home *** CD-ROM | disk | FTP | other *** search
/ Language/OS - Multiplatform Resource Library / LANGUAGE OS.iso / scheme / pcscheme / geneva / pcscheme.exe / SAMPLES / RECUR.SW < prev    next >
LaTeX Document  |  1992-12-10  |  3.7 KB

open in: MacOS 8.1     |     Win98     |     DOS

browse contents    |     view JSON data     |     view as text


This file was processed as: LaTeX Document (document/latex).

ConfidenceProgramDetectionMatch TypeSupport
100% dexvert LaTeX Document (document/latex) magic Supported
1% dexvert Text File (text/txt) fallback Supported
100% file LaTeX document text default
99% file LaTeX document, ASCII text, with CRLF line terminators default
100% TrID LaTeX 2e document (with rem) default
100% checkBytes Printable ASCII default
100% perlTextCheck Likely Text (Perl) default
100% siegfried fmt/281 LaTeX (Subdocument) default
100% detectItEasy Format: plain text[CRLF] default (weak)



hex view
+--------+-------------------------+-------------------------+--------+--------+
|00000000| 25 2a 20 52 45 43 55 52 | 2e 53 57 0d 0a 25 2a 2a |%* RECUR|.SW..%**|
|00000010| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000020| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000030| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000040| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000050| 2a 2a 2a 2a 2a 2a 0d 0a | 25 2a 09 09 09 09 09 09 |******..|%*......|
|00000060| 09 09 09 2a 0d 0a 25 2a | 09 09 50 43 20 53 63 68 |...*..%*|..PC Sch|
|00000070| 65 6d 65 2f 47 65 6e 65 | 76 61 20 34 2e 30 30 20 |eme/Gene|va 4.00 |
|00000080| 53 63 68 65 6d 65 20 73 | 75 70 70 6f 72 74 20 63 |Scheme s|upport c|
|00000090| 6f 64 65 09 09 2a 0d 0a | 25 2a 09 09 09 09 09 09 |ode..*..|%*......|
|000000a0| 09 09 09 2a 0d 0a 25 2a | 20 28 63 29 20 31 39 38 |...*..%*| (c) 198|
|000000b0| 35 2d 31 39 38 38 20 62 | 79 20 54 65 78 61 73 20 |5-1988 b|y Texas |
|000000c0| 49 6e 73 74 72 75 6d 65 | 6e 74 73 2c 20 49 6e 63 |Instrume|nts, Inc|
|000000d0| 2e 20 53 65 65 20 43 4f | 50 59 52 49 47 48 54 2e |. See CO|PYRIGHT.|
|000000e0| 54 58 54 09 09 2a 0d 0a | 25 2a 20 28 63 29 20 31 |TXT..*..|%* (c) 1|
|000000f0| 39 39 32 20 62 79 20 4c | 2e 20 42 61 72 74 68 6f |992 by L|. Bartho|
|00000100| 6c 64 69 20 26 20 4d 2e | 20 56 75 69 6c 6c 65 75 |ldi & M.| Vuilleu|
|00000110| 6d 69 65 72 2c 20 55 6e | 69 76 65 72 73 69 74 79 |mier, Un|iversity|
|00000120| 20 6f 66 20 47 65 6e 65 | 76 61 09 2a 0d 0a 25 2a | of Gene|va.*..%*|
