* Implementations of arithmetic operations handle {@code NaN} and * infinite values according to the rules for {@link java.lang.Double}, i.e. * {@link #equals} is an equivalence relation for all instances that have @@ -42,16 +42,14 @@ import org.apache.commons.math4.util.Precision; *
+ * Note that this contradicts the IEEE-754 standard for floating
* point numbers (according to which the test {@code x == x} must fail if
* {@code x} is {@code NaN}). The method
* {@link org.apache.commons.math4.util.Precision#equals(double,double,int)
* equals for primitive double} in {@link org.apache.commons.math4.util.Precision}
* conforms with IEEE-754 while this class conforms with the standard behavior
- * for Java object types.
- *
- * Implements Serializable since 2.0
+ * for Java object types.
- *
- * (a + bi) + (c + di) = (a+c) + (b+d)i
- *
- *
- * + * {@code (a + bi) + (c + di) = (a+c) + (b+d)i} + *
* If either {@code this} or {@code addend} has a {@code NaN} value in * either part, {@link #NaN} is returned; otherwise {@code Infinite} * and {@code NaN} values are returned in the parts of the result @@ -181,17 +176,17 @@ public class Complex implements FieldElement
* {@link #NaN} is returned if either the real or imaginary
* part of this Complex number equals {@code Double.NaN}.
- *
+ *
* If the imaginary part is infinite, and the real part is not * {@code NaN}, the returned value has infinite imaginary part * of the opposite sign, e.g. the conjugate of * {@code 1 + POSITIVE_INFINITY i} is {@code 1 - NEGATIVE_INFINITY i}. - * + *
* @return the conjugate of this Complex object. */ public Complex conjugate() { @@ -217,7 +212,7 @@ public class Complex implements FieldElement* {@code Infinite} and {@code NaN} values are handled according to the * following rules, applied in the order presented: *
- *
- * (a + bi)(c + di) = (ac - bd) + (ad + bc)i
- *
- *
+ * + * {@code (a + bi)(c + di) = (ac - bd) + (ad + bc)i} + *
* Returns {@link #NaN} if either {@code this} or {@code factor} has one or * more {@code NaN} parts. - *
* Returns {@link #INF} if neither {@code this} nor {@code factor} has one
* or more {@code NaN} parts and if either {@code this} or {@code factor}
* has one or more infinite parts (same result is returned regardless of
* the sign of the components).
- *
+ *
* Returns finite values in components of the result per the definitional - * formula in all remaining cases. + * formula in all remaining cases.
* * @param factor value to be multiplied by this {@code Complex}. * @return {@code this * factor}. @@ -585,7 +578,7 @@ public class Complex implements FieldElement
- *
- * (a + bi) - (c + di) = (a-c) + (b-d)i
- *
- *
+ * + * {@code (a + bi) - (c + di) = (a-c) + (b-d)i} + *
* If either {@code this} or {@code subtrahend} has a {@code NaN]} value in either part, * {@link #NaN} is returned; otherwise infinite and {@code NaN} values are * returned in the parts of the result according to the rules for @@ -648,11 +639,9 @@ public class Complex implements FieldElement
- *
- * acos(z) = -i (log(z + i (sqrt(1 - z2))))
- *
- *
+ * + * {@code acos(z) = -i (log(z + i (sqrt(1 - z2))))} + *
* Returns {@link Complex#NaN} if either real or imaginary part of the * input argument is {@code NaN} or infinite. * @@ -672,13 +661,11 @@ public class Complex implements FieldElement
- *
- * asin(z) = -i (log(sqrt(1 - z2) + iz))
- *
- *
+ * + * {@code asin(z) = -i (log(sqrt(1 - z2) + iz))} + *
* Returns {@link Complex#NaN} if either real or imaginary part of the - * input argument is {@code NaN} or infinite. + * input argument is {@code NaN} or infinite.
* * @return the inverse sine of this complex number. * @since 1.2 @@ -696,13 +683,11 @@ public class Complex implements FieldElement
- *
- * atan(z) = (i/2) log((i + z)/(i - z))
- *
- *
+ * + * {@code atan(z) = (i/2) log((i + z)/(i - z))} + *
* Returns {@link Complex#NaN} if either real or imaginary part of the - * input argument is {@code NaN} or infinite. + * input argument is {@code NaN} or infinite.
* * @return the inverse tangent of this complex number * @since 1.2 @@ -719,27 +704,24 @@ public class Complex implements FieldElement
- *
- * cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i
- *
- *
+ * + * {@code cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i} + *
* where the (real) functions on the right-hand side are
* {@link FastMath#sin}, {@link FastMath#cos},
* {@link FastMath#cosh} and {@link FastMath#sinh}.
