Pathological floating point problems: Difference between revisions

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Line 1,980: =={{header\|Fōrmulæ}}== {{FormulaeEntry\|page=https://formulae.org/?script=examples/Pathological_floating_point_problems}} Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition. '''Solution''' Programs in Fōrmulæ are created/edited online in its [https://formulae.org website], However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used. '''Case 1. Introduction example''' ~~In '''[https://formulae.org/?example=Pathological_floating_point_problems this]''' page you can see the program(s) related to this task and their results.~~ [[File:Fōrmulæ - Pathological floating point problems 01.png]] [[File:Fōrmulæ - Pathological floating point problems 02.png]] '''Case 2. A sequence that seems to converge to a wrong limit''' [[File:Fōrmulæ - Pathological floating point problems 03.png]] [[File:Fōrmulæ - Pathological floating point problems 04.png]] '''Case 3. The Chaotic Bank Society''' [[File:Fōrmulæ - Pathological floating point problems 05.png]] [[File:Fōrmulæ - Pathological floating point problems 06.png]] '''Case 4. Siegfried Rump's example''' [[File:Fōrmulæ - Pathological floating point problems 07.png]] [[File:Fōrmulæ - Pathological floating point problems 08.png]] =={{header\|Go}}== Line 2,782 ⟶ 2,804: f(77617.0, 33096.0) is -0.8273960599468214 </pre> =={{header\|M2000 Interpreter}}== From n=26 we get wrong numbers (not shown here). For Task 2 only Decimal can show a good result, although has less accuracy. <syntaxhighlight lang="m2000 interpreter"> module Pathological_floating_point_problems{ decimal vn[3] vn[1]=2 vn[2]=-4 for i=3 to 100 vn[i]=111@-1130@/vn[i-1]+3000@/(vn[i-1]vn[i-2]) next n=list:=3,4,5,6,7,8,20,25 k=each(n) while k report "n = "+eval$(k)+chr$(9)+(vn[eval(k)]) end while } print "Task 1" Pathological_floating_point_problems print print "Task 2" module Chaotic_Bank_Society { decimal Balance=2.7182818284590452353602874713@-1@ string frmt="year {0::-2} Balance:{1}" for i=1 to 25 Balance=Balancei-1@ rem print format$(frmt, i, Balance) next i Print "Starting balance: $e-1" Print "Balance = (Balance * year) - 1 for 25 years" print "Balance after 25 years: $"+Balance } Chaotic_Bank_Society </syntaxhighlight> {{out}} <pre> Task 1 n = 3 18.5 n = 4 9.378378378378378378378378378 n = 5 7.80115273775216138328530259 n = 6 7.154414480975249353527890606 n = 7 6.806784736923632983941755925 n = 8 6.592632768704438392741992887 n = 20 6.04355210719488789087813234 n = 25 6.01330401514055310928530167 Task 2 Starting balance: $e-1 Balance = (Balance * year) - 1 for 25 years Balance after 25 years: $0.0391218706091111022592 </pre> =={{header\|Mathematica}}/{{header\|Wolfram Language}}== Line 4,442 ⟶ 4,518: {{libheader\|Wren-big}} {{libheader\|Wren-fmt}} <syntaxhighlight lang="~~ecmascript~~wren">import "./big" for BigRat import "./fmt" for Fmt var LIMIT = 100 Line 4,582 ⟶ 4,658: f(77617.0, 33096.0) is -0.8273960599468214 </pre> =={{header\|XPL0}}== This shows the results from the IEEE 754 double precision (64-bit) FPU built into the Raspberry Pi 4. Identical results were obtained from EXPL-32 on an Intel Inspiron. A Duron 850 gave identical results for the first task, but the second task diverged to positive values after 17 years. The Duron also gave a large positive value for the third task. <syntaxhighlight lang "XPL0">func real F(A, B); real A, B; return 333.75Pow(B,6.) + AA(11.AABB - Pow(B,6.) - 121.Pow(B,4.) - 2.) + 5.5Pow(B,8.) + A/(2.B); real V1, V2, V3, Bal; int N, Year; [V1:= 2.; V2:= -4.; \task 1 for N:= 3 to 100 do [V3:= 111. - 1130./V2 + 3000./(V1V2); case N of 3,4,5,6,7,8,20,30,50,100: [Format(3, 0); RlOut(0, float(N)); Format(5, 16); RlOut(0, V3); CrLf(0); ] other []; V1:= V2; V2:= V3; ]; CrLf(0); \task 2 Bal:= Exp(1.) - 1.; for Year:= 1 to 25 do [Bal:= Balfloat(Year) - 1.; Format(2, 0); RlOut(0, float(Year)); Format(12, 16); RlOut(0, Bal); CrLf(0); ]; CrLf(0); \task 3 RlOut(0, F(77617., 33096.)); CrLf(0); ]</syntaxhighlight> {{out}} <pre> 3 18.5000000000000000 4 9.3783783783783800 5 7.8011527377521700 6 7.1544144809753300 7 6.8067847369248100 8 6.5926327687217900 20 98.3495031221654000 30 99.9999999999989000 50 100.0000000000000000 100 100.0000000000000000 1 0.7182818284590450 2 0.4365636569180900 3 0.3096909707542710 4 0.2387638830170820 5 0.1938194150854110 6 0.1629164905124650 7 0.1404154335872580 8 0.1233234686980610 9 0.1099112182825480 10 0.0991121828254790 11 0.0902340110802700 12 0.0828081329632370 13 0.0765057285220790 14 0.0710801993091080 15 0.0662029896366220 16 0.0592478341859530 17 0.0072131811612050 18 -0.8701627390983050 19 -17.5330920428678000 20 -351.6618408573560000 21 -7385.8986580044700000 22 -162490.7704760980000000 23 -3737288.7209502600000000 24 -89694930.3028063000000000 25 -2242373258.5701600000000000 -1180591620717410000000.0000000000000000 </pre>