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Text of the page (random words):
od yes no floored forth mod yes no implementation defined fm mod yes no floored sm rem yes no truncated fortran mod yes yes truncated 42 modulo yes yes floored 43 frink mod yes yes floored 44 full basic mod yes yes floored 45 remainder yes yes truncated 46 glsl yes no undefined 47 mod no yes floored 48 gamemaker studio gml mod yes no truncated gdscript godot yes no truncated 49 posmod yes no euclidean 50 fmod no yes truncated 51 fposmod no yes euclidean 52 go yes no truncated 53 math mod no yes truncated 54 big int mod yes no euclidean 55 big int rem yes no truncated 56 groovy yes no truncated haskell mod yes no floored 57 rem yes no truncated 57 data fixed mod ghc no yes floored haxe yes yes truncated 58 hlsl yes yes undefined 59 j c yes no floored java yes yes truncated 60 integer remainderunsigned long remainderunsigned yes no n a 61 62 math ceilmod strictmath ceilmod yes no ceiling 63 64 65 66 67 68 math floormod strictmath floormod yes no floored 69 70 71 72 73 74 math ieeeremainder strictmath ieeeremainder no yes rounded 75 76 a mod b biginteger yes no euclidean 77 a remainder b biginteger yes no truncated 78 a remainder b a remainder b mathcontext bigdecimal no yes truncated 79 80 javascript typescript yes yes truncated julia mod yes yes floored 81 rem yes yes truncated 82 kotlin rem yes yes truncated 83 mod yes yes floored 84 ksh yes no truncated same as posix sh fmod no yes truncated labview mod yes yes truncated libreoffice mod yes yes floored 85 logo modulo yes no floored remainder yes no truncated lua 5 yes yes floored lua 4 mod x y yes yes truncated liberty basic mod yes no truncated mathcad mod x y yes no floored maple e mod m by default modp e m yes no euclidean mods e m yes no rounded frem e m yes yes rounded mathematica mod a b yes yes floored 86 matlab mod yes yes floored 87 rem yes yes truncated 88 maxima mod yes no floored remainder yes no truncated maya embedded language yes no truncated fmod no yes truncated same as c 89 microsoft excel mod yes yes floored 90 minitab mod yes no floored modula 2 mod yes no floored rem yes no truncated mumps yes no floored 91 netwide assembler nasm nasmx div unsigned yes no n a signed yes no implementation defined 92 nim mod yes yes truncated 93 94 floormod yes yes floored 95 oberon mod yes no floored like e objective c yes no truncated same as c99 object pascal delphi mod yes no truncated ocaml mod yes no truncated 96 mod_float no yes truncated 97 occam yes no truncated pascal iso 7185 and 10206 mod yes no euclidean like f perl yes no floored g posix fmod no yes truncated same as c 99 php yes no truncated 100 fmod no yes truncated 101 pic basic pro yes no truncated pl i mod yes no floored ansi pl i powershell yes no truncated programming code prc math op mod yes no undefined progress modulo yes no truncated prolog mod yes no floored rem yes no truncated purebasic yes no truncated mod x y no yes truncated 102 purescript mod yes no euclidean 103 pure data yes no truncated same as c mod yes no floored python yes yes floored 104 math fmod no yes truncated 105 math remainder no yes rounded 106 q yes no truncated 107 r yes yes floored 108 racket modulo yes some h floored 110 remainder yes some h truncated 111 raku no yes floored realbasic mod yes no truncated reason mod yes no truncated rexx yes yes truncated rpg rem yes no truncated ruby modulo yes yes floored remainder yes yes truncated rust yes yes truncated 112 rem_euclid yes yes euclidean 113 sas mod yes no truncated scala yes yes truncated scheme modulo yes no floored remainder yes no truncated scheme r 6 rs mod yes no euclidean 114 mod0 yes no rounded 114 flmod no yes euclidean flmod0 no yes rounded scratch mod yes yes floored seed7 mod yes yes floored rem yes yes truncated sensetalk modulo yes no floored rem yes no truncated sh posix includes bash mksh c yes no truncated same as c 115 smalltalk yes yes floored 116 sec 5 6 2 9 rem yes yes truncated 116 sec 5 6 2 30 snap mod yes no floored spin yes no floored solidity yes no truncated 117 sql sql 1999 mod x y yes no truncated sql sql 2011 yes no truncated standard ml mod yes no floored int rem yes no truncated real rem no yes truncated stata mod x y yes no euclidean swift yes no truncated 118 remainder dividingby no yes rounded 119 truncatingremainder dividingby no yes truncated 120 tcl expr a n tcl mathop a n i yes no floored 122 123 expr fmod a n tcl mathfunc fmod a n j no yes truncated same as c tcsh yes no truncated torque yes no truncated turing mod yes no floored verilog 2001 yes no truncated vhdl mod yes no floored rem yes no truncated viml yes no truncated visual basic mod yes no truncated webassembly i32 rem_u i64 rem_u unsigned yes no n a 125 i32 rem_s i64 rem_s signed yes no truncated 125 x86 assembly div unsigned yes no n a idiv signed yes no truncated fprem no yes truncated fprem1 no yes rounded xbase yes yes truncated mod yes yes floored zig rem yes yes truncated 126 mod yes yes floored