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Ingy döt Net 2015-02-20 00:35:01 -05:00
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commit 00a190b0a6
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Task/Forward-difference/REXX/forward-difference-1.rexx
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@ -1,44 +1,41 @@
/*REXX program to compute the forward difference of a list of numbers.*/
/* ┌───────────────────────────────────────────────────────────────────┐
│ /\ n n n-k │
│ {delta} / \ n [ƒ] (x) ≡ Σ Ç ∙ (-1) ∙ ƒ(x+k) │
│ /____\ k=0 k │
│ │
│ {n=order} {Ç=comb or binomial coeff.} │
└───────────────────────────────────────────────────────────────────┘*/
numeric digits 100 /*ensure enough accuracy. */
arg numbers ',' ord /*input: x1 x2 x3 x4 ... ,ORD */
if numbers=='' then numbers='90 47 58 29 22 32 55 5 55 73' /*default?*/
w=words(numbers) /*set W to # of numbers in list.*/
do i=1 for w /*validate input (valid numbers?)*/
@.i=word(numbers,i) /*assign the next # in the list. */
if \datatype(@.i,'N') then call ser @.i "isn't a valid number"
@.i=@.i/1 /*normalize the #, prettify the #*/
end /*i*/
/*═════════════════════════════════════════process the (optional) input.*/
if w==0 then call ser 'no numbers were specified'
if ord\=='' & ord<0 then call ser ord "(ner) can't be negative"
if ord\=='' & ord>w then call ser ord "(ner) can't be greater than" w
say right(w 'numbers: ' numbers,64) /*sloppy way to do a header, ... */
say right(copies('─',length(numbers)),64) /* and the header fence.*/
if ord=='' then do; bot=0; top=w; end /*define default ners.*/
else do; bot=n; top=n; end /*just a specific ner?*/
butchers/mangles some of the characters in the documentation box. -->
<lang>/*REXX program computes the forward difference of a list of numbers.
╔════════════════════════════════════════════════════════════════════╗
║ /\ n n n-k ║
║ / \ n [ƒ] (x) ≡ Σ C ∙ (-1) ∙ ƒ(x+k) ║
║ /____\ k=0 k ║
║ ↑ ↑ ↑ ║
║ │ │ │ ║
║ {delta}─────┘ {n=order} {C=comb or binomial coeff.} ║
╚════════════════════════════════════════════════════════════════════╝*/
numeric digits 100 /*ensure enough accuracy (digits)*/
parse arg xxx ',' N /*input: ε1 ε2 ε3 ε4 ··· , order*/
if xxx=='' then xxx='90 47 58 29 22 32 55 5 55 73' /*default numbers.*/
w=words(xxx) /*set W to # of numbers in list.*/
/* [↓] validate the input numbers*/
do i=1 for w; _=word(xxx,i) /*process each number 1 at a time*/
if \datatype(_,'N') then call ser _ "isn't a valid number"
@.i=_/1 /*normalize the #, prettify the #*/
end /*i*/ /* [↑] removes superfluous stuff*/
/* [↓] process (optional) order.*/
if w==0 then call ser 'no numbers were specified.'
if N\=='' & N<0 then call ser N "(order) can't be negative."
if N\=='' & N>w then call ser N "(order) can't be greater than" w
say right(w 'numbers:', 44) xxx /*display the header ··· */
say left('', 44)copies('─', length(xxx)+2) /* and the header fence.*/
if N=='' then do; bot=0; top=w; end /*define default orders. */
else do; bot=N; top=N; end /*just a specific order? */
/*═════════════════════════════════════════where da rubber meets da road*/
do order=bot to top; do r=1 for w; !.r=@.r; end; $=
do j=1 for order; d=!.j; do k=j+1 to w /*order diff.*/
parse value !.k !.k-d with d !.k
end /*k*/
do #=bot to top; do r=1 for w; !.r=@.r; end; $=
do j=1 for #; d=!.j; do k=j+1 to w
parse value !.k !.k-d with d !.k
end /*k*/
end /*j*/
do i=order+1 to w /*build list.*/
$=$ !.i/1 /*append it. */
end /*i*/
if $=='' then $='[null]' /*pretty null*/
what=right(order,length(w))th(order)'-order' /*nice format*/
say what 'forward difference vector = ' strip($) /*display it.*/
do i=#+1 to w; $=$ !.i/1; end
if $=='' then $='[null]'
say right(#, 7)th(#)'-order forward difference vector = ' strip($)
end /*o*/
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────SER subroutine──────────────────────*/
ser: say; say '*** error! ***'; say arg(1); say; exit 13
/*──────────────────────────────────TH subroutine───────────────────────*/
th: parse arg ?; return word('th st nd rd',1+?//10*(?//100%10\==1)*(?//10<4))
/*──────────────────────────────────one─liner subroutines───────────────*/
ser: say; say '***error!***'; say arg(1); say; exit 13
th: arg ?; return word('th st nd rd',1+?//10*(?//100%10\==1)*(?//10<4))