js-hexfloat

Rudimentary C99 Hexadecimal Floating Point Support in JS

SYNOPSIS

var pi = parseHexFloat('0x1.921fb54442d18p+1'); // 3.14159265358982
var piHex = Math.PI.toHexString();              // '0x1.921fb54442d18p+1'
parseHexFloat(piHex) == Math.PI;                // true

DESCRIPTION

This script adds the following:

parseHexFloat(theString)

Parses C99 hexadecimal floating point in theString. Returns NaN if fails.

Unlike parseInt and parseFloat, the number must be prepended with '0x' and ended with 'p' and exponent in decimal number.

also available as Number.parseHexFloat().

parseHexFloat as a callback

From version 0.4.0, you can use parseHexFloat with String.prototype.replace.

var text = 'e=0x1.5bf0a8b145769p+1, pi=0x1.921fb54442d18p+1';
text.replace(RE_HEXFLOAT_G, parseHexFloat); // 'e=2.718281828459045, pi=3.141592653589793';

In the case above, parseHexFloat does not apply regexp by itself. Instead it just takes its arguments as the matched result.

Unfortunately text.replace(RE_HEXFLOAT, parseHexFloat, 'g') is not standard so RE_HEXFLOAT_G is added.

RE_HEXFLOAT

RegExp object used in parseHexFloat:

/([\+\-]?)0x([0-9A-F]+)\.?([0-9A-F]*)p([\+\-]?[0-9]+)/i

RE_HEXFLOAT_G

RE_HEXFLOAT with a g (global) flag. See above for usage.

Number.prototype.toHexString()

Stringifies the number as a C99 hexadecimal notation like "%a" in C99 sprintf().

Why Canonical Form?

From version 0.3.0, .toHexString() always returns the canonical notation.

Math.PI.toString(16);   // 3.243f6a8885a3 -> 0x3.243f6a8885a3p0 is valid yet uncanonical
Math.PI.toHexString();  // 0x1.921fb54442d18p+1 is valid and canonical

It seems ok to just prepend '0x' and append 'p0' to .toString(16) to make a hex float. Turns out it isn't. It sometimes drops the last bits in some occasions.

Math.log(2).toString(16)  // 0.b17217f7d1cf78
Math.log(2).toHexString() // 0x1.62e42fefa39efp-1

% perl -E 'say 0x0.b17217f7d1cf78p0 - 0x1.62e42fefa39efp-1'
-1.11022302462516e-16
% perl -E 'say sprintf "%a", 0x0.b17217f7d1cf78p0 - 0x1.62e42fefa39efp-1'
-0x1p-53

And abs(-0x1p-53) is DBL_EPSILON.

SEE ALSO

• http://www.exploringbinary.com/hexadecimal-floating-point-constants/
• https://github.com/dankogai/js-sion
• https://dankogai.github.com/SION/

Appendix: HexFloat in Other Languages

• C
  • Standard since C99
  • Literals, output via %a in printf format, input via strtod(), ...
  • https://gcc.gnu.org/onlinedocs/gcc/Hex-Floats.html
• C++
  • Standard since C++11
  • C features plus std::hexfloat, ...
  • http://www.cplusplus.com/reference/ios/hexfloat/
• Perl 5
  • Supported since 5.22
  • Pretty much like C99: literals, the %a format, POSIX::strtod(), ...
  • http://perldoc.perl.org/perl5220delta.html
  • http://www.effectiveperlprogramming.com/2015/06/perl-v5-22-adds-hexadecimal-floating-point-literals/
• Ruby
  • Supported since 1.9?
    • http://docs.ruby-lang.org/ja/1.9.3/doc/print_format.html
    • http://docs.ruby-lang.org/ja/1.8.7/doc/print_format.html
  • No literals, output via %a for sprintf, input via Float()
• Swift
  • Supported from the beginning
  • Literals, output via String(format:"%a", ...), input via Double(), ...
  • https://developer.apple.com/library/ios/documentation/Swift/Conceptual/Swift_Programming_Language/