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Posted to commits@commons.apache.org by lu...@apache.org on 2015/09/10 11:12:15 UTC
[math] Ported pow function re-implementation from 4.X to 3.X.
Repository: commons-math
Updated Branches:
refs/heads/MATH_3_X 50c5eae1a -> 252a0137b
Ported pow function re-implementation from 4.X to 3.X.
JIRA: MATH-1272
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/252a0137
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/252a0137
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/252a0137
Branch: refs/heads/MATH_3_X
Commit: 252a0137b147469b18625eb4e7622a85f44ecfe8
Parents: 50c5eae
Author: Luc Maisonobe <lu...@apache.org>
Authored: Thu Sep 10 10:24:44 2015 +0200
Committer: Luc Maisonobe <lu...@apache.org>
Committed: Thu Sep 10 10:24:44 2015 +0200
----------------------------------------------------------------------
src/changes/changes.xml | 7 +
.../org/apache/commons/math3/util/FastMath.java | 423 +++++++++++--------
.../distribution/GammaDistributionTest.java | 2 +-
.../scalar/noderiv/BOBYQAOptimizerTest.java | 2 +-
.../direct/BOBYQAOptimizerTest.java | 2 +-
.../apache/commons/math3/util/FastMathTest.java | 59 ++-
6 files changed, 308 insertions(+), 187 deletions(-)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/252a0137/src/changes/changes.xml
----------------------------------------------------------------------
diff --git a/src/changes/changes.xml b/src/changes/changes.xml
index 6f437b4..1698f0f 100644
--- a/src/changes/changes.xml
+++ b/src/changes/changes.xml
@@ -51,6 +51,13 @@ If the output is not quite correct, check for invisible trailing spaces!
</properties>
<body>
<release version="3.6" date="XXXX-XX-XX" description="">
+ <action dev="luc" type="add" >
+ Reimplemented pow(double, double) in FastMath, for better accuracy in
+ integral power cases and trying to fix erroneous JIT optimization again.
+ </action>
+ <action dev="luc" type="add" >
+ Added a pow(double, long) method in FastMath.
+ </action>
<action dev="luc" type="fix" issue="MATH-1266">
Fixed split/side inconsistencies in BSP trees.
</action>
http://git-wip-us.apache.org/repos/asf/commons-math/blob/252a0137/src/main/java/org/apache/commons/math3/util/FastMath.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/util/FastMath.java b/src/main/java/org/apache/commons/math3/util/FastMath.java
index 3a05c6b..ce710a0 100644
--- a/src/main/java/org/apache/commons/math3/util/FastMath.java
+++ b/src/main/java/org/apache/commons/math3/util/FastMath.java
@@ -315,10 +315,17 @@ public class FastMath {
/** Mask used to clear the non-sign part of a long. */
private static final long MASK_NON_SIGN_LONG = 0x7fffffffffffffffl;
+ /** Mask used to extract exponent from double bits. */
+ private static final long MASK_DOUBLE_EXPONENT = 0x7ff0000000000000L;
+
+ /** Mask used to extract mantissa from double bits. */
+ private static final long MASK_DOUBLE_MANTISSA = 0x000fffffffffffffL;
+
+ /** Mask used to add implicit high order bit for normalized double. */
+ private static final long IMPLICIT_HIGH_BIT = 0x0010000000000000L;
+
/** 2^52 - double numbers this large must be integral (no fraction) or NaN or Infinite */
private static final double TWO_POWER_52 = 4503599627370496.0;
- /** 2^53 - double numbers this large must be even. */
- private static final double TWO_POWER_53 = 2 * TWO_POWER_52;
/** Constant: {@value}. */
