8139688: Port fdlibm exp to Java
Reviewed-by: bpb, nadezhin
This commit is contained in:
Joe Darcy
parent
2e27b2e68a
commit
be91309965
@ -150,7 +150,6 @@ SUNWprivate_1.1 {
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Java_java_lang_StrictMath_atan;
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Java_java_lang_StrictMath_atan2;
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Java_java_lang_StrictMath_cos;
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Java_java_lang_StrictMath_exp;
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Java_java_lang_StrictMath_log;
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Java_java_lang_StrictMath_log10;
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Java_java_lang_StrictMath_sin;
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@ -1,5 +1,5 @@
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/*
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* Copyright (c) 1998, 2015, Oracle and/or its affiliates. All rights reserved.
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* Copyright (c) 1998, 2016, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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@ -79,7 +79,8 @@ class FdLibm {
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*/
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private static double __LO(double x, int low) {
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long transX = Double.doubleToRawLongBits(x);
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return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low );
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return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L) |
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(low & 0x0000_0000_FFFF_FFFFL));
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}
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/**
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@ -96,7 +97,8 @@ class FdLibm {
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*/
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private static double __HI(double x, int high) {
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long transX = Double.doubleToRawLongBits(x);
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return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 );
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return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL) |
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( ((long)high)) << 32 );
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}
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/**
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@ -580,4 +582,152 @@ class FdLibm {
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return s * z;
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}
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}
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/**
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* Returns the exponential of x.
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*
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* Method
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* 1. Argument reduction:
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* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
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* Given x, find r and integer k such that
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*
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* x = k*ln2 + r, |r| <= 0.5*ln2.
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*
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* Here r will be represented as r = hi-lo for better
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* accuracy.
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*
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* 2. Approximation of exp(r) by a special rational function on
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* the interval [0,0.34658]:
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* Write
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* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
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* We use a special Reme algorithm on [0,0.34658] to generate
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* a polynomial of degree 5 to approximate R. The maximum error
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* of this polynomial approximation is bounded by 2**-59. In
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* other words,
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* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
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* (where z=r*r, and the values of P1 to P5 are listed below)
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* and
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* | 5 | -59
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* | 2.0+P1*z+...+P5*z - R(z) | <= 2
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* | |
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* The computation of exp(r) thus becomes
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* 2*r
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* exp(r) = 1 + -------
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* R - r
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* r*R1(r)
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* = 1 + r + ----------- (for better accuracy)
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* 2 - R1(r)
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* where
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* 2 4 10
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* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
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*
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* 3. Scale back to obtain exp(x):
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* From step 1, we have
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* exp(x) = 2^k * exp(r)
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*
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* Special cases:
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* exp(INF) is INF, exp(NaN) is NaN;
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* exp(-INF) is 0, and
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* for finite argument, only exp(0)=1 is exact.
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*
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* Accuracy:
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* according to an error analysis, the error is always less than
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* 1 ulp (unit in the last place).
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*
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* Misc. info.
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* For IEEE double
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* if x > 7.09782712893383973096e+02 then exp(x) overflow
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* if x < -7.45133219101941108420e+02 then exp(x) underflow
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following
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* constants. The decimal values may be used, provided that the
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* compiler will convert from decimal to binary accurately enough
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* to produce the hexadecimal values shown.
