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Implementation"},{"level":2,"text":"References","anchor":"references","htmlText":"References"},{"level":2,"text":"Copyright","anchor":"copyright","htmlText":"Copyright"}],"lineInfo":{"truncatedLoc":"1239","truncatedSloc":"899"},"mode":"file"},"image":false,"isCodeownersFile":null,"isPlain":false,"isValidLegacyIssueTemplate":false,"issueTemplate":null,"discussionTemplate":null,"language":"reStructuredText","languageID":419,"large":false,"planSupportInfo":{"repoIsFork":null,"repoOwnedByCurrentUser":null,"requestFullPath":"/python/peps/blob/main/peps/pep-0327.rst","showFreeOrgGatedFeatureMessage":null,"showPlanSupportBanner":null,"upgradeDataAttributes":null,"upgradePath":null},"publishBannersInfo":{"dismissActionNoticePath":"/settings/dismiss-notice/publish_action_from_dockerfile","releasePath":"/python/peps/releases/new?marketplace=true","showPublishActionBanner":false},"rawBlobUrl":"https://github.com/python/peps/raw/refs/heads/main/peps/pep-0327.rst","renderImageOrRaw":false,"richText":"\u003carticle class=\"markdown-body entry-content container-lg\" itemprop=\"text\"\u003e\u003cp dir=\"auto\"\u003ePEP: 327\nTitle: Decimal Data Type\nAuthor: Facundo Batista \u0026lt;\u003ca href=\"mailto:facundo@taniquetil.com.ar\"\u003efacundo@taniquetil.com.ar\u003c/a\u003e\u0026gt;\nStatus: Final\nType: Standards Track\nCreated: 17-Oct-2003\nPython-Version: 2.4\nPost-History: 30-Nov-2003, 02-Jan-2004, 29-Jan-2004\u003c/p\u003e\n\u003ca name=\"user-content-abstract\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAbstract\u003c/h2\u003e\u003ca id=\"user-content-abstract\" class=\"anchor\" aria-label=\"Permalink: Abstract\" href=\"#abstract\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe idea is to have a Decimal data type, for every use where decimals\nare needed but binary floating point is too inexact.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe Decimal data type will support the Python standard functions and\noperations, and must comply with the decimal arithmetic ANSI standard\nX3.274-1996 \u003ca href=\"#id19\" id=\"user-content-id1\"\u003e[1]\u003c/a\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eDecimal will be floating point (as opposed to fixed point) and will\nhave bounded precision (the precision is the upper limit on the\nnumber of significant digits in a result). However, precision is\nuser-settable, and a notion of significant trailing zeroes is supported\nso that fixed-point usage is also possible.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThis work is based on code and test functions written by Eric Price,\nAahz and Tim Peters. Just before Python 2.4a1, the decimal.py\n\u003ca href=\"#reference-implementation\"\u003ereference implementation\u003c/a\u003e was moved into the standard library; along\nwith the documentation and the test suite, this was the work of\nRaymond Hettinger. Much of the explanation in this PEP is taken from\nCowlishaw's work \u003ca href=\"#id20\" id=\"user-content-id2\"\u003e[2]\u003c/a\u003e, comp.lang.python and python-dev.\u003c/p\u003e\n\u003ca name=\"user-content-motivation\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eMotivation\u003c/h2\u003e\u003ca id=\"user-content-motivation\" class=\"anchor\" aria-label=\"Permalink: Motivation\" href=\"#motivation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eHere I'll expose the reasons of why I think a Decimal data type is\nneeded and why other numeric data types are not enough.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eI wanted a Money data type, and after proposing a pre-PEP in\ncomp.lang.python, the community agreed to have a numeric data type\nwith the needed arithmetic behaviour, and then build Money over it:\nall the considerations about quantity of digits after the decimal\npoint, rounding, etc., will be handled through Money. It is not the\npurpose of this PEP to have a data type that can be used as Money\nwithout further effort.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eOne of the biggest advantages of implementing a standard is that\nsomeone already thought out all the creepy cases for you. And to a\nstandard GvR redirected me: Mike Cowlishaw's General Decimal\nArithmetic specification \u003ca href=\"#id20\" id=\"user-content-id3\"\u003e[2]\u003c/a\u003e. This document defines a general\npurpose decimal arithmetic. A correct implementation of this\nspecification will conform to the decimal arithmetic defined in\nANSI/IEEE standard 854-1987, except for some minor restrictions, and\nwill also provide unrounded decimal arithmetic and integer arithmetic\nas proper subsets.\u003c/p\u003e\n\u003ca name=\"user-content-the-problem-with-binary-float\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThe problem with binary float\u003c/h3\u003e\u003ca id=\"user-content-the-problem-with-binary-float\" class=\"anchor\" aria-label=\"Permalink: The problem with binary float\" href=\"#the-problem-with-binary-float\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn decimal math, there are many numbers that can't be represented with\na fixed number of decimal digits, e.g. 1/3 = 0.3333333333.......\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIn base 2 (the way that standard floating point is calculated), 1/2 =\n0.1, 1/4 = 0.01, 1/8 = 0.001, etc. Decimal 0.2 equals 2/10 equals\n1/5, resulting in the binary fractional number\n0.001100110011001... As you can see, the problem is that some decimal\nnumbers can't be represented exactly in binary, resulting in small\nroundoff errors.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSo we need a decimal data type that represents exactly decimal\nnumbers. Instead of a binary data type, we need a decimal one.\u003c/p\u003e\n\u003ca name=\"user-content-why-floating-point\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eWhy floating point?\u003c/h3\u003e\u003ca id=\"user-content-why-floating-point\" class=\"anchor\" aria-label=\"Permalink: Why floating point?\" href=\"#why-floating-point\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eSo we go to decimal, but why \u003cem\u003efloating point\u003c/em\u003e?\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFloating point numbers use a fixed quantity of digits (precision) to\nrepresent a number, working with an exponent when the number gets too\nbig or too small. For example, with a precision of 5:\u003c/p\u003e\n\u003cpre\u003e 1234 ==\u0026gt; 1234e0\n 12345 ==\u0026gt; 12345e0\n123456 ==\u0026gt; 12346e1\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003e(note that in the last line the number got rounded to fit in five digits).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIn contrast, we have the example of a \u003ccode\u003elong\u003c/code\u003e integer with infinite\nprecision, meaning that you can have the number as big as you want,\nand you'll never lose any information.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIn a fixed point number, the position of the decimal point is fixed.\nFor a fixed point data type, check Tim Peter's FixedPoint at\nSourceForge \u003ca href=\"#id22\" id=\"user-content-id4\"\u003e[4]\u003c/a\u003e. I'll go for floating point because it's easier to\nimplement the arithmetic behaviour of the standard, and then you can\nimplement a fixed point data type over Decimal.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBut why can't we have a floating point number with infinite precision?\nIt's not so easy, because of inexact divisions. E.g.: 1/3 =\n0.3333333333333... ad infinitum. In this case you should store an\ninfinite amount of 3s, which takes too much memory, ;).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eJohn Roth proposed to eliminate the division operator and force the\nuser to use an explicit method, just to avoid this kind of trouble.\nThis generated adverse reactions in comp.lang.python, as everybody\nwants to have support for the \u003ccode\u003e/\u003c/code\u003e operator in a numeric data type.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWith this exposed maybe you're thinking \"Hey! Can we just store the 1\nand the 3 as numerator and denominator?\", which takes us to the next\npoint.\u003c/p\u003e\n\u003ca name=\"user-content-why-not-rational\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eWhy not rational?\u003c/h3\u003e\u003ca id=\"user-content-why-not-rational\" class=\"anchor\" aria-label=\"Permalink: Why not rational?\" href=\"#why-not-rational\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eRational numbers are stored using two integer numbers, the numerator\nand the denominator. This implies that the arithmetic operations\ncan't be executed directly (e.g. to add two rational numbers you first\nneed to calculate the common denominator).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eQuoting Alex Martelli:\u003c/p\u003e\n\u003cblockquote\u003e\nThe performance implications of the fact that summing two\nrationals (which take O(M) and O(N) space respectively) gives a\nrational which takes O(M+N) memory space is just too troublesome.\nThere are excellent Rational implementations in both pure Python\nand as extensions (e.g., gmpy), but they'll always be a \"niche\nmarket\" IMHO. Probably worth PEPping, not worth doing without\nDecimal -- which is the right way to represent sums of money, a\ntruly major use case in the real world.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eAnyway, if you're interested in this data type, you maybe will want to\ntake a look at \u003ca href=\"http://www.python.org/dev/peps/pep-0239\" rel=\"nofollow\"\u003ePEP 239\u003c/a\u003e: Adding a Rational Type to Python.\u003c/p\u003e\n\u003ca name=\"user-content-so-what-do-we-have\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eSo, what do we have?\u003c/h3\u003e\u003ca id=\"user-content-so-what-do-we-have\" class=\"anchor\" aria-label=\"Permalink: So, what do we have?\" href=\"#so-what-do-we-have\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe result is a Decimal data type, with bounded precision and floating\npoint.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWill it be useful? I can't say it better than Alex Martelli:\u003c/p\u003e\n\u003cblockquote\u003e\nPython (out of the box) doesn't let you have binary floating point\nnumbers \u003cem\u003ewith whatever precision you specify\u003c/em\u003e: you're limited to\nwhat your hardware supplies. Decimal, be it used as a fixed or\nfloating point number, should suffer from no such limitation:\nwhatever bounded precision you may specify on number creation\n(your memory permitting) should work just as well. Most of the\nexpense of programming simplicity can be hidden from application\nprograms and placed in a suitable decimal arithmetic type. As per\n\u003ca href=\"http://speleotrove.com/decimal/\" rel=\"nofollow\"\u003ehttp://speleotrove.com/decimal/\u003c/a\u003e, \u003cem\u003ea single data type can be\nused for integer, fixed-point, and floating-point decimal\narithmetic\u003c/em\u003e -- and for money arithmetic which doesn't drive the\napplication programmer crazy.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eThere are several uses for such a data type. As I said before, I will\nuse it as base for Money. In this case the bounded precision is not\nan issue; quoting Tim Peters:\u003c/p\u003e\n\u003cblockquote\u003e\nA precision of 20 would be way more than enough to account for\ntotal world economic output, down to the penny, since the\nbeginning of time.\u003c/blockquote\u003e\n\u003ca name=\"user-content-general-decimal-arithmetic-specification\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eGeneral Decimal Arithmetic Specification\u003c/h2\u003e\u003ca id=\"user-content-general-decimal-arithmetic-specification\" class=\"anchor\" aria-label=\"Permalink: General Decimal Arithmetic Specification\" href=\"#general-decimal-arithmetic-specification\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eHere I'll include information and descriptions that are part of the\nspecification \u003ca href=\"#id20\" id=\"user-content-id5\"\u003e[2]\u003c/a\u003e (the structure of the number, the context, etc.).\nAll the requirements included in this section are not for discussion\n(barring typos or other mistakes), as they are in the standard, and\nthe PEP is just for implementing the standard.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBecause of copyright restrictions, I can not copy here explanations\ntaken from the specification, so I'll try to explain it in my own\nwords. I firmly encourage you to read the original specification\ndocument \u003ca href=\"#id20\" id=\"user-content-id6\"\u003e[2]\u003c/a\u003e for details or if you have any doubt.\u003c/p\u003e\n\u003ca name=\"user-content-the-arithmetic-model\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eThe Arithmetic Model\u003c/h3\u003e\u003ca id=\"user-content-the-arithmetic-model\" class=\"anchor\" aria-label=\"Permalink: The Arithmetic Model\" href=\"#the-arithmetic-model\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe specification is based on a decimal arithmetic model, as defined\nby the relevant standards: IEEE 854 \u003ca href=\"#id21\" id=\"user-content-id7\"\u003e[3]\u003c/a\u003e, ANSI X3-274 \u003ca href=\"#id19\" id=\"user-content-id8\"\u003e[1]\u003c/a\u003e, and the\nproposed revision \u003ca href=\"#id23\" id=\"user-content-id9\"\u003e[5]\u003c/a\u003e of IEEE 754 \u003ca href=\"#id24\" id=\"user-content-id10\"\u003e[6]\u003c/a\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe model has three components:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eNumbers: just the values that the operation uses as input or output.\u003c/li\u003e\n\u003cli\u003eOperations: addition, multiplication, etc.\u003c/li\u003e\n\u003cli\u003eContext: a set of parameters and rules that the user can select and\nwhich govern the results of operations (for example, the precision\nto be used).\u003c/li\u003e\n\u003c/ul\u003e\n\u003ca name=\"user-content-numbers\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eNumbers\u003c/h3\u003e\u003ca id=\"user-content-numbers\" class=\"anchor\" aria-label=\"Permalink: Numbers\" href=\"#numbers\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eNumbers may be finite or special values. The former can be\nrepresented exactly. The latter are infinites and undefined (such as\n0/0).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFinite numbers are defined by three parameters:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eSign: 0 (positive) or 1 (negative).\u003c/li\u003e\n\u003cli\u003eCoefficient: a non-negative integer.\u003c/li\u003e\n\u003cli\u003eExponent: a signed integer, the power of ten of the coefficient\nmultiplier.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eThe numerical value of a finite number is given by:\u003c/p\u003e\n\u003cpre\u003e(-1)**sign * coefficient * 10**exponent\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eSpecial values are named as following:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eInfinity: a value which is infinitely large. Could be positive or\nnegative.\u003c/li\u003e\n\u003cli\u003eQuiet NaN (\"qNaN\"): represent undefined results (\u003cem\u003eNot a Number\u003c/em\u003e).\nDoes not cause an Invalid operation condition. The sign in a NaN\nhas no meaning.\u003c/li\u003e\n\u003cli\u003eSignaling NaN (\"sNaN\"): also \u003cem\u003eNot a Number\u003c/em\u003e, but will cause an\nInvalid operation condition if used in any operation.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ca name=\"user-content-context\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eContext\u003c/h3\u003e\u003ca id=\"user-content-context\" class=\"anchor\" aria-label=\"Permalink: Context\" href=\"#context\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe context is a set of parameters and rules that the user can select\nand which govern the results of operations (for example, the precision\nto be used).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe context gets that name because it surrounds the Decimal numbers,\nwith parts of context acting as input to, and output of, operations.\nIt's up to the application to work with one or several contexts,\nbut definitely the idea is not to get a context per Decimal number.\nFor example, a typical use would be to set the context's precision to\n20 digits at the start of a program, and never explicitly use context\nagain.