private static final double F_1_3 = 1d / 3d;
@@ -1457,145 +1464,142 @@ public class FastMath {
* @param y a double
* @return double
*/
- public static double pow(double x, double y) {
- final double lns[] = new double[2];
+ public static double pow(final double x, final double y) {
- if (y == 0.0) {
+ if (y == 0) {
+ // y = -0 or y = +0
return 1.0;
- } else if (x != x) { // X is NaN
- return x;
- } else if (y != y) { // y is NaN
- return y;
- } else if (x == 0) {
- long bits = Double.doubleToRawLongBits(x);
- if ((bits & 0x8000000000000000L) != 0) {
- // -zero
- long yi = (long) y;
-
- if (y < 0 && y == yi && (yi & 1) == 1) {
- return Double.NEGATIVE_INFINITY;
- }
+ } else {
- if (y > 0 && y == yi && (yi & 1) == 1) {
- return -0.0;
+ final long yBits = Double.doubleToRawLongBits(y);
+ final int yRawExp = (int) ((yBits & MASK_DOUBLE_EXPONENT) >> 52);
+ final long yRawMantissa = yBits & MASK_DOUBLE_MANTISSA;
+ final long xBits = Double.doubleToRawLongBits(x);
+ final int xRawExp = (int) ((xBits & MASK_DOUBLE_EXPONENT) >> 52);
+ final long xRawMantissa = xBits & MASK_DOUBLE_MANTISSA;
+
+ if (yRawExp > 1085) {
+ // y is either a very large integral value that does not fit in a long or it is a special number
+
+ if ((yRawExp == 2047 && yRawMantissa != 0) ||
+ (xRawExp == 2047 && xRawMantissa != 0)) {
+ // NaN
+ return Double.NaN;
+ } else if (xRawExp == 1023 && xRawMantissa == 0) {
+ // x = -1.0 or x = +1.0
+ if (yRawExp == 2047) {
+ // y is infinite
+ return Double.NaN;
+ } else {
+ // y is a large even integer
+ return 1.0;
+ }
+ } else {
+ // the absolute value of x is either greater or smaller than 1.0
+
+ // if yRawExp == 2047 and mantissa is 0, y = -infinity or y = +infinity
+ // if 1085 < yRawExp < 2047, y is simply a large number, however, due to limited
+ // accuracy, at this magnitude it behaves just like infinity with regards to x
+ if ((y > 0) ^ (xRawExp < 1023)) {
+ // either y = +infinity (or large engouh) and abs(x) > 1.0
+ // or y = -infinity (or large engouh) and abs(x) < 1.0
+ return Double.POSITIVE_INFINITY;
+ } else {
+ // either y = +infinity (or large engouh) and abs(x) < 1.0
+ // or y = -infinity (or large engouh) and abs(x) > 1.0
+ return +0.0;
+ }
}
- }
- if (y < 0) {
- return Double.POSITIVE_INFINITY;
- }
- if (y > 0) {
- return 0.0;
- }
-
- return Double.NaN;
- } else if (x == Double.POSITIVE_INFINITY) {
- if (y < 0.0) {
- return 0.0;
- } else {
- return Double.POSITIVE_INFINITY;
- }
- } else if (y == Double.POSITIVE_INFINITY) {
- if (x * x == 1.0) {
- return Double.NaN;
- }
-
- if (x * x > 1.0) {
- return Double.POSITIVE_INFINITY;
} else {
- return 0.0;
- }
- } else if (x == Double.NEGATIVE_INFINITY) {
- if (y < 0) {
- long yi = (long) y;
- if (y == yi && (yi & 1) == 1) {
- return -0.0;
+ // y is a regular non-zero number
+
+ if (yRawExp >= 1023) {
+ // y may be an integral value, which should be handled specifically
+ final long yFullMantissa = IMPLICIT_HIGH_BIT | yRawMantissa;
+ if (yRawExp < 1075) {
+ // normal number with negative shift that may have a fractional part
+ final long integralMask = (-1L) << (1075 - yRawExp);
+ if ((yFullMantissa & integralMask) == yFullMantissa) {
+ // all fractional bits are 0, the number is really integral
+ final long l = yFullMantissa >> (1075 - yRawExp);
+ return FastMath.pow(x, (y < 0) ? -l : l);
+ }
+ } else {
+ // normal number with positive shift, always an integral value
