2_lo; return k*ln2_hi+c;}
		}
		R = hfsq*(1.0-0.66666666666666666*f);
		if(k==0) return f-R; else
				 return k*ln2_hi-((R-(k*ln2_lo+c))-f);
	}
	s = f/(2.0+f);
	z = s*s;
	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
	if(k==0) return f-(hfsq-s*(hfsq+R)); else
		return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);

}

OVERLOADABLE double logb(double x)
{
	int lx,ix;
	ix = (__HI(x))&0x7fffffff;	/* high |x| */
	lx = __LO(x);			/* low x */
	if((ix|lx)==0) return -1.0/fabs(x);
	if(ix>=0x7ff00000) return x*x;
	if((ix>>=20)==0) 			/* IEEE 754 logb */
	{
		long qx = as_long(x);
		qx = qx & DF_ABS_MASK;
		int msbOne = clz(qx);
		return (double)(-1022 - (53 -(64 -msbOne)));
	}
	else
		return (double) (ix-1023);
}

OVERLOADABLE int ilogb(double x)
{
	int hx,lx,ix;

	hx  = (__HI(x))&0x7fffffff;	/* high word of x */
	if(hx == 0x7ff00000 && __LO(x) == 0) return 0x7fffffff;

	if(hx<0x00100000) {
		lx = __LO(x);
		if((hx|lx)==0)
		return 0x80000000;	/* ilogb(0) = 0x80000000 */
		else			/* subnormal x */
		if(hx==0) {
			for (ix = -1043; lx>0; lx<<=1) ix -=1;
		} else {
			for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;
		}
		return ix;
	}
	else if (hx<0x7ff00000) return (hx>>20)-1023;
	else return 0x80000000;
}

CONST OVERLOADABLE double __gen_ocl_mad(double a, double b, double c) __asm("llvm.fma" ".f64");
OVERLOADABLE double mad(double a, double b, double c)
{
	return __gen_ocl_mad(a, b, c);
}

OVERLOADABLE double nan(ulong code)
{
	return as_double(DF_POSITIVE_INF + (code&DF_MAN_MASK));
}

OVERLOADABLE double nextafter(double x, double y)
{
	long hx, hy, ix, iy;
	hx = as_long(x);
	hy = as_long(y);
	ix = hx & DF_ABS_MASK;
	iy = hy & DF_ABS_MASK;

	if(ix>DF_POSITIVE_INF|| iy>DF_POSITIVE_INF)
	  return x+y;
	if(hx == hy)
	  return y;
	if(ix == 0) {
	  if(iy == 0)
		return y;
	  else
		return as_double((hy&DF_SIGN_MASK) | 1);
	}
	if(hx >= 0) {
	  if(hx > hy) {
		hx -= 1;
	  } else {
		hx += 1;
	  }
	} else {
	  if(hy >= 0 || hx > hy){
		hx -= 1;
	  } else {
		hx += 1;
	  }
	}
	return as_double(hx);
}

OVERLOADABLE double fmax(double a, double b)
{
	ulong ua = as_ulong(a);
	ulong ub =as_ulong(b);

	if((ua & DF_ABS_MASK) > DF_MAX_NORMAL) return b;
	if((ub & DF_ABS_MASK) > DF_MAX_NORMAL) return a;
	if(ua == DF_POSITIVE_INF) return a;
	if(ub == DF_POSITIVE_INF) return b;

	double c = a - b;
	return (c >= 0) ? a:b;
}

OVERLOADABLE double fmin(double a, double b)
{
	ulong ua = as_ulong(a);
	ulong ub =as_ulong(b);

	if((ua & DF_ABS_MASK) > DF_MAX_NORMAL) return b;
	if((ub & DF_ABS_MASK) > DF_MAX_NORMAL) return a;
	if(ua == DF_NEGTIVE_INF) return a;
	if(ub == DF_NEGTIVE_INF) return b;

	double c = a - b;
	return (c <= 0) ? a:b;
}

OVERLOADABLE double fmod (double x, double y)
{
	const double one = 1.0, Zero[] = {0.0, -0.0,};
	int n,hx,hy,hz,ix,iy,sx,i;
	uint lx,ly,lz;

	hx = __HI(x);
	lx = __LO(x);
	hy = __HI(y);
	ly = __LO(y);
	sx = hx&0x80000000;		/* sign of x */
	hx ^=sx;		/* |x| */
	hy &= 0x7fffffff;	/* |y| */

