Properties of the Correction Loop in David Gay’s strtod()

The infinite loop I discovered in PHP was caused by a bug in its decimal to floating-point conversion routine, which is based on David Gay’s widely used strtod() function. strtod() has a “correction loop,” the purpose of which is to refine an initial estimate of a converted double-precision value to its correctly rounded result. This got me thinking: infinite loops notwithstanding, how many times should the loop execute? Does it depend on the accuracy of the initial estimate? I instrumented strtod() and gathered some data to help answer these questions.

The most interesting thing I discovered was this: strtod()’s correction procedure can execute at most three times. So why was it coded as an infinite loop?

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A Better Fix for the PHP 2.2250738585072011e-308 Bug

Recently I discovered a bug in PHP’s decimal to floating-point conversion routine, zend_strtod(): it went into an infinite loop trying to convert the decimal string 2.2250738585072011e-308 to floating-point. zend_strtod() is based on David Gay’s strtod() function in dtoa.c, as are the decimal to floating-point conversion routines of many other open source projects. So why hasn’t this bug affected these other projects?

zend_strtod() is based on a very old copy of dtoa.c. The current version of dtoa.c is immune to the 2.2250738585072011e-308 bug — and has been since 1997 by my reckoning. So while the ‘volatile’ keyword fixes the PHP problem, I think there’s a better solution: upgrade zend_strtod() to the latest dtoa.c.

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Nondeterministic Floating-Point Conversions in Java

Recently I discovered that Java converts some very small decimal numbers to double-precision floating-point incorrectly. While investigating that bug, I stumbled upon something very strange: Java’s decimal to floating-point conversion routine, Double.parseDouble(), sometimes returns two different results for the same decimal string. The culprit appears to be just-in-time compilation of Double.parseDouble() into SSE instructions, which exposes an architecture-dependent bug in Java’s conversion algorithm — and another real-world example of a double rounding on underflow error. I’ll describe the problem, and take you through the detective work to find its cause.

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Incorrectly Rounded Subnormal Conversions in Java

While verifying the fix to the Java 2.2250738585072012e-308 bug I found an OpenJDK testcase for verifying conversions of edge case subnormal double-precision numbers. I ran the testcase, expecting it to work — but it failed! I determined it fails because Java converts some subnormal numbers incorrectly.

(By the way, this bug exists in prior versions of Java — it has nothing to do with the fix.)

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FPUpdater Fixes the Java 2.2250738585072012e-308 Bug

Oracle has released a fix for security alert CVE-2010-4476 — the “Java Hangs on 2.2250738585072012e-308 bug.” The fix comes in the form of something called the FPUpdater Tool, which updates rt.jar. I tested it on my Windows XP system and it works.

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A Closer Look at the Java 2.2250738585072012e-308 Bug

Java’s decimal to floating-point conversion routine, the doubleValue() method of its FloatingDecimal class, goes into an infinite loop when converting the decimal string 2.2250738585072012e-308 to double-precision binary floating-point. I took a closer look at the bug, by tracing the doubleValue() method in the Eclipse IDE for Java (thanks to Konstantin Preißer for helping me set that up). What I found was that our initial analysis of the bug was wrong; what actually happens is that doubleValue()’s correction loop oscillates between two values, 0x1p-1022 and 0x0.fffffffffffffp-1022.

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Java Hangs When Converting 2.2250738585072012e-308

Konstantin Preißer made an interesting discovery, after reading my article “PHP Hangs On Numeric Value 2.2250738585072011e-308”: Java — both its runtime and compiler — go into an infinite loop when converting the decimal number 2.2250738585072012e-308 to double-precision binary floating-point. This number is supposed to convert to 0x1p-1022, which is DBL_MIN; instead, Java gets stuck, oscillating between 0x1p-1022 and 0x0.fffffffffffffp-1022, the largest subnormal double-precision floating-point number.

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Why “Volatile” Fixes the 2.2250738585072011e-308 Bug

Recently I discovered a serious bug in x87 builds of PHP: PHP’s decimal to floating-point conversion routine, zend_strtod(), went into an infinite loop when converting the decimal string 2.2250738585072011e-308 to double-precision binary floating-point. This problem was fixed with a simple one line of code change to zend_strtod.c:

This line

double aadj, aadj1, adj;

was changed to

volatile double aadj, aadj1, adj;

Why does this fix the problem? I uncovered the very specific reason: it prevents a double rounding on underflow error.

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PHP Hangs On Numeric Value 2.2250738585072011e-308

I stumbled upon a very strange bug in PHP; this statement sends it into an infinite loop:

<?php $d = 2.2250738585072011e-308; ?>

(The same thing happens if you write the number without scientific notation — 324 decimal places.)

I hit this bug in the two places I tested for it: on Windows (PHP 5.3.1 under XAMPP 1.7.3), and on Linux (PHP Version 5.3.2-1ubuntu4.5) — both on an Intel Core Duo processor. I’ve written a bug report.

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