+ // we know it fits in a primitive long because yRawExp > 1085 has been handled above
+ final long l = yFullMantissa << (yRawExp - 1075);
+ return FastMath.pow(x, (y < 0) ? -l : l);
+ }
}
- return 0.0;
- }
+ // y is a non-integral value
+
+ if (x == 0) {
+ // x = -0 or x = +0
+ // the integer powers have already been handled above
+ return y < 0 ? Double.POSITIVE_INFINITY : +0.0;
+ } else if (xRawExp == 2047) {
+ if (xRawMantissa == 0) {
+ // x = -infinity or x = +infinity
+ return (y < 0) ? +0.0 : Double.POSITIVE_INFINITY;
+ } else {
+ // NaN
+ return Double.NaN;
+ }
+ } else if (x < 0) {
+ // the integer powers have already been handled above
+ return Double.NaN;
+ } else {
- if (y > 0) {
- long yi = (long) y;
- if (y == yi && (yi & 1) == 1) {
- return Double.NEGATIVE_INFINITY;
- }
+ // this is the general case, for regular fractional numbers x and y
- return Double.POSITIVE_INFINITY;
- }
- } else if (y == Double.NEGATIVE_INFINITY) {
- if (x * x == 1.0) {
- return Double.NaN;
- }
+ // Split y into ya and yb such that y = ya+yb
+ final double tmp = y * HEX_40000000;
+ final double ya = (y + tmp) - tmp;
+ final double yb = y - ya;
- if (x * x < 1.0) {
- return Double.POSITIVE_INFINITY;
- } else {
- return 0.0;
- }
- } else if (x < 0) { // Handle special case x<0
- // y is an even integer in this case
- if (y >= TWO_POWER_53 || y <= -TWO_POWER_53) {
- return pow(-x, y);
- }
+ /* Compute ln(x) */
+ final double lns[] = new double[2];
+ final double lores = log(x, lns);
+ if (Double.isInfinite(lores)) { // don't allow this to be converted to NaN
+ return lores;
+ }
- if (y == (long) y) {
- // If y is an integer
- return ((long)y & 1) == 0 ? pow(-x, y) : -pow(-x, y);
- } else {
- return Double.NaN;
- }
- }
+ double lna = lns[0];
+ double lnb = lns[1];
- /* Split y into ya and yb such that y = ya+yb */
- double ya;
- double yb;
- if (y < 8e298 && y > -8e298) {
- double tmp1 = y * HEX_40000000;
- ya = y + tmp1 - tmp1;
- yb = y - ya;
- } else {
- double tmp1 = y * 9.31322574615478515625E-10;
- double tmp2 = tmp1 * 9.31322574615478515625E-10;
- ya = (tmp1 + tmp2 - tmp1) * HEX_40000000 * HEX_40000000;
- yb = y - ya;
- }
+ /* resplit lns */
+ final double tmp1 = lna * HEX_40000000;
+ final double tmp2 = (lna + tmp1) - tmp1;
+ lnb += lna - tmp2;
+ lna = tmp2;
- /* Compute ln(x) */
- final double lores = log(x, lns);
- if (Double.isInfinite(lores)){ // don't allow this to be converted to NaN
- return lores;
- }
+ // y*ln(x) = (aa+ab)
+ final double aa = lna * ya;
+ final double ab = lna * yb + lnb * ya + lnb * yb;
- double lna = lns[0];
- double lnb = lns[1];
+ lna = aa+ab;
+ lnb = -(lna - aa - ab);
- /* resplit lns */
- double tmp1 = lna * HEX_40000000;
- double tmp2 = lna + tmp1 - tmp1;
- lnb += lna - tmp2;
- lna = tmp2;
+ double z = 1.0 / 120.0;
+ z = z * lnb + (1.0 / 24.0);
+ z = z * lnb + (1.0 / 6.0);
+ z = z * lnb + 0.5;
+ z = z * lnb + 1.0;
+ z *= lnb;
- // y*ln(x) = (aa+ab)
- final double aa = lna * ya;
- final double ab = lna * yb + lnb * ya + lnb * yb;
+ final double result = exp(lna, z, null);
+ //result = result + result * z;
+ return result;
- lna = aa+ab;
- lnb = -(lna - aa - ab);
+ }
+ }
- double z = 1.0 / 120.0;
- z = z * lnb + (1.0 / 24.0);
- z = z * lnb + (1.0 / 6.0);
- z = z * lnb + 0.5;
- z = z * lnb + 1.0;
- z *= lnb;
+ }
- final double result = exp(lna, z, null);
- //result = result + result * z;
- return result;
}
-
/**
* Raise a double to an int power.