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThese definitions don't affect the internal storage of the Decimal\nnumbers, just the way that the arithmetic operations are performed.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe context is mainly defined by the following parameters (see\n\u003ca href=\"#context-attributes\"\u003eContext Attributes\u003c/a\u003e for all context attributes):\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003ePrecision: The maximum number of significant digits that can result\nfrom an arithmetic operation (integer \u0026gt; 0). There is no maximum for\nthis value.\u003c/li\u003e\n\u003cli\u003eRounding: The name of the algorithm to be used when rounding is\nnecessary, one of \"round-down\", \"round-half-up\", \"round-half-even\",\n\"round-ceiling\", \"round-floor\", \"round-half-down\", and \"round-up\".\nSee \u003ca href=\"#rounding-algorithms\"\u003eRounding Algorithms\u003c/a\u003e below.\u003c/li\u003e\n\u003cli\u003eFlags and trap-enablers: \u003ca href=\"#exceptional-conditions\"\u003eExceptional conditions\u003c/a\u003e are grouped into\nsignals, controllable individually, each consisting of a flag\n(boolean, set when the signal occurs) and a trap-enabler (a boolean\nthat controls behavior). The signals are: \"clamped\",\n\"division-by-zero\", \"inexact\", \"invalid-operation\", \"overflow\",\n\"rounded\", \"subnormal\" and \"underflow\".\u003c/li\u003e\n\u003c/ul\u003e\n\u003ca name=\"user-content-default-contexts\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDefault Contexts\u003c/h3\u003e\u003ca id=\"user-content-default-contexts\" class=\"anchor\" aria-label=\"Permalink: Default Contexts\" href=\"#default-contexts\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe specification defines two default contexts, which should be easily\nselectable by the user.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBasic Default Context:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eflags: all set to 0\u003c/li\u003e\n\u003cli\u003etrap-enablers: inexact, rounded, and subnormal are set to 0; all\nothers are set to 1\u003c/li\u003e\n\u003cli\u003eprecision: is set to 9\u003c/li\u003e\n\u003cli\u003erounding: is set to round-half-up\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eExtended Default Context:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eflags: all set to 0\u003c/li\u003e\n\u003cli\u003etrap-enablers: all set to 0\u003c/li\u003e\n\u003cli\u003eprecision: is set to 9\u003c/li\u003e\n\u003cli\u003erounding: is set to round-half-even\u003c/li\u003e\n\u003c/ul\u003e\n\u003ca name=\"user-content-exceptional-conditions\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eExceptional Conditions\u003c/h3\u003e\u003ca id=\"user-content-exceptional-conditions\" class=\"anchor\" aria-label=\"Permalink: Exceptional Conditions\" href=\"#exceptional-conditions\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe table below lists the exceptional conditions that may arise during\nthe arithmetic operations, the corresponding signal, and the defined\nresult. For details, see the specification \u003ca href=\"#id20\" id=\"user-content-id11\"\u003e[2]\u003c/a\u003e.\u003c/p\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable\u003e\n\n\n\n\n\n\u003cthead valign=\"bottom\"\u003e\n\u003ctr\u003e\u003cth\u003eCondition\u003c/th\u003e\n\u003cth\u003eSignal\u003c/th\u003e\n\u003cth\u003eResult\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003eClamped\u003c/td\u003e\n\u003ctd\u003eclamped\u003c/td\u003e\n\u003ctd\u003esee spec \u003ca href=\"#id20\" id=\"user-content-id12\"\u003e[2]\u003c/a\u003e\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\u003ctd\u003eDivision by zero\u003c/td\u003e\n\u003ctd\u003edivision-by-zero\u003c/td\u003e\n\u003ctd\u003e[sign,inf]\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\u003ctd\u003eInexact\u003c/td\u003e\n\u003ctd\u003einexact\u003c/td\u003e\n\u003ctd\u003eunchanged\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\u003ctd\u003eInvalid operation\u003c/td\u003e\n\u003ctd\u003einvalid-operation\u003c/td\u003e\n\u003ctd\u003e[0,qNaN] (or [s,qNaN] or [s,qNaN,d]\nwhen the cause is a signaling NaN)\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\u003ctd\u003eOverflow\u003c/td\u003e\n\u003ctd\u003eoverflow\u003c/td\u003e\n\u003ctd\u003edepends on the rounding mode\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\u003ctd\u003eRounded\u003c/td\u003e\n\u003ctd\u003erounded\u003c/td\u003e\n\u003ctd\u003eunchanged\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\u003ctd\u003eSubnormal\u003c/td\u003e\n\u003ctd\u003esubnormal\u003c/td\u003e\n\u003ctd\u003eunchanged\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\u003ctd\u003eUnderflow\u003c/td\u003e\n\u003ctd\u003eunderflow\u003c/td\u003e\n\u003ctd\u003esee spec \u003ca href=\"#id20\" id=\"user-content-id13\"\u003e[2]\u003c/a\u003e\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cp dir=\"auto\"\u003eNote: when the standard talks about \"Insufficient storage\", as long as\nthis is implementation-specific behaviour about not having enough\nstorage to keep the internals of the number, this implementation will\nraise MemoryError.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eRegarding Overflow and Underflow, there's been a long discussion in\npython-dev about artificial limits. The general consensus is to keep\nthe artificial limits only if there are important reasons to do that.\nTim Peters gives us three:\u003c/p\u003e\n\u003cblockquote\u003e\n\u003cp dir=\"auto\"\u003e...eliminating bounds on exponents effectively means overflow\n(and underflow) can never happen. But overflow \u003cem\u003eis\u003c/em\u003e a valuable\nsafety net in real life fp use, like a canary in a coal mine,\ngiving danger signs early when a program goes insane.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eVirtually all implementations of 854 use (and as IBM's standard\neven suggests) \"forbidden\" exponent values to encode non-finite\nnumbers (infinities and NaNs). A bounded exponent can do this at\nvirtually no extra storage cost. If the exponent is unbounded,\nthen additional bits have to be used instead. This cost remains\nhidden until more time- and space- efficient implementations are\nattempted.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBig as it is, the IBM standard is a tiny start at supplying a\ncomplete numeric facility. Having no bound on exponent size will\nenormously complicate the implementations of, e.g., decimal sin()\nand cos() (there's then no a priori limit on how many digits of\npi effectively need to be known in order to perform argument\nreduction).\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eEdward Loper give us an example of when the limits are to be crossed:\nprobabilities.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThat said, Robert Brewer and Andrew Lentvorski want the limits to be\neasily modifiable by the users. Actually, this is quite possible:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d1 = Decimal(\"1e999999999\") # at the exponent limit\n\u0026gt;\u0026gt;\u0026gt; d1\nDecimal(\"1E+999999999\")\n\u0026gt;\u0026gt;\u0026gt; d1 * 10 # exceed the limit, got infinity\nTraceback (most recent call last):\n File \"\u0026lt;pyshell#3\u0026gt;\", line 1, in ?\n d1 * 10\n ...\n ...\nOverflow: above Emax\n\u0026gt;\u0026gt;\u0026gt; getcontext().Emax = 1000000000 # increase the limit\n\u0026gt;\u0026gt;\u0026gt; d1 * 10 # does not exceed any more\nDecimal(\"1.0E+1000000000\")\n\u0026gt;\u0026gt;\u0026gt; d1 * 100 # exceed again\nTraceback (most recent call last):\n File \"\u0026lt;pyshell#3\u0026gt;\", line 1, in ?\n d1 * 100\n ...\n ...\nOverflow: above Emax\n\u003c/pre\u003e\n\u003ca name=\"user-content-rounding-algorithms\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRounding Algorithms\u003c/h3\u003e\u003ca id=\"user-content-rounding-algorithms\" class=\"anchor\" aria-label=\"Permalink: Rounding Algorithms\" href=\"#rounding-algorithms\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eround-down\u003c/code\u003e: The discarded digits are ignored; the result is\nunchanged (round toward 0, truncate):\u003c/p\u003e\n\u003cpre\u003e1.123 --\u0026gt; 1.12\n1.128 --\u0026gt; 1.12\n1.125 --\u0026gt; 1.12\n1.135 --\u0026gt; 1.13\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eround-half-up\u003c/code\u003e: If the discarded digits represent greater than or\nequal to half (0.5) then the result should be incremented by 1;\notherwise the discarded digits are ignored:\u003c/p\u003e\n\u003cpre\u003e1.123 --\u0026gt; 1.12\n1.128 --\u0026gt; 1.13\n1.125 --\u0026gt; 1.13\n1.135 --\u0026gt; 1.14\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eround-half-even\u003c/code\u003e: If the discarded digits represent greater than\nhalf (0.5) then the result coefficient is incremented by 1; if they\nrepresent less than half, then the result is not adjusted; otherwise\nthe result is unaltered if its rightmost digit is even, or incremented\nby 1 if its rightmost digit is odd (to make an even digit):\u003c/p\u003e\n\u003cpre\u003e1.123 --\u0026gt; 1.12\n1.128 --\u0026gt; 1.13\n1.125 --\u0026gt; 1.12\n1.135 --\u0026gt; 1.14\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eround-ceiling\u003c/code\u003e: If all of the discarded digits are zero or if the\nsign is negative the result is unchanged; otherwise, the result is\nincremented by 1 (round toward positive infinity):\u003c/p\u003e\n\u003cpre\u003e 1.123 --\u0026gt; 1.13\n 1.128 --\u0026gt; 1.13\n-1.123 --\u0026gt; -1.12\n-1.128 --\u0026gt; -1.12\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eround-floor\u003c/code\u003e: If all of the discarded digits are zero or if the\nsign is positive the result is unchanged; otherwise, the absolute\nvalue of the result is incremented by 1 (round toward negative\ninfinity):\u003c/p\u003e\n\u003cpre\u003e 1.123 --\u0026gt; 1.12\n 1.128 --\u0026gt; 1.12\n-1.123 --\u0026gt; -1.13\n-1.128 --\u0026gt; -1.13\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eround-half-down\u003c/code\u003e: If the discarded digits represent greater than\nhalf (0.5) then the result is incremented by 1; otherwise the\ndiscarded digits are ignored:\u003c/p\u003e\n\u003cpre\u003e1.123 --\u0026gt; 1.12\n1.128 --\u0026gt; 1.13\n1.125 --\u0026gt; 1.12\n1.135 --\u0026gt; 1.13\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003e\u003ccode\u003eround-up\u003c/code\u003e: If all of the discarded digits are zero the result is\nunchanged, otherwise the result is incremented by 1 (round away from\n0):\u003c/p\u003e\n\u003cpre\u003e1.123 --\u0026gt; 1.13\n1.128 --\u0026gt; 1.13\n1.125 --\u0026gt; 1.13\n1.135 --\u0026gt; 1.14\n\u003c/pre\u003e\n\u003ca name=\"user-content-rationale\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRationale\u003c/h2\u003e\u003ca id=\"user-content-rationale\" class=\"anchor\" aria-label=\"Permalink: Rationale\" href=\"#rationale\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eI must separate the requirements in two sections. The first is to\ncomply with the ANSI standard. All the requirements for this are\nspecified in the Mike Cowlishaw's work \u003ca href=\"#id20\" id=\"user-content-id14\"\u003e[2]\u003c/a\u003e. He also provided a\n\u003cstrong\u003every large\u003c/strong\u003e suite of test cases.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe second section of requirements (standard Python functions support,\nusability, etc.) is detailed from here, where I'll include all the\ndecisions made and why, and all the subjects still being discussed.\u003c/p\u003e\n\u003ca name=\"user-content-explicit-construction\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eExplicit construction\u003c/h3\u003e\u003ca id=\"user-content-explicit-construction\" class=\"anchor\" aria-label=\"Permalink: Explicit construction\" href=\"#explicit-construction\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe explicit construction does not get affected by the context (there\nis no rounding, no limits by the precision, etc.), because the context\naffects just operations' results. The only exception to this is when\nyou're \u003ca href=\"#creating-from-context\"\u003eCreating from Context\u003c/a\u003e.\u003c/p\u003e\n\u003ca name=\"user-content-from-int-or-long\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom int or long\u003c/h4\u003e\u003ca id=\"user-content-from-int-or-long\" class=\"anchor\" aria-label=\"Permalink: From int or long\" href=\"#from-int-or-long\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThere's no loss and no need to specify any other information:\u003c/p\u003e\n\u003cpre\u003eDecimal(35)\nDecimal(-124)\n\u003c/pre\u003e\n\u003ca name=\"user-content-from-string\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom string\u003c/h4\u003e\u003ca id=\"user-content-from-string\" class=\"anchor\" aria-label=\"Permalink: From string\" href=\"#from-string\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eStrings containing Python decimal integer literals and Python float\nliterals will be supported. In this transformation there is no loss\nof information, as the string is directly converted to Decimal (there\nis not an intermediate conversion through float):\u003c/p\u003e\n\u003cpre\u003eDecimal(\"-12\")\nDecimal(\"23.2e-7\")\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eAlso, you can construct in this way all special values (Infinity and\nNot a Number):\u003c/p\u003e\n\u003cpre\u003eDecimal(\"Inf\")\nDecimal(\"NaN\")\n\u003c/pre\u003e\n\u003ca name=\"user-content-from-float\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom float\u003c/h4\u003e\u003ca id=\"user-content-from-float\" class=\"anchor\" aria-label=\"Permalink: From float\" href=\"#from-float\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe initial discussion on this item was what should\nhappen when passing floating point to the constructor:\u003c/p\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003e\u003ccode\u003eDecimal(1.1) == Decimal('1.1')\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003e\u003ccode\u003eDecimal(1.1) ==\nDecimal('110000000000000008881784197001252...e-51')\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003ean exception is raised\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp dir=\"auto\"\u003eSeveral people alleged that (1) is the better option here, because\nit's what you expect when writing \u003ccode\u003eDecimal(1.1)\u003c/code\u003e. And quoting John\nRoth, it's easy to implement:\u003c/p\u003e\n\u003cblockquote\u003e\nIt's not at all difficult to find where the actual number ends and\nwhere the fuzz begins. You can do it visually, and the algorithms\nto do it are quite well known.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eBut If I \u003cem\u003ereally\u003c/em\u003e want my number to be\n\u003ccode\u003eDecimal('110000000000000008881784197001252...e-51')\u003c/code\u003e, why can't I\nwrite \u003ccode\u003eDecimal(1.1)\u003c/code\u003e? Why should I expect Decimal to be \"rounding\"\nit? Remember that \u003ccode\u003e1.1\u003c/code\u003e \u003cem\u003eis\u003c/em\u003e binary floating point, so I can\npredict the result. It's not intuitive to a beginner, but that's the\nway it is.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAnyway, Paul Moore showed that (1) can't work, because:\u003c/p\u003e\n\u003cpre\u003e(1) says D(1.1) == D('1.1')\nbut 1.1 == 1.1000000000000001\nso D(1.1) == D(1.1000000000000001)\ntogether: D(1.1000000000000001) == D('1.1')\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003ewhich is wrong, because if I write \u003ccode\u003eDecimal('1.1')\u003c/code\u003e it is exact, not\n\u003ccode\u003eD(1.1000000000000001)\u003c/code\u003e. He also proposed to have an explicit\nconversion to float. bokr says you need to put the precision in the\nconstructor and mwilson agreed:\u003c/p\u003e\n\u003cpre\u003ed = Decimal (1.1, 1) # take float value to 1 decimal place\nd = Decimal (1.1) # gets `places` from pre-set context\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eBut Alex Martelli says that:\u003c/p\u003e\n\u003cblockquote\u003e\nConstructing with some specified precision would be fine. Thus,\nI think \"construction from float with some default precision\" runs\na substantial risk of tricking naive users.