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commit ff1b7d1d197fac7ce58864a8c89d032132ee53f0 Author: Alex Herbert <[email protected]> AuthorDate: Tue Dec 10 23:23:08 2019 +0000 Ensure log() and log10() avoid overflow. --- .../apache/commons/numbers/complex/Complex.java | 54 +++++++++++++++++++--- 1 file changed, 48 insertions(+), 6 deletions(-) diff --git a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java index c9cd5ea..0181189 100644 --- a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java +++ b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java @@ -96,6 +96,21 @@ public final class Complex implements Serializable { } /** + * Define a unary operation on a double. + * This is used in the log() and log10() functions. + */ + @FunctionalInterface + private interface UnaryOperation { + /** + * Apply an operation to a value. + * + * @param value The value. + * @return The result. + */ + double apply(double value); + } + + /** * Private default constructor. * * @param real Real part. @@ -1469,13 +1484,11 @@ public final class Complex implements Serializable { * @see #arg() */ public Complex log() { - // All edge cases satisfied by the Math library - return new Complex(Math.log(abs()), - arg()); + return log(Math::log); } /** - * Compute the base 10 or + * Compute the base 10 * <a href="http://mathworld.wolfram.com/CommonLogarithm.html";> * common logarithm</a> of this complex number. * Implements the formula: @@ -1489,8 +1502,37 @@ public final class Complex implements Serializable { * @see #arg() */ public Complex log10() { - // All edge cases satisfied by the Math library - return new Complex(Math.log10(abs()), + return log(Math::log10); + } + + /** + * Compute the logarithm of this complex number using the provided function. + * Implements the formula: + * <pre> + * log(a + bi) = log(|a + b i|) + i arg(a + b i) + * </pre> + * + * @param log Log function. + * @return the logarithm of {@code this}. + * @see #abs() + * @see #arg() + */ + private Complex log(UnaryOperation log) { + // All ISO C99 edge cases satisfied by the Math library. + // Make computation overflow safe. + final double abs = abs(); + if (abs == Double.POSITIVE_INFINITY && isFinite()) { + // Edge-case where the |a + b i| overflows. + // |a + b i| = sqrt(a^2 + b^2) + // This can be scaled linearly. + // Scale the absolute and exploit: + // ln(abs / s) = ln(abs) - ln(s) + // ln(abs) = ln(abs / s) + ln(s) + final double s = Math.max(Math.abs(real), Math.abs(imaginary)); + final double absOs = Math.hypot(real / s, imaginary / s); + return new Complex(log.apply(absOs) + log.apply(s), arg()); + } + return new Complex(log.apply(abs), arg()); }