*
@@ -1605,68 +1609,149 @@ public class FastMath {
* @since 3.1
*/
public static double pow(double d, int e) {
+ return pow(d, (long) e);
+ }
+ /**
+ * Raise a double to a long power.
+ *
+ * @param d Number to raise.
+ * @param e Exponent.
+ * @return d<sup>e</sup>
+ * @since 3.6
+ */
+ public static double pow(double d, long e) {
if (e == 0) {
return 1.0;
- } else if (e < 0) {
- e = -e;
- d = 1.0 / d;
- }
-
- // split d as one 26 bits number and one 27 bits number
- // beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties
- final double d1High = Double.longBitsToDouble(Double.doubleToRawLongBits(d) & ((-1L) << 27));
- final double d1Low = d - d1High;
-
- // prepare result
- double resultHigh = 1;
- double resultLow = 0;
-
- // d^(2p)
- double d2p = d;
- double d2pHigh = d1High;
- double d2pLow = d1Low;
-
- while (e != 0) {
-
- if ((e & 0x1) != 0) {
- // accurate multiplication result = result * d^(2p) using Veltkamp TwoProduct algorithm
- // beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties
- final double tmpHigh = resultHigh * d2p;
- final double rHH = Double.longBitsToDouble(Double.doubleToRawLongBits(resultHigh) & ((-1L) << 27));
- final double rHL = resultHigh - rHH;
- final double tmpLow = rHL * d2pLow - (((tmpHigh - rHH * d2pHigh) - rHL * d2pHigh) - rHH * d2pLow);
- resultHigh = tmpHigh;
- resultLow = resultLow * d2p + tmpLow;
- }
+ } else if (e > 0) {
+ return new Split(d).pow(e).full;
+ } else {
+ return new Split(d).reciprocal().pow(-e).full;
+ }
+ }
+
+ /** Class operator on double numbers split into one 26 bits number and one 27 bits number. */
+ private static class Split {
+
+ /** Split version of NaN. */
+ public static final Split NAN = new Split(Double.NaN, 0);
+
+ /** Split version of positive infinity. */
+ public static final Split POSITIVE_INFINITY = new Split(Double.POSITIVE_INFINITY, 0);
+
+ /** Split version of negative infinity. */
+ public static final Split NEGATIVE_INFINITY = new Split(Double.NEGATIVE_INFINITY, 0);
+
+ /** Full number. */
+ private final double full;
- // accurate squaring d^(2(p+1)) = d^(2p) * d^(2p) using Veltkamp TwoProduct algorithm
+ /** High order bits. */
+ private final double high;
+
+ /** Low order bits. */
+ private final double low;
+
+ /** Simple constructor.
+ * @param x number to split
+ */
+ public Split(final double x) {
+ full = x;
+ high = Double.longBitsToDouble(Double.doubleToRawLongBits(x) & ((-1L) << 27));
+ low = x - high;
+ }
+
+ /** Simple constructor.
+ * @param high high order bits
+ * @param low low order bits
+ */
+ public Split(final double high, final double low) {
+ this(high + low, high, low);
+ }
+
+ /** Simple constructor.
+ * @param full full number
+ * @param high high order bits
+ * @param low low order bits
+ */
+ public Split(final double full, final double high, final double low) {
+ this.full = full;
+ this.high = high;
+ this.low = low;
+ }
+
+ /** Multiply the instance by another one.
+ * @param b other instance to multiply by
+ * @return product
+ */
+ public Split multiply(final Split b) {
+ // beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties
+ final Split mulBasic = new Split(full * b.full);
+ final double mulError = low * b.low - (((mulBasic.full - high * b.high) - low * b.high) - high * b.low);
+ return new Split(mulBasic.high, mulBasic.low + mulError);
+ }
+
+ /** Compute the reciprocal of the instance.