|00000130| 09 09 09 09 09 09 09 09 | 09 2a 0d 0a 25 2a 2d 2d |........|.*..%*--|
|00000140| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000150| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000160| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000170| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000180| 2d 2d 2d 2d 2a 0d 0a 25 | 2a 09 09 09 09 09 09 09 |----*..%|*.......|
|00000190| 09 09 2a 0d 0a 25 2a 09 | 09 41 20 66 65 77 20 66 |..*..%*.|.A few f|
|000001a0| 75 6e 20 64 65 6d 6f 73 | 20 6f 66 20 72 65 63 75 |un demos| of recu|
|000001b0| 72 73 69 76 65 20 66 75 | 6e 63 74 69 6f 6e 73 09 |rsive fu|nctions.|
|000001c0| 09 09 2a 0d 0a 25 2a 09 | 09 09 09 09 09 09 09 09 |..*..%*.|........|
|000001d0| 2a 0d 0a 25 2a 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |*..%*---|--------|
|000001e0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000001f0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000200| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000210| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2a 0d 0a 25 2a |--------|---*..%*|
|00000220| 09 09 09 09 09 09 09 09 | 09 2a 0d 0a 25 2a 20 43 |........|.*..%* C|
|00000230| 72 65 61 74 65 64 20 62 | 79 3a 20 4c 2e 20 42 61 |reated b|y: L. Ba|
|00000240| 72 74 68 6f 6c 64 69 09 | 09 44 61 74 65 3a 20 31 |rtholdi.|.Date: 1|
|00000250| 39 39 32 09 09 09 2a 0d | 0a 25 2a 20 52 65 76 69 |992...*.|.%* Revi|
|00000260| 73 69 6f 6e 20 68 69 73 | 74 6f 72 79 3a 09 09 09 |sion his|tory:...|
|00000270| 09 09 09 09 2a 0d 0a 25 | 2a 20 2d 20 20 31 20 4f |....*..%|* - 1 O|
|00000280| 63 74 20 39 32 3a 09 52 | 65 6e 61 69 73 73 61 6e |ct 92:.R|enaissan|
|00000290| 63 65 20 28 42 6f 72 6c | 61 6e 64 20 43 6f 6d 70 |ce (Borl|and Comp|
|000002a0| 69 6c 65 72 73 2c 20 2e | 2e 2e 29 09 09 09 2a 0d |ilers, .|..)...*.|
|000002b0| 0a 25 2a 09 09 09 09 09 | 09 09 09 09 2a 0d 0a 25 |.%*.....|....*..%|
|000002c0| 2a 09 09 09 09 09 60 60 | 49 6e 20 6e 6f 6d 69 6e |*.....``|In nomin|
|000002d0| 65 20 6f 6d 6e 69 70 6f | 74 65 6e 74 69 69 20 64 |e omnipo|tentii d|
|000002e0| 65 69 27 27 09 2a 0d 0a | 25 2a 2a 2a 2a 2a 2a 2a |ei''.*..|%*******|
|000002f0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000300| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000310| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000320| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000330| 2a 0d 0a 0d 0a 5c 64 6f | 63 75 6d 65 6e 74 73 74 |*....\do|cumentst|
