--- old/make/mapfiles/libjava/mapfile-vers 2016-12-15 12:13:36.959083091 -0800
+++ new/make/mapfiles/libjava/mapfile-vers 2016-12-15 12:13:36.647083076 -0800
@@ -150,7 +150,6 @@
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;
--- old/src/java.base/share/classes/java/lang/FdLibm.java 2016-12-15 12:13:37.791083131 -0800
+++ new/src/java.base/share/classes/java/lang/FdLibm.java 2016-12-15 12:13:37.419083113 -0800
@@ -96,7 +96,8 @@
*/
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 +581,151 @@
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= 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 */
+
+ // 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;
+ }
+ }
+ }
}
--- old/src/java.base/share/classes/java/lang/StrictMath.java 2016-12-15 12:13:38.591083169 -0800
+++ new/src/java.base/share/classes/java/lang/StrictMath.java 2016-12-15 12:13:38.267083154 -0800
@@ -227,7 +227,9 @@
* @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}
--- old/src/java.base/share/native/libjava/StrictMath.c 2016-12-15 12:13:39.399083208 -0800
+++ new/src/java.base/share/native/libjava/StrictMath.c 2016-12-15 12:13:39.079083193 -0800
@@ -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
@@ -65,12 +65,6 @@
}
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)
{
return (jdouble) jlog((double)d);
--- old/test/java/lang/StrictMath/FdlibmTranslit.java 2016-12-15 12:13:40.195083246 -0800
+++ new/test/java/lang/StrictMath/FdlibmTranslit.java 2016-12-15 12:13:39.843083229 -0800
@@ -65,7 +65,8 @@
*/
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 +251,136 @@
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;
+ }
+ }
+ }
}
--- /dev/null 2016-12-04 10:29:16.690761514 -0800
+++ new/test/java/lang/StrictMath/ExpTests.java 2016-12-15 12:13:40.647083267 -0800
@@ -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 4123456
+ * @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();
+ }
+ }
+
+ static int testExp() {
+ int failures = 0;
+
+ // From the fdlibm source, the overflow threshold in hex is:
+ // 0x4086_2E42_FEFA_39EF.
+ final double OVERFLOW_THRESH = Double.longBitsToDouble(0x4086_2E42_FEFA_39EFL);
+
+ // From the fdlibm source, the underflow threshold in hex is:
+ // 0xc087_4910_D52D_3051L.
+ final double UNDERFLOW_THRESH = Double.longBitsToDouble(0xc087_4910_D52D_3051L);
+
+ 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},
+ {OVERFLOW_THRESH, 0x1.ffff_ffff_fff2ap1023},
+ {Math.nextUp(OVERFLOW_THRESH), Double.POSITIVE_INFINITY},
+ {Math.nextDown(UNDERFLOW_THRESH), +0.0},
+ {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
+ Double.longBitsToDouble(0x4086_2E42_FEFA_39EFL - 512L),
+
+ // Near underflow threshold
+ Double.longBitsToDouble(0xc087_4910_D52D_3051L - 512L),
+
+ // 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;
+ }
+}
--- old/src/java.base/share/native/libfdlibm/e_exp.c 2016-12-15 12:13:41.715083318 -0800
+++ /dev/null 2016-12-04 10:29:16.690761514 -0800
@@ -1,169 +0,0 @@
-/*
- * Copyright (c) 1998, 2001, 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. Oracle designates this
- * particular file as subject to the "Classpath" exception as provided
- * by Oracle in the LICENSE file that accompanied this code.
- *
- * 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.
- */
-
-/* __ieee754_exp(x)
- * 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.
- */
-
-#include "fdlibm.h"
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-one = 1.0,
-halF[2] = {0.5,-0.5,},
-huge = 1.0e+300,
-twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
-o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
-u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
-ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
- -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
-ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
- -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
-invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
-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 */
-
-
-#ifdef __STDC__
- double __ieee754_exp(double x) /* default IEEE double exp */
-#else
- double __ieee754_exp(x) /* default IEEE double exp */
- double x;
-#endif
-{
- double y,hi=0,lo=0,c,t;
- int k=0,xsb;
- unsigned 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 = 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) {
- __HI(y) += (k<<20); /* add k to y's exponent */
- return y;
- } else {
- __HI(y) += ((k+1000)<<20);/* add k to y's exponent */
- return y*twom1000;
- }
-}
--- old/src/java.base/share/native/libfdlibm/w_exp.c 2016-12-15 12:13:42.275083345 -0800
+++ /dev/null 2016-12-04 10:29:16.690761514 -0800
@@ -1,62 +0,0 @@
-
-/*
- * Copyright (c) 1998, 2001, 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. Oracle designates this
- * particular file as subject to the "Classpath" exception as provided
- * by Oracle in the LICENSE file that accompanied this code.
- *
- * 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.
- */
-
-/*
- * wrapper exp(x)
- */
-
-#include "fdlibm.h"
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
-u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
-
-#ifdef __STDC__
- double exp(double x) /* wrapper exp */
-#else
- double exp(x) /* wrapper exp */
- double x;
-#endif
-{
-#ifdef _IEEE_LIBM
- return __ieee754_exp(x);
-#else
- double z;
- z = __ieee754_exp(x);
- if(_LIB_VERSION == _IEEE_) return z;
- if(finite(x)) {
- if(x>o_threshold)
- return __kernel_standard(x,x,6); /* exp overflow */
- else if(x