+ * @return reciprocal of the instance
+ */
+ public Split reciprocal() {
+
+ final double approximateInv = 1.0 / full;
+ final Split splitInv = new Split(approximateInv);
+
+ // if 1.0/d were computed perfectly, remultiplying it by d should give 1.0
+ // we want to estimate the error so we can fix the low order bits of approximateInvLow
// beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties
- final double tmpHigh = d2pHigh * d2p;
- final double cD2pH = Double.longBitsToDouble(Double.doubleToRawLongBits(d2pHigh) & ((-1L) << 27));
- final double d2pHH = cD2pH - (cD2pH - d2pHigh);
- final double d2pHL = d2pHigh - d2pHH;
- final double tmpLow = d2pHL * d2pLow - (((tmpHigh - d2pHH * d2pHigh) - d2pHL * d2pHigh) - d2pHH * d2pLow);
- d2pHigh = Double.longBitsToDouble(Double.doubleToRawLongBits(tmpHigh) & ((-1L) << 27));
- d2pLow = d2pLow * d2p + tmpLow + (tmpHigh - d2pHigh);
- d2p = d2pHigh + d2pLow;
+ final Split product = multiply(splitInv);
+ final double error = (product.high - 1) + product.low;
- e >>= 1;
+ // better accuracy estimate of reciprocal
+ return Double.isNaN(error) ? splitInv : new Split(splitInv.high, splitInv.low - error / full);
}
- final double result = resultHigh + resultLow;
+ /** Computes this^e.
+ * @param e exponent (beware, here it MUST be > 0; the only exclusion is Long.MIN_VALUE)
+ * @return d^e, split in high and low bits
+ * @since 3.6
+ */
+ private Split pow(final long e) {
- if (Double.isNaN(result)) {
- if (Double.isNaN(d)) {
- return Double.NaN;
+ // prepare result
+ Split result = new Split(1);
+
+ // d^(2p)
+ Split d2p = new Split(full, high, low);
+
+ for (long p = e; p != 0; p >>>= 1) {
+
+ if ((p & 0x1) != 0) {
+ // accurate multiplication result = result * d^(2p) using Veltkamp TwoProduct algorithm
+ result = result.multiply(d2p);
+ }
+
+ // accurate squaring d^(2(p+1)) = d^(2p) * d^(2p) using Veltkamp TwoProduct algorithm
+ d2p = d2p.multiply(d2p);
+
+ }
+
+ if (Double.isNaN(result.full)) {
+ if (Double.isNaN(full)) {
+ return Split.NAN;
+ } else {
+ // some intermediate numbers exceeded capacity,
+ // and the low order bits became NaN (because infinity - infinity = NaN)
+ if (FastMath.abs(full) < 1) {
+ return new Split(FastMath.copySign(0.0, full), 0.0);
+ } else if (full < 0 && (e & 0x1) == 1) {
+ return Split.NEGATIVE_INFINITY;
+ } else {
+ return Split.POSITIVE_INFINITY;
+ }
+ }
} else {
- // some intermediate numbers exceeded capacity,
- // and the low order bits became NaN (because infinity - infinity = NaN)
- return (d < 0 && (e & 0x1) == 1) ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
+ return result;
}
- } else {
- return result;
+
}
}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/252a0137/src/test/java/org/apache/commons/math3/distribution/GammaDistributionTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math3/distribution/GammaDistributionTest.java b/src/test/java/org/apache/commons/math3/distribution/GammaDistributionTest.java
index 6f5fa38..c07bbe1 100644
--- a/src/test/java/org/apache/commons/math3/distribution/GammaDistributionTest.java
+++ b/src/test/java/org/apache/commons/math3/distribution/GammaDistributionTest.java
@@ -347,7 +347,7 @@ public class GammaDistributionTest extends RealDistributionAbstractTest {