|00000340| 79 6c 65 5b 61 73 74 79 | 70 65 64 2c 61 34 2c 31 |yle[asty|ped,a4,1|
|00000350| 32 70 74 5d 7b 61 72 74 | 69 63 6c 65 7d 0d 0a 5c |2pt]{art|icle}..\|
|00000360| 61 75 74 68 6f 72 7b 4c | 61 72 72 79 20 42 61 72 |author{L|arry Bar|
|00000370| 74 68 6f 6c 64 69 20 5c | 26 20 68 69 73 20 67 61 |tholdi \|& his ga|
|00000380| 6e 67 7d 0d 0a 5c 74 69 | 74 6c 65 7b 52 65 63 75 |ng}..\ti|tle{Recu|
|00000390| 72 73 69 76 65 20 73 61 | 6d 70 6c 65 73 7d 0d 0a |rsive sa|mples}..|
|000003a0| 5c 64 61 74 65 7b 5c 74 | 6f 64 61 79 7d 0d 0a 5c |\date{\t|oday}..\|
|000003b0| 73 65 74 6c 65 6e 67 74 | 68 7b 5c 74 65 78 74 68 |setlengt|h{\texth|
|000003c0| 65 69 67 68 74 7d 7b 32 | 34 30 6d 6d 7d 0d 0a 0d |eight}{2|40mm}...|
|000003d0| 0a 5c 6e 65 77 63 6f 6d | 6d 61 6e 64 7b 5c 70 63 |.\newcom|mand{\pc|
|000003e0| 73 7d 7b 7b 5c 73 63 20 | 50 63 53 63 68 65 6d 65 |s}{{\sc |PcScheme|
|000003f0| 7d 7d 0d 0a 5c 6e 65 77 | 63 6f 6d 6d 61 6e 64 7b |}}..\new|command{|
|00000400| 5c 73 63 68 65 6d 65 7d | 7b 5c 76 65 72 62 7d 0d |\scheme}|{\verb}.|
|00000410| 0a 0d 0a 5c 62 65 67 69 | 6e 7b 64 6f 63 75 6d 65 |...\begi|n{docume|
|00000420| 6e 74 7d 0d 0a 5c 6d 61 | 6b 65 74 69 74 6c 65 0d |nt}..\ma|ketitle.|
|00000430| 0a 0d 0a 54 68 69 73 20 | 69 73 20 74 68 65 20 7b |...This |is the {|
|00000440| 5c 65 6d 20 6f 6e 6c 79 | 7d 20 74 72 75 65 20 64 |\em only|} true d|
|00000450| 65 66 69 6e 69 74 69 6f | 6e 20 6f 66 20 66 61 63 |efinitio|n of fac|
|00000460| 74 6f 72 69 61 6c 20 6f | 76 65 72 20 24 5c 63 61 |torial o|ver $\ca|
|00000470| 6c 20 5a 24 2e 0d 0a 4e | 6f 74 65 20 5c 73 63 68 |l Z$...N|ote \sch|
|00000480| 65 6d 65 2b 28 66 61 63 | 74 20 2d 31 29 2b 20 69 |eme+(fac|t -1)+ i|
|00000490| 73 20 24 5c 47 61 6d 6d | 61 28 30 29 24 2c 20 61 |s $\Gamm|a(0)$, a|
|000004a0| 6e 64 20 24 5c 47 61 6d | 6d 61 28 30 29 5c 63 64 |nd $\Gam|ma(0)\cd|
|000004b0| 6f 74 20 30 24 20 6d 75 | 73 74 20 62 65 0d 0a 24 |ot 0$ mu|st be..$|
|000004c0| 5c 47 61 6d 6d 61 28 31 | 29 24 20 6f 72 20 24 31 |\Gamma(1|)$ or $1|
|000004d0| 24 2c 20 73 6f 20 5c 73 | 63 68 65 6d 65 2b 28 66 |$, so \s|cheme+(f|
|000004e0| 61 63 74 20 2d 31 29 2b | 20 69 73 20 24 5c 69 6e |act -1)+| is $\in|
|000004f0| 66 74 79 24 0d 0a 20 28 | 73 6f 20 69 73 20 5c 73 |fty$.. (|so is \s|
|00000500| 63 68 65 6d 65 2b 28 67 | 61 6d 6d 61 20 2d 6e 29 |cheme+(g|amma -n)|
|00000510| 2b 20 66 6f 72 20 69 6e | 74 65 67 72 61 6c 20 24 |+ for in|tegral $|
