Articles with the ‘Java’ Tag

Direct Generation of Double Rounding Error Conversions in Kotlin

By Rick Regan November 10th, 2020

For my recent search for short examples of double rounding errors in decimal to double to float conversions I wrote a Kotlin program to generate and test random decimal strings. While this was sufficient to find examples, I realized I could do a more direct search by generating only decimal strings with the underlying double rounding error bit patterns. I’ll show you the Java BigDecimal based Kotlin program I wrote for this purpose.

Continue reading “Direct Generation of Double Rounding Error Conversions in Kotlin”

Maximum Number of Decimal Digits In Binary Floating-Point Numbers

By Rick Regan December 5th, 2016

I’ve written about the formulas used to compute the number of decimal digits in a binary integer and the number of decimal digits in a binary fraction. In this article, I’ll use those formulas to determine the maximum number of digits required by the double-precision (double), single-precision (float), and quadruple-precision (quad) IEEE binary floating-point formats.

The maximum digit counts are useful if you want to print the full decimal value of a floating-point number (worst case format specifier and buffer size) or if you are writing or trying to understand a decimal to floating-point conversion routine (worst case number of input digits that must be converted).

Continue reading “Maximum Number of Decimal Digits In Binary Floating-Point Numbers”

Java Doesn’t Print The Shortest Strings That Round-Trip

By Rick Regan May 1st, 2016

I’ve always thought Java was one of the languages that prints the shortest decimal strings that round-trip back to floating-point. I was wrong.

Continue reading “Java Doesn’t Print The Shortest Strings That Round-Trip”

Floating-Point Questions Are Endless on stackoverflow.com

By Rick Regan November 7th, 2013

For years I’ve followed, through RSS, floating-point related questions on stackoverflow.com. Every day it seems there is a question like “why does 19.24 plus 6.95 equal 26.189999999999998?” I decided to track these questions, to see if my sense of their frequency was correct. I found that, in the last 40 days, there were 18 such questions. That’s not one per day, but still — a lot!

Continue reading “Floating-Point Questions Are Endless on stackoverflow.com”

Decimal/Binary Conversion Using “Deci-Binary”

By Rick Regan September 2nd, 2013

I read about an interesting method for decimal/binary conversion in chapter two of Gerald R. Rising’s book “Inside Your Calculator”. Unlike the standard string-oriented conversion algorithms, the algorithms in his book perform arithmetic on an encoding I’ve dubbed “deci-binary”. Using this encoding, binary numbers are input and output as decimal strings consisting of only ones and zeros, exploiting built-in language facilities for decimal input and output. I will demonstrate this conversion process with Java code I have written.

Continue reading “Decimal/Binary Conversion Using “Deci-Binary””

Fast Path Decimal to Floating-Point Conversion

By Rick Regan September 1st, 2011

In general, to convert an arbitrary decimal number into a binary floating-point number, arbitrary-precision arithmetic is required. However, a subset of decimal numbers can be converted correctly with just ordinary limited-precision IEEE floating-point arithmetic, taking what I call the fast path to conversion. Fast path conversion is an optimization used in practice: it’s in David Gay’s strtod() function and in Java’s FloatingDecimal class. I will explain how fast path conversion works, and describe the set of numbers that qualify for it.

Continue reading “Fast Path Decimal to Floating-Point Conversion”

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

By Rick Regan March 23rd, 2011

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?

Continue reading “Properties of the Correction Loop in David Gay’s strtod()”

Nondeterministic Floating-Point Conversions in Java

By Rick Regan February 21st, 2011

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.

Continue reading “Nondeterministic Floating-Point Conversions in Java”

Incorrectly Rounded Subnormal Conversions in Java

By Rick Regan February 16th, 2011

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.)

Continue reading “Incorrectly Rounded Subnormal Conversions in Java”

FPUpdater Fixes the Java 2.2250738585072012e-308 Bug

By Rick Regan February 9th, 2011

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.

Continue reading “FPUpdater Fixes the Java 2.2250738585072012e-308 Bug”

A Closer Look at the Java 2.2250738585072012e-308 Bug

By Rick Regan February 7th, 2011

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.

Continue reading “A Closer Look at the Java 2.2250738585072012e-308 Bug”

Java Hangs When Converting 2.2250738585072012e-308

By Rick Regan January 31st, 2011

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.

Continue reading “Java Hangs When Converting 2.2250738585072012e-308”