- *
+ *
* Returns {@link Complex#NaN} if either real or imaginary part of the
* input argument is {@code NaN}.
- *
+ *
* Infinite values in real or imaginary parts of the input may result in - * infinite or NaN values returned in parts of the result. + * infinite or NaN values returned in parts of the result.
*
* Examples:
*
- * cos(1 ± INFINITY i) = 1 ∓ INFINITY i
+ * cos(1 ± INFINITY i) = 1 \u2213 INFINITY i
* cos(±INFINITY + i) = NaN + NaN i
* cos(±INFINITY ± INFINITY i) = NaN + NaN i
*
@@ -764,16 +746,16 @@ public class Complex implements FieldElement, Serializable {
* Implements the formula:
*
*
- * cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i}
+ * cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i
*
*
* where the (real) functions on the right-hand side are
* {@link FastMath#sin}, {@link FastMath#cos},
* {@link FastMath#cosh} and {@link FastMath#sinh}.
- *
+ *
* Returns {@link Complex#NaN} if either real or imaginary part of the
* input argument is {@code NaN}.
- *
+ *
* Infinite values in real or imaginary parts of the input may result in
* infinite or NaN values returned in parts of the result.
*
@@ -810,10 +792,10 @@ public class Complex implements FieldElement, Serializable {
* where the (real) functions on the right-hand side are
* {@link FastMath#exp}, {@link FastMath#cos}, and
* {@link FastMath#sin}.
- *
+ *
* Returns {@link Complex#NaN} if either real or imaginary part of the
* input argument is {@code NaN}.
- *
+ *
* Infinite values in real or imaginary parts of the input may result in
* infinite or NaN values returned in parts of the result.
*
@@ -852,10 +834,10 @@ public class Complex implements FieldElement, Serializable {
* where ln on the right hand side is {@link FastMath#log},
* {@code |a + bi|} is the modulus, {@link Complex#abs}, and
* {@code arg(a + bi) = }{@link FastMath#atan2}(b, a).
- *
+ *
* Returns {@link Complex#NaN} if either real or imaginary part of the
* input argument is {@code NaN}.
- *
+ *
* Infinite (or critical) values in real or imaginary parts of the input may
* result in infinite or NaN values returned in parts of the result.
*
@@ -893,13 +875,13 @@ public class Complex implements FieldElement, Serializable {
*
* where {@code exp} and {@code log} are {@link #exp} and
* {@link #log}, respectively.
- *
+ *
* Returns {@link Complex#NaN} if either real or imaginary part of the
* input argument is {@code NaN} or infinite, or if {@code y}
- * equals {@link Complex#ZERO}.
+ * equals {@link Complex#ZERO}.
*
* @param x exponent to which this {@code Complex} is to be raised.
- * @return this{@code x}.
+ * @return thisx.
* @throws NullArgumentException if x is {@code null}.
* @since 1.2
*/
@@ -934,10 +916,10 @@ public class Complex implements FieldElement, Serializable {
* where the (real) functions on the right-hand side are
* {@link FastMath#sin}, {@link FastMath#cos},
* {@link FastMath#cosh} and {@link FastMath#sinh}.
- *
+ *
* Returns {@link Complex#NaN} if either real or imaginary part of the
* input argument is {@code NaN}.
- *
+ *
* Infinite values in real or imaginary parts of the input may result in
* infinite or {@code NaN} values returned in parts of the result.
*
@@ -974,10 +956,10 @@ public class Complex implements FieldElement, Serializable {
* where the (real) functions on the right-hand side are
* {@link FastMath#sin}, {@link FastMath#cos},
* {@link FastMath#cosh} and {@link FastMath#sinh}.
- *
+ *
* Returns {@link Complex#NaN} if either real or imaginary part of the
* input argument is {@code NaN}.
- *
+ *
* Infinite values in real or imaginary parts of the input may result in
* infinite or NaN values returned in parts of the result.
*
@@ -1015,10 +997,10 @@ public class Complex implements FieldElement, Serializable {
* - {@code |a + bi| = }{@link Complex#abs}(a + bi)
* - {@code sign(b) = }{@link FastMath#copySign(double,double) copySign(1d, b)}
*
* Returns {@link Complex#NaN} if either real or imaginary part of the
* input argument is {@code NaN}.
