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/* ====================================================
* 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.
* ====================================================
*/
package com.oracle.truffle.js.builtins.math;
import com.oracle.truffle.api.CompilerDirectives.TruffleBoundary;
import com.oracle.truffle.api.dsl.Specialization;
import com.oracle.truffle.js.nodes.function.JSBuiltin;
import com.oracle.truffle.js.runtime.JSContext;
public abstract class Log2Node extends MathOperation {
public Log2Node(JSContext context, JSBuiltin builtin) {
super(context, builtin);
}
Return a double with its low-order bits of the second argument and the high-order bits of the
first argument.
/**
* Return a double with its low-order bits of the second argument and the high-order bits of the
* first argument.
*/
private static double lowBits(double x, int low) {
long transX = Double.doubleToRawLongBits(x);
return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L) | low);
}
Return the high-order 32 bits of the double argument as an int.
/**
* Return the high-order 32 bits of the double argument as an int.
*/
private static int highBits(double x) {
long transducer = Double.doubleToRawLongBits(x);
return (int) (transducer >> 32);
}
Return a double with its high-order bits of the second argument and the low-order bits of the
first argument.
/**
* Return a double with its high-order bits of the second argument and the low-order bits of the
* first argument.
*/
private static double highBits(double x, int high) {
long transX = Double.doubleToRawLongBits(x);
return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL) | (((long) high)) << 32);
}
Returns the base 2 logarithm. The algorithm comes from FDLIBM library. This library does not have an explicit log2 function but its pow function implements log2 function as part of the pow implementation. The implementation of this function is an extract of log2 function from the Java port of pow function found in java.lang.FdLibm class. Params: - x – value whose logarithm should be returned.
Returns: base 2 logarithm.
/**
* Returns the base 2 logarithm. The algorithm comes from FDLIBM library. This library does not
* have an explicit log2 function but its pow function implements log2 function as part of the
* pow implementation. The implementation of this function is an extract of log2 function from
* the Java port of pow function found in {@code java.lang.FdLibm} class.
*
* @param x value whose logarithm should be returned.
* @return base 2 logarithm.
*/
@TruffleBoundary
private static strictfp double log2Impl(final double x) {
double xAbs = Math.abs(x);
final int hx = highBits(x);
int ix = hx & 0x7fffffff;
final double cp = 0x1.ec70_9dc3_a03fdp-1; // 9.61796693925975554329e-01 = 2/(3ln2)
final double cph = 0x1.ec709ep-1; // 9.61796700954437255859e-01 = (float)cp
final double cpl = -0x1.e2fe_0145_b01f5p-28; // -7.02846165095275826516e-09 = tail of cph
int n = 0;
// Take care of subnormal numbers
if (ix < 0x00100000) {
xAbs *= 0x1.0p53; // 2^53 = 9007199254740992.0
n -= 53;
ix = highBits(xAbs);
}
n += ((ix) >> 20) - 0x3ff;
int j = ix & 0x000fffff;
// Determine interval
ix = j | 0x3ff00000; // Normalize ix
int k;
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;
}
xAbs = highBits(xAbs, ix);
// Compute ss = s_h + s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5)
final double[] bp = {1.0, 1.5};
final double[] dph = {0.0, 0x1.2b80_34p-1}; // 5.84962487220764160156e-01
final double[] dpl = {0.0, 0x1.cfde_b43c_fd006p-27}; // 1.35003920212974897128e-08
// Poly coefs for (3/2)*(log(x)-2s-2/3*s**3
final double l1 = 0x1.3333_3333_33303p-1; // 5.99999999999994648725e-01
final double l2 = 0x1.b6db_6db6_fabffp-2; // 4.28571428578550184252e-01
final double l3 = 0x1.5555_5518_f264dp-2; // 3.33333329818377432918e-01
final double l4 = 0x1.1746_0a91_d4101p-2; // 2.72728123808534006489e-01
final double l5 = 0x1.d864_a93c_9db65p-3; // 2.30660745775561754067e-01
final double l6 = 0x1.a7e2_84a4_54eefp-3; // 2.06975017800338417784e-01
double u = xAbs - bp[k]; // BP[0]=1.0, BP[1]=1.5
double v = 1.0 / (xAbs + bp[k]);
double ss = u * v;
double sh = ss;
sh = lowBits(sh, 0);
// t_h=xAbs + BP[k] High
double th = 0.0;
th = highBits(th, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
double tl = xAbs - (th - bp[k]);
double sl = v * ((u - sh * th) - sh * tl);
// Compute log(xAbs)
double s2 = ss * ss;
double r = s2 * s2 * (l1 + s2 * (l2 + s2 * (l3 + s2 * (l4 + s2 * (l5 + s2 * l6)))));
r += sl * (sh + ss);
s2 = sh * sh;
th = 3.0 + s2 + r;
th = lowBits(th, 0);
tl = r - ((th - 3.0) - s2);
// u+v = ss*(1+...)
u = sh * th;
v = sl * th + tl * ss;
// 2/(3log2)*(ss + ...)
double ph = u + v;
ph = lowBits(ph, 0);
double pl = v - (ph - u);
double zh = cph * ph; // cph + cpl = 2/(3*log2)
double zl = cpl * ph + pl * cp + dpl[k];
// log2(x_abs) = (ss + ..)*2/(3*log2) = n + DP_H + z_h + z_l
double t = n;
double t1 = (((zh + zl) + dph[k]) + t);
t1 = lowBits(t1, 0);
double t2 = zl - (((t1 - t) - dph[k]) - zh);
return t1 + t2;
}
@Specialization
protected double log2(final double x) {
if (x < 0 || Double.isNaN(x)) {
return Double.NaN;
}
if (x == 0) {
return Double.NEGATIVE_INFINITY;
}
if (x == Double.POSITIVE_INFINITY) {
return Double.POSITIVE_INFINITY;
}
return log2Impl(x);
}
@Specialization
protected double log2(Object a) {
return log2(toDouble(a));
}
}