MathObject.cpp   [plain text]

/*
 *  Copyright (C) 1999-2000 Harri Porten (porten@kde.org)
 *  Copyright (C) 2007, 2008 Apple Inc. All Rights Reserved.
 *
 *  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 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, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */

#include "config.h"
#include "MathObject.h"

#include "Lookup.h"
#include "ObjectPrototype.h"
#include "Operations.h"
#include <time.h>
#include <wtf/Assertions.h>
#include <wtf/MathExtras.h>
#include <wtf/RandomNumber.h>
#include <wtf/RandomNumberSeed.h>

namespace JSC {

ASSERT_CLASS_FITS_IN_CELL(MathObject);

static EncodedJSValue JSC_HOST_CALL mathProtoFuncAbs(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncACos(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncASin(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncATan(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncATan2(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncCeil(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncCos(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncExp(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncFloor(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncLog(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncMax(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncMin(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncPow(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncRandom(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncRound(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncSin(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncSqrt(ExecState*);
static EncodedJSValue JSC_HOST_CALL mathProtoFuncTan(ExecState*);

}

#include "MathObject.lut.h"

namespace JSC {

ASSERT_HAS_TRIVIAL_DESTRUCTOR(MathObject);

const ClassInfo MathObject::s_info = { "Math", &JSNonFinalObject::s_info, 0, ExecState::mathTable, CREATE_METHOD_TABLE(MathObject) };

/* Source for MathObject.lut.h
@begin mathTable
  abs           mathProtoFuncAbs               DontEnum|Function 1
  acos          mathProtoFuncACos              DontEnum|Function 1
  asin          mathProtoFuncASin              DontEnum|Function 1
  atan          mathProtoFuncATan              DontEnum|Function 1
  atan2         mathProtoFuncATan2             DontEnum|Function 2
  ceil          mathProtoFuncCeil              DontEnum|Function 1
  cos           mathProtoFuncCos               DontEnum|Function 1
  exp           mathProtoFuncExp               DontEnum|Function 1
  floor         mathProtoFuncFloor             DontEnum|Function 1
  log           mathProtoFuncLog               DontEnum|Function 1
  max           mathProtoFuncMax               DontEnum|Function 2
  min           mathProtoFuncMin               DontEnum|Function 2
  pow           mathProtoFuncPow               DontEnum|Function 2
  random        mathProtoFuncRandom            DontEnum|Function 0 
  round         mathProtoFuncRound             DontEnum|Function 1
  sin           mathProtoFuncSin               DontEnum|Function 1
  sqrt          mathProtoFuncSqrt              DontEnum|Function 1
  tan           mathProtoFuncTan               DontEnum|Function 1
@end
*/

MathObject::MathObject(JSGlobalObject* globalObject, Structure* structure)
    : JSNonFinalObject(globalObject->globalData(), structure)
{
}

void MathObject::finishCreation(ExecState* exec, JSGlobalObject* globalObject)
{
    Base::finishCreation(globalObject->globalData());
    ASSERT(inherits(&s_info));

    putDirectWithoutTransition(exec->globalData(), Identifier(exec, "E"), jsNumber(exp(1.0)), DontDelete | DontEnum | ReadOnly);
    putDirectWithoutTransition(exec->globalData(), Identifier(exec, "LN2"), jsNumber(log(2.0)), DontDelete | DontEnum | ReadOnly);
    putDirectWithoutTransition(exec->globalData(), Identifier(exec, "LN10"), jsNumber(log(10.0)), DontDelete | DontEnum | ReadOnly);
    putDirectWithoutTransition(exec->globalData(), Identifier(exec, "LOG2E"), jsNumber(1.0 / log(2.0)), DontDelete | DontEnum | ReadOnly);
    putDirectWithoutTransition(exec->globalData(), Identifier(exec, "LOG10E"), jsNumber(0.4342944819032518), DontDelete | DontEnum | ReadOnly); // See ECMA-262 15.8.1.5
    putDirectWithoutTransition(exec->globalData(), Identifier(exec, "PI"), jsNumber(piDouble), DontDelete | DontEnum | ReadOnly);
    putDirectWithoutTransition(exec->globalData(), Identifier(exec, "SQRT1_2"), jsNumber(sqrt(0.5)), DontDelete | DontEnum | ReadOnly);
    putDirectWithoutTransition(exec->globalData(), Identifier(exec, "SQRT2"), jsNumber(sqrt(2.0)), DontDelete | DontEnum | ReadOnly);
}