@Test
public void testMath753Shape142() throws IOException {
- doTestMath753(142.0, 0.5, 1.5, 40.0, 40.0, "gamma-distribution-shape-142.csv");
+ doTestMath753(142.0, 3.3, 1.6, 40.0, 40.0, "gamma-distribution-shape-142.csv");
}
@Test
http://git-wip-us.apache.org/repos/asf/commons-math/blob/252a0137/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/BOBYQAOptimizerTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/BOBYQAOptimizerTest.java b/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/BOBYQAOptimizerTest.java
index f2f36e9..c214e4b 100644
--- a/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/BOBYQAOptimizerTest.java
+++ b/src/test/java/org/apache/commons/math3/optim/nonlinear/scalar/noderiv/BOBYQAOptimizerTest.java
@@ -188,7 +188,7 @@ public class BOBYQAOptimizerTest {
new PointValuePair(point(DIM/2,0.0),0.0);
doTest(new DiffPow(), startPoint, boundaries,
GoalType.MINIMIZE,
- 1e-8, 1e-1, 12000, expected);
+ 1e-8, 1e-1, 21000, expected);
}
@Test
http://git-wip-us.apache.org/repos/asf/commons-math/blob/252a0137/src/test/java/org/apache/commons/math3/optimization/direct/BOBYQAOptimizerTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math3/optimization/direct/BOBYQAOptimizerTest.java b/src/test/java/org/apache/commons/math3/optimization/direct/BOBYQAOptimizerTest.java
index a957637..f89da18 100644
--- a/src/test/java/org/apache/commons/math3/optimization/direct/BOBYQAOptimizerTest.java
+++ b/src/test/java/org/apache/commons/math3/optimization/direct/BOBYQAOptimizerTest.java
@@ -187,7 +187,7 @@ public class BOBYQAOptimizerTest {
new PointValuePair(point(DIM/2,0.0),0.0);
doTest(new DiffPow(), startPoint, boundaries,
GoalType.MINIMIZE,
- 1e-8, 1e-1, 12000, expected);
+ 1e-8, 1e-1, 21000, expected);
}
@Test
http://git-wip-us.apache.org/repos/asf/commons-math/blob/252a0137/src/test/java/org/apache/commons/math3/util/FastMathTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math3/util/FastMathTest.java b/src/test/java/org/apache/commons/math3/util/FastMathTest.java
index b1dce92..86a3145 100644
--- a/src/test/java/org/apache/commons/math3/util/FastMathTest.java
+++ b/src/test/java/org/apache/commons/math3/util/FastMathTest.java
@@ -319,9 +319,9 @@ public class FastMathTest {
@Test
public void testLogSpecialCases() {
- Assert.assertTrue("Log of zero should be -Inf", Double.isInfinite(FastMath.log(0.0)));
+ Assert.assertEquals("Log of zero should be -Inf", Double.NEGATIVE_INFINITY, FastMath.log(0.0), 1.0);
- Assert.assertTrue("Log of -zero should be -Inf", Double.isInfinite(FastMath.log(-0.0)));
+ Assert.assertEquals("Log of -zero should be -Inf", Double.NEGATIVE_INFINITY, FastMath.log(-0.0), 1.0);
Assert.assertTrue("Log of NaN should be NaN", Double.isNaN(FastMath.log(Double.NaN)));
@@ -329,8 +329,9 @@ public class FastMathTest {
Assert.assertEquals("Log of Double.MIN_VALUE should be -744.4400719213812", -744.4400719213812, FastMath.log(Double.MIN_VALUE), Precision.EPSILON);
- Assert.assertTrue("Log of infinity should be infinity", Double.isInfinite(FastMath.log(Double.POSITIVE_INFINITY)));
+ Assert.assertEquals("Log of infinity should be infinity", Double.POSITIVE_INFINITY, FastMath.log(Double.POSITIVE_INFINITY), 1.0);
}
+
@Test