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eSo, the accepted solution through c.l.p is that you can not call Decimal\nwith a float. Instead you must use a method: Decimal.from_float(). The\nsyntax:\u003c/p\u003e\n\u003cpre\u003eDecimal.from_float(floatNumber, [decimal_places])\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003ewhere \u003ccode\u003efloatNumber\u003c/code\u003e is the float number origin of the construction\nand \u003ccode\u003edecimal_places\u003c/code\u003e are the number of digits after the decimal\npoint where you apply a round-half-up rounding, if any. In this way\nyou can do, for example:\u003c/p\u003e\n\u003cpre\u003eDecimal.from_float(1.1, 2): The same as doing Decimal('1.1').\nDecimal.from_float(1.1, 16): The same as doing Decimal('1.1000000000000001').\nDecimal.from_float(1.1): The same as doing Decimal('1100000000000000088817841970012523233890533447265625e-51').\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eBased on later discussions, it was decided to omit from_float() from the\nAPI for Py2.4. Several ideas contributed to the thought process:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eInteractions between decimal and binary floating point force the user to\ndeal with tricky issues of representation and round-off. Avoidance of those\nissues is a primary reason for having the module in the first place.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eThe first release of the module should focus on that which is safe, minimal,\nand essential.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eWhile theoretically nice, real world use cases for interactions between floats\nand decimals are lacking. Java included float/decimal conversions to handle\nan obscure case where calculations are best performed in decimal even though\na legacy data structure requires the inputs and outputs to be stored in\nbinary floating point.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eIf the need arises, users can use string representations as an intermediate\ntype. The advantage of this approach is that it makes explicit the\nassumptions about precision and representation (no wondering what is going\non under the hood).\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eThe Java docs for BigDecimal(double val) reflected their experiences with\nthe constructor:\u003c/p\u003e\n\u003cpre\u003eThe results of this constructor can be somewhat\nunpredictable and its use is generally not recommended.\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003ca name=\"user-content-from-tuples\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom tuples\u003c/h4\u003e\u003ca id=\"user-content-from-tuples\" class=\"anchor\" aria-label=\"Permalink: From tuples\" href=\"#from-tuples\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAahz suggested to construct from tuples: it's easier\nto implement \u003ccode\u003eeval()\u003c/code\u003e's round trip and \"someone who has numeric\nvalues representing a Decimal does not need to convert them to a\nstring.\"\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe structure will be a tuple of three elements: sign, number and\nexponent. The sign is 1 or 0, the number is a tuple of decimal digits\nand the exponent is a signed int or long:\u003c/p\u003e\n\u003cpre\u003eDecimal((1, (3, 2, 2, 5), -2)) # for -32.25\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eOf course, you can construct in this way all special values:\u003c/p\u003e\n\u003cpre\u003eDecimal( (0, (0,), 'F') ) # for Infinity\nDecimal( (0, (0,), 'n') ) # for Not a Number\n\u003c/pre\u003e\n\u003ca name=\"user-content-from-decimal\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom Decimal\u003c/h4\u003e\u003ca id=\"user-content-from-decimal\" class=\"anchor\" aria-label=\"Permalink: From Decimal\" href=\"#from-decimal\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eNo mystery here, just a copy.\u003c/p\u003e\n\u003ca name=\"user-content-syntax-for-all-cases\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eSyntax for All Cases\u003c/h4\u003e\u003ca id=\"user-content-syntax-for-all-cases\" class=\"anchor\" aria-label=\"Permalink: Syntax for All Cases\" href=\"#syntax-for-all-cases\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cpre\u003eDecimal(value1)\nDecimal.from_float(value2, [decimal_places])\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003ewhere \u003ccode\u003evalue1\u003c/code\u003e can be int, long, string, 3-tuple or Decimal,\n\u003ccode\u003evalue2\u003c/code\u003e can only be float, and \u003ccode\u003edecimal_places\u003c/code\u003e is an optional\nnon negative int.\u003c/p\u003e\n\u003ca name=\"user-content-creating-from-context\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eCreating from Context\u003c/h4\u003e\u003ca id=\"user-content-creating-from-context\" class=\"anchor\" aria-label=\"Permalink: Creating from Context\" href=\"#creating-from-context\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis item arose in python-dev from two sources in parallel. Ka-Ping\nYee proposes to pass the context as an argument at instance creation\n(he wants the context he passes to be used only in creation time: \"It\nwould not be persistent\"). Tony Meyer asks from_string to honor the\ncontext if it receives a parameter \"honour_context\" with a True value.\n(I don't like it, because the doc specifies that the context be\nhonored and I don't want the method to comply with the specification\nregarding the value of an argument.)\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTim Peters gives us a reason to have a creation that uses context:\u003c/p\u003e\n\u003cblockquote\u003e\nIn general number-crunching, literals may be given to high\nprecision, but that precision isn't free and \u003cem\u003eusually\u003c/em\u003e isn't\nneeded\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eCasey Duncan wants to use another method, not a bool arg:\u003c/p\u003e\n\u003cblockquote\u003e\nI find boolean arguments a general anti-pattern, especially given\nwe have class methods. Why not use an alternate constructor like\nDecimal.rounded_to_context(\"3.14159265\").\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eIn the process of deciding the syntax of that, Tim came up with a\nbetter idea: he proposes not to have a method in Decimal to create\nwith a different context, but having instead a method in Context to\ncreate a Decimal instance. Basically, instead of:\u003c/p\u003e\n\u003cpre\u003eD.using_context(number, context)\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eit will be:\u003c/p\u003e\n\u003cpre\u003econtext.create_decimal(number)\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eFrom Tim:\u003c/p\u003e\n\u003cblockquote\u003e\nWhile all operations in the spec except for the two to-string\noperations use context, no operations in the spec support an\noptional local context. That the Decimal() constructor ignores\ncontext by default is an extension to the spec. We must supply a\ncontext-honoring from-string operation to meet the spec. I\nrecommend against any concept of \"local context\" in any operation\n-- it complicates the model and isn't necessary.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eSo, we decided to use a context method to create a Decimal that will\nuse (only to be created) that context in particular (for further\noperations it will use the context of the thread). But, a method with\nwhat name?\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTim Peters proposes three methods to create from diverse sources\n(from_string, from_int, from_float). I proposed to use one method,\n\u003ccode\u003ecreate_decimal()\u003c/code\u003e, without caring about the data type. Michael\nChermside: \"The name just fits my brain. The fact that it uses the\ncontext is obvious from the fact that it's Context method\".\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe community agreed with that. I think that it's OK because a newbie\nwill not be using the creation method from Context (the separate\nmethod in Decimal to construct from float is just to prevent newbies\nfrom encountering binary floating point issues).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSo, in short, if you want to create a Decimal instance using a\nparticular context (that will be used just at creation time and not\nany further), you'll have to use a method of that context:\u003c/p\u003e\n\u003cpre\u003e# n is any datatype accepted in Decimal(n) plus float\nmycontext.create_decimal(n)\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eExample:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; # create a standard decimal instance\n\u0026gt;\u0026gt;\u0026gt; Decimal(\"11.2233445566778899\")\nDecimal(\"11.2233445566778899\")\n\u0026gt;\u0026gt;\u0026gt;\n\u0026gt;\u0026gt;\u0026gt; # create a decimal instance using the thread context\n\u0026gt;\u0026gt;\u0026gt; thread_context = getcontext()\n\u0026gt;\u0026gt;\u0026gt; thread_context.prec\n28\n\u0026gt;\u0026gt;\u0026gt; thread_context.create_decimal(\"11.2233445566778899\")\nDecimal(\"11.2233445566778899\")\n\u0026gt;\u0026gt;\u0026gt;\n\u0026gt;\u0026gt;\u0026gt; # create a decimal instance using other context\n\u0026gt;\u0026gt;\u0026gt; other_context = thread_context.copy()\n\u0026gt;\u0026gt;\u0026gt; other_context.prec = 4\n\u0026gt;\u0026gt;\u0026gt; other_context.create_decimal(\"11.2233445566778899\")\nDecimal(\"11.22\")\n\u003c/pre\u003e\n\u003ca name=\"user-content-implicit-construction\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eImplicit construction\u003c/h3\u003e\u003ca id=\"user-content-implicit-construction\" class=\"anchor\" aria-label=\"Permalink: Implicit construction\" href=\"#implicit-construction\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAs the implicit construction is the consequence of an operation, it\nwill be affected by the context as is detailed in each point.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eJohn Roth suggested that \"The other type should be handled in the same\nway the decimal() constructor would handle it\". But Alex Martelli\nthinks that\u003c/p\u003e\n\u003cblockquote\u003e\nthis total breach with Python tradition would be a terrible\nmistake. 23+\"43\" is NOT handled in the same way as 23+int(\"45\"),\nand a VERY good thing that is too. It's a completely different\nthing for a user to EXPLICITLY indicate they want construction\n(conversion) and to just happen to sum two objects one of which by\nmistake could be a string.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eSo, here I define the behaviour again for each data type.\u003c/p\u003e\n\u003ca name=\"user-content-id15\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom int or long\u003c/h4\u003e\u003ca id=\"user-content-from-int-or-long-1\" class=\"anchor\" aria-label=\"Permalink: From int or long\" href=\"#from-int-or-long-1\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAn int or long is a treated like a Decimal explicitly constructed from\nDecimal(str(x)) in the current context (meaning that the to-string rules\nfor rounding are applied and the appropriate flags are set). This\nguarantees that expressions like \u003ccode\u003eDecimal('1234567') + 13579\u003c/code\u003e match\nthe mental model of \u003ccode\u003eDecimal('1234567') + Decimal('13579')\u003c/code\u003e. That\nmodel works because all integers are representable as strings without\nrepresentation error.\u003c/p\u003e\n\u003ca name=\"user-content-id16\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom string\u003c/h4\u003e\u003ca id=\"user-content-from-string-1\" class=\"anchor\" aria-label=\"Permalink: From string\" href=\"#from-string-1\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eEverybody agrees to raise an exception here.\u003c/p\u003e\n\u003ca name=\"user-content-id17\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom float\u003c/h4\u003e\u003ca id=\"user-content-from-float-1\" class=\"anchor\" aria-label=\"Permalink: From float\" href=\"#from-float-1\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAahz is strongly opposed to interact with float, suggesting an\nexplicit conversion:\u003c/p\u003e\n\u003cblockquote\u003e\nThe problem is that Decimal is capable of greater precision,\naccuracy, and range than float.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eThe example of the valid python expression, \u003ccode\u003e35 + 1.1\u003c/code\u003e, seems to suggest\nthat \u003ccode\u003eDecimal(35) + 1.1\u003c/code\u003e should also be valid. However, a closer look\nshows that it only demonstrates the feasibility of integer to floating\npoint conversions. Hence, the correct analog for decimal floating point\nis \u003ccode\u003e35 + Decimal(1.1)\u003c/code\u003e. Both coercions, int-to-float and int-to-Decimal,\ncan be done without incurring representation error.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe question of how to coerce between binary and decimal floating point\nis more complex. I proposed allowing the interaction with float,\nmaking an exact conversion and raising ValueError if exceeds the\nprecision in the current context (this is maybe too tricky, because\nfor example with a precision of 9, \u003ccode\u003eDecimal(35) + 1.2\u003c/code\u003e is OK but\n\u003ccode\u003eDecimal(35) + 1.1\u003c/code\u003e raises an error).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThis resulted to be too tricky. So tricky, that c.l.p agreed to raise\nTypeError in this case: you could not mix Decimal and float.\u003c/p\u003e\n\u003ca name=\"user-content-id18\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eFrom Decimal\u003c/h4\u003e\u003ca id=\"user-content-from-decimal-1\" class=\"anchor\" aria-label=\"Permalink: From Decimal\" href=\"#from-decimal-1\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThere isn't any issue here.\u003c/p\u003e\n\u003ca name=\"user-content-use-of-context\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUse of Context\u003c/h3\u003e\u003ca id=\"user-content-use-of-context\" class=\"anchor\" aria-label=\"Permalink: Use of Context\" href=\"#use-of-context\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn the last pre-PEP I said that \"The Context must be omnipresent,\nmeaning that changes to it affects all the current and future Decimal\ninstances\". I was wrong. In response, John Roth said:\u003c/p\u003e\n\u003cblockquote\u003e\nThe context should be selectable for the particular usage. That\nis, it should be possible to have several different contexts in\nplay at one time in an application.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eIn comp.lang.python, Aahz explained that the idea is to have a\n\"context per thread\". So, all the instances of a thread belongs to a\ncontext, and you can change a context in thread A (and the behaviour\nof the instances of that thread) without changing nothing in thread B.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAlso, and again correcting me, he said:\u003c/p\u003e\n\u003cblockquote\u003e\n(the) Context applies only to operations, not to Decimal\ninstances; changing the Context does not affect existing instances\nif there are no operations on them.\u003c/blockquote\u003e\n\u003cp dir=\"auto\"\u003eArguing about special cases when there's need to perform operations\nwith other rules that those of the current context, Tim Peters said\nthat the context will have the operations as methods. This way, the\nuser \"can create whatever private context object(s) it needs, and\nspell arithmetic as explicit method calls on its private context\nobject(s), so that the default thread context object is neither\nconsulted nor modified\".\u003c/p\u003e\n\u003ca name=\"user-content-python-usability\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003ePython Usability\u003c/h3\u003e\u003ca id=\"user-content-python-usability\" class=\"anchor\" aria-label=\"Permalink: Python Usability\" href=\"#python-usability\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eDecimal should support the basic arithmetic (\u003ccode\u003e+, -, *, /, //, **,\n%, divmod\u003c/code\u003e) and comparison (\u003ccode\u003e==, !=, \u0026lt;, \u0026gt;, \u0026lt;=, \u0026gt;=, cmp\u003c/code\u003e)\noperators in the following cases (check \u003ca href=\"#implicit-construction\"\u003eImplicit Construction\u003c/a\u003e to\nsee what types could OtherType be, and what happens in each case):\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eDecimal op Decimal\u003c/li\u003e\n\u003cli\u003eDecimal op otherType\u003c/li\u003e\n\u003cli\u003eotherType op Decimal\u003c/li\u003e\n\u003cli\u003eDecimal op= Decimal\u003c/li\u003e\n\u003cli\u003eDecimal op= otherType\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eDecimal should support unary operators (\u003ccode\u003e-, +, abs\u003c/code\u003e).