|00000520| 6e 24 29 2e 0d 0a 28 64 | 65 66 69 6e 65 20 28 66 |n$)...(d|efine (f|
|00000530| 61 63 74 20 6e 29 0d 0a | 20 20 28 69 66 20 28 3c |act n)..| (if (<|
|00000540| 3d 20 6e 20 30 29 0d 0a | 20 20 20 20 20 20 28 69 |= n 0)..| (i|
|00000550| 66 20 28 3d 20 6e 20 30 | 29 20 31 20 28 2f 20 31 |f (= n 0|) 1 (/ 1|
|00000560| 20 30 29 29 0d 0a 20 20 | 20 20 20 20 28 2a 20 6e | 0)).. | (* n|
|00000570| 20 28 66 61 63 74 20 28 | 2d 31 2b 20 6e 29 29 29 | (fact (|-1+ n)))|
|00000580| 29 29 0d 0a 0d 0a 54 68 | 69 73 20 63 6f 64 65 20 |))....Th|is code |
|00000590| 65 78 70 65 63 74 20 69 | 73 20 69 6e 74 65 6e 64 |expect i|s intend|
|000005a0| 65 64 20 61 73 20 61 20 | 70 72 6f 76 6f 63 61 74 |ed as a |provocat|
|000005b0| 69 6f 6e 5c 6c 64 6f 74 | 73 0d 0a 4e 6f 74 69 63 |ion\ldot|s..Notic|
|000005c0| 65 20 74 68 65 20 73 70 | 65 65 64 20 69 6d 70 72 |e the sp|eed impr|
|000005d0| 6f 76 65 6d 65 6e 74 73 | 20 61 72 65 20 6d 61 72 |ovements| are mar|
|000005e0| 67 69 6e 61 6c 2c 20 74 | 68 65 20 61 72 67 75 6d |ginal, t|he argum|
|000005f0| 65 6e 74 73 20 61 72 65 | 20 6e 6f 74 20 74 65 73 |ents are| not tes|
|00000600| 74 65 64 0d 0a 61 73 20 | 63 6c 65 61 6e 6c 79 20 |ted..as |cleanly |
|00000610| 61 73 20 61 62 6f 76 65 | 2c 20 77 69 74 68 6f 75 |as above|, withou|
|00000620| 74 20 6d 65 6d 74 69 6f | 6e 69 6e 67 20 70 6f 6f |t memtio|ning poo|
|00000630| 72 20 70 6f 72 74 61 62 | 69 6c 69 74 79 20 28 74 |r portab|ility (t|
|00000640| 68 65 20 6f 6e 65 20 74 | 68 69 6e 67 0d 0a 75 73 |he one t|hing..us|
|00000650| 20 53 63 68 65 6d 65 20 | 67 75 79 73 20 73 68 6f | Scheme |guys sho|
|00000660| 75 6c 64 20 62 65 20 70 | 72 6f 75 64 20 6f 66 29 |uld be p|roud of)|
|00000670| 2e 0d 0a 28 64 65 66 69 | 6e 65 20 66 61 73 74 66 |...(defi|ne fastf|
|00000680| 61 63 74 20 28 69 6e 6c | 69 6e 65 2d 6c 61 6d 62 |act (inl|ine-lamb|
|00000690| 64 61 20 31 20 27 28 70 | 63 73 2d 63 6f 64 65 2d |da 1 '(p|cs-code-|
|000006a0| 62 6c 6f 63 6b 20 30 20 | 32 35 20 28 29 0d 0a 09 |block 0 |25 ()...|
|000006b0| 28 30 20 31 32 20 34 09 | 09 09 09 3b 09 6d 6f 76 |(0 12 4.|...;.mov|
|000006c0| 2e 72 09 72 33 2c 20 72 | 31 0d 0a 09 32 20 34 20 |.r.r3, r|1...2 4 |
|000006d0| 31 09 09 09 09 3b 09 6d | 6f 76 2e 69 09 72 31 2c |1....;.m|ov.i.r1,|
|000006e0| 20 5c 23 31 0d 0a 09 32 | 20 38 20 31 09 09 09 09 | \#1...2| 8 1....|
|000006f0| 3b 09 6d 6f 76 2e 69 09 | 72 32 2c 20 5c 23 31 0d |;.mov.i.|r2, \#1.|
|00000700| 0a 09 38 33 20 34 20 38 | 09 09 09 09 3b 40 40 6c |..83 4 8|....;@@l|
