{"id":937,"date":"2009-08-10T16:00:36","date_gmt":"2009-08-11T00:00:36","guid":{"rendered":"https:\/\/www.reenigne.org\/blog\/?p=937"},"modified":"2009-07-19T20:10:36","modified_gmt":"2009-07-20T04:10:36","slug":"floating-point-is-not-evil","status":"publish","type":"post","link":"https:\/\/www.reenigne.org\/blog\/floating-point-is-not-evil\/","title":{"rendered":"Floating point is not evil"},"content":{"rendered":"

In response to this<\/a>:<\/p>\n

Floating point is not evil and it is deterministic, but you need to know what the values you’re working with actually are. Basically, floating point is like scientific notation, except with 2s instead of 10s. In other words, instead storing numbers like 1.234*104<\/sup> it stores numbers like 1.00110100102<\/sub>*210<\/sup>. It’s actually stored as a pair of numbers, a mantissa and an exponent. The number of bits in the mantissa is fixed (it’s 23 bits for single precision and 52 for double) and the leading “1” is implied. Each number representable as an IEEE floating point constant has exactly one representation except for zero (+0 and -0 have different bit patterns for complicated reasons). There are complications (denormals, NaNs and infinities) which can usually be ignored and which I won’t go into.<\/p>\n

Floating point numbers are handy for lots of purposes but they do have a couple of problems.<\/p>\n

The first problem is that floating point numbers are inefficient. They are very quick with today’s hardware but consider what you’d do if neither floating point hardware nor floating point libraries were available. For most applications, you’d use fixed point numbers – you’d store an integer and it would be implied by the type of number you’re working with that the actual numeric value is obtained by dividing this integer value by 2n<\/sup> for some n. For most purposes you probably wouldn’t store that n with each integer – all your numbers have the same number of significant digits. For example, if you’re writing a graphics program you might decide that units of 1\/256 of a pixel width are always enough, so n would always be -8. When writing floating-point programs, most programmers don’t do this calculation to figure out what the precision needs to be, they just use single precision floating point or switch to double if that isn’t precise enough. While constant precision is preferable for a general purpose calculator, most actual applications are better served by constant resolution.<\/p>\n

The other problem is that sooner or later you’ll run out of precision. If you’re plotting Mandelbrot sets, sooner or later you’ll zoom in far enough that adjacent pixels have complex numbers with the same floating-point representation. If you’re using FFTs to multiply big integers, sooner or later you’ll want to multiply integers so large that floating-point numbers won’t have sufficient precision. If you’re using hardware floating point, this is quite difficult to solve (you need to find or write a big-float library) and will cause a big speed hit, so most people will give up at that point. However, if you’re already using fixed point bignums, it’s just a question of adding another digit.<\/p>\n","protected":false},"excerpt":{"rendered":"

In response to this: Floating point is not evil and it is deterministic, but you need to know what the values you’re working with actually are. Basically, floating point is like scientific notation, except with 2s instead of 10s. In other words, instead storing numbers like 1.234*104 it stores numbers like 1.00110100102*210. It’s actually stored […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-937","post","type-post","status-publish","format-standard","hentry","category-computer"],"_links":{"self":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts\/937","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/comments?post=937"}],"version-history":[{"count":1,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts\/937\/revisions"}],"predecessor-version":[{"id":938,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/posts\/937\/revisions\/938"}],"wp:attachment":[{"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/media?parent=937"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/categories?post=937"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reenigne.org\/blog\/wp-json\/wp\/v2\/tags?post=937"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}