    /* purge off exception values */
	if((hy|ly)==0||(hx>=0x7ff00000)||	/* y=0,or x not finite */
	  ((hy|((ly|-ly)>>31))>0x7ff00000))	/* or y is NaN */
	    return (x*y)/(x*y);
	if(hx<=hy) {
	    if((hx<hy)||(lx<ly)) return x;	/* |x|<|y| return x */
	    if(lx==ly) 
		return Zero[(uint)sx>>31];	/* |x|=|y| return x*0*/
	}

    /* determine ix = ilogb(x) */
	if(hx<0x00100000) {	/* subnormal x */
	    if(hx==0) {
		for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
	    } else {
		for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
	    }
	} else ix = (hx>>20)-1023;

    /* determine iy = ilogb(y) */
	if(hy<0x00100000) {	/* subnormal y */
	    if(hy==0) {
		for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
	    } else {
		for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
	    }
	} else iy = (hy>>20)-1023;

    /* set up {hx,lx}, {hy,ly} and align y to x */
	if(ix >= -1022) 
	    hx = 0x00100000|(0x000fffff&hx);
	else {		/* subnormal x, shift x to normal */
	    n = -1022-ix;
	    if(n<=31) {
	        hx = (hx<<n)|(lx>>(32-n));
	        lx <<= n;
	    } else {
		hx = lx<<(n-32);
		lx = 0;
	    }
	}
	if(iy >= -1022) 
	    hy = 0x00100000|(0x000fffff&hy);
	else {		/* subnormal y, shift y to normal */
	    n = -1022-iy;
	    if(n<=31) {
	        hy = (hy<<n)|(ly>>(32-n));
	        ly <<= n;
	    } else {
		hy = ly<<(n-32);
		ly = 0;
	    }
	}

    /* fix point fmod */
	n = ix - iy;
	while(n--) {
	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
	    if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
	    else {
	    	if((hz|lz)==0) 		/* return sign(x)*0 */
		    return Zero[(uint)sx>>31];
	    	hx = hz+hz+(lz>>31); lx = lz+lz;
	    }
	}
	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
	if(hz>=0) {hx=hz;lx=lz;}

    /* convert back to floating value and restore the sign */
	if((hx|lx)==0) 			/* return sign(x)*0 */
	    return Zero[(uint)sx>>31];	
	while(hx<0x00100000) {		/* normalize x */
	    hx = hx+hx+(lx>>31); lx = lx+lx;
	    iy -= 1;
	}
	if(iy>= -1022) {	/* normalize output */
		hx = ((hx-0x00100000)|((iy+1023)<<20));
		__setHigh(&x,hx|sx);
		__setLow(&x, lx);
	} else {		/* subnormal output */
	    n = -1022 - iy;
	    if(n<=20) {
		lx = (lx>>n)|((uint)hx<<(32-n));
		hx >>= n;
	    } else if (n<=31) {
		lx = (hx<<(32-n))|(lx>>n); hx = sx;
	    } else {
		lx = hx>>(n-32); hx = sx;
	    }
	__setHigh(&x,hx|sx);
	__setLow(&x, lx);

	    x *= one;		/* create necessary signal */
	}
	return x;		/* exact output */

}

OVERLOADABLE double rint(double x)
{
	long ret;
	long lval = as_long(x);
	int exp = ((lval & DF_EXP_MASK) >> DF_EXP_OFFSET) - DF_EXP_BIAS;
	long sign = (lval & DF_SIGN_MASK)?1:0;
	long ma = (lval &DF_MAN_MASK);

	if((lval & DF_ABS_MASK) == 0)
		return as_double(sign << 63);

	if(exp < -1)
	{
		ret = ((sign << 63)) ;
		return as_double(ret);
	}

	if(exp > 51) return x;

