/**
* Copyright (c) 2012-2016 André Bargull
* Alle Rechte vorbehalten / All Rights Reserved. Use is subject to license terms.
*
* <https://github.com/anba/es6draft>
*/
package com.github.anba.es6draft.runtime.internal;
/**
* Java port of fdlibm functions.
*/
public final class MathImpl {
private MathImpl() {
}
/* @formatter:off */
private static final double
log2e = 1.442695040888963407359924, /* 3FF71547 652B82FE */
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
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 */
zero = 0d, /* 00000000 00000000 */
one = 1.0d, /* 3FF00000 00000000 */
two = 2.0,
ln2 = Math.log(2d), /* 3FE62E42 FEFA39EF */
huge = 1e300,
tiny = 1.0e-300,
/* 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*/
private static final double[]
bp = {1.0, 1.5,},
dp_h = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l = { 0.0, 1.35003920212974897128e-08,}; /* 0x3E4CFDEB, 0x43CFD006 */
/* @formatter:on */
/* @formatter:off */
/* @(#)e_log.c 1.3 95/01/18 */
/*
* ====================================================
* 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.
* ====================================================
*/
/**
* Returns the base 2 logarithm of {@code x}.
* <p>
* This method computes {@code Math.log(x) / Math.log(2.0)}, but may yield better accuracy.
*
* @param x
* a double value
* @return the base 2 logarithm of {@code x}
*/
public static double
log2(double x)
{
double hfsq,f,s,z,R,w,t1,t2,dk;
int k,hx,i,j;
/* unsigned */ int lx;
long bits = Double.doubleToRawLongBits(x);
hx = __HI(bits); /* high word of x */
lx = __LO(bits); /* 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;
x = __HI(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;
dk=(double)k;
return dk;
}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return (f - R) * log2e;
dk=(double)k;
return dk - (R - f) * log2e;
}
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))) * log2e;
return dk - (hfsq - s * (hfsq + R) - f) * log2e;
} else {
if(k==0) return (f - s * (f - R)) * log2e;
return dk - (s * (f - R) - f) * log2e;
}
}
/* @formatter:on */
/* @formatter:off */
/* @(#)e_acosh.c 1.3 95/01/18 */
/*
* ====================================================
* 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.
* ====================================================
*
*/
/**
* Returns the hyperbolic arc-cosine of {@code x}.
*
* @param x
* a double value
* @return the hyperbolic arc-cosine of {@code x}
*/
public static double
acosh(final double x)
{
final long bits = Double.doubleToRawLongBits(x);
final int hx = __HI(bits);
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 Math.log(x) + ln2; /* acosh(huge)=log(2x) */
} else if (((hx - 0x3ff00000) | __LO(bits)) == 0) {
return 0.0; /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
final double t = x * x;
return Math.log(2.0 * x - one / (x + Math.sqrt(t - one)));
} else { /* 1<x<2 */
final double t = x - one;
return Math.log1p(t + Math.sqrt(2.0 * t + t * t));
}
}
/* @formatter:on */
/* @formatter:off */
/* @(#)s_asinh.c 1.3 95/01/18 */
/*
* ====================================================
* 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.
* ====================================================
*/
/**
* Returns the hyperbolic arc-sine of {@code x}.
*
* @param x
* a double value
* @return the hyperbolic arc-sine of {@code x}
*/
public static double
asinh(final double x)
{
final long bits = Double.doubleToRawLongBits(x);
final int hx = __HI(bits);
final int 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 */
}
final double w;
if (ix > 0x41b00000) { /* |x| > 2**28 */
w = Math.log(Math.abs(x)) + ln2;
} else if (ix > 0x40000000) { /* 2**28 > |x| > 2.0 */
final double t = Math.abs(x);
w = Math.log(2.0 * t + one / (Math.sqrt(x * x + one) + t));
} else { /* 2.0 > |x| > 2**-28 */
final double t = x * x;
w = Math.log1p(Math.abs(x) + t / (one + Math.sqrt(one + t)));
}
if (hx > 0)
return w;
else
return -w;
}
/* @formatter:on */
/* @formatter:off */
/* @(#)e_atanh.c 1.3 95/01/18 */
/*
* ====================================================
* 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.
* ====================================================
*
*/
/**
* Returns the hyperbolic arc-tangent of {@code x}.
*
* @param x
* a double value
* @return the hyperbolic arc-tangent of {@code x}
*/
public static double
atanh(double x)
{
final long bits = Double.doubleToRawLongBits(x);
double t;
final int hx = __HI(bits); /* high word */
final int lx = __LO(bits); /* low word */
final int 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 */
x = toDouble(ix, lx); /* x <- |x| */
if (ix < 0x3fe00000) { /* x < 0.5 */
t = x + x;
t = 0.5 * Math.log1p(t + t * x / (one - x));
} else
t = 0.5 * Math.log1p((x + x) / (one - x));
if (hx >= 0)
return t;
else
return -t;
}
/* @formatter:on */
/* @formatter:on */
/* @(#)e_pow.c 1.5 04/04/22 SMI */
/*
* ====================================================
* 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.
* ====================================================
*/
public static double
pow(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 i,j,k,yisint,n;
int hx,hy,ix,iy;
/*unsigned*/ int lx,ly;
// int i0, i1;
// 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((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 Math.sqrt(x);
}
}
ax = Math.abs(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;
// Remove if-condition to pass FindBugs validation.
// if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
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;
t1 = __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;
ax = __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;
s_h = __LO(s_h, 0);
/* t_h=ax+bp[k] High */
t_h = zero;
// __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
t_h = __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_h = __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_h = __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;
t1 = __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;
y1 = __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));
t = __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;
t = __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 = Math.scalb(z,n); /* subnormal output */
// else __HI(z) += (n<<20);
else z = __HI(z, __HI(z) + (n<<20));
return s*z;
}
/* @formatter:off */
private static int __HI(long bits) {
return (int) (bits >>> 32);
}
private static int __LO(long bits) {
return (int) bits;
}
private static int __HI(double value) {
return __HI(Double.doubleToRawLongBits(value));
}
private static int __LO(double value) {
return __LO(Double.doubleToRawLongBits(value));
}
private static double __HI(double value, int hi) {
return Double.longBitsToDouble(((long) hi << 32) | ((long) __LO(value) & 0xFFFF_FFFFL));
}
private static double __LO(double value, int lo) {
return Double.longBitsToDouble(((long) __HI(value) << 32) | ((long) lo & 0xFFFF_FFFFL));
}
private static double toDouble(int hi, int lo) {
return Double.longBitsToDouble(((long) hi << 32) | ((long) lo & 0xFFFF_FFFFL));
}
}