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commit a0e56e1fd241d9fd77973c137c0608dc12ff44f0
Author: Alex Herbert <aherb...@apache.org>
AuthorDate: Thu Oct 14 08:21:15 2021 +0100
NUMBERS-172: Use Boost Error function implementation
Replace the use of the regularized gamma functions P and Q to evaluate
the error function.
---
.../org/apache/commons/numbers/gamma/BoostErf.java | 301 ++++++++++++
.../java/org/apache/commons/numbers/gamma/Erf.java | 39 +-
.../org/apache/commons/numbers/gamma/Erfc.java | 44 +-
.../apache/commons/numbers/gamma/BoostErfTest.java | 159 ++++++-
.../commons/numbers/gamma/erf_close_to_1_data.csv | 159 +++++++
.../org/apache/commons/numbers/gamma/erf_data.csv | 522 +++++++++++++++++++++
.../commons/numbers/gamma/erf_large_data.csv | 92 ++++
.../commons/numbers/gamma/erf_small_data.csv | 172 +++++++
src/main/resources/pmd/pmd-ruleset.xml | 13 +
9 files changed, 1449 insertions(+), 52 deletions(-)
diff --git
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/BoostErf.java
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/BoostErf.java
index 08845fc..3569099 100644
---
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/BoostErf.java
+++
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/BoostErf.java
@@ -34,6 +34,14 @@ package org.apache.commons.numbers.gamma;
* Boost C++ Error functions</a>
*/
final class BoostErf {
+ /**
+ * The multiplier used to split the double value into high and low parts.
From
+ * Dekker (1971): "The constant should be chosen equal to 2^(p - p/2) + 1,
+ * where p is the number of binary digits in the mantissa". Here p is 53
+ * and the multiplier is {@code 2^27 + 1}.
+ */
+ private static final double MULTIPLIER = 1.0 + 0x1.0p27;
+
/** Private constructor. */
private BoostErf() {
// intentionally empty.
@@ -51,6 +59,12 @@ final class BoostErf {
// - Explicitly inline the polynomial function evaluation
// using Horner's method
(https://en.wikipedia.org/wiki/Horner%27s_method)
// - Support odd function for f(0.0) = -f(-0.0)
+ // Erf:
+ // - Change extended precision z*z to compute the square round-off
+ // using Dekker's method
+ // - Change the erf threshold for z when p=1 from
+ // z > 5.8f to z > 5.930664
+ // - Change edge case detection for integer z
// Inverse erf:
// - Change inverse erf edge case detection to include NaN
//
@@ -61,6 +75,211 @@ final class BoostErf {
// The values are unchanged from the Boost reference.
/**
+ * Returns the complementary error function.
+ *
+ * @param x the value.
+ * @return the complementary error function.
+ */
+ static double erfc(double x) {
+ return erfImp(x, true);
+ }
+
+ /**
+ * Returns the error function.
+ *
+ * @param x the value.
+ * @return the error function.
+ */
+ static double erf(double x) {
+ return erfImp(x, false);
+ }
+
+ /**
+ * 53-bit implementation for the error function.