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*/
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static class Exp {
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private static final double one = 1.0;
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private static final double[] half = {0.5, -0.5,};
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private static final double huge = 1.0e+300;
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private static final double twom1000= 0x1.0p-1000; // 9.33263618503218878990e-302 = 2^-1000
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private static final double o_threshold= 0x1.62e42fefa39efp9; // 7.09782712893383973096e+02
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private static final double u_threshold= -0x1.74910d52d3051p9; // -7.45133219101941108420e+02;
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private static final double[] ln2HI ={ 0x1.62e42feep-1, // 6.93147180369123816490e-01
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-0x1.62e42feep-1}; // -6.93147180369123816490e-01
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private static final double[] ln2LO ={ 0x1.a39ef35793c76p-33, // 1.90821492927058770002e-10
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-0x1.a39ef35793c76p-33}; // -1.90821492927058770002e-10
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private static final double invln2 = 0x1.71547652b82fep0; // 1.44269504088896338700e+00
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private static final double P1 = 0x1.555555555553ep-3; // 1.66666666666666019037e-01
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private static final double P2 = -0x1.6c16c16bebd93p-9; // -2.77777777770155933842e-03
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private static final double P3 = 0x1.1566aaf25de2cp-14; // 6.61375632143793436117e-05
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private static final double P4 = -0x1.bbd41c5d26bf1p-20; // -1.65339022054652515390e-06
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private static final double P5 = 0x1.6376972bea4d0p-25; // 4.13813679705723846039e-08
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// should be able to forgo strictfp due to controlled over/underflow
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public static strictfp double compute(double x) {
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double y;
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double hi = 0.0;
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double lo = 0.0;
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double c;
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double t;
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int k = 0;
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int xsb;
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/*unsigned*/ int hx;
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hx = __HI(x); /* high word of x */
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xsb = (hx >> 31) & 1; /* sign bit of x */
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hx &= 0x7fffffff; /* high word of |x| */
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/* filter out non-finite argument */
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if (hx >= 0x40862E42) { /* if |x| >= 709.78... */
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if (hx >= 0x7ff00000) {
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if (((hx & 0xfffff) | __LO(x)) != 0)
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return x + x; /* NaN */
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else
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return (xsb == 0) ? x : 0.0; /* exp(+-inf) = {inf, 0} */
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}
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if (x > o_threshold)
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return huge * huge; /* overflow */
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if (x < u_threshold) // unsigned compare needed here?
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return twom1000 * twom1000; /* underflow */
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}
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/* argument reduction */
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if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
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if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
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hi = x - ln2HI[xsb];
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lo=ln2LO[xsb];
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k = 1 - xsb - xsb;
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} else {
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k = (int)(invln2 * x + half[xsb]);
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t = k;
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hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
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lo = t*ln2LO[0];
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}
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x = hi - lo;
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} else if (hx < 0x3e300000) { /* when |x|<2**-28 */
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if (huge + x > one)
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return one + x; /* trigger inexact */
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} else {
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k = 0;
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}
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/* x is now in primary range */
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t = x * x;
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c = x - t*(P1 + t*(P2 + t*(P3 + t*(P4 + t*P5))));
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if (k == 0)
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return one - ((x*c)/(c - 2.0) - x);
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else
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y = one - ((lo - (x*c)/(2.0 - c)) - hi);
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if(k >= -1021) {
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y = __HI(y, __HI(y) + (k << 20)); /* add k to y's exponent */
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return y;
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} else {
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y = __HI(y, __HI(y) + ((k + 1000) << 20)); /* add k to y's exponent */
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return y * twom1000;
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}
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}
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}
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}
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@ -227,7 +227,9 @@ public final class StrictMath {
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* @return the value <i>e</i><sup>{@code a}</sup>,
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* where <i>e</i> is the base of the natural logarithms.
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*/
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public static native double exp(double a);
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public static double exp(double a) {
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return FdLibm.Exp.compute(a);
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}
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/**
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* Returns the natural logarithm (base <i>e</i>) of a {@code double}
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@ -1,5 +1,5 @@
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/*
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* Copyright (c) 1994, 2015, Oracle and/or its affiliates. All rights reserved.
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* Copyright (c) 1994, 2016, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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@ -64,12 +64,6 @@ Java_java_lang_StrictMath_atan(JNIEnv *env, jclass unused, jdouble d)
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return (jdouble) jatan((double)d);
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}
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JNIEXPORT jdouble JNICALL
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Java_java_lang_StrictMath_exp(JNIEnv *env, jclass unused, jdouble d)
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{
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return (jdouble) jexp((double)d);
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}
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JNIEXPORT jdouble JNICALL
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Java_java_lang_StrictMath_log(JNIEnv *env, jclass unused, jdouble d)
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{
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147
jdk/test/java/lang/StrictMath/ExpTests.java
Normal file
147
jdk/test/java/lang/StrictMath/ExpTests.java
Normal file
@ -0,0 +1,147 @@
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/*
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* Copyright (c) 2015, 2016, Oracle and/or its affiliates. All rights reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*/
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/*
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* @test
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* @bug 8139688
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* @key randomness
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* @library /lib/testlibrary/
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* @build jdk.testlibrary.RandomFactory
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* @build Tests
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* @build FdlibmTranslit
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* @build ExpTests
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* @run main ExpTests
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* @summary Tests specifically for StrictMath.exp
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*/
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import jdk.testlibrary.RandomFactory;
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/**
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* The role of this test is to verify that the FDLIBM exp algorithm is
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* being used by running golden file style tests on values that may
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* vary from one conforming exponential implementation to another.