\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003erepr() should round trip, meaning that:\u003c/p\u003e\n\u003cpre\u003em = Decimal(...)\nm == eval(repr(m))\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eDecimal should be immutable.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eDecimal should support the built-in methods:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003emin, max\u003c/li\u003e\n\u003cli\u003efloat, int, long\u003c/li\u003e\n\u003cli\u003estr, repr\u003c/li\u003e\n\u003cli\u003ehash\u003c/li\u003e\n\u003cli\u003ebool (0 is false, otherwise true)\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eThere's been some discussion in python-dev about the behaviour of\n\u003ccode\u003ehash()\u003c/code\u003e. The community agrees that if the values are the same, the\nhashes of those values should also be the same. So, while Decimal(25)\n== 25 is True, hash(Decimal(25)) should be equal to hash(25).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe detail is that you can NOT compare Decimal to floats or strings,\nso we should not worry about them giving the same hashes. In short:\u003c/p\u003e\n\u003cpre\u003ehash(n) == hash(Decimal(n)) # Only if n is int, long, or Decimal\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eRegarding str() and repr() behaviour, Ka-Ping Yee proposes that repr()\nhave the same behaviour as str() and Tim Peters proposes that str()\nbehave like the to-scientific-string operation from the Spec.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThis is possible, because (from Aahz): \"The string form already\ncontains all the necessary information to reconstruct a Decimal\nobject\".\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAnd it also complies with the Spec; Tim Peters:\u003c/p\u003e\n\u003cblockquote\u003e\nThere's no requirement to have a method \u003cem\u003enamed\u003c/em\u003e \"to_sci_string\",\nthe only requirement is that \u003cem\u003esome\u003c/em\u003e way to spell to-sci-string's\nfunctionality be supplied. The meaning of to-sci-string is\nprecisely specified by the standard, and is a good choice for both\nstr(Decimal) and repr(Decimal).\u003c/blockquote\u003e\n\u003ca name=\"user-content-documentation\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDocumentation\u003c/h2\u003e\u003ca id=\"user-content-documentation\" class=\"anchor\" aria-label=\"Permalink: Documentation\" href=\"#documentation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis section explains all the public methods and attributes of Decimal\nand Context.\u003c/p\u003e\n\u003ca name=\"user-content-decimal-attributes\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDecimal Attributes\u003c/h3\u003e\u003ca id=\"user-content-decimal-attributes\" class=\"anchor\" aria-label=\"Permalink: Decimal Attributes\" href=\"#decimal-attributes\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eDecimal has no public attributes. The internal information is stored\nin slots and should not be accessed by end users.\u003c/p\u003e\n\u003ca name=\"user-content-decimal-methods\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eDecimal Methods\u003c/h3\u003e\u003ca id=\"user-content-decimal-methods\" class=\"anchor\" aria-label=\"Permalink: Decimal Methods\" href=\"#decimal-methods\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eFollowing are the conversion and arithmetic operations defined in the\nSpec, and how that functionality can be achieved with the actual\nimplementation.\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eto-scientific-string: Use builtin function \u003ccode\u003estr()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('123456789012.345')\n\u0026gt;\u0026gt;\u0026gt; str(d)\n'1.23456789E+11'\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eto-engineering-string: Use method \u003ccode\u003eto_eng_string()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('123456789012.345')\n\u0026gt;\u0026gt;\u0026gt; d.to_eng_string()\n'123.456789E+9'\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eto-number: Use Context method \u003ccode\u003ecreate_decimal()\u003c/code\u003e. The standard\nconstructor or \u003ccode\u003efrom_float()\u003c/code\u003e constructor cannot be used because\nthese do not use the context (as is specified in the Spec for this\nconversion).\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eabs: Use builtin function \u003ccode\u003eabs()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('-15.67')\n\u0026gt;\u0026gt;\u0026gt; abs(d)\nDecimal('15.67')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eadd: Use operator \u003ccode\u003e+\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('15.6')\n\u0026gt;\u0026gt;\u0026gt; d + 8\nDecimal('23.6')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003esubtract: Use operator \u003ccode\u003e-\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('15.6')\n\u0026gt;\u0026gt;\u0026gt; d - 8\nDecimal('7.6')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003ecompare: Use method \u003ccode\u003ecompare()\u003c/code\u003e. This method (and not the\nbuilt-in function cmp()) should only be used when dealing with\n\u003cem\u003especial values\u003c/em\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('-15.67')\n\u0026gt;\u0026gt;\u0026gt; nan = Decimal('NaN')\n\u0026gt;\u0026gt;\u0026gt; d.compare(23)\n'-1'\n\u0026gt;\u0026gt;\u0026gt; d.compare(nan)\n'NaN'\n\u0026gt;\u0026gt;\u0026gt; cmp(d, 23)\n-1\n\u0026gt;\u0026gt;\u0026gt; cmp(d, nan)\n1\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003edivide: Use operator \u003ccode\u003e/\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('-15.67')\n\u0026gt;\u0026gt;\u0026gt; d / 2\nDecimal('-7.835')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003edivide-integer: Use operator \u003ccode\u003e//\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('-15.67')\n\u0026gt;\u0026gt;\u0026gt; d // 2\nDecimal('-7')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003emax: Use method \u003ccode\u003emax()\u003c/code\u003e. Only use this method (and not the\nbuilt-in function max()) when dealing with \u003cem\u003especial values\u003c/em\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('15')\n\u0026gt;\u0026gt;\u0026gt; nan = Decimal('NaN')\n\u0026gt;\u0026gt;\u0026gt; d.max(8)\nDecimal('15')\n\u0026gt;\u0026gt;\u0026gt; d.max(nan)\nDecimal('NaN')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003emin: Use method \u003ccode\u003emin()\u003c/code\u003e. Only use this method (and not the\nbuilt-in function min()) when dealing with \u003cem\u003especial values\u003c/em\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('15')\n\u0026gt;\u0026gt;\u0026gt; nan = Decimal('NaN')\n\u0026gt;\u0026gt;\u0026gt; d.min(8)\nDecimal('8')\n\u0026gt;\u0026gt;\u0026gt; d.min(nan)\nDecimal('NaN')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eminus: Use unary operator \u003ccode\u003e-\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('-15.67')\n\u0026gt;\u0026gt;\u0026gt; -d\nDecimal('15.67')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eplus: Use unary operator \u003ccode\u003e+\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('-15.67')\n\u0026gt;\u0026gt;\u0026gt; +d\nDecimal('-15.67')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003emultiply: Use operator \u003ccode\u003e*\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('5.7')\n\u0026gt;\u0026gt;\u0026gt; d * 3\nDecimal('17.1')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003enormalize: Use method \u003ccode\u003enormalize()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('123.45000')\n\u0026gt;\u0026gt;\u0026gt; d.normalize()\nDecimal('123.45')\n\u0026gt;\u0026gt;\u0026gt; d = Decimal('120.00')\n\u0026gt;\u0026gt;\u0026gt; d.normalize()\nDecimal('1.2E+2')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003equantize: Use method \u003ccode\u003equantize()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('2.17')\n\u0026gt;\u0026gt;\u0026gt; d.quantize(Decimal('0.001'))\nDecimal('2.170')\n\u0026gt;\u0026gt;\u0026gt; d.quantize(Decimal('0.1'))\nDecimal('2.2')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eremainder: Use operator \u003ccode\u003e%\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('10')\n\u0026gt;\u0026gt;\u0026gt; d % 3\nDecimal('1')\n\u0026gt;\u0026gt;\u0026gt; d % 6\nDecimal('4')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eremainder-near: Use method \u003ccode\u003eremainder_near()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('10')\n\u0026gt;\u0026gt;\u0026gt; d.remainder_near(3)\nDecimal('1')\n\u0026gt;\u0026gt;\u0026gt; d.remainder_near(6)\nDecimal('-2')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003eround-to-integral-value: Use method \u003ccode\u003eto_integral()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('-123.456')\n\u0026gt;\u0026gt;\u0026gt; d.to_integral()\nDecimal('-123')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003esame-quantum: Use method \u003ccode\u003esame_quantum()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('123.456')\n\u0026gt;\u0026gt;\u0026gt; d.same_quantum(Decimal('0.001'))\nTrue\n\u0026gt;\u0026gt;\u0026gt; d.same_quantum(Decimal('0.01'))\nFalse\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003esquare-root: Use method \u003ccode\u003esqrt()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('123.456')\n\u0026gt;\u0026gt;\u0026gt; d.sqrt()\nDecimal('11.1110756')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003epower: User operator \u003ccode\u003e**\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('12.56')\n\u0026gt;\u0026gt;\u0026gt; d ** 2\nDecimal('157.7536')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eFollowing are other methods and why they exist:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003eadjusted()\u003c/code\u003e: Returns the adjusted exponent. This concept is\ndefined in the Spec: the adjusted exponent is the value of the\nexponent of a number when that number is expressed as though in\nscientific notation with one digit before any decimal point:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('12.56')\n\u0026gt;\u0026gt;\u0026gt; d.adjusted()\n1\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003efrom_float()\u003c/code\u003e: Class method to create instances from float data\ntypes:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal.from_float(12.35)\n\u0026gt;\u0026gt;\u0026gt; d\nDecimal('12.3500000')\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003eas_tuple()\u003c/code\u003e: Show the internal structure of the Decimal, the\ntriple tuple. This method is not required by the Spec, but Tim\nPeters proposed it and the community agreed to have it (it's useful\nfor developing and debugging):\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; d = Decimal('123.4')\n\u0026gt;\u0026gt;\u0026gt; d.as_tuple()\n(0, (1, 2, 3, 4), -1)\n\u0026gt;\u0026gt;\u0026gt; d = Decimal('-2.34e5')\n\u0026gt;\u0026gt;\u0026gt; d.as_tuple()\n(1, (2, 3, 4), 3)\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003ca name=\"user-content-context-attributes\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eContext Attributes\u003c/h3\u003e\u003ca id=\"user-content-context-attributes\" class=\"anchor\" aria-label=\"Permalink: Context Attributes\" href=\"#context-attributes\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThese are the attributes that can be changed to modify the context.\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003eprec\u003c/code\u003e (int): the precision:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.prec\n9\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003erounding\u003c/code\u003e (str): rounding type (how to round):\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.rounding\n'half_even'\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003etrap_enablers\u003c/code\u003e (dict): if trap_enablers[exception] = 1, then an\nexception is raised when it is caused:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.trap_enablers[Underflow]\n0\n\u0026gt;\u0026gt;\u0026gt; c.trap_enablers[Clamped]\n0\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003eflags\u003c/code\u003e (dict): when an exception is caused, flags[exception] is\nincremented (whether or not the trap_enabler is set). Should be\nreset by the user of Decimal instance:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.flags[Underflow]\n0\n\u0026gt;\u0026gt;\u0026gt; c.flags[Clamped]\n0\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003eEmin\u003c/code\u003e (int): minimum exponent:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.Emin\n-999999999\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003eEmax\u003c/code\u003e (int): maximum exponent:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.Emax\n999999999\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003ecapitals\u003c/code\u003e (int): boolean flag to use 'E' (True/1) or 'e'\n(False/0) in the string (for example, '1.32e+2' or '1.32E+2'):\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.capitals\n1\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003ca name=\"user-content-context-methods\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eContext Methods\u003c/h3\u003e\u003ca id=\"user-content-context-methods\" class=\"anchor\" aria-label=\"Permalink: Context Methods\" href=\"#context-methods\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe following methods comply with Decimal functionality from the Spec.\nBe aware that the operations that are called through a specific\ncontext use that context and not the thread context.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTo use these methods, take note that the syntax changes when the\noperator is binary or unary, for example:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; mycontext.abs(Decimal('-2'))\n'2'\n\u0026gt;\u0026gt;\u0026gt; mycontext.multiply(Decimal('2.3'), 5)\n'11.5'\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eSo, the following are the Spec operations and conversions and how to\nachieve them through a context (where \u003ccode\u003ed\u003c/code\u003e is a Decimal instance and\n\u003ccode\u003en\u003c/code\u003e a number that can be used in an \u003ca href=\"#implicit-construction\"\u003eImplicit construction\u003c/a\u003e):\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eto-scientific-string: \u003ccode\u003eto_sci_string(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eto-engineering-string: \u003ccode\u003eto_eng_string(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eto-number: \u003ccode\u003ecreate_decimal(number)\u003c/code\u003e, see \u003ca href=\"#explicit-construction\"\u003eExplicit construction\u003c/a\u003e\nfor \u003ccode\u003enumber\u003c/code\u003e.\u003c/li\u003e\n\u003cli\u003eabs: \u003ccode\u003eabs(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eadd: \u003ccode\u003eadd(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003esubtract: \u003ccode\u003esubtract(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003ecompare: \u003ccode\u003ecompare(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003edivide: \u003ccode\u003edivide(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003edivide-integer: \u003ccode\u003edivide_int(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003emax: \u003ccode\u003emax(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003emin: \u003ccode\u003emin(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eminus: \u003ccode\u003eminus(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eplus: \u003ccode\u003eplus(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003emultiply: \u003ccode\u003emultiply(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003enormalize: \u003ccode\u003enormalize(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003equantize: \u003ccode\u003equantize(d, d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eremainder: \u003ccode\u003eremainder(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eremainder-near: \u003ccode\u003eremainder_near(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003eround-to-integral-value: \u003ccode\u003eto_integral(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003esame-quantum: \u003ccode\u003esame_quantum(d, d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003esquare-root: \u003ccode\u003esqrt(d)\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003epower: \u003ccode\u003epower(d, n)\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eThe \u003ccode\u003edivmod(d, n)\u003c/code\u003e method supports decimal functionality through\nContext.