|00000710| 6f 6f 70 3a 6d 75 6c 2e | 72 09 72 31 2c 20 72 32 |oop:mul.|r.r1, r2|
|00000720| 0d 0a 09 38 31 20 38 20 | 31 09 09 09 09 3b 09 61 |...81 8 |1....;.a|
|00000730| 64 64 2e 69 09 72 32 2c | 20 5c 23 31 0d 0a 09 30 |dd.i.r2,| \#1...0|
|00000740| 20 31 36 20 38 09 09 09 | 09 3b 09 6d 6f 76 2e 69 | 16 8...|.;.mov.i|
|00000750| 09 72 34 2c 20 72 32 0d | 0a 09 39 35 20 31 36 20 |.r4, r2.|..95 16 |
|00000760| 31 32 09 09 09 3b 09 67 | 74 2e 72 09 72 34 2c 20 |12...;.g|t.r.r4, |
|00000770| 72 33 0d 0a 09 33 34 20 | 31 36 20 32 34 31 09 09 |r3...34 |16 241..|
|00000780| 09 3b 09 6a 6e 69 6c 2e | 73 09 72 34 2c 20 40 40 |.;.jnil.|s.r4, @@|
|00000790| 6c 6f 6f 70 0d 0a 20 20 | 20 20 20 20 20 20 20 20 |loop.. | |
|000007a0| 20 35 39 29 29 29 29 09 | 09 09 09 3b 09 72 65 74 | 59)))).|...;.ret|
|000007b0| 0d 0a 0d 0a 41 6c 6c 20 | 74 68 65 73 65 20 65 78 |....All |these ex|
|000007c0| 61 6d 70 6c 65 73 20 61 | 72 65 20 65 78 74 72 61 |amples a|re extra|
|000007d0| 63 74 65 64 20 66 72 6f | 6d 0d 0a 60 60 47 5c 22 |cted fro|m..``G\"|
|000007e0| 6f 65 64 65 6c 2c 20 45 | 73 63 68 65 72 2c 20 42 |oedel, E|scher, B|
|000007f0| 61 63 68 3a 20 61 6e 20 | 45 74 65 72 6e 61 6c 20 |ach: an |Eternal |
|00000800| 47 6f 6c 64 65 6e 20 42 | 72 61 69 64 27 27 0d 0a |Golden B|raid''..|
|00000810| 62 79 20 44 6f 75 67 20 | 48 6f 66 73 74 61 64 74 |by Doug |Hofstadt|
|00000820| 65 72 2c 20 63 68 61 70 | 74 65 72 20 56 2c 20 70 |er, chap|ter V, p|
|00000830| 61 67 65 73 20 31 33 36 | 20 66 66 2e 20 54 68 65 |ages 136| ff. The|
|00000840| 69 72 20 62 65 68 61 76 | 69 6f 75 72 20 69 73 0d |ir behav|iour is.|
|00000850| 0a 64 65 74 65 72 6d 69 | 6e 69 73 74 69 63 2c 20 |.determi|nistic, |
|00000860| 62 75 74 20 63 61 6e 20 | 62 65 20 66 65 6c 74 20 |but can |be felt |
|00000870| 61 73 20 63 68 61 6f 74 | 69 63 2c 20 61 20 66 61 |as chaot|ic, a fa|
|00000880| 63 74 20 65 78 70 72 65 | 73 73 65 64 20 62 79 20 |ct expre|ssed by |
|00000890| 74 68 65 0d 0a 61 62 73 | 65 6e 63 65 20 6f 66 20 |the..abs|ence of |
|000008a0| 63 6c 6f 73 65 64 20 66 | 6f 72 6d 20 61 6e 64 20 |closed f|orm and |
|000008b0| 74 68 65 20 27 72 75 67 | 67 65 64 6e 65 73 73 27 |the 'rug|gedness'|
|000008c0| 20 6f 66 20 74 68 65 69 | 72 20 67 72 61 70 68 2e | of thei|r graph.|
|000008d0| 0d 0a 28 64 65 66 69 6e | 65 20 28 67 20 6e 29 0d |..(defin|e (g n).|
|000008e0| 0a 20 20 28 69 66 20 28 | 3d 20 6e 20 30 29 0d 0a |. (if (|= n 0)..|