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*/
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public class ExpTests {
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private ExpTests(){}
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public static void main(String [] argv) {
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int failures = 0;
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failures += testExp();
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failures += testAgainstTranslit();
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if (failures > 0) {
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System.err.println("Testing the exponential incurred "
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+ failures + " failures.");
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throw new RuntimeException();
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}
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}
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// From the fdlibm source, the overflow threshold in hex is:
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// 0x4086_2E42_FEFA_39EF.
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static final double EXP_OVERFLOW_THRESH = Double.longBitsToDouble(0x4086_2E42_FEFA_39EFL);
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// From the fdlibm source, the underflow threshold in hex is:
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// 0xc087_4910_D52D_3051L.
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static final double EXP_UNDERFLOW_THRESH = Double.longBitsToDouble(0xc087_4910_D52D_3051L);
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static int testExp() {
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int failures = 0;
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double [][] testCases = {
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// Some of these could be moved to common Math/StrictMath exp testing.
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{Double.NaN, Double.NaN},
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{Double.MAX_VALUE, Double.POSITIVE_INFINITY},
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{Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY},
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{Double.NEGATIVE_INFINITY, +0.0},
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{EXP_OVERFLOW_THRESH, 0x1.ffff_ffff_fff2ap1023},
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{Math.nextUp(EXP_OVERFLOW_THRESH), Double.POSITIVE_INFINITY},
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{Math.nextDown(EXP_UNDERFLOW_THRESH), +0.0},
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{EXP_UNDERFLOW_THRESH, +Double.MIN_VALUE},
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};
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for(double[] testCase: testCases)
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failures+=testExpCase(testCase[0], testCase[1]);
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return failures;
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}
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static int testExpCase(double input, double expected) {
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int failures = 0;
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failures+=Tests.test("StrictMath.exp(double)", input,
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StrictMath.exp(input), expected);
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return failures;
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}
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// Initialize shared random number generator
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private static java.util.Random random = RandomFactory.getRandom();
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/**
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* Test StrictMath.exp against transliteration port of exp.
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*/
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private static int testAgainstTranslit() {
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int failures = 0;
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double[] decisionPoints = {
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// Near overflow threshold
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EXP_OVERFLOW_THRESH - 512*Math.ulp(EXP_OVERFLOW_THRESH),
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// Near underflow threshold
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EXP_UNDERFLOW_THRESH - 512*Math.ulp(EXP_UNDERFLOW_THRESH),
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// Straddle algorithm conditional checks
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Double.longBitsToDouble(0x4086_2E42_0000_0000L - 512L),
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Double.longBitsToDouble(0x3fd6_2e42_0000_0000L - 512L),
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Double.longBitsToDouble(0x3FF0_A2B2_0000_0000L - 512L),
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Double.longBitsToDouble(0x3e30_0000_0000_0000L - 512L),
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// Other notable points
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Double.MIN_NORMAL - Math.ulp(Double.MIN_NORMAL)*512,
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-Double.MIN_VALUE*512,
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};
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for (double decisionPoint : decisionPoints) {
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double ulp = Math.ulp(decisionPoint);
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failures += testRange(decisionPoint - 1024*ulp, ulp, 1_024);
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}
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// Try out some random values
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for (int i = 0; i < 100; i++) {
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double x = Tests.createRandomDouble(random);
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failures += testRange(x, Math.ulp(x), 100);
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}
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return failures;
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}
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private static int testRange(double start, double increment, int count) {
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int failures = 0;
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double x = start;
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for (int i = 0; i < count; i++, x += increment) {
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failures += testExpCase(x, FdlibmTranslit.Exp.compute(x));
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}
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return failures;
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}
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}
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@ -1,5 +1,5 @@
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/*
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* Copyright (c) 1998, 2015, Oracle and/or its affiliates. All rights reserved.
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* Copyright (c) 1998, 2016, Oracle and/or its affiliates. All rights reserved.
|
||||
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
|
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*
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* This code is free software; you can redistribute it and/or modify it
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@ -48,7 +48,8 @@ public class FdlibmTranslit {
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*/
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private static double __LO(double x, int low) {
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long transX = Double.doubleToRawLongBits(x);
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return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low );
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return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L) |
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(low & 0x0000_0000_FFFF_FFFFL));
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}
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/**
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@ -65,7 +66,8 @@ public class FdlibmTranslit {
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*/
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private static double __HI(double x, int high) {
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long transX = Double.doubleToRawLongBits(x);
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return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 );
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return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL) |
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( ((long)high)) << 32 );
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}
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public static double hypot(double x, double y) {
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@ -250,4 +252,136 @@ public class FdlibmTranslit {
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return w;
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}
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}
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/**
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* Returns the exponential of x.