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThese are methods that return useful information from the Context:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003eEtiny()\u003c/code\u003e: Minimum exponent considering precision.\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.Emin\n-999999999\n\u0026gt;\u0026gt;\u0026gt; c.Etiny()\n-1000000007\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003eEtop()\u003c/code\u003e: Maximum exponent considering precision.\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; c.Emax\n999999999\n\u0026gt;\u0026gt;\u0026gt; c.Etop()\n999999991\n\u003c/pre\u003e\n\u003c/li\u003e\n\u003cli\u003e\u003cp dir=\"auto\"\u003e\u003ccode\u003ecopy()\u003c/code\u003e: Returns a copy of the context.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e\n\u003ca name=\"user-content-reference-implementation\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eReference Implementation\u003c/h2\u003e\u003ca id=\"user-content-reference-implementation\" class=\"anchor\" aria-label=\"Permalink: Reference Implementation\" href=\"#reference-implementation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eAs of Python 2.4-alpha, the code has been checked into the standard\nlibrary. The latest version is available from:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"http://svn.python.org/view/python/trunk/Lib/decimal.py\" rel=\"nofollow\"\u003ehttp://svn.python.org/view/python/trunk/Lib/decimal.py\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe test cases are here:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e\u003ca href=\"http://svn.python.org/view/python/trunk/Lib/test/test_decimal.py\" rel=\"nofollow\"\u003ehttp://svn.python.org/view/python/trunk/Lib/test/test_decimal.py\u003c/a\u003e\u003c/p\u003e\n\u003ca name=\"user-content-references\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eReferences\u003c/h2\u003e\u003ca id=\"user-content-references\" class=\"anchor\" aria-label=\"Permalink: References\" href=\"#references\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-id19\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e[1]\u003c/td\u003e\u003ctd\u003e\u003cem\u003e(\u003ca href=\"#id1\"\u003e1\u003c/a\u003e, \u003ca href=\"#id8\"\u003e2\u003c/a\u003e)\u003c/em\u003e ANSI standard X3.274-1996 (Programming Language REXX):\n\u003ca href=\"http://www.rexxla.org/Standards/ansi.html\" rel=\"nofollow\"\u003ehttp://www.rexxla.org/Standards/ansi.html\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-id20\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e[2]\u003c/td\u003e\u003ctd\u003e\u003cem\u003e(\u003ca href=\"#id2\"\u003e1\u003c/a\u003e, \u003ca href=\"#id3\"\u003e2\u003c/a\u003e, \u003ca href=\"#id5\"\u003e3\u003c/a\u003e, \u003ca href=\"#id6\"\u003e4\u003c/a\u003e, \u003ca href=\"#id11\"\u003e5\u003c/a\u003e, \u003ca href=\"#id12\"\u003e6\u003c/a\u003e, \u003ca href=\"#id13\"\u003e7\u003c/a\u003e, \u003ca href=\"#id14\"\u003e8\u003c/a\u003e)\u003c/em\u003e General Decimal Arithmetic specification (Cowlishaw):\n\u003ca href=\"http://speleotrove.com/decimal/decarith.html\" rel=\"nofollow\"\u003ehttp://speleotrove.com/decimal/decarith.html\u003c/a\u003e (related\ndocuments and links at \u003ca href=\"http://speleotrove.com/decimal/\" rel=\"nofollow\"\u003ehttp://speleotrove.com/decimal/\u003c/a\u003e)\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-id21\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id7\"\u003e[3]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003eANSI/IEEE standard 854-1987 (Radix-Independent Floating-Point\nArithmetic):\n\u003ca href=\"http://www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html\" rel=\"nofollow\"\u003ehttp://www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html\u003c/a\u003e\n(unofficial text; official copies can be ordered from\n\u003ca href=\"http://standards.ieee.org/catalog/ordering.html\" rel=\"nofollow\"\u003ehttp://standards.ieee.org/catalog/ordering.html\u003c/a\u003e)\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-id22\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id4\"\u003e[4]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003eTim Peter's FixedPoint at SourceForge:\n\u003ca href=\"http://fixedpoint.sourceforge.net/\" rel=\"nofollow\"\u003ehttp://fixedpoint.sourceforge.net/\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-id23\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id9\"\u003e[5]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003eIEEE 754 revision:\n\u003ca href=\"http://grouper.ieee.org/groups/754/revision.html\" rel=\"nofollow\"\u003ehttp://grouper.ieee.org/groups/754/revision.html\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-id24\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id10\"\u003e[6]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003eIEEE 754 references:\n\u003ca href=\"http://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html\" rel=\"nofollow\"\u003ehttp://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003ca name=\"user-content-copyright\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eCopyright\u003c/h2\u003e\u003ca id=\"user-content-copyright\" class=\"anchor\" aria-label=\"Permalink: Copyright\" href=\"#copyright\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis document has been placed in the public 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class="Box-sc-g0xbh4-0 eoaCFS js-snippet-clipboard-copy-unpositioned undefined" data-hpc="true"><article class="markdown-body entry-content container-lg" itemprop="text"><p dir="auto">PEP: 327 Title: Decimal Data Type Author: Facundo Batista <<a href="mailto:facundo@taniquetil.com.ar">facundo@taniquetil.com.ar</a>> Status: Final Type: Standards Track Created: 17-Oct-2003 Python-Version: 2.4 Post-History: 30-Nov-2003, 02-Jan-2004, 29-Jan-2004</p> <a name="user-content-abstract"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Abstract</h2><a id="user-content-abstract" class="anchor" aria-label="Permalink: Abstract" href="#abstract"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The idea is to have a Decimal data type, for every use where decimals are needed but binary floating point is too inexact.</p> <p dir="auto">The Decimal data type will support the Python standard functions and operations, and must comply with the decimal arithmetic ANSI standard X3.274-1996 <a href="#id19" id="user-content-id1">[1]</a>.</p> <p dir="auto">Decimal will be floating point (as opposed to fixed point) and will have bounded precision (the precision is the upper limit on the number of significant digits in a result). However, precision is user-settable, and a notion of significant trailing zeroes is supported so that fixed-point usage is also possible.</p> <p dir="auto">This work is based on code and test functions written by Eric Price, Aahz and Tim Peters. Just before Python 2.4a1, the decimal.py <a href="#reference-implementation">reference implementation</a> was moved into the standard library; along with the documentation and the test suite, this was the work of Raymond Hettinger. Much of the explanation in this PEP is taken from Cowlishaw's work <a href="#id20" id="user-content-id2">[2]</a>, comp.lang.python and python-dev.</p> <a name="user-content-motivation"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Motivation</h2><a id="user-content-motivation" class="anchor" aria-label="Permalink: Motivation" href="#motivation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Here I'll expose the reasons of why I think a Decimal data type is needed and why other numeric data types are not enough.</p> <p dir="auto">I wanted a Money data type, and after proposing a pre-PEP in comp.lang.python, the community agreed to have a numeric data type with the needed arithmetic behaviour, and then build Money over it: all the considerations about quantity of digits after the decimal point, rounding, etc., will be handled through Money. It is not the purpose of this PEP to have a data type that can be used as Money without further effort.</p> <p dir="auto">One of the biggest advantages of implementing a standard is that someone already thought out all the creepy cases for you. And to a standard GvR redirected me: Mike Cowlishaw's General Decimal Arithmetic specification <a href="#id20" id="user-content-id3">[2]</a>. This document defines a general purpose decimal arithmetic. A correct implementation of this specification will conform to the decimal arithmetic defined in ANSI/IEEE standard 854-1987, except for some minor restrictions, and will also provide unrounded decimal arithmetic and integer arithmetic as proper subsets.</p> <a name="user-content-the-problem-with-binary-float"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">The problem with binary float</h3><a id="user-content-the-problem-with-binary-float" class="anchor" aria-label="Permalink: The problem with binary float" href="#the-problem-with-binary-float"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">In decimal math, there are many numbers that can't be represented with a fixed number of decimal digits, e.g. 1/3 = 0.3333333333.......</p> <p dir="auto">In base 2 (the way that standard floating point is calculated), 1/2 = 0.1, 1/4 = 0.01, 1/8 = 0.001, etc. Decimal 0.2 equals 2/10 equals 1/5, resulting in the binary fractional number 0.001100110011001... As you can see, the problem is that some decimal numbers can't be represented exactly in binary, resulting in small roundoff errors.</p> <p dir="auto">So we need a decimal data type that represents exactly decimal numbers. Instead of a binary data type, we need a decimal one.</p> <a name="user-content-why-floating-point"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Why floating point?</h3><a id="user-content-why-floating-point" class="anchor" aria-label="Permalink: Why floating point?" href="#why-floating-point"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">So we go to decimal, but why <em>floating point</em>?</p> <p dir="auto">Floating point numbers use a fixed quantity of digits (precision) to represent a number, working with an exponent when the number gets too big or too small. For example, with a precision of 5:</p> <pre> 1234 ==> 1234e0 12345 ==> 12345e0 123456 ==> 12346e1 </pre> <p dir="auto">(note that in the last line the number got rounded to fit in five digits).</p> <p dir="auto">In contrast, we have the example of a <code>long</code> integer with infinite precision, meaning that you can have the number as big as you want, and you'll never lose any information.</p> <p dir="auto">In a fixed point number, the position of the decimal point is fixed. For a fixed point data type, check Tim Peter's FixedPoint at SourceForge <a href="#id22" id="user-content-id4">[4]</a>. I'll go for floating point because it's easier to implement the arithmetic behaviour of the standard, and then you can implement a fixed point data type over Decimal.</p> <p dir="auto">But why can't we have a floating point number with infinite precision? It's not so easy, because of inexact divisions. E.g.: 1/3 = 0.3333333333333... ad infinitum. In this case you should store an infinite amount of 3s, which takes too much memory, ;).</p> <p dir="auto">John Roth proposed to eliminate the division operator and force the user to use an explicit method, just to avoid this kind of trouble. This generated adverse reactions in comp.lang.python, as everybody wants to have support for the <code>/</code> operator in a numeric data type.</p> <p dir="auto">With this exposed maybe you're thinking "Hey! Can we just store the 1 and the 3 as numerator and denominator?", which takes us to the next point.</p> <a name="user-content-why-not-rational"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Why not rational?</h3><a id="user-content-why-not-rational" class="anchor" aria-label="Permalink: Why not rational?" href="#why-not-rational"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Rational numbers are stored using two integer numbers, the numerator and the denominator. This implies that the arithmetic operations can't be executed directly (e.g. to add two rational numbers you first need to calculate the common denominator).</p> <p dir="auto">Quoting Alex Martelli:</p> <blockquote> The performance implications of the fact that summing two rationals (which take O(M) and O(N) space respectively) gives a rational which takes O(M+N) memory space is just too troublesome. There are excellent Rational implementations in both pure Python and as extensions (e.g., gmpy), but they'll always be a "niche market" IMHO. Probably worth PEPping, not worth doing without Decimal -- which is the right way to represent sums of money, a truly major use case in the real world.</blockquote> <p dir="auto">Anyway, if you're interested in this data type, you maybe will want to take a look at <a href="http://www.python.org/dev/peps/pep-0239" rel="nofollow">PEP 239</a>: Adding a Rational Type to Python.</p> <a name="user-content-so-what-do-we-have"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">So, what do we have?</h3><a id="user-content-so-what-do-we-have" class="anchor" aria-label="Permalink: So, what do we have?" href="#so-what-do-we-have"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The result is a Decimal data type, with bounded precision and floating point.</p> <p dir="auto">Will it be useful? I can't say it better than Alex Martelli:</p> <blockquote> Python (out of the box) doesn't let you have binary floating point numbers <em>with whatever precision you specify</em>: you're limited to what your hardware supplies. Decimal, be it used as a fixed or floating point number, should suffer from no such limitation: whatever bounded precision you may specify on number creation (your memory permitting) should work just as well. Most of the expense of programming simplicity can be hidden from application programs and placed in a suitable decimal arithmetic type. As per <a href="http://speleotrove.com/decimal/" rel="nofollow">http://speleotrove.com/decimal/</a>, <em>a single data type can be used for integer, fixed-point, and floating-point decimal arithmetic</em> -- and for money arithmetic which doesn't drive the application programmer crazy.</blockquote> <p dir="auto">There are several uses for such a data type. As I said before, I will use it as base for Money. In this case the bounded precision is not an issue; quoting Tim Peters:</p> <blockquote> A precision of 20 would be way more than enough to account for total world economic output, down to the penny, since the beginning of time.</blockquote> <a name="user-content-general-decimal-arithmetic-specification"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">General Decimal Arithmetic Specification</h2><a id="user-content-general-decimal-arithmetic-specification" class="anchor" aria-label="Permalink: General Decimal Arithmetic Specification" href="#general-decimal-arithmetic-specification"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Here I'll include information and descriptions that are part of the specification <a href="#id20" id="user-content-id5">[2]</a> (the structure of the number, the context, etc.). All the requirements included in this section are not for discussion (barring typos or other mistakes), as they are in the standard, and the PEP is just for implementing the standard.</p> <p dir="auto">Because of copyright restrictions, I can not copy here explanations taken from the specification, so I'll try to explain it in my own words. I firmly encourage you to read the original specification document <a href="#id20" id="user-content-id6">[2]</a> for details or if you have any doubt.