From be91309965a532db4cf4fa794987753cfacbadd7 Mon Sep 17 00:00:00 2001 From: Joe Darcy Date: Fri, 16 Dec 2016 21:43:29 -0800 Subject: [PATCH] 8139688: Port fdlibm exp to Java Reviewed-by: bpb, nadezhin --- jdk/make/mapfiles/libjava/mapfile-vers | 1 - .../share/classes/java/lang/FdLibm.java | 156 +++++++++++++++++- .../share/classes/java/lang/StrictMath.java | 4 +- .../share/native/libjava/StrictMath.c | 8 +- jdk/test/java/lang/StrictMath/ExpTests.java | 147 +++++++++++++++++ .../java/lang/StrictMath/FdlibmTranslit.java | 140 +++++++++++++++- 6 files changed, 441 insertions(+), 15 deletions(-) create mode 100644 jdk/test/java/lang/StrictMath/ExpTests.java diff --git a/jdk/make/mapfiles/libjava/mapfile-vers b/jdk/make/mapfiles/libjava/mapfile-vers index 5d7cc4a655f..65336defa6d 100644 --- a/jdk/make/mapfiles/libjava/mapfile-vers +++ b/jdk/make/mapfiles/libjava/mapfile-vers @@ -150,7 +150,6 @@ SUNWprivate_1.1 { Java_java_lang_StrictMath_atan; Java_java_lang_StrictMath_atan2; Java_java_lang_StrictMath_cos; - Java_java_lang_StrictMath_exp; Java_java_lang_StrictMath_log; Java_java_lang_StrictMath_log10; Java_java_lang_StrictMath_sin; diff --git a/jdk/src/java.base/share/classes/java/lang/FdLibm.java b/jdk/src/java.base/share/classes/java/lang/FdLibm.java index dfecf79bb18..e1d3085ba70 100644 --- a/jdk/src/java.base/share/classes/java/lang/FdLibm.java +++ b/jdk/src/java.base/share/classes/java/lang/FdLibm.java @@ -1,5 +1,5 @@ /* - * Copyright (c) 1998, 2015, Oracle and/or its affiliates. All rights reserved. + * Copyright (c) 1998, 2016, 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 @@ -79,7 +79,8 @@ class FdLibm { */ private static double __LO(double x, int low) { long transX = Double.doubleToRawLongBits(x); - return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low ); + return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L) | + (low & 0x0000_0000_FFFF_FFFFL)); } /** @@ -96,7 +97,8 @@ class FdLibm { */ private static double __HI(double x, int high) { long transX = Double.doubleToRawLongBits(x); - return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 ); + return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL) | + ( ((long)high)) << 32 ); } /** @@ -580,4 +582,152 @@ class FdLibm { return s * z; } } + + /** + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Reme algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * 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= 0x1.0p-1000; // 9.33263618503218878990e-302 = 2^-1000 + private static final double o_threshold= 0x1.62e42fefa39efp9; // 7.09782712893383973096e+02 + private static final double u_threshold= -0x1.74910d52d3051p9; // -7.45133219101941108420e+02; + private static final double[] ln2HI ={ 0x1.62e42feep-1, // 6.93147180369123816490e-01 + -0x1.62e42feep-1}; // -6.93147180369123816490e-01 + private static final double[] ln2LO ={ 0x1.a39ef35793c76p-33, // 1.90821492927058770002e-10 + -0x1.a39ef35793c76p-33}; // -1.90821492927058770002e-10 + private static final double invln2 = 0x1.71547652b82fep0; // 1.44269504088896338700e+00 + + private static final double P1 = 0x1.555555555553ep-3; // 1.66666666666666019037e-01 + private static final double P2 = -0x1.6c16c16bebd93p-9; // -2.77777777770155933842e-03 + private static final double P3 = 0x1.1566aaf25de2cp-14; // 6.61375632143793436117e-05 + private static final double P4 = -0x1.bbd41c5d26bf1p-20; // -1.65339022054652515390e-06 + private static final double P5 = 0x1.6376972bea4d0p-25; // 4.13813679705723846039e-08 + + // should be able to forgo strictfp due to controlled over/underflow + public static strictfp double compute(double x) { + double y; + double hi = 0.0; + double lo = 0.0; + double c; + double t; + int k = 0; + int 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) // unsigned compare needed here? + 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; + } + } + } } diff --git a/jdk/src/java.base/share/classes/java/lang/StrictMath.java b/jdk/src/java.base/share/classes/java/lang/StrictMath.java index 1491a8478bc..63d895fa13c 100644 --- a/jdk/src/java.base/share/classes/java/lang/StrictMath.java +++ b/jdk/src/java.base/share/classes/java/lang/StrictMath.java @@ -227,7 +227,9 @@ public final class StrictMath { * @return the value e{@code a}, * where e is the base of the natural logarithms. */ - public static native double exp(double a); + public static double exp(double a) { + return FdLibm.Exp.compute(a); + } /** * Returns the natural logarithm (base e) of a {@code double} diff --git a/jdk/src/java.base/share/native/libjava/StrictMath.c b/jdk/src/java.base/share/native/libjava/StrictMath.c index 6c5ba3151c4..32d42217c5e 100644 --- a/jdk/src/java.base/share/native/libjava/StrictMath.c +++ b/jdk/src/java.base/share/native/libjava/StrictMath.c @@ -1,5 +1,5 @@ /* - * Copyright (c) 1994, 2015, Oracle and/or its affiliates. All rights reserved. + * Copyright (c) 1994, 2016, 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 @@ -64,12 +64,6 @@ Java_java_lang_StrictMath_atan(JNIEnv *env, jclass unused, jdouble d) return (jdouble) jatan((double)d); } -JNIEXPORT jdouble JNICALL -Java_java_lang_StrictMath_exp(JNIEnv *env, jclass unused, jdouble d) -{ - return (jdouble) jexp((double)d); -} - JNIEXPORT jdouble JNICALL Java_java_lang_StrictMath_log(JNIEnv *env, jclass unused, jdouble d) { diff --git a/jdk/test/java/lang/StrictMath/ExpTests.java b/jdk/test/java/lang/StrictMath/ExpTests.java new file mode 100644 index 00000000000..0a2e1f0304d --- /dev/null +++ b/jdk/test/java/lang/StrictMath/ExpTests.java @@ -0,0 +1,147 @@ +/* + * Copyright (c) 2015, 2016, 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 8139688 + * @key randomness + * @library /lib/testlibrary/ + * @build jdk.testlibrary.RandomFactory + * @build Tests + * @build FdlibmTranslit + * @build ExpTests + * @run main ExpTests + * @summary Tests specifically for StrictMath.exp + */ + +import jdk.testlibrary.RandomFactory; + +/** + * The role of this test is to verify that the FDLIBM exp algorithm is + * being used by running golden file style tests on values that may + * vary from one conforming exponential implementation to another. + */ + +public class ExpTests { + private ExpTests(){} + + public static void main(String [] argv) { + int failures = 0; + + failures += testExp(); + failures += testAgainstTranslit(); + + if (failures > 0) { + System.err.println("Testing the exponential incurred " + + failures + " failures."); + throw new RuntimeException(); + } + } + + // From the fdlibm source, the overflow threshold in hex is: + // 0x4086_2E42_FEFA_39EF. + static final double EXP_OVERFLOW_THRESH = Double.longBitsToDouble(0x4086_2E42_FEFA_39EFL); + + // From the fdlibm source, the underflow threshold in hex is: + // 0xc087_4910_D52D_3051L. + static final double EXP_UNDERFLOW_THRESH = Double.longBitsToDouble(0xc087_4910_D52D_3051L); + + static int testExp() { + int failures = 0; + + double [][] testCases = { + // Some of these could be moved to common Math/StrictMath exp testing. + {Double.NaN, Double.NaN}, + {Double.MAX_VALUE, Double.POSITIVE_INFINITY}, + {Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY}, + {Double.NEGATIVE_INFINITY, +0.0}, + {EXP_OVERFLOW_THRESH, 0x1.ffff_ffff_fff2ap1023}, + {Math.nextUp(EXP_OVERFLOW_THRESH), Double.POSITIVE_INFINITY}, + {Math.nextDown(EXP_UNDERFLOW_THRESH), +0.0}, + {EXP_UNDERFLOW_THRESH, +Double.MIN_VALUE}, + }; + + for(double[] testCase: testCases) + failures+=testExpCase(testCase[0], testCase[1]); + + return failures; + } + + static int testExpCase(double input, double expected) { + int failures = 0; + + failures+=Tests.test("StrictMath.exp(double)", input, + StrictMath.exp(input), expected); + return failures; + } + + // Initialize shared random number generator + private static java.util.Random random = RandomFactory.getRandom(); + + /** + * Test StrictMath.exp against transliteration port of exp. + */ + private static int testAgainstTranslit() { + int failures = 0; + + double[] decisionPoints = { + // Near overflow threshold + EXP_OVERFLOW_THRESH - 512*Math.ulp(EXP_OVERFLOW_THRESH), + + // Near underflow threshold + EXP_UNDERFLOW_THRESH - 512*Math.ulp(EXP_UNDERFLOW_THRESH), + + // Straddle algorithm conditional checks + Double.longBitsToDouble(0x4086_2E42_0000_0000L - 512L), + Double.longBitsToDouble(0x3fd6_2e42_0000_0000L - 512L), + Double.longBitsToDouble(0x3FF0_A2B2_0000_0000L - 512L), + Double.longBitsToDouble(0x3e30_0000_0000_0000L - 512L), + + // Other notable points + Double.MIN_NORMAL - Math.ulp(Double.MIN_NORMAL)*512, + -Double.MIN_VALUE*512, + }; + + for (double decisionPoint : decisionPoints) { + double ulp = Math.ulp(decisionPoint); + failures += testRange(decisionPoint - 1024*ulp, ulp, 1_024); + } + + // Try out some random values + for (int i = 0; i < 100; i++) { + double x = Tests.createRandomDouble(random); + failures += testRange(x, Math.ulp(x), 100); + } + + 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 += testExpCase(x, FdlibmTranslit.Exp.compute(x)); + } + return failures; + } +} diff --git a/jdk/test/java/lang/StrictMath/FdlibmTranslit.java b/jdk/test/java/lang/StrictMath/FdlibmTranslit.java index 64d4ca6112a..5ad48cb4b44 100644 --- a/jdk/test/java/lang/StrictMath/FdlibmTranslit.java +++ b/jdk/test/java/lang/StrictMath/FdlibmTranslit.java @@ -1,5 +1,5 @@ /* - * Copyright (c) 1998, 2015, Oracle and/or its affiliates. All rights reserved. + * Copyright (c) 1998, 2016, 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 @@ -48,7 +48,8 @@ public class FdlibmTranslit { */ private static double __LO(double x, int low) { long transX = Double.doubleToRawLongBits(x); - return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low ); + return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L) | + (low & 0x0000_0000_FFFF_FFFFL)); } /** @@ -65,7 +66,8 @@ public class FdlibmTranslit { */ private static double __HI(double x, int high) { long transX = Double.doubleToRawLongBits(x); - return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 ); + return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL) | + ( ((long)high)) << 32 ); } public static double hypot(double x, double y) { @@ -250,4 +252,136 @@ public class FdlibmTranslit { return w; } } + + /** + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Reme algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * 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; + } + } + } }