bool MathObject::getOwnPropertySlot(JSCell* cell, ExecState* exec, const Identifier& propertyName, PropertySlot &slot)
{
    return getStaticFunctionSlot<JSObject>(exec, ExecState::mathTable(exec), jsCast<MathObject*>(cell), propertyName, slot);
}

bool MathObject::getOwnPropertyDescriptor(JSObject* object, ExecState* exec, const Identifier& propertyName, PropertyDescriptor& descriptor)
{
    return getStaticFunctionDescriptor<JSObject>(exec, ExecState::mathTable(exec), jsCast<MathObject*>(object), propertyName, descriptor);
}

// ------------------------------ Functions --------------------------------

EncodedJSValue JSC_HOST_CALL mathProtoFuncAbs(ExecState* exec)
{
    return JSValue::encode(jsNumber(fabs(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncACos(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(acos(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncASin(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(asin(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncATan(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(atan(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncATan2(ExecState* exec)
{
    double arg0 = exec->argument(0).toNumber(exec);
    double arg1 = exec->argument(1).toNumber(exec);
    return JSValue::encode(jsDoubleNumber(atan2(arg0, arg1)));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncCeil(ExecState* exec)
{
    return JSValue::encode(jsNumber(ceil(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncCos(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(cos(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncExp(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(exp(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncFloor(ExecState* exec)
{
    return JSValue::encode(jsNumber(floor(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncLog(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(log(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncMax(ExecState* exec)
{
    unsigned argsCount = exec->argumentCount();
    double result = -std::numeric_limits<double>::infinity();
    for (unsigned k = 0; k < argsCount; ++k) {
        double val = exec->argument(k).toNumber(exec);
        if (isnan(val)) {
            result = std::numeric_limits<double>::quiet_NaN();
            break;
        }
        if (val > result || (val == 0 && result == 0 && !signbit(val)))
            result = val;
    }
    return JSValue::encode(jsNumber(result));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncMin(ExecState* exec)
{
    unsigned argsCount = exec->argumentCount();
    double result = +std::numeric_limits<double>::infinity();
    for (unsigned k = 0; k < argsCount; ++k) {
        double val = exec->argument(k).toNumber(exec);
        if (isnan(val)) {
            result = std::numeric_limits<double>::quiet_NaN();
            break;
        }
        if (val < result || (val == 0 && result == 0 && signbit(val)))
            result = val;
    }
    return JSValue::encode(jsNumber(result));
}

#if CPU(ARM_THUMB2)

static double fdlibmPow(double x, double y);

static ALWAYS_INLINE bool isDenormal(double x)
{
        static const uint64_t signbit = 0x8000000000000000ULL;
        static const uint64_t minNormal = 0x0001000000000000ULL;
        return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 < minNormal - 1;
}

static ALWAYS_INLINE bool isEdgeCase(double x)
{
        static const uint64_t signbit = 0x8000000000000000ULL;
        static const uint64_t infinity = 0x7fffffffffffffffULL;
        return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 >= infinity - 1;
}

static ALWAYS_INLINE double mathPow(double x, double y)
{
    if (!isDenormal(x) && !isDenormal(y)) {
        double libmResult = pow(x,y);
        if (libmResult || isEdgeCase(x) || isEdgeCase(y))
            return libmResult;
    }
    return fdlibmPow(x,y);
}