- *
+ *
@@ -1060,10 +1042,10 @@ public class Complex implements FieldElement, Serializable { * number. * Computes the result directly as * {@code sqrt(ONE.subtract(z.multiply(z)))}. - *
+ ** Returns {@link Complex#NaN} if either real or imaginary part of the * input argument is {@code NaN}. - *
* Infinite values in real or imaginary parts of the input may result in * infinite or NaN values returned in parts of the result. * @@ -1087,10 +1069,10 @@ public class Complex implements FieldElement
+ *, Serializable { * where the (real) functions on the right-hand side are * {@link FastMath#sin}, {@link FastMath#cos}, {@link FastMath#cosh} and * {@link FastMath#sinh}. - *
+ ** Returns {@link Complex#NaN} if either real or imaginary part of the * input argument is {@code NaN}. - *
* Infinite (or critical) values in real or imaginary parts of the input may * result in infinite or NaN values returned in parts of the result. *
+ *@@ -1138,10 +1120,10 @@ public class Complex implements FieldElement, Serializable { * where the (real) functions on the right-hand side are * {@link FastMath#sin}, {@link FastMath#cos}, {@link FastMath#cosh} and * {@link FastMath#sinh}. - *
+ ** Returns {@link Complex#NaN} if either real or imaginary part of the * input argument is {@code NaN}. - *
* Infinite values in real or imaginary parts of the input may result in * infinite or NaN values returned in parts of the result. *
+ *@@ -1184,7 +1166,7 @@ public class Complex implements FieldElement, Serializable { * The value returned is between -PI (not inclusive) * and PI (inclusive), with negative values returned for numbers with * negative imaginary parts. - *
+ ** If either real or imaginary part (or both) is NaN, NaN is returned. * Infinite parts are handled as {@code Math.atan2} handles them, * essentially treating finite parts as zero in the presence of an @@ -1209,14 +1191,14 @@ public class Complex implements FieldElement
, Serializable { * for {@code k=0, 1, ..., n-1}, where {@code abs} and {@code phi} * are respectively the {@link #abs() modulus} and * {@link #getArgument() argument} of this complex number. - *
+ ** If one or both parts of this complex number is NaN, a list with just * one element, {@link #NaN} is returned. * if neither part is NaN, but at least one part is infinite, the result * is a one-element list containing {@link #INF}. * * @param n Degree of root. - * @return a List
of all {@code n}-th roots of {@code this}. + * @return a List of all {@code n}-th roots of {@code this}. * @throws NotPositiveException if {@code n <= 0}. * @since 2.0 */ diff --git a/src/main/java/org/apache/commons/math4/util/Precision.java b/src/main/java/org/apache/commons/math4/util/Precision.java index e2d0cc95d..91b0cb77b 100644 --- a/src/main/java/org/apache/commons/math4/util/Precision.java +++ b/src/main/java/org/apache/commons/math4/util/Precision.java @@ -99,7 +99,8 @@ public class Precision { * @param eps the amount of error to allow when checking for equality * @return + *
- 0 if {@link #equals(double, double, double) equals(x, y, eps)}
*- < 0 if !{@link #equals(double, double, double) equals(x, y, eps)} && x < y
- *- > 0 if !{@link #equals(double, double, double) equals(x, y, eps)} && x > y
> 0 if !{@link #equals(double, double, double) equals(x, y, eps)} && x > y or + * either argument is NaN */ public static int compareTo(double x, double y, double eps) { if (equals(x, y, eps)) { @@ -117,7 +118,7 @@ public class Precision { * point numbers are considered equal. * Adapted from - * Bruce Dawson + * Bruce Dawson. Returns {@code false} if either of the arguments is NaN. * * @param x first value * @param y second value @@ -125,7 +126,8 @@ public class Precision { * values between {@code x} and {@code y}. * @return+ *
- 0 if {@link #equals(double, double, int) equals(x, y, maxUlps)}
*- < 0 if !{@link #equals(double, double, int) equals(x, y, maxUlps)} && x < y
- *- > 0 if !{@link #equals(double, double, int) equals(x, y, maxUlps)} && x > y
