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GeezerVison is showing reference.wolfram.com — FoldWhile—Wolfram Documentation FoldWhile[f,x,{a1,a2,…},test] returns the first expression f[… f[f[x,a1],a2]…,ak] to which applying test does not yield True. FoldWhile[f,x,{a1,a2,…},test,m] supplies the most recent m results as arguments for test at each step. FoldWhile[f,x,{a1,a2,…},test,m,n] returns the result after applying f an extra n times after test fails. FoldWhile[f,x,{a1,a2,…},test,m,-n] returns the result found when f had been applied n fewer times. Details
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FoldWhileFoldWhile[f,x,{a1,a2,…},test] returns the first expression f[… f[f[x,a1],a2]…,ak] to which applying test does not yield True. FoldWhile[f,x,{a1,a2,…},test,m] supplies the most recent m results as arguments for test at each step. FoldWhile[f,x,{a1,a2,…},test,m,n] returns the result after applying f an extra n times after test fails. FoldWhile[f,x,{a1,a2,…},test,m,-n] returns the result found when f had been applied n fewer times. Details
Examplesopen all close allBasic Examples (3)Divide 5! by consecutive positive integers, until the result is a non-integer: FoldWhile[Divide, 5!, Range[10], IntegerQ]Add 1/n6 terms until Unequal yields False for two consecutive results in machine arithmetic: FoldWhile[Plus, 0., 1 / Range[1000] ^ 6, Unequal, 2]Divide 5! by consecutive positive integers and return the last integer result: FoldWhile[Divide, 5!, Range[10], IntegerQ, 1, -1]Scope (9)Starting with 12, subtract increasing integers while the remainder is still positive: FoldWhile[Subtract, 12, {1, 2, 3, 4, 5, 6}, Positive]Use Echo to display the intermediate results: FoldWhile[Echo @* Subtract, 12, {1, 2, 3, 4, 5, 6}, Positive]Display the results of the corresponding tests: FoldWhile[Subtract, 12, {1, 2, 3, 4, 5, 6}, Echo @* Positive]Compute a random walk starting from the origin, and return the first point whose norm is beyond 10: FoldWhile[Plus, {0, 0}, AngleVector /@ RandomReal[2Pi, 200], Norm /* LessThan[10]]Norm[%]Fold Cross over a list of random unit vectors while the norm of the result is larger than 0.1: FoldWhile[Cross, Normalize /@ RandomReal[1, {100, 3}], Norm /* GreaterThan[0.1]]Norm[%]Add 1/n8 terms until Unequal yields False for two consecutive results in machine arithmetic: FoldWhile[Plus, 0., 1 / Range[200] ^ 8, Unequal, 2]Add random integers to 0 while all results are different, returning the first value that was repeated: SeedRandom[123];FoldWhile[Plus, 0, DeleteCases[RandomInteger[{-10, 10}, 100], 0], UnsameQ, All]Divide 5! by consecutive positive integers, returning the first non-integer result: FoldWhile[Divide, 5!, Range[10], IntegerQ, 1, 0]Return the last integer result: FoldWhile[Divide, 5!, Range[10], IntegerQ, 1, -1]Return the next-to-last integer result: FoldWhile[Divide, 5!, Range[10], IntegerQ, 1, -2]Abort the computation before it is finished: Catch[FoldWhile[If[# > 25, Divide[#1, #2], Throw[#1]]&, 5!, Range[10], IntegerQ]]Use FoldWhile in operator form: FoldWhile[Subtract, Positive][12, {1, 2, 3, 4, 5, 6}]FoldWhile[Plus, LessThan[20]][Range[10]]FoldWhile admits operator forms of three or four arguments when the third and fourth arguments are explicit integers: FoldWhile[Subtract, Positive, 1, -1][12, {1, 2, 3, 4, 5, 6}]Properties & Relations (4)If test[x] does not yield True, FoldWhile[f,x,alist,test] returns x: FoldWhile[Divide, 0, {2, 3, 4, 5}, Positive]FoldWhile[f,x,alist,test,…] is equivalent to Last[FoldWhileList[f,x,alist,test,…]]: FoldWhileList[Divide, 5!, Range[10], IntegerQ]Last[%]FoldWhile[Divide, 5!, Range[10], IntegerQ]FoldWhile[f,x,list,True&] is equivalent to Fold[f,x,list]: FoldWhile[Plus, 0, Range[10], True&]Fold[Plus, 0, Range[10]]FoldWhile[f,x,list,test,m,n] is equivalent to NestWhile[f,x,test,m,Length[list],n] for a function f taking only one argument: FoldWhile[Sqrt[#]&, 10 ^ 6, Range[4], GreaterThan[2], 1, 0]NestWhile[Sqrt[#]&, 10 ^ 6, GreaterThan[2], 1, 4, 0]See AlsoRelated GuidesHistory
Wolfram Research (2020), FoldWhile, Wolfram Language function, https://reference.wolfram.com/language/ref/FoldWhile.html.
TextWolfram Research (2020), FoldWhile, Wolfram Language function, https://reference.wolfram.com/language/ref/FoldWhile.html. CMSWolfram Language. 2020. "FoldWhile." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FoldWhile.html. APAWolfram Language. (2020). FoldWhile. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FoldWhile.html BibTeX@misc{reference.wolfram_2026_foldwhile, author="Wolfram Research", title="{FoldWhile}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/FoldWhile.html}", note=[Accessed: 12-November-2026]} BibLaTeX@online{reference.wolfram_2026_foldwhile, organization={Wolfram Research}, title={FoldWhile}, year={2020}, url={https://reference.wolfram.com/language/ref/FoldWhile.html}, note=[Accessed: 12-November-2026]} |
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