|000008f0| 20 20 20 20 20 20 30 0d | 0a 20 20 20 20 20 20 28 | 0.|. (|
|00000900| 2d 20 6e 20 28 67 20 28 | 67 20 28 2d 31 2b 20 6e |- n (g (|g (-1+ n|
|00000910| 29 29 29 29 29 29 0d 0a | 28 64 65 66 69 6e 65 20 |))))))..|(define |
|00000920| 28 68 20 6e 29 0d 0a 20 | 20 28 69 66 20 28 3d 20 |(h n).. | (if (= |
|00000930| 6e 20 30 29 0d 0a 20 20 | 20 20 20 20 30 0d 0a 20 |n 0).. | 0.. |
|00000940| 20 20 20 20 20 28 2d 20 | 6e 20 28 68 20 28 68 20 | (- |n (h (h |
|00000950| 28 68 20 28 2d 31 2b 20 | 6e 29 29 29 29 29 29 29 |(h (-1+ |n)))))))|
|00000960| 0d 0a 28 64 65 66 69 6e | 65 20 28 66 65 6d 61 6c |..(defin|e (femal|
|00000970| 65 20 6e 29 0d 0a 20 20 | 28 69 66 20 28 3d 20 6e |e n).. |(if (= n|
|00000980| 20 30 29 0d 0a 20 20 20 | 20 20 20 31 0d 0a 20 20 | 0).. | 1.. |
|00000990| 20 20 20 20 28 2d 20 6e | 20 28 6d 61 6c 65 20 28 | (- n| (male (|
|000009a0| 66 65 6d 61 6c 65 20 28 | 2d 31 2b 20 6e 29 29 29 |female (|-1+ n)))|
|000009b0| 29 29 29 0d 0a 28 64 65 | 66 69 6e 65 20 28 6d 61 |)))..(de|fine (ma|
|000009c0| 6c 65 20 6e 29 0d 0a 20 | 20 28 69 66 20 28 3d 20 |le n).. | (if (= |
|000009d0| 6e 20 30 29 0d 0a 20 20 | 20 20 20 20 30 0d 0a 20 |n 0).. | 0.. |
|000009e0| 20 20 20 20 20 28 2d 20 | 6e 20 28 66 65 6d 61 6c | (- |n (femal|
|000009f0| 65 20 28 6d 61 6c 65 20 | 28 2d 31 2b 20 6e 29 29 |e (male |(-1+ n))|
|00000a00| 29 29 29 29 0d 0a 28 64 | 65 66 69 6e 65 20 28 71 |))))..(d|efine (q|
|00000a10| 20 6e 29 0d 0a 20 20 28 | 69 66 20 28 3c 3d 20 6e | n).. (|if (<= n|
|00000a20| 20 32 29 0d 0a 20 20 20 | 20 20 20 31 0d 0a 20 20 | 2).. | 1.. |
|00000a30| 20 20 20 20 28 2b 20 28 | 71 20 28 2d 20 6e 20 28 | (+ (|q (- n (|
|00000a40| 71 20 28 2d 20 6e 20 31 | 29 29 29 29 0d 0a 20 20 |q (- n 1|)))).. |
|00000a50| 20 20 20 20 20 20 20 28 | 71 20 28 2d 20 6e 20 28 | (|q (- n (|
|00000a60| 71 20 28 2d 20 6e 20 32 | 29 29 29 29 29 29 29 0d |q (- n 2|))))))).|
|00000a70| 0a 28 64 65 66 69 6e 65 | 20 28 66 69 62 6f 20 6e |.(define| (fibo n|
|00000a80| 29 0d 0a 20 20 28 69 66 | 20 28 3c 3d 20 6e 20 32 |).. (if| (<= n 2|
|00000a90| 29 0d 0a 20 20 20 20 20 | 20 31 0d 0a 20 20 20 20 |).. | 1.. |
|00000aa0| 20 20 28 2b 20 28 66 69 | 62 6f 20 28 2d 20 6e 20 | (+ (fi|bo (- n |
|00000ab0| 31 29 29 0d 0a 20 20 20 | 20 20 20 20 20 20 28 66 |1)).. | (f|
|00000ac0| 69 62 6f 20 28 2d 20 6e | 20 32 29 29 29 29 29 0d |ibo (- n| 2))))).|
|00000ad0| 0a 0d 0a 4e 6f 77 20 63 | 6f 6d 65 73 20 61 20 63 |...Now c|omes a c|
|00000ae0| 6f 64 65 20 74 68 61 74 | 20 69 73 6e 27 74 20 70 |ode that| isn't p|