#else

ALWAYS_INLINE double mathPow(double x, double y)
{
    return pow(x, y);
}

#endif

EncodedJSValue JSC_HOST_CALL mathProtoFuncPow(ExecState* exec)
{
    // ECMA 15.8.2.1.13

    double arg = exec->argument(0).toNumber(exec);
    double arg2 = exec->argument(1).toNumber(exec);

    if (isnan(arg2))
        return JSValue::encode(jsNaN());
    if (isinf(arg2) && fabs(arg) == 1)
        return JSValue::encode(jsNaN());
    return JSValue::encode(jsNumber(mathPow(arg, arg2)));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncRandom(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(exec->lexicalGlobalObject()->weakRandomNumber()));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncRound(ExecState* exec)
{
    double arg = exec->argument(0).toNumber(exec);
    double integer = ceil(arg);
    return JSValue::encode(jsNumber(integer - (integer - arg > 0.5)));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncSin(ExecState* exec)
{
    return JSValue::encode(exec->globalData().cachedSin(exec->argument(0).toNumber(exec)));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncSqrt(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(sqrt(exec->argument(0).toNumber(exec))));
}

EncodedJSValue JSC_HOST_CALL mathProtoFuncTan(ExecState* exec)
{
    return JSValue::encode(jsDoubleNumber(tan(exec->argument(0).toNumber(exec))));
}

#if CPU(ARM_THUMB2)

// The following code is taken from netlib.org:
//   http://www.netlib.org/fdlibm/fdlibm.h
//   http://www.netlib.org/fdlibm/e_pow.c
//   http://www.netlib.org/fdlibm/s_scalbn.c
//
// And was originally distributed under the following license:

/*
 * ====================================================
 * 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.
 * ====================================================
 */
/*
 * ====================================================
 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
 *
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* __ieee754_pow(x,y) return x**y
 *
 *		      n
 * Method:  Let x =  2   * (1+f)
 *	1. Compute and return log2(x) in two pieces:
 *		log2(x) = w1 + w2,
 *	   where w1 has 53-24 = 29 bit trailing zeros.
 *	2. Perform y*log2(x) = n+y' by simulating muti-precision 
 *	   arithmetic, where |y'|<=0.5.
 *	3. Return x**y = 2**n*exp(y'*log2)
 *
 * Special cases:
 *	1.  (anything) ** 0  is 1
 *	2.  (anything) ** 1  is itself
 *	3.  (anything) ** NAN is NAN
 *	4.  NAN ** (anything except 0) is NAN
 *	5.  +-(|x| > 1) **  +INF is +INF
 *	6.  +-(|x| > 1) **  -INF is +0
 *	7.  +-(|x| < 1) **  +INF is +0
 *	8.  +-(|x| < 1) **  -INF is +INF
 *	9.  +-1         ** +-INF is NAN
 *	10. +0 ** (+anything except 0, NAN)               is +0
 *	11. -0 ** (+anything except 0, NAN, odd integer)  is +0
 *	12. +0 ** (-anything except 0, NAN)               is +INF
 *	13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
 *	14. -0 ** (odd integer) = -( +0 ** (odd integer) )
 *	15. +INF ** (+anything except 0,NAN) is +INF
 *	16. +INF ** (-anything except 0,NAN) is +0
 *	17. -INF ** (anything)  = -0 ** (-anything)
 *	18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
 *	19. (-anything except 0 and inf) ** (non-integer) is NAN
 *
 * Accuracy:
 *	pow(x,y) returns x**y nearly rounded. In particular
 *			pow(integer,integer)
 *	always returns the correct integer provided it is 
 *	representable.
 *
 * Constants :
 * The hexadecimal values are the intended ones for the following 
 * constants. The decimal values may be used, provided that the 
 * compiler will convert from decimal to binary accurately enough 
 * to produce the hexadecimal values shown.
 */