	long i = (1L << (52 - exp));
	i = 0x10000000000000 - i;
	unsigned long uv = 0xFFF0000000000000 + i;
	ulong vv = lval & uv;
	double	dp = as_double(vv);
	if(exp == -1) dp = 0;

	long fval = ma | DF_IMPLICITE_ONE;
	long lastBit = (fval & (1L << (52 -exp)));
	long roundBits = (fval & ( (1L << (52 -exp)) -1));

	if(roundBits > (1L << (51 -exp)))
		dp = (sign) ? dp-1.0:dp+1.0;
	else if((roundBits == (1L << (51 -exp))) && lastBit)
		dp = (sign) ? dp-1.0:dp+1.0;

	return dp;
}

OVERLOADABLE double round(double x)
{
	long ret;
	long lval = as_long(x);
	int exp = ((lval & DF_EXP_MASK) >> DF_EXP_OFFSET) - DF_EXP_BIAS;
	long sign = (lval & DF_SIGN_MASK)?1:0;
	long ma = (lval &DF_MAN_MASK);

	if((lval & DF_ABS_MASK) == 0)
		return as_double(sign << 63);

	if(exp < -1)
	{
		ret = ((sign << 63)) ;
		return as_double(ret);
	}

	if(exp > 51) return x;

	long i = (1L << (52 - exp));
	i = 0x10000000000000 - i;
	unsigned long uv = 0xFFF0000000000000 + i;
	ulong vv = lval & uv;
	double	dp = as_double(vv);
	if(exp == -1) dp = 0;

	long fval = ma | DF_IMPLICITE_ONE;
	long roundBits = (fval & ( (1L << (52 -exp)) -1));

	if(roundBits > (1L << (51 -exp)))
		dp = (sign) ? dp-1.0:dp+1.0;
	else if(roundBits == (1L << (51 -exp)))
		dp = (sign) ? dp-1.0:dp+1.0;

	return dp;
}

OVERLOADABLE double sin(double x)
{
	double y[2],z=0.0;
	int n, ix;

	/* High word of x. */
	ix = __HI(x);

	/* |x| ~< pi/4 */
	ix &= 0x7fffffff;
	if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);

	/* sin(Inf or NaN) is NaN */
	else if (ix>=0x7ff00000) return x-x;

	/* argument reduction needed */
	else {
		n = __ieee754_rem_pio2(x,y);
		switch(n&3) {
		case 0: return  __kernel_sin(y[0],y[1],1);
		case 1: return  __kernel_cos(y[0],y[1]);
		case 2: return -__kernel_sin(y[0],y[1],1);
		default:
			return -__kernel_cos(y[0],y[1]);
		}
	}
}

OVERLOADABLE double sinh(double x)
{
	double one = 1.0, shuge = 1.0e307;
	double t,w,h;
	int ix,jx;
	unsigned lx;

	/* High word of |x|. */
	jx = __HI(x);
	ix = jx&0x7fffffff;

	/* x is INF or NaN */
	if(ix>=0x7ff00000) return x+x;

	h = 0.5;
	if (jx<0) h = -h;
	/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
	if (ix < 0x40360000) {		/* |x|<22 */
		if (ix<0x3e300000) 		/* |x|<2**-28 */
		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
		t = expm1(fabs(x));
		if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
		return h*(t+t/(t+one));
	}

	/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
	if (ix < 0x40862E42)  return h*exp(fabs(x));

	/* |x| in [log(maxdouble), overflowthresold] */
	lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
	if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
		w = exp(0.5*fabs(x));
		t = h*w;
		return t*w;
	}

	/* |x| > overflowthresold, sinh(x) overflow */
	return x*shuge;
}

OVERLOADABLE double sqrt(double x)
{
    double z;
    int     sign = (int)0x80000000;
    unsigned r,t1,s1,ix1,q1;
    int ix0,s0,q,m,t,i;
    const double    one = 1.0, tiny=1.0e-300;

    ix0 = __HI(x);          /* high word of x */
    ix1 = __LO(x);      /* low word of x */