|00000af0| 72 65 63 69 73 65 6c 79 | 20 72 65 63 75 72 73 69 |recisely| recursi|
|00000b00| 76 65 2e 20 41 73 20 79 | 6f 75 20 63 65 72 74 61 |ve. As y|ou certa|
|00000b10| 69 6e 6c 79 20 6b 6e 6f | 77 2c 0d 0a 5c 73 63 68 |inly kno|w,..\sch|
|00000b20| 65 6d 65 2b 64 6f 2b 2d | 2d 6c 6f 6f 70 73 20 61 |eme+do+-|-loops a|
|00000b30| 72 65 20 68 61 6e 67 69 | 6e 67 20 6f 66 66 65 6e |re hangi|ng offen|
|00000b40| 73 65 73 3b 20 62 75 74 | 20 6f 6e 20 74 68 65 20 |ses; but| on the |
|00000b50| 6f 74 68 65 72 20 73 69 | 64 65 2c 20 5c 70 63 73 |other si|de, \pcs|
|00000b60| 5c 0d 0a 69 73 20 6b 69 | 6e 64 20 65 6e 6f 75 67 |\..is ki|nd enoug|
|00000b70| 68 20 74 6f 20 74 72 61 | 6e 73 6c 61 74 65 20 74 |h to tra|nslate t|
|00000b80| 68 65 20 6c 6f 6f 70 73 | 20 69 6e 20 74 61 69 6c |he loops| in tail|
|00000b90| 2d 72 65 63 75 72 73 69 | 76 65 20 63 6f 64 65 2c |-recursi|ve code,|
|00000ba0| 20 73 6f 5c 6c 64 6f 74 | 73 0d 0a 54 68 65 20 61 | so\ldot|s..The a|
|00000bb0| 6c 67 6f 72 69 74 68 6d | 20 69 73 20 62 61 73 65 |lgorithm| is base|
|00000bc0| 64 20 6f 6e 20 61 20 66 | 61 73 74 20 73 65 72 69 |d on a f|ast seri|
|00000bd0| 65 73 20 66 6f 72 20 24 | 34 5c 61 72 63 74 61 6e |es for $|4\arctan|
|00000be0| 28 31 29 24 20 28 73 65 | 65 20 41 62 72 61 6d 6f |(1)$ (se|e Abramo|
|00000bf0| 77 69 74 7a 0d 0a 5c 26 | 20 53 74 65 67 75 6e 2c |witz..\&| Stegun,|
|00000c00| 20 66 6f 72 6d 75 6c 61 | 20 34 2e 34 2e 34 32 29 | formula| 4.4.42)|
|00000c10| 3a 0d 0a 24 24 5c 61 72 | 63 74 61 6e 20 7a 20 3d |:..$$\ar|ctan z =|
|00000c20| 20 5c 66 72 61 63 7b 7a | 7d 7b 31 2b 7a 5e 32 7d | \frac{z|}{1+z^2}|
|00000c30| 5c 62 69 67 5c 7b 31 2b | 5c 66 72 61 63 7b 32 7d |\big\{1+|\frac{2}|
|00000c40| 7b 33 7d 5c 66 72 61 63 | 7b 7a 5e 32 7d 7b 31 2b |{3}\frac|{z^2}{1+|
|00000c50| 7a 5e 32 7d 5c 62 69 67 | 5b 31 2b 5c 66 72 61 63 |z^2}\big|[1+\frac|
|00000c60| 7b 34 7d 7b 35 7d 0d 0a | 09 5c 66 72 61 63 7b 7a |{4}{5}..|.\frac{z|
|00000c70| 5e 32 7d 7b 31 2b 7a 5e | 32 7d 5c 62 69 67 28 31 |^2}{1+z^|2}\big(1|
|00000c80| 2b 5c 6c 64 6f 74 73 5c | 62 69 67 29 5c 62 69 67 |+\ldots\|big)\big|
|00000c90| 5d 5c 62 69 67 5c 7d 2e | 24 24 0d 0a 28 64 65 66 |]\big\}.|$$..(def|
|00000ca0| 69 6e 65 20 28 70 69 20 | 6e 29 0d 0a 20 20 28 6c |ine (pi |n).. (l|
|00000cb0| 65 74 20 28 28 75 6e 69 | 74 79 20 28 64 6f 20 28 |et ((uni|ty (do (|
|00000cc0| 28 69 20 30 20 28 31 2b | 20 69 29 29 0d 0a 20 20 |(i 0 (1+| i)).. |