</p> <a name="user-content-the-arithmetic-model"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">The Arithmetic Model</h3><a id="user-content-the-arithmetic-model" class="anchor" aria-label="Permalink: The Arithmetic Model" href="#the-arithmetic-model"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The specification is based on a decimal arithmetic model, as defined by the relevant standards: IEEE 854 <a href="#id21" id="user-content-id7">[3]</a>, ANSI X3-274 <a href="#id19" id="user-content-id8">[1]</a>, and the proposed revision <a href="#id23" id="user-content-id9">[5]</a> of IEEE 754 <a href="#id24" id="user-content-id10">[6]</a>.</p> <p dir="auto">The model has three components:</p> <ul dir="auto"> <li>Numbers: just the values that the operation uses as input or output.</li> <li>Operations: addition, multiplication, etc.</li> <li>Context: a set of parameters and rules that the user can select and which govern the results of operations (for example, the precision to be used).</li> </ul> <a name="user-content-numbers"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Numbers</h3><a id="user-content-numbers" class="anchor" aria-label="Permalink: Numbers" href="#numbers"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Numbers may be finite or special values. The former can be represented exactly. The latter are infinites and undefined (such as 0/0).</p> <p dir="auto">Finite numbers are defined by three parameters:</p> <ul dir="auto"> <li>Sign: 0 (positive) or 1 (negative).</li> <li>Coefficient: a non-negative integer.</li> <li>Exponent: a signed integer, the power of ten of the coefficient multiplier.</li> </ul> <p dir="auto">The numerical value of a finite number is given by:</p> <pre>(-1)**sign * coefficient * 10**exponent </pre> <p dir="auto">Special values are named as following:</p> <ul dir="auto"> <li>Infinity: a value which is infinitely large. Could be positive or negative.</li> <li>Quiet NaN ("qNaN"): represent undefined results (<em>Not a Number</em>). Does not cause an Invalid operation condition. The sign in a NaN has no meaning.</li> <li>Signaling NaN ("sNaN"): also <em>Not a Number</em>, but will cause an Invalid operation condition if used in any operation.</li> </ul> <a name="user-content-context"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Context</h3><a id="user-content-context" class="anchor" aria-label="Permalink: Context" href="#context"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The context is a set of parameters and rules that the user can select and which govern the results of operations (for example, the precision to be used).</p> <p dir="auto">The context gets that name because it surrounds the Decimal numbers, with parts of context acting as input to, and output of, operations. It's up to the application to work with one or several contexts, but definitely the idea is not to get a context per Decimal number. For example, a typical use would be to set the context's precision to 20 digits at the start of a program, and never explicitly use context again.</p> <p dir="auto">These definitions don't affect the internal storage of the Decimal numbers, just the way that the arithmetic operations are performed.</p> <p dir="auto">The context is mainly defined by the following parameters (see <a href="#context-attributes">Context Attributes</a> for all context attributes):</p> <ul dir="auto"> <li>Precision: The maximum number of significant digits that can result from an arithmetic operation (integer > 0). There is no maximum for this value.</li> <li>Rounding: The name of the algorithm to be used when rounding is necessary, one of "round-down", "round-half-up", "round-half-even", "round-ceiling", "round-floor", "round-half-down", and "round-up". See <a href="#rounding-algorithms">Rounding Algorithms</a> below.</li> <li>Flags and trap-enablers: <a href="#exceptional-conditions">Exceptional conditions</a> are grouped into signals, controllable individually, each consisting of a flag (boolean, set when the signal occurs) and a trap-enabler (a boolean that controls behavior). The signals are: "clamped", "division-by-zero", "inexact", "invalid-operation", "overflow", "rounded", "subnormal" and "underflow".</li> </ul> <a name="user-content-default-contexts"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Default Contexts</h3><a id="user-content-default-contexts" class="anchor" aria-label="Permalink: Default Contexts" href="#default-contexts"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The specification defines two default contexts, which should be easily selectable by the user.</p> <p dir="auto">Basic Default Context:</p> <ul dir="auto"> <li>flags: all set to 0</li> <li>trap-enablers: inexact, rounded, and subnormal are set to 0; all others are set to 1</li> <li>precision: is set to 9</li> <li>rounding: is set to round-half-up</li> </ul> <p dir="auto">Extended Default Context:</p> <ul dir="auto"> <li>flags: all set to 0</li> <li>trap-enablers: all set to 0</li> <li>precision: is set to 9</li> <li>rounding: is set to round-half-even</li> </ul> <a name="user-content-exceptional-conditions"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Exceptional Conditions</h3><a id="user-content-exceptional-conditions" class="anchor" aria-label="Permalink: Exceptional Conditions" href="#exceptional-conditions"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The table below lists the exceptional conditions that may arise during the arithmetic operations, the corresponding signal, and the defined result. For details, see the specification <a href="#id20" id="user-content-id11">[2]</a>.</p> <markdown-accessiblity-table><table> <thead valign="bottom"> <tr><th>Condition</th> <th>Signal</th> <th>Result</th> </tr> </thead> <tbody valign="top"> <tr><td>Clamped</td> <td>clamped</td> <td>see spec <a href="#id20" id="user-content-id12">[2]</a></td> </tr> <tr><td>Division by zero</td> <td>division-by-zero</td> <td>[sign,inf]</td> </tr> <tr><td>Inexact</td> <td>inexact</td> <td>unchanged</td> </tr> <tr><td>Invalid operation</td> <td>invalid-operation</td> <td>[0,qNaN] (or [s,qNaN] or [s,qNaN,d] when the cause is a signaling NaN)</td> </tr> <tr><td>Overflow</td> <td>overflow</td> <td>depends on the rounding mode</td> </tr> <tr><td>Rounded</td> <td>rounded</td> <td>unchanged</td> </tr> <tr><td>Subnormal</td> <td>subnormal</td> <td>unchanged</td> </tr> <tr><td>Underflow</td> <td>underflow</td> <td>see spec <a href="#id20" id="user-content-id13">[2]</a></td> </tr> </tbody> </table></markdown-accessiblity-table> <p dir="auto">Note: when the standard talks about "Insufficient storage", as long as this is implementation-specific behaviour about not having enough storage to keep the internals of the number, this implementation will raise MemoryError.</p> <p dir="auto">Regarding Overflow and Underflow, there's been a long discussion in python-dev about artificial limits. The general consensus is to keep the artificial limits only if there are important reasons to do that. Tim Peters gives us three:</p> <blockquote> <p dir="auto">...eliminating bounds on exponents effectively means overflow (and underflow) can never happen. But overflow <em>is</em> a valuable safety net in real life fp use, like a canary in a coal mine, giving danger signs early when a program goes insane.</p> <p dir="auto">Virtually all implementations of 854 use (and as IBM's standard even suggests) "forbidden" exponent values to encode non-finite numbers (infinities and NaNs). A bounded exponent can do this at virtually no extra storage cost. If the exponent is unbounded, then additional bits have to be used instead. This cost remains hidden until more time- and space- efficient implementations are attempted.</p> <p dir="auto">Big as it is, the IBM standard is a tiny start at supplying a complete numeric facility. Having no bound on exponent size will enormously complicate the implementations of, e.g., decimal sin() and cos() (there's then no a priori limit on how many digits of pi effectively need to be known in order to perform argument reduction).</p> </blockquote> <p dir="auto">Edward Loper give us an example of when the limits are to be crossed: probabilities.</p> <p dir="auto">That said, Robert Brewer and Andrew Lentvorski want the limits to be easily modifiable by the users. Actually, this is quite possible:</p> <pre>>>> d1 = Decimal("1e999999999") # at the exponent limit >>> d1 Decimal("1E+999999999") >>> d1 * 10 # exceed the limit, got infinity Traceback (most recent call last): File "<pyshell#3>", line 1, in ? d1 * 10 ... ... Overflow: above Emax >>> getcontext().Emax = 1000000000 # increase the limit >>> d1 * 10 # does not exceed any more Decimal("1.0E+1000000000") >>> d1 * 100 # exceed again Traceback (most recent call last): File "<pyshell#3>", line 1, in ? d1 * 100 ... ... Overflow: above Emax </pre> <a name="user-content-rounding-algorithms"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Rounding Algorithms</h3><a id="user-content-rounding-algorithms" class="anchor" aria-label="Permalink: Rounding Algorithms" href="#rounding-algorithms"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto"><code>round-down</code>: The discarded digits are ignored; the result is unchanged (round toward 0, truncate):</p> <pre>1.123 --> 1.12 1.128 --> 1.12 1.125 --> 1.12 1.135 --> 1.13 </pre> <p dir="auto"><code>round-half-up</code>: If the discarded digits represent greater than or equal to half (0.5) then the result should be incremented by 1; otherwise the discarded digits are ignored:</p> <pre>1.123 --> 1.12 1.128 --> 1.13 1.125 --> 1.13 1.135 --> 1.14 </pre> <p dir="auto"><code>round-half-even</code>: If the discarded digits represent greater than half (0.5) then the result coefficient is incremented by 1; if they represent less than half, then the result is not adjusted; otherwise the result is unaltered if its rightmost digit is even, or incremented by 1 if its rightmost digit is odd (to make an even digit):</p> <pre>1.123 --> 1.12 1.128 --> 1.13 1.125 --> 1.12 1.135 --> 1.14 </pre> <p dir="auto"><code>round-ceiling</code>: If all of the discarded digits are zero or if the sign is negative the result is unchanged; otherwise, the result is incremented by 1 (round toward positive infinity):</p> <pre> 1.123 --> 1.13 1.128 --> 1.13 -1.123 --> -1.12 -1.128 --> -1.12 </pre> <p dir="auto"><code>round-floor</code>: If all of the discarded digits are zero or if the sign is positive the result is unchanged; otherwise, the absolute value of the result is incremented by 1 (round toward negative infinity):</p> <pre> 1.123 --> 1.12 1.128 --> 1.12 -1.123 --> -1.13 -1.128 --> -1.13 </pre> <p dir="auto"><code>round-half-down</code>: If the discarded digits represent greater than half (0.5) then the result is incremented by 1; otherwise the discarded digits are ignored:</p> <pre>1.123 --> 1.12 1.128 --> 1.13 1.125 --> 1.12 1.135 --> 1.13 </pre> <p dir="auto"><code>round-up</code>: If all of the discarded digits are zero the result is unchanged, otherwise the result is incremented by 1 (round away from 0):</p> <pre>1.123 --> 1.13 1.128 --> 1.13 1.125 --> 1.13 1.135 --> 1.14 </pre> <a name="user-content-rationale"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Rationale</h2><a id="user-content-rationale" class="anchor" aria-label="Permalink: Rationale" href="#rationale"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">I must separate the requirements in two sections. The first is to comply with the ANSI standard. All the requirements for this are specified in the Mike Cowlishaw's work <a href="#id20" id="user-content-id14">[2]</a>. He also provided a <strong>very large</strong> suite of test cases.</p> <p dir="auto">The second section of requirements (standard Python functions support, usability, etc.) is detailed from here, where I'll include all the decisions made and why, and all the subjects still being discussed.</p> <a name="user-content-explicit-construction"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Explicit construction</h3><a id="user-content-explicit-construction" class="anchor" aria-label="Permalink: Explicit construction" href="#explicit-construction"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The explicit construction does not get affected by the context (there is no rounding, no limits by the precision, etc.), because the context affects just operations' results. The only exception to this is when you're <a href="#creating-from-context">Creating from Context</a>.</p> <a name="user-content-from-int-or-long"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From int or long</h4><a id="user-content-from-int-or-long" class="anchor" aria-label="Permalink: From int or long" href="#from-int-or-long"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">There's no loss and no need to specify any other information:</p> <pre>Decimal(35) Decimal(-124) </pre> <a name="user-content-from-string"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From string</h4><a id="user-content-from-string" class="anchor" aria-label="Permalink: From string" href="#from-string"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Strings containing Python decimal integer literals and Python float literals will be supported. In this transformation there is no loss of information, as the string is directly converted to Decimal (there is not an intermediate conversion through float):</p> <pre>Decimal("-12") Decimal("23.2e-7") </pre> <p dir="auto">Also, you can construct in this way all special values (Infinity and Not a Number):</p> <pre>Decimal("Inf") Decimal("NaN") </pre> <a name="user-content-from-float"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From float</h4><a id="user-content-from-float" class="anchor" aria-label="Permalink: From float" href="#from-float"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The initial discussion on this item was what should happen when passing floating point to the constructor:</p> <ol dir="auto"> <li><code>Decimal(1.1) == Decimal('1.1')</code></li> <li><code>Decimal(1.1) == Decimal('110000000000000008881784197001252...e-51')</code></li> <li>an exception is raised</li> </ol> <p dir="auto">Several people alleged that (1) is the better option here, because it's what you expect when writing <code>Decimal(1.1)</code>. And quoting John Roth, it's easy to implement:</p> <blockquote> It's not at all difficult to find where the actual number ends and where the fuzz begins. You can do it visually, and the algorithms to do it are quite well known.</blockquote> <p dir="auto">But If I <em>really</em> want my number to be <code>Decimal('110000000000000008881784197001252...e-51')</code>, why can't I write <code>Decimal(1.1)</code>? Why should I expect Decimal to be "rounding" it? Remember that <code>1.1</code> <em>is</em> binary floating point, so I can predict the result. It's not intuitive to a beginner, but that's the way it is.</p> <p dir="auto">Anyway, Paul Moore showed that (1) can't work, because:</p> <pre>(1) says D(1.1) == D('1.1') but 1.1 == 1.1000000000000001 so D(1.1) == D(1.1000000000000001) together: D(1.1000000000000001) == D('1.1') </pre> <p dir="auto">which is wrong, because if I write <code>Decimal('1.1')</code> it is exact, not <code>D(1.1000000000000001)</code>. He also proposed to have an explicit conversion to float. bokr says you need to put the precision in the constructor and mwilson agreed:</p> <pre>d = Decimal (1.1, 1) # take float value to 1 decimal place d = Decimal (1.1) # gets `places` from pre-set context </pre> <p dir="auto">But Alex Martelli says that:</p> <blockquote> Constructing with some specified precision would be fine. Thus, I think "construction from float with some default precision" runs a substantial risk of tricking naive users.</blockquote> <p dir="auto">So, the accepted solution through c.l.p is that you can not call Decimal with a float. Instead you must use a method: Decimal.from_float(). The syntax:</p> <pre>Decimal.from_float(floatNumber, [decimal_places]) </pre> <p dir="auto">where <code>floatNumber</code> is the float number origin of the construction and <code>decimal_places</code> are the number of digits after the decimal point where you apply a round-half-up rounding, if any. In this way you can do, for example:</p> <pre>Decimal.from_float(1.1, 2): The same as doing Decimal('1.1'). Decimal.from_float(1.1, 16): The same as doing Decimal('1.1000000000000001'). Decimal.from_float(1.1): The same as doing Decimal('1100000000000000088817841970012523233890533447265625e-51'). </pre> <p dir="auto">Based on later discussions, it was decided to omit from_float() from the API for Py2.4. Several ideas contributed to the thought process:</p> <ul dir="auto"> <li><p dir="auto">Interactions between decimal and binary floating point force the user to deal with tricky issues of representation and round-off. Avoidance of those issues is a primary reason for having the module in the first place.