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8301202: Port fdlibm log to Java

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Reviewed-by: bpb
This commit is contained in:
Joe Darcy 2023-02-11 02:15:46 +00:00
parent 98e98e9049
commit 919a6da2a7
5 changed files with 498 additions and 2 deletions
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140
src/java.base/share/classes/java/lang/FdLibm.java
View file

@ -747,6 +747,146 @@ class FdLibm {
}
}
/**
* Return the (natural) logarithm of x
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Approximation of log(1+f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lg1*s +...+Lg7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log(1+f) = f - s*(f - R) (if f is not too large)
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
*
* 3. Finally, log(x) = k*ln2 + log(1+f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* 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 final class Log {
private Log() {throw new UnsupportedOperationException();}
private static final double
ln2_hi = 0x1.62e42feep-1, // 6.93147180369123816490e-01
ln2_lo = 0x1.a39ef35793c76p-33, // 1.90821492927058770002e-10
Lg1 = 0x1.5555555555593p-1, // 6.666666666666735130e-01
Lg2 = 0x1.999999997fa04p-2, // 3.999999999940941908e-01
Lg3 = 0x1.2492494229359p-2, // 2.857142874366239149e-01
Lg4 = 0x1.c71c51d8e78afp-3, // 2.222219843214978396e-01
Lg5 = 0x1.7466496cb03dep-3, // 1.818357216161805012e-01
Lg6 = 0x1.39a09d078c69fp-3, // 1.531383769920937332e-01
Lg7 = 0x1.2f112df3e5244p-3; // 1.479819860511658591e-01
private static final double zero = 0.0;
static double compute(double x) {
double hfsq, f, s, z, R, w, t1, t2, dk;
int k, hx, i, j;
/*unsigned*/ int lx;
hx = __HI(x); // high word of x
lx = __LO(x); // low word of x
k=0;
if (hx < 0x0010_0000) { // x < 2**-1022
if (((hx & 0x7fff_ffff) | lx) == 0) { // log(+-0) = -inf
return -TWO54/zero;
}
if (hx < 0) { // log(-#) = NaN
return (x - x)/zero;
}
k -= 54;
x *= TWO54; // subnormal number, scale up x
hx = __HI(x); // high word of x
}
if (hx >= 0x7ff0_0000) {
return x + x;
}
k += (hx >> 20) - 1023;
hx &= 0x000f_ffff;
i = (hx + 0x9_5f64) & 0x10_0000;
x =__HI(x, hx | (i ^ 0x3ff0_0000)); // normalize x or x/2
k += (i >> 20);
f = x - 1.0;
if ((0x000f_ffff & (2 + hx)) < 3) {// |f| < 2**-20
if (f == zero) {
if (k == 0) {
return zero;
} else {
dk = (double)k;
return dk*ln2_hi + dk*ln2_lo;
}
}
R = f*f*(0.5 - 0.33333333333333333*f);
if (k == 0) {
return f - R;
} else {
dk = (double)k;
return dk*ln2_hi - ((R - dk*ln2_lo) - f);
}
}
s = f/(2.0 + f);
dk = (double)k;
z = s*s;
i = hx - 0x6_147a;
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));
} else {
return dk*ln2_hi - ((hfsq - (s*(hfsq + R) + dk*ln2_lo)) - f);
}
} else {
if (k == 0) {
return f - s*(f - R);
} else {
return dk*ln2_hi - ((s*(f - R) - dk*ln2_lo) - f);
}
}
}
}
/**
* Return the base 10 logarithm of x
*

4
src/java.base/share/classes/java/lang/StrictMath.java
View file

@ -259,7 +259,9 @@ public final class StrictMath {
* @return the value ln&nbsp;{@code a}, the natural logarithm of
* {@code a}.
*/
public static native double log(double a);
public static double log(double a) {
return FdLibm.Log.compute(a);
}
/**
* Returns the base 10 logarithm of a {@code double} value.

95
test/jdk/java/lang/Math/LogTests.java Normal file
View file

@ -0,0 +1,95 @@
/*
* Copyright (c) 2003, 2023, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation.
*
* This code 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 General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* @test
* @bug 8301202
* @build Tests
* @build LogTests
* @run main LogTests
* @summary Tests for {Math, StrictMath}.log
*/
public class LogTests {
private LogTests(){}
public static void main(String... args) {
int failures = 0;
failures += testLogSpecialCases();
if (failures > 0) {
System.err.println("Testing log incurred "
+ failures + " failures.");
throw new RuntimeException();
}
}
private static final double infinityD = Double.POSITIVE_INFINITY;
private static final double NaNd = Double.NaN;
/**
* From the spec for Math.log:
* "Special cases:
*
* If the argument is NaN or less than zero, then the result is NaN.
* If the argument is positive infinity, then the result is positive infinity.
* If the argument is positive zero or negative zero, then the result is negative infinity.
* If the argument is 1.0, then the result is positive zero.
*/
private static int testLogSpecialCases() {
int failures = 0;
double [][] testCases = {
{Double.NaN, NaNd},
{Double.NEGATIVE_INFINITY, NaNd},
{-Double.MAX_VALUE, NaNd},
{-1.0, NaNd},
{-Double.MIN_NORMAL, NaNd},
{-Double.MIN_VALUE, NaNd},
{Double.POSITIVE_INFINITY, infinityD},
{-0.0, -infinityD},
{+0.0, -infinityD},
{+1.0, 0.0},
};
for(int i = 0; i < testCases.length; i++) {
failures += testLogCase(testCases[i][0],
testCases[i][1]);
}
return failures;
}
private static int testLogCase(double input, double expected) {
int failures=0;
failures+=Tests.test("Math.log", input, Math::log, expected);
failures+=Tests.test("StrictMath.log", input, StrictMath::log, expected);
return failures;
}
}