+ *
+ * @param z Point to evaluate
+ * @param invert true to invert the result (for the complementary error
function)
+ * @return the error function result
+ */
+ private static double erfImp(double z, boolean invert) {
+ if (Double.isNaN(z)) {
+ return Double.NaN;
+ }
+
+ if (z < 0) {
+ if (!invert) {
+ return -erfImp(-z, invert);
+ } else if (z < -0.5) {
+ return 2 - erfImp(-z, invert);
+ } else {
+ return 1 + erfImp(-z, false);
+ }
+ }
+
+ double result;
+
+ //
+ // Big bunch of selection statements now to pick
+ // which implementation to use,
+ // try to put most likely options first:
+ //
+ if (z < 0.5) {
+ //
+ // We're going to calculate erf:
+ //
+ if (z < 1e-10) {
+ if (z == 0) {
+ result = z;
+ } else {
+ final double c = 0.003379167095512573896158903121545171688;
+ result = z * 1.125f + z * c;
+ }
+ } else {
+ // Maximum Deviation Found: 1.561e-17
+ // Expected Error Term: 1.561e-17
+ // Maximum Relative Change in Control Points: 1.155e-04
+ // Max Error found at double precision = 2.961182e-17
+
+ final double Y = 1.044948577880859375f;
+ final double zz = z * z;
+ double P;
+ P = -0.000322780120964605683831;
+ P = -0.00772758345802133288487 + P * zz;
+ P = -0.0509990735146777432841 + P * zz;
+ P = -0.338165134459360935041 + P * zz;
+ P = 0.0834305892146531832907 + P * zz;
+ double Q;
+ Q = 0.000370900071787748000569;
+ Q = 0.00858571925074406212772 + Q * zz;
+ Q = 0.0875222600142252549554 + Q * zz;
+ Q = 0.455004033050794024546 + Q * zz;
+ Q = 1.0 + Q * zz;
+ result = z * (Y + P / Q);
+ }
+ // Note: Boost threshold of 5.8f has been raised to approximately 5.93
(6073 / 1024)
+ } else if (invert ? (z < 28) : (z < 5.9306640625f)) {
+ //
+ // We'll be calculating erfc:
+ //
+ invert = !invert;
+ if (z < 1.5f) {
+ // Maximum Deviation Found: 3.702e-17
+ // Expected Error Term: 3.702e-17
+ // Maximum Relative Change in Control Points: 2.845e-04
+ // Max Error found at double precision = 4.841816e-17
+ final double Y = 0.405935764312744140625f;
+ final double zm = z - 0.5;
+ double P;
+ P = 0.00180424538297014223957;
+ P = 0.0195049001251218801359 + P * zm;
+ P = 0.0888900368967884466578 + P * zm;
+ P = 0.191003695796775433986 + P * zm;
+ P = 0.178114665841120341155 + P * zm;
+ P = -0.098090592216281240205 + P * zm;
+ double Q;
+ Q = 0.337511472483094676155e-5;
+ Q = 0.0113385233577001411017 + Q * zm;
+ Q = 0.12385097467900864233 + Q * zm;
+ Q = 0.578052804889902404909 + Q * zm;
+ Q = 1.42628004845511324508 + Q * zm;
+ Q = 1.84759070983002217845 + Q * zm;
+ Q = 1.0 + Q * zm;
+ result = Y + P / Q;
+ result *= Math.exp(-z * z) / z;
+ } else if (z < 2.5f) {
+ // Max Error found at double precision = 6.599585e-18
+ // Maximum Deviation Found: 3.909e-18
+ // Expected Error Term: 3.909e-18
+ // Maximum Relative Change in Control Points: 9.886e-05
+ final double Y = 0.50672817230224609375f;
+ final double zm = z - 1.5;
+ double P;
+ P = 0.000235839115596880717416;
+ P = 0.00323962406290842133584 + P * zm;
+ P = 0.0175679436311802092299 + P * zm;
+ P = 0.04394818964209516296 + P * zm;
+ P = 0.0386540375035707201728 + P * zm;
+ P = -0.0243500476207698441272 + P * zm;
+ double Q;
+ Q = 0.00410369723978904575884;
+ Q = 0.0563921837420478160373 + Q * zm;
+ Q = 0.325732924782444448493 + Q * zm;
+ Q = 0.982403709157920235114 + Q * zm;
+ Q = 1.53991494948552447182 + Q * zm;
+ Q = 1.0 + Q * zm;
+ result = Y + P / Q;
+ final double sq = z * z;
+ final double errSqr = squareLowUnscaled(z, sq);