    /* take care of Inf and NaN */
    if((ix0&0x7ff00000)==0x7ff00000) {
        return x*x+x;       /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
                       sqrt(-inf)=sNaN */
    }
    /* take care of zero */
    if(ix0<=0) {
        if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
        else if(ix0<0)
        return (x-x)/(x-x);     /* sqrt(-ve) = sNaN */
    }
    /* normalize x */
    m = (ix0>>20);
    if(m==0) {              /* subnormal x */
        while(ix0==0) {
        m -= 21;
        ix0 |= (ix1>>11); ix1 <<= 21;
        }
        for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
        m -= i-1;
        ix0 |= (ix1>>(32-i));
        ix1 <<= i;
    }
    m -= 1023;  /* unbias exponent */
    ix0 = (ix0&0x000fffff)|0x00100000;
    if(m&1){    /* odd m, double x to make it even */
        ix0 += ix0 + ((ix1&sign)>>31);
        ix1 += ix1;
    }
    m >>= 1;    /* m = [m/2] */

    /* generate sqrt(x) bit by bit */
    ix0 += ix0 + ((ix1&sign)>>31);
    ix1 += ix1;
    q = q1 = s0 = s1 = 0;   /* [q,q1] = sqrt(x) */
    r = 0x00200000;     /* r = moving bit from right to left */

    while(r!=0) {
        t = s0+r;
        if(t<=ix0) {
        s0   = t+r;
        ix0 -= t;
        q   += r;
        }
        ix0 += ix0 + ((ix1&sign)>>31);
        ix1 += ix1;
        r>>=1;
    }

    r = sign;
    while(r!=0) {
        t1 = s1+r;
        t  = s0;
        if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
        s1  = t1+r;
        if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
        ix0 -= t;
        if (ix1 < t1) ix0 -= 1;
        ix1 -= t1;
        q1  += r;
        }
        ix0 += ix0 + ((ix1&sign)>>31);
        ix1 += ix1;
        r>>=1;
    }

    /* use floating add to find out rounding direction */
    if((ix0|ix1)!=0) {
        z = one-tiny; /* trigger inexact flag */
        if (z>=one) {
            z = one+tiny;
            if (q1==(unsigned)0xffffffff) { q1=0; q += 1;}
        else if (z>one) {
            if (q1==(unsigned)0xfffffffe) q+=1;
            q1+=2;
        } else
                q1 += (q1&1);
        }
    }
    ix0 = (q>>1)+0x3fe00000;
    ix1 =  q1>>1;
    if ((q&1)==1) ix1 |= sign;
    ix0 += (m <<20);
    __setHigh(&z, ix0);
    __setLow(&z, ix1);
    return z;
}

double __kernel_tan(double x, double y, int iy)
{
		 const double xxx[] = {
			 3.33333333333334091986e-01,	/* 3FD55555, 55555563 */
			 1.33333333333201242699e-01,	/* 3FC11111, 1110FE7A */
			 5.39682539762260521377e-02,	/* 3FABA1BA, 1BB341FE */
			 2.18694882948595424599e-02,	/* 3F9664F4, 8406D637 */
			 8.86323982359930005737e-03,	/* 3F8226E3, E96E8493 */
			 3.59207910759131235356e-03,	/* 3F6D6D22, C9560328 */
			 1.45620945432529025516e-03,	/* 3F57DBC8, FEE08315 */
			 5.88041240820264096874e-04,	/* 3F4344D8, F2F26501 */
			 2.46463134818469906812e-04,	/* 3F3026F7, 1A8D1068 */
			 7.81794442939557092300e-05,	/* 3F147E88, A03792A6 */
			 7.14072491382608190305e-05,	/* 3F12B80F, 32F0A7E9 */
			-1.85586374855275456654e-05,	/* BEF375CB, DB605373 */
			 2.59073051863633712884e-05,	/* 3EFB2A70, 74BF7AD4 */
	/* one */	1.00000000000000000000e+00,	/* 3FF00000, 00000000 */
	/* pio4 */   7.85398163397448278999e-01,	/* 3FE921FB, 54442D18 */
	/* pio4lo */	 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */
	};
#define	one	xxx[13]
#define	pio4	xxx[14]
#define	pio4lo	xxx[15]
#define	T	xxx