z3 theorem prover div mod yes no euclidean in addition many computer systems provide a divmod functionality which produces the quotient and the remainder at the same time examples include the x86 architecture s div and idiv instructions the c programming language s div function and python s divmod function generalizations edit modulo with offset edit sometimes it is useful for the result of a modulo n to lie not between 0 and n 1 but between some number d and d n 1 in that case d is called an offset and d 1 is particularly common there does not seem to be a standard notation for this operation so let us tentatively use a mod d n we thus have the following definition 127 x a mod d n just in case d x d n 1 and x mod n a mod n clearly the usual modulo operation corresponds to zero offset a mod n a mod 0 n the operation of modulo with offset is related to the floor function as follows a mod d n a n a d n displaystyle a operatorname mod _ d n a n left lfloor frac a d n right rfloor to see this let x a n a d n textstyle x a n left lfloor frac a d n right rfloor we first show that x mod n a mod n it is in general true that a bn mod n a mod n for all integers b thus this is true also in the particular case when b a d n textstyle b left lfloor frac a d n right rfloor but that means that x mod n a n a d n mod n a mod n textstyle x bmod n left a n left lfloor frac a d n right rfloor right bmod n a bmod n which is what we wanted to prove it remains to be shown that d x d n 1 let k and r be the integers such that a d kn r with 0 r n 1 see euclidean division then a d n k textstyle left lfloor frac a d n right rfloor k thus x a n a d n a n k d r textstyle x a n left lfloor frac a d n right rfloor a nk d r now take 0 r n 1 and add d to both sides obtaining d d r d n 1 but we ve seen that x d r so we are done the modulo with offset a mod d n is implemented in mathematica as mod a n d 127 implementing other modulo definitions using truncation edit despite the mathematical elegance of knuth s floored division and euclidean division it is generally much more common to find a truncated division based modulo in programming languages leijen provides the following algorithms for calculating the two divisions given a truncated integer division euclidean and floored divmod in the style of c s ldiv typedef struct this structure is part of the c stdlib h but is reproduced here for clarity long int quot long int rem ldiv_t euclidean division inline ldiv_t ldive long numer long denom the c99 and c 11 languages define both of these as truncating long q numer denom long r numer denom if r 0 if denom 0 q q 1 r r denom else q q 1 r r denom return ldiv_t quot q rem r floored division inline ldiv_t ldivf long numer long denom long q numer denom long r numer denom if r 0 denom 0 r 0 denom 0 q q 1 r r denom return ldiv_t quot q rem r for both cases the remainder can be calculated independently of the quotient but not vice versa the operations are combined here to save screen space as the logical branches are the same see also edit modulo disambiguation many uses of the word modulo all of which grew out of carl f gauss approach to modular arithmetic in 1801 modulo mathematics general use of the term in mathematics modular exponentiation turn angle notes edit mathematically these two choices are but two of the infinite number of choices available for the inequality satisfied by a remainder the revised report uses boldface to distinguish between keywords and identifiers but permits other formats including capitalization e g mod 1 2 argument order reverses i e α ω computes ω mod α displaystyle omega bmod alpha the remainder when dividing ω by α c99 and c 11 define the behavior of to be truncated 14 the standards before then leave the behavior implementation defined 15 divisor must be positive otherwise undefined as discussed by boute iso pascal s definitions of div and mod do not obey the division identity of d d d d d d and are thus fundamentally broken perl usually uses arithmetic modulo operator that is machine independent for examples and exceptions see the perl documentation on multiplicative operators 98 1 2 racket defines an integer as a rational number for which round produces the same number when applied this includes some inexact numbers like 42 0 but excludes others like 3 14 109 the expr command is defined independently of commands in the tcl mathop namespace 121 the expr command is defined in terms of commands in the tcl mathfunc namespace 124 references edit weisstein eric w congruence wolfram mathworld retrieved 2020 08 27 caldwell chris residue prime glossary retrieved august 27 2020 knuth donald e 1972 the art of computer programming addison wesley boute raymond t april 1992 the euclidean definition of the functions div and mod acm transactions on programming languages and systems 14 2 acm press new york ny usa 127 144 doi 10 1145 128861 128862 hdl 1854 lu 314490 s2cid 8321674 peterson doctor 5 july 2001 mod function and negative numbers math forum ask dr