</p> </li> <li><p dir="auto">The first release of the module should focus on that which is safe, minimal, and essential.</p> </li> <li><p dir="auto">While theoretically nice, real world use cases for interactions between floats and decimals are lacking. Java included float/decimal conversions to handle an obscure case where calculations are best performed in decimal even though a legacy data structure requires the inputs and outputs to be stored in binary floating point.</p> </li> <li><p dir="auto">If the need arises, users can use string representations as an intermediate type. The advantage of this approach is that it makes explicit the assumptions about precision and representation (no wondering what is going on under the hood).</p> </li> <li><p dir="auto">The Java docs for BigDecimal(double val) reflected their experiences with the constructor:</p> <pre>The results of this constructor can be somewhat unpredictable and its use is generally not recommended. </pre> </li> </ul> <a name="user-content-from-tuples"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From tuples</h4><a id="user-content-from-tuples" class="anchor" aria-label="Permalink: From tuples" href="#from-tuples"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Aahz suggested to construct from tuples: it's easier to implement <code>eval()</code>'s round trip and "someone who has numeric values representing a Decimal does not need to convert them to a string."</p> <p dir="auto">The structure will be a tuple of three elements: sign, number and exponent. The sign is 1 or 0, the number is a tuple of decimal digits and the exponent is a signed int or long:</p> <pre>Decimal((1, (3, 2, 2, 5), -2)) # for -32.25 </pre> <p dir="auto">Of course, you can construct in this way all special values:</p> <pre>Decimal( (0, (0,), 'F') ) # for Infinity Decimal( (0, (0,), 'n') ) # for Not a Number </pre> <a name="user-content-from-decimal"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From Decimal</h4><a id="user-content-from-decimal" class="anchor" aria-label="Permalink: From Decimal" href="#from-decimal"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">No mystery here, just a copy.</p> <a name="user-content-syntax-for-all-cases"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Syntax for All Cases</h4><a id="user-content-syntax-for-all-cases" class="anchor" aria-label="Permalink: Syntax for All Cases" href="#syntax-for-all-cases"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <pre>Decimal(value1) Decimal.from_float(value2, [decimal_places]) </pre> <p dir="auto">where <code>value1</code> can be int, long, string, 3-tuple or Decimal, <code>value2</code> can only be float, and <code>decimal_places</code> is an optional non negative int.</p> <a name="user-content-creating-from-context"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">Creating from Context</h4><a id="user-content-creating-from-context" class="anchor" aria-label="Permalink: Creating from Context" href="#creating-from-context"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This item arose in python-dev from two sources in parallel. Ka-Ping Yee proposes to pass the context as an argument at instance creation (he wants the context he passes to be used only in creation time: "It would not be persistent"). Tony Meyer asks from_string to honor the context if it receives a parameter "honour_context" with a True value. (I don't like it, because the doc specifies that the context be honored and I don't want the method to comply with the specification regarding the value of an argument.)</p> <p dir="auto">Tim Peters gives us a reason to have a creation that uses context:</p> <blockquote> In general number-crunching, literals may be given to high precision, but that precision isn't free and <em>usually</em> isn't needed</blockquote> <p dir="auto">Casey Duncan wants to use another method, not a bool arg:</p> <blockquote> I find boolean arguments a general anti-pattern, especially given we have class methods. Why not use an alternate constructor like Decimal.rounded_to_context("3.14159265").</blockquote> <p dir="auto">In the process of deciding the syntax of that, Tim came up with a better idea: he proposes not to have a method in Decimal to create with a different context, but having instead a method in Context to create a Decimal instance. Basically, instead of:</p> <pre>D.using_context(number, context) </pre> <p dir="auto">it will be:</p> <pre>context.create_decimal(number) </pre> <p dir="auto">From Tim:</p> <blockquote> While all operations in the spec except for the two to-string operations use context, no operations in the spec support an optional local context. That the Decimal() constructor ignores context by default is an extension to the spec. We must supply a context-honoring from-string operation to meet the spec. I recommend against any concept of "local context" in any operation -- it complicates the model and isn't necessary.</blockquote> <p dir="auto">So, we decided to use a context method to create a Decimal that will use (only to be created) that context in particular (for further operations it will use the context of the thread). But, a method with what name?</p> <p dir="auto">Tim Peters proposes three methods to create from diverse sources (from_string, from_int, from_float). I proposed to use one method, <code>create_decimal()</code>, without caring about the data type. Michael Chermside: "The name just fits my brain. The fact that it uses the context is obvious from the fact that it's Context method".</p> <p dir="auto">The community agreed with that. I think that it's OK because a newbie will not be using the creation method from Context (the separate method in Decimal to construct from float is just to prevent newbies from encountering binary floating point issues).</p> <p dir="auto">So, in short, if you want to create a Decimal instance using a particular context (that will be used just at creation time and not any further), you'll have to use a method of that context:</p> <pre># n is any datatype accepted in Decimal(n) plus float mycontext.create_decimal(n) </pre> <p dir="auto">Example:</p> <pre>>>> # create a standard decimal instance >>> Decimal("11.2233445566778899") Decimal("11.2233445566778899") >>> >>> # create a decimal instance using the thread context >>> thread_context = getcontext() >>> thread_context.prec 28 >>> thread_context.create_decimal("11.2233445566778899") Decimal("11.2233445566778899") >>> >>> # create a decimal instance using other context >>> other_context = thread_context.copy() >>> other_context.prec = 4 >>> other_context.create_decimal("11.2233445566778899") Decimal("11.22") </pre> <a name="user-content-implicit-construction"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Implicit construction</h3><a id="user-content-implicit-construction" class="anchor" aria-label="Permalink: Implicit construction" href="#implicit-construction"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">As the implicit construction is the consequence of an operation, it will be affected by the context as is detailed in each point.</p> <p dir="auto">John Roth suggested that "The other type should be handled in the same way the decimal() constructor would handle it". But Alex Martelli thinks that</p> <blockquote> this total breach with Python tradition would be a terrible mistake. 23+"43" is NOT handled in the same way as 23+int("45"), and a VERY good thing that is too. It's a completely different thing for a user to EXPLICITLY indicate they want construction (conversion) and to just happen to sum two objects one of which by mistake could be a string.</blockquote> <p dir="auto">So, here I define the behaviour again for each data type.</p> <a name="user-content-id15"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From int or long</h4><a id="user-content-from-int-or-long-1" class="anchor" aria-label="Permalink: From int or long" href="#from-int-or-long-1"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">An int or long is a treated like a Decimal explicitly constructed from Decimal(str(x)) in the current context (meaning that the to-string rules for rounding are applied and the appropriate flags are set). This guarantees that expressions like <code>Decimal('1234567') + 13579</code> match the mental model of <code>Decimal('1234567') + Decimal('13579')</code>. That model works because all integers are representable as strings without representation error.</p> <a name="user-content-id16"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From string</h4><a id="user-content-from-string-1" class="anchor" aria-label="Permalink: From string" href="#from-string-1"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Everybody agrees to raise an exception here.</p> <a name="user-content-id17"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From float</h4><a id="user-content-from-float-1" class="anchor" aria-label="Permalink: From float" href="#from-float-1"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Aahz is strongly opposed to interact with float, suggesting an explicit conversion:</p> <blockquote> The problem is that Decimal is capable of greater precision, accuracy, and range than float.</blockquote> <p dir="auto">The example of the valid python expression, <code>35 + 1.1</code>, seems to suggest that <code>Decimal(35) + 1.1</code> should also be valid. However, a closer look shows that it only demonstrates the feasibility of integer to floating point conversions. Hence, the correct analog for decimal floating point is <code>35 + Decimal(1.1)</code>. Both coercions, int-to-float and int-to-Decimal, can be done without incurring representation error.</p> <p dir="auto">The question of how to coerce between binary and decimal floating point is more complex. I proposed allowing the interaction with float, making an exact conversion and raising ValueError if exceeds the precision in the current context (this is maybe too tricky, because for example with a precision of 9, <code>Decimal(35) + 1.2</code> is OK but <code>Decimal(35) + 1.1</code> raises an error).</p> <p dir="auto">This resulted to be too tricky. So tricky, that c.l.p agreed to raise TypeError in this case: you could not mix Decimal and float.</p> <a name="user-content-id18"></a> <div class="markdown-heading" dir="auto"><h4 tabindex="-1" class="heading-element" dir="auto">From Decimal</h4><a id="user-content-from-decimal-1" class="anchor" aria-label="Permalink: From Decimal" href="#from-decimal-1"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">There isn't any issue here.</p> <a name="user-content-use-of-context"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Use of Context</h3><a id="user-content-use-of-context" class="anchor" aria-label="Permalink: Use of Context" href="#use-of-context"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">In the last pre-PEP I said that "The Context must be omnipresent, meaning that changes to it affects all the current and future Decimal instances". I was wrong. In response, John Roth said:</p> <blockquote> The context should be selectable for the particular usage. That is, it should be possible to have several different contexts in play at one time in an application.</blockquote> <p dir="auto">In comp.lang.python, Aahz explained that the idea is to have a "context per thread". So, all the instances of a thread belongs to a context, and you can change a context in thread A (and the behaviour of the instances of that thread) without changing nothing in thread B.</p> <p dir="auto">Also, and again correcting me, he said:</p> <blockquote> (the) Context applies only to operations, not to Decimal instances; changing the Context does not affect existing instances if there are no operations on them.</blockquote> <p dir="auto">Arguing about special cases when there's need to perform operations with other rules that those of the current context, Tim Peters said that the context will have the operations as methods. This way, the user "can create whatever private context object(s) it needs, and spell arithmetic as explicit method calls on its private context object(s), so that the default thread context object is neither consulted nor modified".</p> <a name="user-content-python-usability"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Python Usability</h3><a id="user-content-python-usability" class="anchor" aria-label="Permalink: Python Usability" href="#python-usability"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li><p dir="auto">Decimal should support the basic arithmetic (<code>+, -, *, /, //, **, %, divmod</code>) and comparison (<code>==, !=, <, >, <=, >=, cmp</code>) operators in the following cases (check <a href="#implicit-construction">Implicit Construction</a> to see what types could OtherType be, and what happens in each case):</p> <ul dir="auto"> <li>Decimal op Decimal</li> <li>Decimal op otherType</li> <li>otherType op Decimal</li> <li>Decimal op= Decimal</li> <li>Decimal op= otherType</li> </ul> </li> <li><p dir="auto">Decimal should support unary operators (<code>-, +, abs</code>).</p> </li> <li><p dir="auto">repr() should round trip, meaning that:</p> <pre>m = Decimal(...) m == eval(repr(m)) </pre> </li> <li><p dir="auto">Decimal should be immutable.</p> </li> <li><p dir="auto">Decimal should support the built-in methods:</p> <ul dir="auto"> <li>min, max</li> <li>float, int, long</li> <li>str, repr</li> <li>hash</li> <li>bool (0 is false, otherwise true)</li> </ul> </li> </ul> <p dir="auto">There's been some discussion in python-dev about the behaviour of <code>hash()</code>. The community agrees that if the values are the same, the hashes of those values should also be the same. So, while Decimal(25) == 25 is True, hash(Decimal(25)) should be equal to hash(25).</p> <p dir="auto">The detail is that you can NOT compare Decimal to floats or strings, so we should not worry about them giving the same hashes. In short:</p> <pre>hash(n) == hash(Decimal(n)) # Only if n is int, long, or Decimal </pre> <p dir="auto">Regarding str() and repr() behaviour, Ka-Ping Yee proposes that repr() have the same behaviour as str() and Tim Peters proposes that str() behave like the to-scientific-string operation from the Spec.</p> <p dir="auto">This is possible, because (from Aahz): "The string form already contains all the necessary information to reconstruct a Decimal object".</p> <p dir="auto">And it also complies with the Spec; Tim Peters:</p> <blockquote> There's no requirement to have a method <em>named</em> "to_sci_string", the only requirement is that <em>some</em> way to spell to-sci-string's functionality be supplied. The meaning of to-sci-string is precisely specified by the standard, and is a good choice for both str(Decimal) and repr(Decimal).</blockquote> <a name="user-content-documentation"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Documentation</h2><a id="user-content-documentation" class="anchor" aria-label="Permalink: Documentation" href="#documentation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This section explains all the public methods and attributes of Decimal and Context.</p> <a name="user-content-decimal-attributes"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Decimal Attributes</h3><a id="user-content-decimal-attributes" class="anchor" aria-label="Permalink: Decimal Attributes" href="#decimal-attributes"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Decimal has no public attributes. The internal information is stored in slots and should not be accessed by end users.</p> <a name="user-content-decimal-methods"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Decimal Methods</h3><a id="user-content-decimal-methods" class="anchor" aria-label="Permalink: Decimal Methods" href="#decimal-methods"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Following are the conversion and arithmetic operations defined in the Spec, and how that functionality can be achieved with the actual implementation.