+ result *= Math.exp(-sq) * Math.exp(-errSqr) / z;
+ } else if (z < 4.5f) {
+ // Maximum Deviation Found: 1.512e-17
+ // Expected Error Term: 1.512e-17
+ // Maximum Relative Change in Control Points: 2.222e-04
+ // Max Error found at double precision = 2.062515e-17
+ final double Y = 0.5405750274658203125f;
+ final double zm = z - 3.5;
+ double P;
+ P = 0.113212406648847561139e-4;
+ P = 0.000250269961544794627958 + P * zm;
+ P = 0.00212825620914618649141 + P * zm;
+ P = 0.00840807615555585383007 + P * zm;
+ P = 0.0137384425896355332126 + P * zm;
+ P = 0.00295276716530971662634 + P * zm;
+ double Q;
+ Q = 0.000479411269521714493907;
+ Q = 0.0105982906484876531489 + Q * zm;
+ Q = 0.0958492726301061423444 + Q * zm;
+ Q = 0.442597659481563127003 + Q * zm;
+ Q = 1.04217814166938418171 + Q * zm;
+ Q = 1.0 + Q * zm;
+ result = Y + P / Q;
+ final double sq = z * z;
+ final double errSqr = squareLowUnscaled(z, sq);
+ result *= Math.exp(-sq) * Math.exp(-errSqr) / z;
+ } else {
+ // Max Error found at double precision = 2.997958e-17
+ // Maximum Deviation Found: 2.860e-17
+ // Expected Error Term: 2.859e-17
+ // Maximum Relative Change in Control Points: 1.357e-05
+ final double Y = 0.5579090118408203125f;
+ final double iz = 1 / z;
+ double P;
+ P = -2.8175401114513378771;
+ P = -3.22729451764143718517 + P * iz;
+ P = -2.5518551727311523996 + P * iz;
+ P = -0.687717681153649930619 + P * iz;
+ P = -0.212652252872804219852 + P * iz;
+ P = 0.0175389834052493308818 + P * iz;
+ P = 0.00628057170626964891937 + P * iz;
+ double Q;
+ Q = 5.48409182238641741584;
+ Q = 13.5064170191802889145 + Q * iz;
+ Q = 22.9367376522880577224 + Q * iz;
+ Q = 15.930646027911794143 + Q * iz;
+ Q = 11.0567237927800161565 + Q * iz;
+ Q = 2.79257750980575282228 + Q * iz;
+ Q = 1.0 + Q * iz;
+ result = Y + P / Q;
+ final double sq = z * z;
+ final double errSqr = squareLowUnscaled(z, sq);
+ result *= Math.exp(-sq) * Math.exp(-errSqr) / z;
+ }
+ } else {
+ //
+ // Any value of z larger than 28 will underflow to zero:
+ //
+ result = 0;
+ invert = !invert;
+ }
+
+ if (invert) {
+ result = 1 - result;
+ }
+
+ return result;
+ }
+
+ /**
* Returns the inverse complementary error function.
*
* @param z Value (in {@code [0, 2]}).
@@ -368,5 +587,87 @@ final class BoostErf {
}
return result;
}
+
+ // Extended precision multiplication specialised for the square adapted
from:
+ // org.apache.commons.numbers.core.ExtendedPrecision
+
+ /**
+ * Compute the low part of the double length number {@code (z,zz)} for the
exact
+ * square of {@code x} using Dekker's mult12 algorithm. The standard
precision product
+ * {@code x*x} must be provided. The number {@code x} is split into high
and low parts
+ * using Dekker's algorithm.
+ *
+ * <p>Warning: This method does not perform scaling in Dekker's split and
large
+ * finite numbers can create NaN results.
+ *
+ * @param x Number to square
+ * @param xx Standard precision product {@code x*x}
+ * @return the low part of the square double length number
+ */
+ private static double squareLowUnscaled(double x, double xx) {
+ // Split the numbers using Dekker's algorithm without scaling
+ final double hx = highPartUnscaled(x);
+ final double lx = x - hx;
+
+ return squareLow(hx, lx, xx);
+ }
+
+ /**
+ * Implement Dekker's method to split a value into two parts. Multiplying
by (2^s + 1) creates
+ * a big value from which to derive the two split parts.