#define __HI(x) *(1+(int*)&x)
#define __LO(x) *(int*)&x

static const double
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
zero    =  0.0,
one	=  1.0,
two	=  2.0,
two53	=  9007199254740992.0,	/* 0x43400000, 0x00000000 */
huge	=  1.0e300,
tiny    =  1.0e-300,
        /* for scalbn */
two54   =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54  =  5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
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 */
lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

inline double fdlibmScalbn (double x, int n)
{
	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 */
	    {__HI(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 */
        __HI(x) = (hx&0x800fffff)|(k<<20);
        return x*twom54;
}

double fdlibmPow(double x, double y)
{
	double z,ax,z_h,z_l,p_h,p_l;
	double y1,t1,t2,r,s,t,u,v,w;
	int i0,i1,i,j,k,yisint,n;
	int hx,hy,ix,iy;
	unsigned lx,ly;

	i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
	hx = __HI(x); lx = __LO(x);
	hy = __HI(y); ly = __LO(y);
	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;

    /* y==zero: x**0 = 1 */
	if((iy|ly)==0) return one; 	

    /* +-NaN return x+y */
	if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
	   iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 
		return x+y;	

    /* determine if y is an odd int when x < 0
     * yisint = 0	... y is not an integer
     * yisint = 1	... y is an odd int
     * yisint = 2	... y is an even int
     */
	yisint  = 0;
	if(hx<0) {	
	    if(iy>=0x43400000) yisint = 2; /* even integer y */
	    else if(iy>=0x3ff00000) {
		k = (iy>>20)-0x3ff;	   /* exponent */
		if(k>20) {
		    j = ly>>(52-k);
		    if(static_cast<unsigned>(j<<(52-k))==ly) yisint = 2-(j&1);
		} else if(ly==0) {
		    j = iy>>(20-k);
		    if((j<<(20-k))==iy) yisint = 2-(j&1);
		}
	    }		
	} 

    /* special value of y */
	if(ly==0) { 	
	    if (iy==0x7ff00000) {	/* y is +-inf */
	        if(((ix-0x3ff00000)|lx)==0)
		    return  y - y;	/* inf**+-1 is NaN */
	        else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
		    return (hy>=0)? y: zero;
	        else			/* (|x|<1)**-,+inf = inf,0 */
		    return (hy<0)?-y: zero;
	    } 
	    if(iy==0x3ff00000) {	/* y is  +-1 */
		if(hy<0) return one/x; else return x;
	    }
	    if(hy==0x40000000) return x*x; /* y is  2 */
	    if(hy==0x3fe00000) {	/* y is  0.5 */
		if(hx>=0)	/* x >= +0 */
		return sqrt(x);	
	    }
	}

	ax   = fabs(x);
    /* special value of x */
	if(lx==0) {
	    if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
		z = ax;			/*x is +-0,+-inf,+-1*/
		if(hy<0) z = one/z;	/* z = (1/|x|) */
		if(hx<0) {
		    if(((ix-0x3ff00000)|yisint)==0) {
			z = (z-z)/(z-z); /* (-1)**non-int is NaN */
		    } else if(yisint==1) 
			z = -z;		/* (x<0)**odd = -(|x|**odd) */
		}
		return z;
	    }
	}
    
	n = (hx>>31)+1;

    /* (x<0)**(non-int) is NaN */
	if((n|yisint)==0) return (x-x)/(x-x);

	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
	if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */

    /* |y| is huge */
	if(iy>0x41e00000) { /* if |y| > 2**31 */
	    if(iy>0x43f00000){	/* if |y| > 2**64, must o/uflow */
		if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
		if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
	    }
	/* over/underflow if x is not close to one */
	    if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
	    if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
	/* now |1-x| is tiny <= 2**-20, suffice to compute 
	   log(x) by x-x^2/2+x^3/3-x^4/4 */
	    t = ax-one;		/* t has 20 trailing zeros */
	    w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
	    u = ivln2_h*t;	/* ivln2_h has 21 sig. bits */
	    v = t*ivln2_l-w*ivln2;
	    t1 = u+v;
	    __LO(t1) = 0;
	    t2 = v-(t1-u);
	} else {
	    double ss,s2,s_h,s_l,t_h,t_l;
	    n = 0;
	/* take care subnormal number */
	    if(ix<0x00100000)
		{ax *= two53; n -= 53; ix = __HI(ax); }
	    n  += ((ix)>>20)-0x3ff;
	    j  = ix&0x000fffff;
	/* determine interval */
	    ix = j|0x3ff00000;		/* normalize ix */
	    if(j<=0x3988E) k=0;		/* |x|<sqrt(3/2) */
	    else if(j<0xBB67A) k=1;	/* |x|<sqrt(3)   */
	    else {k=0;n+=1;ix -= 0x00100000;}
	    __HI(ax) = ix;

	/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
	    u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
	    v = one/(ax+bp[k]);
	    ss = u*v;
	    s_h = ss;
	    __LO(s_h) = 0;
	/* t_h=ax+bp[k] High */
	    t_h = zero;
	    __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18); 
	    t_l = ax - (t_h-bp[k]);
	    s_l = v*((u-s_h*t_h)-s_h*t_l);
	/* compute log(ax) */
	    s2 = ss*ss;
	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
	    r += s_l*(s_h+ss);
	    s2  = s_h*s_h;
	    t_h = 3.0+s2+r;
	    __LO(t_h) = 0;
	    t_l = r-((t_h-3.0)-s2);
	/* u+v = ss*(1+...) */
	    u = s_h*t_h;
	    v = s_l*t_h+t_l*ss;
	/* 2/(3log2)*(ss+...) */
	    p_h = u+v;
	    __LO(p_h) = 0;
	    p_l = v-(p_h-u);
	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
	/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
	    t = (double)n;
	    t1 = (((z_h+z_l)+dp_h[k])+t);
	    __LO(t1) = 0;
	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
	}

    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
	y1  = y;
	__LO(y1) = 0;
	p_l = (y-y1)*t1+y*t2;
	p_h = y1*t1;
	z = p_l+p_h;
	j = __HI(z);
	i = __LO(z);
	if (j>=0x40900000) {				/* z >= 1024 */
	    if(((j-0x40900000)|i)!=0)			/* if z > 1024 */
		return s*huge*huge;			/* overflow */
	    else {
		if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
	    }
	} else if((j&0x7fffffff)>=0x4090cc00 ) {	/* z <= -1075 */
	    if(((j-0xc090cc00)|i)!=0) 		/* z < -1075 */
		return s*tiny*tiny;		/* underflow */
	    else {
		if(p_l<=z-p_h) return s*tiny*tiny;	/* underflow */
	    }
	}
    /*
     * compute 2**(p_h+p_l)
     */
	i = j&0x7fffffff;
	k = (i>>20)-0x3ff;
	n = 0;
	if(i>0x3fe00000) {		/* if |z| > 0.5, set n = [z+0.5] */
	    n = j+(0x00100000>>(k+1));
	    k = ((n&0x7fffffff)>>20)-0x3ff;	/* new k for n */
	    t = zero;
	    __HI(t) = (n&~(0x000fffff>>k));
	    n = ((n&0x000fffff)|0x00100000)>>(20-k);
	    if(j<0) n = -n;
	    p_h -= t;
	} 
	t = p_l+p_h;
	__LO(t) = 0;
	u = t*lg2_h;
	v = (p_l-(t-p_h))*lg2+t*lg2_l;
	z = u+v;
	w = v-(z-u);
	t  = z*z;
	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
	r  = (z*t1)/(t1-two)-(w+z*w);
	z  = one-(r-z);
	j  = __HI(z);
	j += (n<<20);
	if((j>>20)<=0) z = fdlibmScalbn(z,n);	/* subnormal output */
	else __HI(z) += (n<<20);
	return s*z;
}

#endif

} // namespace JSC