public void testExpSpecialCases() {
@@ -341,7 +342,7 @@ public class FastMathTest {
Assert.assertTrue("exp of NaN should be NaN", Double.isNaN(FastMath.exp(Double.NaN)));
- Assert.assertTrue("exp of infinity should be infinity", Double.isInfinite(FastMath.exp(Double.POSITIVE_INFINITY)));
+ Assert.assertEquals("exp of infinity should be infinity", Double.POSITIVE_INFINITY, FastMath.exp(Double.POSITIVE_INFINITY), 1.0);
Assert.assertEquals("exp of -infinity should be 0.0", 0.0, FastMath.exp(Double.NEGATIVE_INFINITY), Precision.EPSILON);
@@ -363,9 +364,9 @@ public class FastMathTest {
Assert.assertTrue("pow(NaN, PI) should be NaN", Double.isNaN(FastMath.pow(Double.NaN, Math.PI)));
- Assert.assertTrue("pow(2.0, Infinity) should be Infinity", Double.isInfinite(FastMath.pow(2.0, Double.POSITIVE_INFINITY)));
+ Assert.assertEquals("pow(2.0, Infinity) should be Infinity", Double.POSITIVE_INFINITY, FastMath.pow(2.0, Double.POSITIVE_INFINITY), 1.0);
- Assert.assertTrue("pow(0.5, -Infinity) should be Infinity", Double.isInfinite(FastMath.pow(0.5, Double.NEGATIVE_INFINITY)));
+ Assert.assertEquals("pow(0.5, -Infinity) should be Infinity", Double.POSITIVE_INFINITY, FastMath.pow(0.5, Double.NEGATIVE_INFINITY), 1.0);
Assert.assertEquals("pow(0.5, Infinity) should be 0.0", 0.0, FastMath.pow(0.5, Double.POSITIVE_INFINITY), Precision.EPSILON);
@@ -375,23 +376,25 @@ public class FastMathTest {
Assert.assertEquals("pow(Infinity, -0.5) should be 0.0", 0.0, FastMath.pow(Double.POSITIVE_INFINITY, -0.5), Precision.EPSILON);
- Assert.assertTrue("pow(0.0, -0.5) should be Inf", Double.isInfinite(FastMath.pow(0.0, -0.5)));
+ Assert.assertEquals("pow(0.0, -0.5) should be Inf", Double.POSITIVE_INFINITY, FastMath.pow(0.0, -0.5), 1.0);
- Assert.assertTrue("pow(Inf, 0.5) should be Inf", Double.isInfinite(FastMath.pow(Double.POSITIVE_INFINITY, 0.5)));
+ Assert.assertEquals("pow(Inf, 0.5) should be Inf", Double.POSITIVE_INFINITY, FastMath.pow(Double.POSITIVE_INFINITY, 0.5), 1.0);
- Assert.assertTrue("pow(-0.0, -3.0) should be -Inf", Double.isInfinite(FastMath.pow(-0.0, -3.0)));
+ Assert.assertEquals("pow(-0.0, -3.0) should be -Inf", Double.NEGATIVE_INFINITY, FastMath.pow(-0.0, -3.0), 1.0);
Assert.assertEquals("pow(-0.0, Infinity) should be 0.0", 0.0, FastMath.pow(-0.0, Double.POSITIVE_INFINITY), Precision.EPSILON);
Assert.assertTrue("pow(-0.0, NaN) should be NaN", Double.isNaN(FastMath.pow(-0.0, Double.NaN)));
- Assert.assertTrue("pow(-0.0, -tiny) should be Infinity", Double.isInfinite(FastMath.pow(-0.0, -Double.MIN_VALUE)));
+ Assert.assertEquals("pow(-0.0, -tiny) should be Infinity", Double.POSITIVE_INFINITY, FastMath.pow(-0.0, -Double.MIN_VALUE), 1.0);
+
+ Assert.assertEquals("pow(-0.0, -huge) should be Infinity", Double.POSITIVE_INFINITY, FastMath.pow(-0.0, -Double.MAX_VALUE), 1.0);
- Assert.assertTrue("pow(-Inf, -3.0) should be -Inf", Double.isInfinite(FastMath.pow(Double.NEGATIVE_INFINITY, 3.0)));
+ Assert.assertEquals("pow(-Inf, -3.0) should be -Inf", Double.NEGATIVE_INFINITY, FastMath.pow(Double.NEGATIVE_INFINITY, 3.0), 1.0);
- Assert.assertTrue("pow(-0.0, -3.5) should be Inf", Double.isInfinite(FastMath.pow(-0.0, -3.5)));
+ Assert.assertEquals("pow(-0.0, -3.5) should be Inf", Double.POSITIVE_INFINITY, FastMath.pow(-0.0, -3.5), 1.0);