	double z, r, v, w, s;
	int ix, hx;

	hx = __HI(x);		/* high word of x */
	ix = hx & 0x7fffffff;			/* high word of |x| */
	if (ix < 0x3e300000) {			/* x < 2**-28 */
		if ((int) x == 0) {		/* generate inexact */
			if (((ix | __LO(x)) | (iy + 1)) == 0)
				return one / fabs(x);
			else {
				if (iy == 1)
					return x;
				else {	/* compute -1 / (x+y) carefully */
					double a, t;

					z = w = x + y;
					__setLow(&z, 0);
					v = y - (z - x);
					t = a = -one / w;
					__setLow(&t, 0);
					s = one + t * z;
					return t + a * (s + t * v);
				}
			}
		}
	}
	if (ix >= 0x3FE59428) {	/* |x| >= 0.6744 */
		if (hx < 0) {
			x = -x;
			y = -y;
		}
		z = pio4 - x;
		w = pio4lo - y;
		x = z + w;
		y = 0.0;
	}
	z = x * x;
	w = z * z;
	/*
	 * Break x^5*(T[1]+x^2*T[2]+...) into
	 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
	 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
	 */
	r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +
		w * T[11]))));
	v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] +
		w * T[12])))));
	s = z * x;
	r = y + z * (s * (r + v) + y);
	r += T[0] * s;
	w = x + r;
	if (ix >= 0x3FE59428) {
		v = (double) iy;
		return (double) (1 - ((hx >> 30) & 2)) *
			(v - 2.0 * (x - (w * w / (w + v) - r)));
	}
	if (iy == 1)
		return w;
	else {
		/*
		 * if allow error up to 2 ulp, simply return
		 * -1.0 / (x+r) here
		 */
		/* compute -1.0 / (x+r) accurately */
		double a, t;
		z = w;
		__setLow(&z, 0);
		v = r - (z - x);	/* z+v = r+x */
		t = a = -1.0 / w;	/* a = -1.0/w */
		__setLow(&t, 0);
		s = 1.0 + t * z;
		return t + a * (s + t * v);
	}

#undef	one
#undef	pio4
#undef	pio4lo
#undef	T
}

OVERLOADABLE double tan(double x)
{
	double y[2],z=0.0;
	int n, ix;

	/* High word of x. */
	ix = __HI(x);

	/* |x| ~< pi/4 */
	ix &= 0x7fffffff;
	if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);

	/* tan(Inf or NaN) is NaN */
	else if (ix>=0x7ff00000) return x-x;		/* NaN */

	/* argument reduction needed */
	else {
		n = __ieee754_rem_pio2(x,y);
		return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
							-1 -- n odd */
	}
}

OVERLOADABLE double tanh(double x)
{
	double one=1.0, two=2.0, tiny = 1.0e-300;
	double t,z;
	int jx,ix;

	/* High word of |x|. */
	jx = __HI(x);
	ix = jx&0x7fffffff;

	/* x is INF or NaN */
	if(ix>=0x7ff00000) {
		if (jx>=0) return one/x+one;	/* tanh(+-inf)=+-1 */
		else	   return one/x-one;	/* tanh(NaN) = NaN */
	}

	/* |x| < 22 */
	if (ix < 0x40360000) {		/* |x|<22 */
		if (ix<0x3c800000) 		/* |x|<2**-55 */
		return x*(one+x);		/* tanh(small) = small */
		if (ix>=0x3ff00000) {	/* |x|>=1  */
		t = expm1(two*fabs(x));
		z = one - two/(t+two);
		} else {
			t = expm1(-two*fabs(x));
			z= -t/(t+two);
		}
	/* |x| > 22, return +-1 */
	} else {
		z = one - tiny;		/* raised inexact flag */
	}
	return (jx>=0)? z: -z;
}

OVERLOADABLE double trunc(double x)
{
	double ret = floor(fabs(x));
	return copysign(ret, x);
}