math archived from the original on 2019 10 22 retrieved 22 october 2019 ada 83 lrm sec 4 5 operators and expression evaluation archive adaic com retrieved 2025 03 03 horvath adam july 5 2012 faster division and modulo operation the power of two abap keyword documentation help sap com 2024 retrieved 2026 01 18 operators adobe actionscript 3 as3 api reference help adobe com retrieved 2026 01 19 1 2 iso iec 8652 2012 information technology programming languages ada iso iec 2012 sec 4 5 5 multiplying operators revised report on the algorithmic language algol 68 ifip wg2 1 1973 sec 10 2 3 3 n awk pubs opengroup org retrieved 2026 01 19 bc pubs opengroup org retrieved 2026 05 23 c99 specification iso iec 9899 tc2 pdf 2005 05 06 sec 6 5 5 multiplicative operators retrieved 16 august 2018 iso iec 14882 2003 programming languages c international organization for standardization iso international electrotechnical commission iec 2003 sec 5 6 4 the binary operator yields the remainder from the division of the first expression by the second if both operands are nonnegative then the remainder is nonnegative if not the sign of the remainder is implementation defined iso iec 9899 1990 programming languages c iso iec 1990 sec 7 5 6 4 the fmod function returns the value x i y for some integer i such that if y is nonzero the result has the same sign as x and magnitude less than the magnitude of y iso iec 9899 1999 programming languages c iso iec 1999 sec 7 12 10 2 the remainder functions compute the remainder x rem y required by iec 60559 expressions c language specification learn microsoft com retrieved 2026 01 19 1 2 dotnet bot math ieeeremainder double double method system microsoft learn retrieved 2022 10 04 clojure core clojure v1 10 3 api documentation clojure github io retrieved 2022 03 16 clojure core clojure v1 10 3 api documentation clojure github io retrieved 2022 03 16 1 2 iso iec jtc 1 sc 22 wg 4 january 2023 iso iec 1989 2023 programming language cobol iso 1 2 coffeescript coffeescript org retrieved 2026 07 22 iso iec jtc 1 sc 22 february 2012 iso iec 23271 2012 information technology common language infrastructure cli iso iii 3 55 56 1 2 clhs function mod rem www lispworks com retrieved 2026 01 20 mod css cascading style sheets mdn developer mozilla org 2024 06 22 retrieved 2024 10 23 rem css cascading style sheets mdn developer mozilla org 2024 10 15 retrieved 2024 10 23 expressions d programming language dlang org retrieved 2021 06 01 operator method num class dart core library dart api api dart dev retrieved 2021 06 01 remainder method num class dart core library dart api api dart dev retrieved 2021 06 01 dc an arbitrary precision calculator www gnu org archived from the original on 2025 12 10 retrieved 2026 05 23 kernel elixir v1 11 3 hexdocs pm retrieved 2021 01 28 integer elixir v1 11 3 hexdocs pm retrieved 2021 01 28 basics core 1 0 5 package elm lang org retrieved 2022 03 16 basics core 1 0 5 package elm lang org retrieved 2022 03 16 erlang math erlang org retrieved 2021 06 01 openeuphoria euphoria v4 0 openeuphoria org retrieved 2026 01 20 openeuphoria euphoria v4 0 openeuphoria org retrieved 2026 01 20 18 the f library fsharp core dll f language specification fsharp github io retrieved 2026 01 19 mod x y z factor documentation docs factorcode org retrieved 2026 01 21 rem x y z factor documentation docs factorcode org retrieved 2026 01 21 manipulation and properties of numeric values fortran programming language fortran lang org retrieved 2026 05 22 manipulation and properties of numeric values fortran programming language fortran lang org retrieved 2026 05 22 frink frinklang org retrieved 2026 07 22 ansi 28 january 1987 programming languages full basic new york american national standards institute 5 4 4 x modulo y i e x y int x y ansi 28 january 1987 programming languages full basic new york american national standards institute 5 4 4 the remainder function i e x y ip x y glsl language specification version 4 50 7 pdf section 5 9 expressions if both operands are non negative then the remainder is non negative results are undefined if one or both operands are negative glsl language specification version 4 50 7 pdf section 8 3 common functions int godot engine documentation retrieved 2026 01 19 globalscope godot engine documentation retrieved 2026 01 19 globalscope godot engine documentation retrieved 2026 01 19 globalscope godot engine documentation retrieved 2026 01 19 the go programming language specification the go programming language go dev retrieved 2022 02 28 math package math pkg go dev pkg go dev retrieved 2022 02 28 big package math big pkg go dev pkg go dev retrieved 2022 02 28 big package math big pkg go dev pkg go dev retrieved 2024 04 12 1 2 6 predefined types and classes www haskell org retrieved 2022 05 22 binary operators haxe the cross platform toolkit retrieved 2026 01 20 operators microsoft 30 june 2021 retrieved 2021 07 19 the operator is defined only in cases where either both sides are positive or both sid...