/**
 * Copyright (c) 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:off */
    /* @(#)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:on */

    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));
    }
}