+ * <pre>
+ * c = (2^s + 1) * a
+ * a_big = c - a
+ * a_hi = c - a_big
+ * a_lo = a - a_hi
+ * a = a_hi + a_lo
+ * </pre>
+ *
+ * <p>The multiplicand allows a p-bit value to be split into
+ * (p-s)-bit value {@code a_hi} and a non-overlapping (s-1)-bit value
{@code a_lo}.
+ * Combined they have (p-1) bits of significand but the sign bit of {@code
a_lo}
+ * contains a bit of information. The constant is chosen so that s is
ceil(p/2) where
+ * the precision p for a double is 53-bits (1-bit of the mantissa is
assumed to be
+ * 1 for a non sub-normal number) and s is 27.
+ *
+ * <p>This conversion does not use scaling and the result of overflow is
NaN. Overflow
+ * may occur when the exponent of the input value is above 996.
+ *
+ * <p>Splitting a NaN or infinite value will return NaN.
+ *
+ * @param value Value.
+ * @return the high part of the value.
+ * @see Math#getExponent(double)
+ */
+ private static double highPartUnscaled(double value) {
+ final double c = MULTIPLIER * value;
+ return c - (c - value);
+ }
+
+ /**
+ * Compute the low part of the double length number {@code (z,zz)} for the
exact
+ * square of {@code x} using Dekker's mult12 algorithm. The standard
+ * precision product {@code x*x} must be provided. The number {@code x}
+ * should already be split into low and high parts.
+ *
+ * <p>Note: This uses the high part of the result {@code (z,zz)} as {@code
x * x} and not
+ * {@code hx * hx + hx * lx + lx * hx} as specified in Dekker's original
paper.
+ * See Shewchuk (1997) for working examples.
+ *
+ * @param hx High part of factor.
+ * @param lx Low part of factor.
+ * @param xx Square of the factor.
+ * @return <code>lx * ly - (((xy - hx * hy) - lx * hy) - hx * ly)</code>
+ * @see <a
href="http://www-2.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-arithmetic.ps";>
+ * Shewchuk (1997) Theorum 18</a>
+ */
+ private static double squareLow(double hx, double lx, double xx) {
+ // Compute the multiply low part:
+ // err1 = xy - hx * hy
+ // err2 = err1 - lx * hy
+ // err3 = err2 - hx * ly
+ // low = lx * ly - err3
+ return lx * lx - ((xx - hx * hx) - 2 * lx * hx);
+ }
}
diff --git
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erf.java
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erf.java
index 0d32074..6d86f6e 100644
---
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erf.java
+++
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erf.java
@@ -17,42 +17,35 @@
package org.apache.commons.numbers.gamma;
/**
- * <a href="http://mathworld.wolfram.com/Erf.html";>Error function</a>.
+ * <a href="https://mathworld.wolfram.com/Erf.html";>Error function</a>.
+ *
+ * <p>\[ \operatorname{erf}(z) = \frac{2}{\sqrt\pi}\int_0^z e^{-t^2}\,dt \]
*/
public final class Erf {
- /** The threshold value for returning the extreme value. */
- private static final double EXTREME_VALUE_BOUND = 40;
-
/** Private constructor. */
private Erf() {
// intentionally empty.
}
/**
- * <p>
- * This implementation computes erf(x) using the
- * {@link RegularizedGamma.P#value(double, double, double, int)
regularized gamma function},
- * following <a href="http://mathworld.wolfram.com/Erf.html";> Erf</a>,
equation (3)
- * </p>
+ * Returns the error function.
*
- * <p>
- * The returned value is always between -1 and 1 (inclusive).
- * If {@code abs(x) > 40}, then {@code Erf.value(x)} is indistinguishable
from
- * either 1 or -1 at {@code double} precision, so the appropriate extreme
value
- * is returned.