</p> <ul dir="auto"> <li><p dir="auto">to-scientific-string: Use builtin function <code>str()</code>:</p> <pre>>>> d = Decimal('123456789012.345') >>> str(d) '1.23456789E+11' </pre> </li> <li><p dir="auto">to-engineering-string: Use method <code>to_eng_string()</code>:</p> <pre>>>> d = Decimal('123456789012.345') >>> d.to_eng_string() '123.456789E+9' </pre> </li> <li><p dir="auto">to-number: Use Context method <code>create_decimal()</code>. The standard constructor or <code>from_float()</code> constructor cannot be used because these do not use the context (as is specified in the Spec for this conversion).</p> </li> <li><p dir="auto">abs: Use builtin function <code>abs()</code>:</p> <pre>>>> d = Decimal('-15.67') >>> abs(d) Decimal('15.67') </pre> </li> <li><p dir="auto">add: Use operator <code>+</code>:</p> <pre>>>> d = Decimal('15.6') >>> d + 8 Decimal('23.6') </pre> </li> <li><p dir="auto">subtract: Use operator <code>-</code>:</p> <pre>>>> d = Decimal('15.6') >>> d - 8 Decimal('7.6') </pre> </li> <li><p dir="auto">compare: Use method <code>compare()</code>. This method (and not the built-in function cmp()) should only be used when dealing with <em>special values</em>:</p> <pre>>>> d = Decimal('-15.67') >>> nan = Decimal('NaN') >>> d.compare(23) '-1' >>> d.compare(nan) 'NaN' >>> cmp(d, 23) -1 >>> cmp(d, nan) 1 </pre> </li> <li><p dir="auto">divide: Use operator <code>/</code>:</p> <pre>>>> d = Decimal('-15.67') >>> d / 2 Decimal('-7.835') </pre> </li> <li><p dir="auto">divide-integer: Use operator <code>//</code>:</p> <pre>>>> d = Decimal('-15.67') >>> d // 2 Decimal('-7') </pre> </li> <li><p dir="auto">max: Use method <code>max()</code>. Only use this method (and not the built-in function max()) when dealing with <em>special values</em>:</p> <pre>>>> d = Decimal('15') >>> nan = Decimal('NaN') >>> d.max(8) Decimal('15') >>> d.max(nan) Decimal('NaN') </pre> </li> <li><p dir="auto">min: Use method <code>min()</code>. Only use this method (and not the built-in function min()) when dealing with <em>special values</em>:</p> <pre>>>> d = Decimal('15') >>> nan = Decimal('NaN') >>> d.min(8) Decimal('8') >>> d.min(nan) Decimal('NaN') </pre> </li> <li><p dir="auto">minus: Use unary operator <code>-</code>:</p> <pre>>>> d = Decimal('-15.67') >>> -d Decimal('15.67') </pre> </li> <li><p dir="auto">plus: Use unary operator <code>+</code>:</p> <pre>>>> d = Decimal('-15.67') >>> +d Decimal('-15.67') </pre> </li> <li><p dir="auto">multiply: Use operator <code>*</code>:</p> <pre>>>> d = Decimal('5.7') >>> d * 3 Decimal('17.1') </pre> </li> <li><p dir="auto">normalize: Use method <code>normalize()</code>:</p> <pre>>>> d = Decimal('123.45000') >>> d.normalize() Decimal('123.45') >>> d = Decimal('120.00') >>> d.normalize() Decimal('1.2E+2') </pre> </li> <li><p dir="auto">quantize: Use method <code>quantize()</code>:</p> <pre>>>> d = Decimal('2.17') >>> d.quantize(Decimal('0.001')) Decimal('2.170') >>> d.quantize(Decimal('0.1')) Decimal('2.2') </pre> </li> <li><p dir="auto">remainder: Use operator <code>%</code>:</p> <pre>>>> d = Decimal('10') >>> d % 3 Decimal('1') >>> d % 6 Decimal('4') </pre> </li> <li><p dir="auto">remainder-near: Use method <code>remainder_near()</code>:</p> <pre>>>> d = Decimal('10') >>> d.remainder_near(3) Decimal('1') >>> d.remainder_near(6) Decimal('-2') </pre> </li> <li><p dir="auto">round-to-integral-value: Use method <code>to_integral()</code>:</p> <pre>>>> d = Decimal('-123.456') >>> d.to_integral() Decimal('-123') </pre> </li> <li><p dir="auto">same-quantum: Use method <code>same_quantum()</code>:</p> <pre>>>> d = Decimal('123.456') >>> d.same_quantum(Decimal('0.001')) True >>> d.same_quantum(Decimal('0.01')) False </pre> </li> <li><p dir="auto">square-root: Use method <code>sqrt()</code>:</p> <pre>>>> d = Decimal('123.456') >>> d.sqrt() Decimal('11.1110756') </pre> </li> <li><p dir="auto">power: User operator <code>**</code>:</p> <pre>>>> d = Decimal('12.56') >>> d ** 2 Decimal('157.7536') </pre> </li> </ul> <p dir="auto">Following are other methods and why they exist:</p> <ul dir="auto"> <li><p dir="auto"><code>adjusted()</code>: Returns the adjusted exponent. This concept is defined in the Spec: the adjusted exponent is the value of the exponent of a number when that number is expressed as though in scientific notation with one digit before any decimal point:</p> <pre>>>> d = Decimal('12.56') >>> d.adjusted() 1 </pre> </li> <li><p dir="auto"><code>from_float()</code>: Class method to create instances from float data types:</p> <pre>>>> d = Decimal.from_float(12.35) >>> d Decimal('12.3500000') </pre> </li> <li><p dir="auto"><code>as_tuple()</code>: Show the internal structure of the Decimal, the triple tuple. This method is not required by the Spec, but Tim Peters proposed it and the community agreed to have it (it's useful for developing and debugging):</p> <pre>>>> d = Decimal('123.4') >>> d.as_tuple() (0, (1, 2, 3, 4), -1) >>> d = Decimal('-2.34e5') >>> d.as_tuple() (1, (2, 3, 4), 3) </pre> </li> </ul> <a name="user-content-context-attributes"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Context Attributes</h3><a id="user-content-context-attributes" class="anchor" aria-label="Permalink: Context Attributes" href="#context-attributes"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">These are the attributes that can be changed to modify the context.</p> <ul dir="auto"> <li><p dir="auto"><code>prec</code> (int): the precision:</p> <pre>>>> c.prec 9 </pre> </li> <li><p dir="auto"><code>rounding</code> (str): rounding type (how to round):</p> <pre>>>> c.rounding 'half_even' </pre> </li> <li><p dir="auto"><code>trap_enablers</code> (dict): if trap_enablers[exception] = 1, then an exception is raised when it is caused:</p> <pre>>>> c.trap_enablers[Underflow] 0 >>> c.trap_enablers[Clamped] 0 </pre> </li> <li><p dir="auto"><code>flags</code> (dict): when an exception is caused, flags[exception] is incremented (whether or not the trap_enabler is set). Should be reset by the user of Decimal instance:</p> <pre>>>> c.flags[Underflow] 0 >>> c.flags[Clamped] 0 </pre> </li> <li><p dir="auto"><code>Emin</code> (int): minimum exponent:</p> <pre>>>> c.Emin -999999999 </pre> </li> <li><p dir="auto"><code>Emax</code> (int): maximum exponent:</p> <pre>>>> c.Emax 999999999 </pre> </li> <li><p dir="auto"><code>capitals</code> (int): boolean flag to use 'E' (True/1) or 'e' (False/0) in the string (for example, '1.32e+2' or '1.32E+2'):</p> <pre>>>> c.capitals 1 </pre> </li> </ul> <a name="user-content-context-methods"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Context Methods</h3><a id="user-content-context-methods" class="anchor" aria-label="Permalink: Context Methods" href="#context-methods"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The following methods comply with Decimal functionality from the Spec. Be aware that the operations that are called through a specific context use that context and not the thread context.</p> <p dir="auto">To use these methods, take note that the syntax changes when the operator is binary or unary, for example:</p> <pre>>>> mycontext.abs(Decimal('-2')) '2' >>> mycontext.multiply(Decimal('2.3'), 5) '11.5' </pre> <p dir="auto">So, the following are the Spec operations and conversions and how to achieve them through a context (where <code>d</code> is a Decimal instance and <code>n</code> a number that can be used in an <a href="#implicit-construction">Implicit construction</a>):</p> <ul dir="auto"> <li>to-scientific-string: <code>to_sci_string(d)</code></li> <li>to-engineering-string: <code>to_eng_string(d)</code></li> <li>to-number: <code>create_decimal(number)</code>, see <a href="#explicit-construction">Explicit construction</a> for <code>number</code>.</li> <li>abs: <code>abs(d)</code></li> <li>add: <code>add(d, n)</code></li> <li>subtract: <code>subtract(d, n)</code></li> <li>compare: <code>compare(d, n)</code></li> <li>divide: <code>divide(d, n)</code></li> <li>divide-integer: <code>divide_int(d, n)</code></li> <li>max: <code>max(d, n)</code></li> <li>min: <code>min(d, n)</code></li> <li>minus: <code>minus(d)</code></li> <li>plus: <code>plus(d)</code></li> <li>multiply: <code>multiply(d, n)</code></li> <li>normalize: <code>normalize(d)</code></li> <li>quantize: <code>quantize(d, d)</code></li> <li>remainder: <code>remainder(d)</code></li> <li>remainder-near: <code>remainder_near(d)</code></li> <li>round-to-integral-value: <code>to_integral(d)</code></li> <li>same-quantum: <code>same_quantum(d, d)</code></li> <li>square-root: <code>sqrt(d)</code></li> <li>power: <code>power(d, n)</code></li> </ul> <p dir="auto">The <code>divmod(d, n)</code> method supports decimal functionality through Context.</p> <p dir="auto">These are methods that return useful information from the Context:</p> <ul dir="auto"> <li><p dir="auto"><code>Etiny()</code>: Minimum exponent considering precision.</p> <pre>>>> c.Emin -999999999 >>> c.Etiny() -1000000007 </pre> </li> <li><p dir="auto"><code>Etop()</code>: Maximum exponent considering precision.</p> <pre>>>> c.Emax 999999999 >>> c.Etop() 999999991 </pre> </li> <li><p dir="auto"><code>copy()</code>: Returns a copy of the context.</p> </li> </ul> <a name="user-content-reference-implementation"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Reference Implementation</h2><a id="user-content-reference-implementation" class="anchor" aria-label="Permalink: Reference Implementation" href="#reference-implementation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">As of Python 2.4-alpha, the code has been checked into the standard library. The latest version is available from:</p> <p dir="auto"><a href="http://svn.python.org/view/python/trunk/Lib/decimal.py" rel="nofollow">http://svn.python.org/view/python/trunk/Lib/decimal.py</a></p> <p dir="auto">The test cases are here:</p> <p dir="auto"><a href="http://svn.python.org/view/python/trunk/Lib/test/test_decimal.py" rel="nofollow">http://svn.python.org/view/python/trunk/Lib/test/test_decimal.py</a></p> <a name="user-content-references"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">References</h2><a id="user-content-references" class="anchor" aria-label="Permalink: References" href="#references"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <markdown-accessiblity-table><table frame="void" id="user-content-id19" rules="none"> <tbody valign="top"> <tr><td>[1]</td><td><em>(<a href="#id1">1</a>, <a href="#id8">2</a>)</em> ANSI standard X3.274-1996 (Programming Language REXX): <a href="http://www.rexxla.org/Standards/ansi.html" rel="nofollow">http://www.rexxla.org/Standards/ansi.html</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-id20" rules="none"> <tbody valign="top"> <tr><td>[2]</td><td><em>(<a href="#id2">1</a>, <a href="#id3">2</a>, <a href="#id5">3</a>, <a href="#id6">4</a>, <a href="#id11">5</a>, <a href="#id12">6</a>, <a href="#id13">7</a>, <a href="#id14">8</a>)</em> General Decimal Arithmetic specification (Cowlishaw): <a href="http://speleotrove.com/decimal/decarith.html" rel="nofollow">http://speleotrove.com/decimal/decarith.html</a> (related documents and links at <a href="http://speleotrove.com/decimal/" rel="nofollow">http://speleotrove.com/decimal/</a>)</td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-id21" rules="none"> <tbody valign="top"> <tr><td><a href="#id7">[3]</a></td><td>ANSI/IEEE standard 854-1987 (Radix-Independent Floating-Point Arithmetic): <a href="http://www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html" rel="nofollow">http://www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html</a> (unofficial text; official copies can be ordered from <a href="http://standards.ieee.org/catalog/ordering.html" rel="nofollow">http://standards.ieee.org/catalog/ordering.html</a>)</td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-id22" rules="none"> <tbody valign="top"> <tr><td><a href="#id4">[4]</a></td><td>Tim Peter's FixedPoint at SourceForge: <a href="http://fixedpoint.sourceforge.net/" rel="nofollow">http://fixedpoint.sourceforge.net/</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-id23" rules="none"> <tbody valign="top"> <tr><td><a href="#id9">[5]</a></td><td>IEEE 754 revision: <a href="http://grouper.ieee.org/groups/754/revision.html" rel="nofollow">http://grouper.ieee.org/groups/754/revision.html</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-id24" rules="none"> <tbody valign="top"> <tr><td><a href="#id10">[6]</a></td><td>IEEE 754 references: <a href="http://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html" rel="nofollow">http://babbage.cs.qc.edu/courses/cs341/IEEE-754references.html</a></td></tr> </tbody> </table></markdown-accessiblity-table> <a name="user-content-copyright"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Copyright</h2><a id="user-content-copyright" class="anchor" aria-label="Permalink: Copyright" href="#copyright"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This document has been placed in the public domain.</p> </article></div><button hidden=""></button></section></div></div></div> <!-- --> <!-- --> </div></div></div><div class="Box-sc-g0xbh4-0"></div></div></div></div></div><div id="find-result-marks-container" class="Box-sc-g0xbh4-0 cCoXib"></div><button hidden="" data-testid="" data-hotkey-scope="read-only-cursor-text-area"></button><button hidden=""></button></div> <!-- --> <!-- --> <script type="application/json" id="__PRIMER_DATA_:R0:__">{"resolvedServerColorMode":"day"}</script></div> </react-app> </turbo-frame> </div> </turbo-frame> </main> </div> </div> <footer class="footer pt-8 pb-6 f6 color-fg-muted p-responsive" role="contentinfo" > <h2 class='sr-only'>Footer</h2> <div class="d-flex flex-justify-center flex-items-center flex-column-reverse flex-lg-row flex-wrap flex-lg-nowrap"> <div 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<ghcc-consent id="ghcc" class="position-fixed bottom-0 left-0" style="z-index: 999999" data-initial-cookie-consent-allowed="" data-cookie-consent-required="false"></ghcc-consent> <div id="ajax-error-message" class="ajax-error-message flash flash-error" hidden> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-alert"> <path d="M6.457 1.047c.659-1.234 2.427-1.234 3.086 0l6.082 11.378A1.75 1.75 0 0 1 14.082 15H1.918a1.75 1.75 0 0 1-1.543-2.575Zm1.763.707a.25.25 0 0 0-.44 0L1.698 13.132a.25.25 0 0 0 .22.368h12.164a.25.25 0 0 0 .22-.368Zm.53 3.996v2.5a.75.75 0 0 1-1.5 0v-2.5a.75.75 0 0 1 1.5 0ZM9 11a1 1 0 1 1-2 0 1 1 0 0 1 2 0Z"></path> </svg> <button type="button" class="flash-close js-ajax-error-dismiss" aria-label="Dismiss error"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg> </button> You can’t perform that action at this time. </div> <template id="site-details-dialog"> <details class="details-reset details-overlay details-overlay-dark lh-default color-fg-default hx_rsm" open> <summary role="button" aria-label="Close dialog"></summary> <details-dialog class="Box Box--overlay d-flex flex-column anim-fade-in fast hx_rsm-dialog hx_rsm-modal"> <button class="Box-btn-octicon m-0 btn-octicon position-absolute right-0 top-0" type="button" aria-label="Close dialog" data-close-dialog> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-x"> <path d="M3.72 3.72a.75.75 0 0 1 1.06 0L8 6.94l3.22-3.22a.749.749 0 0 1 1.275.326.749.749 0 0 1-.215.734L9.06 8l3.22 3.22a.749.749 0 0 1-.326 1.275.749.749 0 0 1-.734-.215L8 9.06l-3.22 3.22a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042L6.94 8 3.72 4.78a.75.75 0 0 1 0-1.06Z"></path> </svg> </button> <div class="octocat-spinner my-6 js-details-dialog-spinner"></div> </details-dialog> </details> </template> <div class="Popover js-hovercard-content position-absolute" style="display: none; outline: none;"> <div class="Popover-message Popover-message--bottom-left Popover-message--large Box color-shadow-large" style="width:360px;"> </div> </div> <template id="snippet-clipboard-copy-button"> <div class="zeroclipboard-container position-absolute right-0 top-0"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn js-clipboard-copy m-2 p-0" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon m-2"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none m-2"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> <template id="snippet-clipboard-copy-button-unpositioned"> <div class="zeroclipboard-container"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn btn-invisible js-clipboard-copy m-2 p-0 d-flex flex-justify-center flex-items-center" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> </div> <div id="js-global-screen-reader-notice" class="sr-only mt-n1" aria-live="polite" aria-atomic="true" ></div> <div id="js-global-screen-reader-notice-assertive" class="sr-only mt-n1" aria-live="assertive" aria-atomic="true"></div> </body> </html>