125
test/jdk/java/lang/StrictMath/FdlibmTranslit.java
View file

@ -78,6 +78,10 @@ public class FdlibmTranslit {
return Cbrt.compute(x);
}
public static double log(double x) {
return Log.compute(x);
}
public static double log10(double x) {
return Log10.compute(x);
}
@ -401,6 +405,125 @@ public class FdlibmTranslit {
}
}
/**
* Return the logarithm of x
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Approximation of log(1+f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lg1*s +...+Lg7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log(1+f) = f - s*(f - R) (if f is not too large)
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
*
* 3. Finally, log(x) = k*ln2 + log(1+f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* 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.
*/
private static final class Log {
private static final double
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
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 */
private static double zero = 0.0;
static double compute(double x) {
double hfsq,f,s,z,R,w,t1,t2,dk;
int k,hx,i,j;
/*unsigned*/ int lx;
hx = __HI(x); /* high word of x */
lx = __LO(x); /* 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;
// __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
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;
else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;}
}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
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)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}
}
/**
* Return the base 10 logarithm of x
*
@ -464,7 +587,7 @@ public class FdlibmTranslit {
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
y = (double)(k+i);
x = __HI(x, hx); //original: __HI(x) = hx;
z = y*log10_2lo + ivln10*StrictMath.log(x); // TOOD: switch to Translit.log when available
z = y*log10_2lo + ivln10*log(x);
return z+y*log10_2hi;
}
}

136
test/jdk/java/lang/StrictMath/LogTests.java Normal file
View file

@ -0,0 +1,136 @@
/*
* Copyright (c) 2023, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation.
*
* This code 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 General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/*
* @test
* @bug 8301202
* @key randomness
* @library /test/lib
* @build jdk.test.lib.RandomFactory
* @build Tests
* @build FdlibmTranslit
* @build LogTests
* @run main LogTests
* @summary Tests for StrictMath.log
*/
import jdk.test.lib.RandomFactory;
public class LogTests {
private LogTests(){}
public static void main(String... args) {
int failures = 0;
failures += testLog();
failures += testAgainstTranslit();
if (failures > 0) {
System.err.println("Testing log incurred "
+ failures + " failures.");
throw new RuntimeException();
}
}
static int testLogCase(double input, double expected) {
return Tests.test("StrictMath.log(double)", input,
StrictMath::log, expected);
}
// Inputs where Math.log and StrictMath.log differ for at least
// one Math.log implementation.
static int testLog() {
int failures = 0;
double [][] testCases = {
{0x1.000000089cd6fp-43, -0x1.dce2a0697a102p4},
{0x1.0000000830698p182, 0x1.f89c7428dd67ap6},
{0x1.0000000744b3ap632, 0x1.b611ab2bd53cep8},
{0x1.000000037d81fp766, 0x1.0979b1dbc4a42p9},
{0x1.000000024028p991, 0x1.577455642bb92p9},
};
for (double[] testCase: testCases)
failures+=testLogCase(testCase[0], testCase[1]);
return failures;
}
// Initialize shared random number generator
private static java.util.Random random = RandomFactory.getRandom();
/**
* Test StrictMath.log against transliteration port of log.
*/
private static int testAgainstTranslit() {
int failures = 0;
double x;
// Test just above subnormal threshold...
x = Double.MIN_NORMAL;
failures += testRange(x, Math.ulp(x), 1000);
// ... and just below subnormal threshold ...
x = Math.nextDown(Double.MIN_NORMAL);
failures += testRange(x, -Math.ulp(x), 1000);
// Probe near decision points in the FDLIBM algorithm.
double[] decisionPoints = {
0x1.0p-1022,
0x1.0p-20,
};
for (double testPoint : decisionPoints) {
failures += testRangeMidpoint(testPoint, Math.ulp(testPoint), 1000);
}
x = Tests.createRandomDouble(random);
// Make the increment twice the ulp value in case the random
// value is near an exponent threshold. Don't worry about test
// elements overflowing to infinity if the starting value is
// near Double.MAX_VALUE.
failures += testRange(x, 2.0 * Math.ulp(x), 1000);
return failures;
}
private static int testRange(double start, double increment, int count) {
int failures = 0;
double x = start;
for (int i = 0; i < count; i++, x += increment) {
failures += testLogCase(x, FdlibmTranslit.log(x));
}
return failures;
}
private static int testRangeMidpoint(double midpoint, double increment, int count) {
int failures = 0;
double x = midpoint - increment*(count / 2) ;
for (int i = 0; i < count; i++, x += increment) {
failures += testLogCase(x, FdlibmTranslit.log(x));
}
return failures;
}
}