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A Problem So Simple That It Took Decades To Solve

What is the ideal default precision for floating-point output? - C/C++

When the Simplest Case Is One Of The Hardest To Get Right

Whenever we do floating-point input, we know exactly what the input is, and we also know exactly what precision the result should have. The hard problem, then, is how to specify the behavior of floating-point output. - C/C++

More Accurate + Faster = Better, Right?

"At least as precise" is sometimes just a polite way of saying "loosely specified." - C/C++

The Temptation For Implementations To Cut Corners

It would be useful if all conversions were as accurate as possible and, independently, were always done in exactly the same way. But complications can impede these goals. - C/C++

Accurate Floating-Point Input: Several Contexts, One Behavior

Let's look at some consequences of floating-point conversion. - C/C++

Floating-Point Input and Output Are Not Symmetric

Floating-point output is difficult because the number of digits needed to represent the result exactly might be very large, and it is not easy to figure out how many of those digits are needed to preserve the values being converted. Floating-point input has almost the opposite problems. - C/C++

Why Is Exact Floating-Point Output So Hard?

Every binary floating-point number is equivalent to what we might call a binary fixed-point number: a sequence of bits with a binary point separating the integer part from the fractional part. - C/C++

Even Simple Floating-Point Output Is Complicated

The root of the problem is that people usually write numbers in base 10 and computers usually store numbers in base 2. - C/C++

Why Language Designers Tolerate Undefined Behavior

Here is my first example of the tension between theoretical and socially inspired solutions to technical problems in programming-language design. - C/C++

Social Processes and the Design of Programming Languages

"A proof does not in itself significantly raise our confidence in the probable truth of the theorem it purports to prove." - C/C++

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