|00000cd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ce0| 20 20 20 20 28 72 20 31 | 20 28 2a 20 72 20 31 30 | (r 1| (* r 10|
|00000cf0| 29 29 29 0d 0a 20 20 20 | 20 20 20 20 20 20 20 20 |))).. | |
|00000d00| 20 20 20 20 20 20 20 20 | 20 20 28 28 3e 3d 20 69 | | ((>= i|
|00000d10| 20 6e 29 20 72 29 29 29 | 0d 0a 20 20 20 20 20 20 | n) r)))|.. |
|00000d20| 20 20 28 69 74 65 72 20 | 28 72 6f 75 6e 64 20 28 | (iter |(round (|
|00000d30| 2b 20 28 2f 20 6e 20 28 | 6c 6f 67 20 32 20 31 30 |+ (/ n (|log 2 10|
|00000d40| 29 29 20 35 30 29 29 29 | 29 0d 0a 20 20 20 20 28 |)) 50)))|).. (|
|00000d50| 64 6f 20 28 28 6e 75 6d | 20 69 74 65 72 20 28 2d |do ((num| iter (-|
|00000d60| 31 2b 20 6e 75 6d 29 29 | 0d 0a 20 20 20 20 20 20 |1+ num))|.. |
|00000d70| 20 20 20 28 64 65 6e 6f | 6d 20 28 2b 20 69 74 65 | (deno|m (+ ite|
|00000d80| 72 20 69 74 65 72 20 31 | 29 20 28 2d 20 64 65 6e |r iter 1|) (- den|
|00000d90| 6f 6d 20 32 29 29 0d 0a | 20 20 20 20 20 20 20 20 |om 2))..| |
|00000da0| 20 28 70 69 20 30 20 28 | 2b 20 75 6e 69 74 79 20 | (pi 0 (|+ unity |
|00000db0| 75 6e 69 74 79 20 28 71 | 75 6f 74 69 65 6e 74 20 |unity (q|uotient |
|00000dc0| 28 2a 20 70 69 20 6e 75 | 6d 29 20 64 65 6e 6f 6d |(* pi nu|m) denom|
|00000dd0| 29 29 29 29 0d 0a 20 20 | 20 20 20 20 20 20 28 28 |)))).. | ((|
|00000de0| 3d 20 6e 75 6d 20 30 29 | 20 28 6e 65 77 6c 69 6e |= num 0)| (newlin|
|00000df0| 65 29 20 70 69 29 0d 0a | 20 20 20 20 20 20 20 20 |e) pi)..| |
|00000e00| 28 77 68 65 6e 20 28 3d | 20 28 72 65 6d 61 69 6e |(when (=| (remain|
|00000e10| 64 65 72 20 6e 75 6d 20 | 31 30 29 20 30 29 0d 0a |der num |10) 0)..|
|00000e20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 28 70 | | (p|
|00000e30| 72 69 6e 63 20 23 5c 72 | 65 74 75 72 6e 29 0d 0a |rinc #\r|eturn)..|
|00000e40| 09 20 20 20 20 20 20 28 | 70 72 69 6e 63 20 22 5b |. (|princ "[|
|00000e50| 22 29 20 28 70 72 69 6e | 63 20 6e 75 6d 29 20 28 |") (prin|c num) (|
|00000e60| 70 72 69 6e 63 20 22 5d | 20 22 29 29 29 29 29 0d |princ "]| "))))).|
|00000e70| 0a 0d 0a 28 77 72 69 74 | 65 6c 6e 20 27 28 66 61 |...(writ|eln '(fa|
|00000e80| 63 74 20 66 61 73 74 66 | 61 63 74 20 67 20 68 20 |ct fastf|act g h |
|00000e90| 66 65 6d 61 6c 65 20 6d | 61 6c 65 20 71 20 66 69 |female m|ale q fi|
|00000ea0| 62 6f 20 70 69 29 29 0d | 0a 5c 65 6e 64 7b 64 6f |bo pi)).|.\end{do|
|00000eb0| 63 75 6d 65 6e 74 7d 0d | 0a |cument}.|. |
+--------+-------------------------+-------------------------+--------+--------+