- * </p>
+ * <p>The returned value is always between -1 and 1 (inclusive).
+ * The appropriate extreme is returned when {@code erf(x)} is
+ * indistinguishable from either -1 or 1 at {@code double} precision.
+ *
+ * <p>Special cases:
+ * <ul>
+ * <li>If the argument is 0, then the result is 0.
+ * <li>If the argument is {@code > 6}, then the result is 1.
+ * <li>If the argument is {@code < 6}, then the result is -1.
+ * <li>If the argument is nan, then the result is nan.
+ * </ul>
*
* @param x the value.
* @return the error function.
- * @throws ArithmeticException if the algorithm fails to converge.
- *
- * @see RegularizedGamma.P#value(double, double, double, int)
*/
public static double value(double x) {
- if (Math.abs(x) > EXTREME_VALUE_BOUND) {
- return x > 0 ? 1 : -1;
- }
- final double ret = RegularizedGamma.P.value(0.5, x * x, 1e-15, 10000);
- return x < 0 ? -ret : ret;
+ return BoostErf.erf(x);
}
}
diff --git
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erfc.java
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erfc.java
index 44a6879..19f62f9 100644
---
a/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erfc.java
+++
b/commons-numbers-gamma/src/main/java/org/apache/commons/numbers/gamma/Erfc.java
@@ -17,45 +17,39 @@
package org.apache.commons.numbers.gamma;
/**
- * <a href="http://mathworld.wolfram.com/Erfc.html";>Complementary error
function</a>.
+ * <a href="https://mathworld.wolfram.com/Erfc.html";>Complementary error
function</a>.
+ *
+ * <p>\[ \begin{aligned} \operatorname{erfc}(z)
+ * &= 1 - \operatorname{erf}(z) \\
+ * &= \frac{2}{\sqrt\pi}\int_z^{\infty} e^{-t^2}\,dt
+ * \end{aligned} \]
*/
public final class Erfc {
- /** The threshold value for returning the extreme value. */
- private static final double EXTREME_VALUE_BOUND = 40;
-
/** Private constructor. */
private Erfc() {
// intentionally empty.
}
/**
- * <p>
- * This implementation computes erfc(x) using the
- * {@link RegularizedGamma.Q#value(double, double, double, int)
regularized gamma function},
- * following <a href="http://mathworld.wolfram.com/Erf.html";>Erf</a>,
equation (3).
- * </p>
+ * Returns the complementary error function.
*
- * <p>
- * The value returned is always between 0 and 2 (inclusive).
- * If {@code abs(x) > 40}, then {@code erf(x)} is indistinguishable from
- * either 0 or 2 at {@code double} precision, so the appropriate extreme
- * value is returned.
- * </p>
+ * <p>The value returned is always between 0 and 2 (inclusive).
+ * The appropriate extreme is returned when {@code erfc(x)} is
+ * indistinguishable from either 0 or 2 at {@code double} precision.
+ *
+ * <p>Special cases:
+ * <ul>
+ * <li>If the argument is 0, then the result is 1.
+ * <li>If the argument is {@code > 28}, then the result is 0.
+ * <li>If the argument is {@code < 6}, then the result is 2.
+ * <li>If the argument is nan, then the result is nan.
+ * </ul>
*
* @param x Value.
* @return the complementary error function.
- * @throws ArithmeticException if the algorithm fails to converge.
- *
- * @see RegularizedGamma.Q#value(double, double, double, int)
*/
public static double value(double x) {
- if (Math.abs(x) > EXTREME_VALUE_BOUND) {
- return x > 0 ? 0 : 2;
- }
- final double ret = RegularizedGamma.Q.value(0.5, x * x, 1e-15, 10000);
- return x < 0 ?