- Assert.assertTrue("pow(Inf, 3.5) should be Inf", Double.isInfinite(FastMath.pow(Double.POSITIVE_INFINITY, 3.5)));
+ Assert.assertEquals("pow(Inf, 3.5) should be Inf", Double.POSITIVE_INFINITY, FastMath.pow(Double.POSITIVE_INFINITY, 3.5), 1.0);
Assert.assertEquals("pow(-2.0, 3.0) should be -8.0", -8.0, FastMath.pow(-2.0, 3.0), Precision.EPSILON);
@@ -407,6 +410,16 @@ public class FastMathTest {
Assert.assertTrue("pow(-huge, huge) should be +Inf", Double.isInfinite(FastMath.pow(-Double.MAX_VALUE, Double.MAX_VALUE)));
+ Assert.assertTrue("pow(NaN, -Infinity) should be NaN", Double.isNaN(FastMath.pow(Double.NaN, Double.NEGATIVE_INFINITY)));
+
+ Assert.assertEquals("pow(NaN, 0.0) should be 1.0", 1.0, FastMath.pow(Double.NaN, 0.0), Precision.EPSILON);
+
+ Assert.assertEquals("pow(-Infinity, -Infinity) should be 0.0", 0.0, FastMath.pow(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY), Precision.EPSILON);
+
+ Assert.assertEquals("pow(-huge, -huge) should be 0.0", 0.0, FastMath.pow(-Double.MAX_VALUE, -Double.MAX_VALUE), Precision.EPSILON);
+
+ Assert.assertEquals("pow(-huge, huge) should be +Inf", Double.POSITIVE_INFINITY, FastMath.pow(-Double.MAX_VALUE, Double.MAX_VALUE), 1.0);
+
// Added tests for a 100% coverage
Assert.assertTrue("pow(+Inf, NaN) should be NaN", Double.isNaN(FastMath.pow(Double.POSITIVE_INFINITY, Double.NaN)));
@@ -419,15 +432,26 @@ public class FastMathTest {
Assert.assertEquals("pow(-Inf, -2.0) should be 0.0", 0.0, FastMath.pow(Double.NEGATIVE_INFINITY, -2.0), Precision.EPSILON);
- Assert.assertTrue("pow(-Inf, 1.0) should be -Inf", Double.isInfinite(FastMath.pow(Double.NEGATIVE_INFINITY, 1.0)));
+ Assert.assertEquals("pow(-Inf, 1.0) should be -Inf", Double.NEGATIVE_INFINITY, FastMath.pow(Double.NEGATIVE_INFINITY, 1.0), 1.0);
- Assert.assertTrue("pow(-Inf, 2.0) should be +Inf", Double.isInfinite(FastMath.pow(Double.NEGATIVE_INFINITY, 2.0)));
+ Assert.assertEquals("pow(-Inf, 2.0) should be +Inf", Double.POSITIVE_INFINITY, FastMath.pow(Double.NEGATIVE_INFINITY, 2.0), 1.0);
Assert.assertTrue("pow(1.0, -Inf) should be NaN", Double.isNaN(FastMath.pow(1.0, Double.NEGATIVE_INFINITY)));
}
@Test
+ public void testPowLargeIntegralDouble() {
+ double y = FastMath.scalb(1.0, 65);
+ Assert.assertEquals(Double.POSITIVE_INFINITY, FastMath.pow(FastMath.nextUp(1.0), y), 1.0);
+ Assert.assertEquals(1.0, FastMath.pow(1.0, y), 1.0);
+ Assert.assertEquals(0.0, FastMath.pow(FastMath.nextDown(1.0), y), 1.0);
+ Assert.assertEquals(0.0, FastMath.pow(FastMath.nextUp(-1.0), y), 1.0);
+ Assert.assertEquals(1.0, FastMath.pow(-1.0, y), 1.0);
+ Assert.assertEquals(Double.POSITIVE_INFINITY, FastMath.pow(FastMath.nextDown(-1.0), y), 1.0);
+ }
+
+ @Test
public void testAtan2SpecialCases() {
Assert.assertTrue("atan2(NaN, 0.0) should be NaN", Double.isNaN(FastMath.atan2(Double.NaN, 0.0)));
@@ -1206,6 +1230,11 @@ public class FastMathTest {
Assert.assertTrue(Double.isInfinite(FastMath.pow(FastMath.scalb(1.0, 500), 4)));
}
+ @Test(timeout=5000L) // This test must finish in finite time.
+ public void testIntPowLongMinValue() {
+ Assert.assertEquals(1.0, FastMath.pow(1.0, Long.MIN_VALUE), -1.0);
+ }
+
@Test
public void testIncrementExactInt() {
int[] specialValues = new int[] {