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*
|
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* Method
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* 1. Argument reduction:
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* Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
|
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* Given x, find r and integer k such that
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*
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* x = k*ln2 + r, |r| <= 0.5*ln2.
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*
|
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* Here r will be represented as r = hi-lo for better
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* accuracy.
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*
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* 2. Approximation of exp(r) by a special rational function on
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* the interval [0,0.34658]:
|
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* Write
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* R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
|
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* We use a special Reme algorithm on [0,0.34658] to generate
|
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* a polynomial of degree 5 to approximate R. The maximum error
|
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* of this polynomial approximation is bounded by 2**-59. In
|
||||
* other words,
|
||||
* R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
|
||||
* (where z=r*r, and the values of P1 to P5 are listed below)
|
||||
* and
|
||||
* | 5 | -59
|
||||
* | 2.0+P1*z+...+P5*z - R(z) | <= 2
|
||||
* | |
|
||||
* The computation of exp(r) thus becomes
|
||||
* 2*r
|
||||
* exp(r) = 1 + -------
|
||||
* R - r
|
||||
* r*R1(r)
|
||||
* = 1 + r + ----------- (for better accuracy)
|
||||
* 2 - R1(r)
|
||||
* where
|
||||
* 2 4 10
|
||||
* R1(r) = r - (P1*r + P2*r + ... + P5*r ).
|
||||
*
|
||||
* 3. Scale back to obtain exp(x):
|
||||
* From step 1, we have
|
||||
* exp(x) = 2^k * exp(r)
|
||||
*
|
||||
* Special cases:
|
||||
* exp(INF) is INF, exp(NaN) is NaN;
|
||||
* exp(-INF) is 0, and
|
||||
* for finite argument, only exp(0)=1 is exact.
|
||||
*
|
||||
* Accuracy:
|
||||
* according to an error analysis, the error is always less than
|
||||
* 1 ulp (unit in the last place).
|
||||
*
|
||||
* Misc. info.
|
||||
* For IEEE double
|
||||
* if x > 7.09782712893383973096e+02 then exp(x) overflow
|
||||
* if x < -7.45133219101941108420e+02 then exp(x) underflow
|
||||
*
|
||||
* 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.
|
||||
*/
|
||||
static class Exp {
|
||||
private static final double one = 1.0;
|
||||
private static final double[] halF = {0.5,-0.5,};
|
||||
private static final double huge = 1.0e+300;
|
||||
private static final double twom1000= 9.33263618503218878990e-302; /* 2**-1000=0x01700000,0*/
|
||||
private static final double o_threshold= 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
|
||||
private static final double u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
|
||||
private static final double[] ln2HI ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
|
||||
-6.93147180369123816490e-01}; /* 0xbfe62e42, 0xfee00000 */
|
||||
private static final double[] ln2LO ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
|
||||
-1.90821492927058770002e-10,}; /* 0xbdea39ef, 0x35793c76 */
|
||||
private static final double invln2 = 1.44269504088896338700e+00; /* 0x3ff71547, 0x652b82fe */
|
||||
private static final double P1 = 1.66666666666666019037e-01; /* 0x3FC55555, 0x5555553E */
|
||||
private static final double P2 = -2.77777777770155933842e-03; /* 0xBF66C16C, 0x16BEBD93 */
|
||||
private static final double P3 = 6.61375632143793436117e-05; /* 0x3F11566A, 0xAF25DE2C */
|
||||
private static final double P4 = -1.65339022054652515390e-06; /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
private static final double P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
|
||||
|
||||
public static strictfp double compute(double x) {
|
||||
double y,hi=0,lo=0,c,t;
|
||||
int k=0,xsb;
|
||||
/*unsigned*/ int 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) {
|
||||
y = __HI(y, __HI(y) + (k<<20)); /* add k to y's exponent */
|
||||
return y;
|
||||
} else {
|
||||
y = __HI(y, __HI(y) + ((k+1000)<<20));/* add k to y's exponent */
|
||||
return y*twom1000;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user