- 2 - ret :
- ret;
+ return BoostErf.erfc(x);
}
}
diff --git
a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/BoostErfTest.java
b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/BoostErfTest.java
index 8f2a6f0..e171269 100644
---
a/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/BoostErfTest.java
+++
b/commons-numbers-gamma/src/test/java/org/apache/commons/numbers/gamma/BoostErfTest.java
@@ -46,6 +46,8 @@ class BoostErfTest {
* This is a utility to identify if the function is an odd function: f(x)
= -f(-x).
*/
private enum TestFunction {
+ ERF(BoostErf::erf, true),
+ ERFC(BoostErf::erfc, false),
ERF_INV(BoostErf::erfInv, true),
ERFC_INV(BoostErf::erfcInv, false);
@@ -94,10 +96,33 @@ class BoostErfTest {
* pass. Spot checks on larger errors have been verified against the
reference
* implementation compiled with promotion of double
<strong>disabled</strong>.
*
+ * <p>For the erf and erfc functions the Boost error is due to the
accuracy of
+ * exponentiation. From the Boost test_erf.cpp:
+ * <pre>
+ * "On MacOS X erfc has much higher error levels than
+ * expected: given that the implementation is basically
+ * just a rational function evaluation combined with
+ * exponentiation, we conclude that exp and pow are less
+ * accurate on this platform, especially when the result
+ * is outside the range of a double."
+ * </pre>
+ *
* @see <a
href="https://www.boost.org/doc/libs/1_77_0/libs/math/doc/html/math_toolkit/relative_error.html";>Relative
error</a>
* @see <a
href="https://www.boost.org/doc/libs/1_77_0/libs/math/doc/html/math_toolkit/pol_tutorial/policy_tut_defaults.html";>Policy
defaults</a>
*/
private enum TestCase {
+ /** Erf Boost data. */
+ ERF(TestFunction.ERF, 1.4, 0.25),
+ /** Erfc Boost data. */
+ ERFC(TestFunction.ERFC, 2.2, 0.5),
+ /** Erf Boost large data (simple case where all z>8, p=1.0). */
+ ERF_LARGE(TestFunction.ERF, 0, 0.0),
+ /** Erfc Boost large data. */
+ ERFC_LARGE(TestFunction.ERFC, 1.99, 0.75),
+ /** Erf Boost small data (no exponentiation required). */
+ ERF_SMALL(TestFunction.ERF, 1.2, 0.25),
+ /** Erfc Boost small data (no exponentiation required: ulp=0). */
+ ERFC_SMALL(TestFunction.ERFC, 0, 0.0),
/** Inverse Erf Boost data. */
ERF_INV(TestFunction.ERF_INV, 1.8, 0.65),
/** Inverse Erfc Boost data. */
@@ -232,6 +257,132 @@ class BoostErfTest {
@ParameterizedTest
@CsvSource({
+ "-Infinity, -1",
+ "Infinity, 1",
+ "0, 0",
+ // Odd function
+ "-0.0, -0.0",
+ "NaN, NaN",
+ // Realistic limits
+ "-6, -1",
+ "6, 1",
+ })
+ void testErfEdgeCases(double z, double p) {
+ Assertions.assertEquals(p, BoostErf.erf(z));
+ }
+
+ @ParameterizedTest
+ @CsvSource({
+ "-Infinity, 2",
+ "Infinity, 0",
+ "0, 1",
+ "NaN, NaN",
+ // Realistic limits
+ "-6, 2",
+ "28, 0",
+ })
+ void testErfcEdgeCases(double z, double q) {
+ Assertions.assertEquals(q, BoostErf.erfc(z));
+ }
+
+ @ParameterizedTest
+ @Order(1)
+ @CsvFileSource(resources = "erf_data.csv")
+ void testErf(double z, BigDecimal p, double q) {
+ assertErf(TestCase.ERF, z, p);
+ }
+
+ @Test
+ @Order(1010)
+ void testErfRMS() {
+ assertRms(TestCase.ERF);
+ }
+
+ @ParameterizedTest
+ @Order(1)
+ @CsvFileSource(resources = "erf_data.csv")
