{"id":6225,"date":"2023-02-09T20:43:42","date_gmt":"2023-02-09T20:43:42","guid":{"rendered":"https:\/\/really.zonky.org\/?p=6225"},"modified":"2023-02-09T20:43:44","modified_gmt":"2023-02-09T20:43:44","slug":"why-do-computers-suck-at-maths","status":"publish","type":"post","link":"https:\/\/really.zonky.org\/?p=6225","title":{"rendered":"Why Do Computers Suck At Maths?"},"content":{"rendered":"\n

Sometimes, computers seem to suck at maths :-<\/p>\n\n\n\n

>>> 1.2 - 1.0\n0.19999999999999996<\/code><\/pre>\n\n\n\n
To be fair, that’s a raw Python interface; an application intended for use as a calculator works a bit better :-<\/p>\n\n\n\n
\u00bb qalc \n> 1.2 - 1.0\n\n  1.2 \u2212 1 = 0.2<\/code><\/pre>\n\n\n\n
The problem is related to low-level numeric types. Computers store numbers in a variety of different formats (called types<\/em> by developers). Whole numbers (integers) are easy – just allocate a certain number of 8-bit bytes (more means you can store bigger numbers; but it takes more memory for each number) and you would have something that would store whole numbers with perfect accuracy.<\/p>\n\n\n\n
Floating point (i.e. numbers with a ‘decimal’ point) on the other hand are much more a compromise between size and accuracy. Floating point in effect uses scientific notation for numbers – 1.23E23. So a number is split into two – the mantissa (effectively the bit before the “E”) and the exponent. Storing two numbers in 32-bits (single precision) limits the precision in which numbers are stored but is usually sufficient and allows a far larger range of numbers :-<\/p>\n\n\n\n
>>> print(\"{:10.4f}\".format(1.2 - 1.0)) \n    0.2000<\/code><\/pre>\n\n\n\n
In other words if you are using a low-level interface as a calculator, you can produce sensible output merely by writing your code properly. Or use a proper calculator program like qalc(ulator). <\/p>\n\n\n\n
This is of course an over simplification<\/a> and the Wikipedia article on single precision floating point<\/a> goes into far more detail than I want to understand. Amongst other things I’ve glossed over is the problem of performing calculations in base 2 (binary) rather than base 10 (decimal).<\/p>\n\n\n\n
Plus there are a whole bunch of other numeric types such as larger floating point types, decimal floating point, bignums (which use whatever memory is necessary to store a number), fixed point, etc. <\/p>\n\n\n\n
Computers aren’t bad at maths; it is just you can trick them into making themselves look bad. <\/p>\n\n\n\n
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Sometimes, computers seem to suck at maths :- To be fair, that’s a raw Python interface; an application intended for use as a calculator works a bit better :- The problem is related to low-level numeric types. Computers store numbers in a variety of different formats (called types by developers). Whole numbers (integers) are easy […]<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_share_on_mastodon":"1"},"categories":[4,7],"tags":[2134,2135,2133,2132],"class_list":["post-6225","post","type-post","status-publish","format-standard","hentry","category-it","category-general","tag-binary","tag-decimal","tag-floating-point","tag-integers","category-4-id","category-7-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"share_on_mastodon":{"url":"https:\/\/mstdn.social\/@grumpygrimnir\/109836725286510308","error":""},"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1f2KI-1Cp","_links":{"self":[{"href":"https:\/\/really.zonky.org\/index.php?rest_route=\/wp\/v2\/posts\/6225","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/really.zonky.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/really.zonky.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/really.zonky.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/really.zonky.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6225"}],"version-history":[{"count":3,"href":"https:\/\/really.zonky.org\/index.php?rest_route=\/wp\/v2\/posts\/6225\/revisions"}],"predecessor-version":[{"id":6235,"href":"https:\/\/really.zonky.org\/index.php?rest_route=\/wp\/v2\/posts\/6225\/revisions\/6235"}],"wp:attachment":[{"href":"https:\/\/really.zonky.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6225"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/really.zonky.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6225"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/really.zonky.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}