> 0 if !{@link #equals(double, double, int) equals(x, y, maxUlps)} && x > y + * or either argument is NaN */ public static int compareTo(final double x, final double y, final int maxUlps) { if (equals(x, y, maxUlps)) { @@ -149,7 +151,7 @@ public class Precision { } /** - * Returns true if both arguments are NaN or neither is NaN and they are + * Returns true if both arguments are NaN or they are * equal as defined by {@link #equals(float,float) equals(x, y, 1)}. * * @param x first value @@ -162,8 +164,9 @@ public class Precision { } /** - * Returns true if both arguments are equal or within the range of allowed - * error (inclusive). + * Returns true if the arguments are equal or within the range of allowed + * error (inclusive). Returns {@code false} if either of the arguments + * is NaN. * * @param x first value * @param y second value @@ -176,7 +179,7 @@ public class Precision { } /** - * Returns true if both arguments are NaN or are equal or within the range + * Returns true if the arguments are both NaN, are equal, or are within the range * of allowed error (inclusive). * * @param x first value @@ -191,14 +194,14 @@ public class Precision { } /** - * Returns true if both arguments are equal or within the range of allowed + * Returns true if the arguments are equal or within the range of allowed * error (inclusive). * Two float numbers are considered equal if there are {@code (maxUlps - 1)} * (or fewer) floating point numbers between them, i.e. two adjacent floating * point numbers are considered equal. * Adapted from - * Bruce Dawson + * Bruce Dawson. Returns {@code false} if either of the arguments is NaN. * * @param x first value * @param y second value @@ -242,7 +245,7 @@ public class Precision { } /** - * Returns true if both arguments are NaN or if they are equal as defined + * Returns true if the arguments are both NaN or if they are equal as defined * by {@link #equals(float,float,int) equals(x, y, maxUlps)}. * * @param x first value @@ -270,7 +273,7 @@ public class Precision { } /** - * Returns true if both arguments are NaN or neither is NaN and they are + * Returns true if the arguments are both NaN or they are * equal as defined by {@link #equals(double,double) equals(x, y, 1)}. * * @param x first value @@ -285,7 +288,8 @@ public class Precision { /** * Returns {@code true} if there is no double value strictly between the * arguments or the difference between them is within the range of allowed - * error (inclusive). + * error (inclusive). Returns {@code false} if either of the arguments + * is NaN. * * @param x First value. * @param y Second value. @@ -299,8 +303,9 @@ public class Precision { /** * Returns {@code true} if there is no double value strictly between the - * arguments or the relative difference between them is smaller or equal - * to the given tolerance. + * arguments or the relative difference between them is less than or equal + * to the given tolerance. Returns {@code false} if either of the arguments + * is NaN. * * @param x First value. * @param y Second value. @@ -321,7 +326,7 @@ public class Precision { } /** - * Returns true if both arguments are NaN or are equal or within the range + * Returns true if the arguments are both NaN, are equal or are within the range * of allowed error (inclusive). * * @param x first value @@ -336,7 +341,7 @@ public class Precision { } /** - * Returns true if both arguments are equal or within the range of allowed + * Returns true if the arguments are equal or within the range of allowed * error (inclusive). ** Two float numbers are considered equal if there are {@code (maxUlps - 1)} @@ -346,7 +351,7 @@ public class Precision { *
* Adapted from - * Bruce Dawson + * Bruce Dawson. Returns {@code false} if either of the arguments is NaN. *
* * @param x first value diff --git a/src/test/java/org/apache/commons/math4/complex/ComplexTest.java b/src/test/java/org/apache/commons/math4/complex/ComplexTest.java index 6694dd6e8..903269245 100644 --- a/src/test/java/org/apache/commons/math4/complex/ComplexTest.java +++ b/src/test/java/org/apache/commons/math4/complex/ComplexTest.java @@ -567,6 +567,15 @@ public class ComplexTest { Assert.assertFalse(Complex.equals(x, y, tol2)); } + @Test + public void testFloatingPointEqualsWithAllowedDeltaNaN() { + final Complex x = new Complex(0, Double.NaN); + final Complex y = new Complex(Double.NaN, 0); + Assert.assertFalse(Complex.equals(x, Complex.ZERO, 0.1)); + Assert.assertFalse(Complex.equals(x, x, 0.1)); + Assert.assertFalse(Complex.equals(x, y, 0.1)); + } + @Test public void testFloatingPointEqualsWithRelativeTolerance() { final double tol = 1e-4; @@ -579,6 +588,15 @@ public class ComplexTest { Assert.assertTrue(Complex.equalsWithRelativeTolerance(x, y, tol)); } + @Test + public void testFloatingPointEqualsWithRelativeToleranceNaN() { + final Complex x = new Complex(0, Double.NaN); + final Complex y = new Complex(Double.NaN, 0); + Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, Complex.ZERO, 0.1)); + Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, x, 0.1)); + Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, y, 0.1)); + } + @Test public void testEqualsTrue() { Complex x = new Complex(3.0, 4.0);