+ void testErfc(double z, double p, BigDecimal q) {
+ assertErf(TestCase.ERFC, z, q);
+ }
+
+ @Test
+ @Order(1020)
+ void testErfcRMS() {
+ assertRms(TestCase.ERFC);
+ }
+
+ @ParameterizedTest
+ @Order(1)
+ @CsvFileSource(resources = "erf_large_data.csv")
+ void testErfLarge(double z, BigDecimal p, double q) {
+ assertErf(TestCase.ERF_LARGE, z, p);
+ }
+
+ @Test
+ @Order(1030)
+ void testErfLargeRMS() {
+ assertRms(TestCase.ERF_LARGE);
+ }
+
+ @ParameterizedTest
+ @Order(1)
+ @CsvFileSource(resources = "erf_large_data.csv")
+ void testErfcLarge(double z, double p, BigDecimal q) {
+ assertErf(TestCase.ERFC_LARGE, z, q);
+ }
+
+ @Test
+ @Order(1040)
+ void testErfcLargeRMS() {
+ assertRms(TestCase.ERFC_LARGE);
+ }
+
+ @ParameterizedTest
+ @Order(1)
+ @CsvFileSource(resources = "erf_small_data.csv")
+ void testErfSmall(double z, BigDecimal p, double q) {
+ assertErf(TestCase.ERF_SMALL, z, p);
+ }
+
+ @Test
+ @Order(1050)
+ void testErfSmallRMS() {
+ assertRms(TestCase.ERF_SMALL);
+ }
+
+ @ParameterizedTest
+ @Order(1)
+ @CsvFileSource(resources = "erf_small_data.csv")
+ void testErfcSmall(double z, double p, BigDecimal q) {
+ assertErf(TestCase.ERFC_SMALL, z, q);
+ }
+
+ @Test
+ @Order(1060)
+ void testErfcSmallRMS() {
+ assertRms(TestCase.ERFC_SMALL);
+ }
+
+ /**
+ * This tests the erf function as the result approaches 1.0. The Boost
threshold
+ * for large z is 5.8f. This is too low and results in 2 ulp errors when z
is
+ * just above 5.8 and the result is 0.9999999999999998.
+ *
+ * @param z Value to test
+ * @param p Expected p
+ */
+ @ParameterizedTest
+ @CsvFileSource(resources = "erf_close_to_1_data.csv")
+ void testErfCloseTo1(double z, double p) {
+ Assertions.assertTrue(5.8 < z, () -> "z not above Boost threshold: " +
z);
+ Assertions.assertTrue(z < 5.95, () -> "z not close to Boost threhsold:
" + z);
+ Assertions.assertTrue(p <= 1.0, () -> "p not <= 1: " + p);
+ Assertions.assertEquals(1.0, p, 0x1.0p-52, "Value not with 2 ulp of
1.0");
+ Assertions.assertEquals(p, BoostErf.erf(z));
+ }
+
+ @ParameterizedTest
+ @CsvSource({
"0, 0",
// Odd function
"-0.0, -0.0",
@@ -331,10 +482,10 @@ class BoostErfTest {
@Test
void testErfRoundTrip() {
assertRoundTrip("erf(erfInv(x))",
- x -> Erf.value(BoostErf.erfInv(x)),
+ x -> BoostErf.erf(BoostErf.erfInv(x)),
// Inverse Erf domain: [-1, 1]
-0.95, 1, 0.125,
- 5L, 2.99);
+ 2L, 0.99);
}
/**
@@ -343,10 +494,10 @@ class BoostErfTest {
@Test
void testErfcRoundTrip() {
assertRoundTrip("erfc(erfcInv(x))",
- x -> Erfc.value(BoostErf.erfcInv(x)),
+ x -> BoostErf.erfc(BoostErf.erfcInv(x)),
// Inverse Erfc domain: [0, 2]
0.125, 2, 0.125,
- 15L, 3.99);
+ 2L, 0.99);
}
/**
diff --git
a/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_close_to_1_data.csv
b/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_close_to_1_data.csv
new file mode 100644
index 0000000..d6ed9f9
--- /dev/null
+++
b/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_close_to_1_data.csv
@@ -0,0 +1,159 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements. See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# Erf close to 1
+#
+# Data generated using the following matlab script
+# using variable precision arithmetic (vpa).
+# Values should be machine representable using double precision.
+#
+# f = fopen('erf_close_to_1_data.csv', 'wt');
+# digits(30);
+# for i = [5950:6080]
+# fprintf(f, "%.17g,%s\n", i/1024, vpa(erf(sym(i/1024))));
+# end
+# fclose(f);
+
+5.810546875,0.999999999999999791958062733146
+5.8115234375,0.999999999999999794339532405692
+5.8125,0.999999999999999796694123729017
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diff --git
a/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_data.csv
b/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_data.csv
new file mode 100644
index 0000000..0c9f923
--- /dev/null
+++
b/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_data.csv
@@ -0,0 +1,522 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements. See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# (C) Copyright John Maddock 2006-7.
+# Use, modification and distribution are subject to the
+# Boost Software License, Version 1.0. (See accompanying file
+# LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# Extracted from: boost/libs/math/test/erf_data.ipp
+
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diff --git
a/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_large_data.csv
b/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_large_data.csv
new file mode 100644
index 0000000..deb90dc
--- /dev/null
+++
b/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_large_data.csv
@@ -0,0 +1,92 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements. See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# (C) Copyright John Maddock 2006-7.
+# Use, modification and distribution are subject to the
+# Boost Software License, Version 1.0. (See accompanying file
+# LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# Extracted from: boost/libs/math/test/erf_large_data.ipp
+
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diff --git
a/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_small_data.csv
b/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_small_data.csv
new file mode 100644
index 0000000..083040e
--- /dev/null
+++
b/commons-numbers-gamma/src/test/resources/org/apache/commons/numbers/gamma/erf_small_data.csv
@@ -0,0 +1,172 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements. See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License. You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# (C) Copyright John Maddock 2006-7.
+# Use, modification and distribution are subject to the
+# Boost Software License, Version 1.0. (See accompanying file
+# LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+# Extracted from: boost/libs/math/test/erf_small_data.ipp
+
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diff --git a/src/main/resources/pmd/pmd-ruleset.xml
b/src/main/resources/pmd/pmd-ruleset.xml
index 4ba91b2..5d11c46 100644
--- a/src/main/resources/pmd/pmd-ruleset.xml
+++ b/src/main/resources/pmd/pmd-ruleset.xml
@@ -67,6 +67,13 @@
<!-- Rule customisations. -->
+ <rule ref="category/java/bestpractices.xml/AvoidReassigningParameters">
+ <properties>
+ <!-- The ported method follows the original C++ usage of the 'invert'
flag. -->
+ <property name="violationSuppressXPath"
value="//ClassOrInterfaceDeclaration[@SimpleName='BoostErf']"/>
+ </properties>
+ </rule>
+
<rule ref="category/java/codestyle.xml/ShortMethodName">
<properties>
<!-- TODO: Current regex effectively disables this rule. -->
@@ -90,6 +97,12 @@
value="//ClassOrInterfaceDeclaration[@SimpleName='BoostErf']"/>
</properties>
</rule>
+ <rule ref="category/java/codestyle.xml/ConfusingTernary">
+ <properties>
+ <!-- Use the original C++ code logic for identifying the erf domain. -->
+ <property name="violationSuppressXPath"
value="//ClassOrInterfaceDeclaration[@SimpleName='BoostErf']"/>
+ </properties>
+ </rule>
<rule ref="category/java/design.xml/CyclomaticComplexity">
<properties>
