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2016 Update

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Tina Müller 2016-12-05 22:15:40 +01:00
parent 948b86eafa
commit dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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Task/Modular-exponentiation/REXX/modular-exponentiation-1.rexx
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@ -1,25 +1,26 @@
/*REXX program displays modular exponentation: a**b mod M */
parse arg a b mm /*get optional args from CL.*/
if a=='' | a==',' then a=2988348162058574136915891421498819466320163312926952423791023078876139
if b=='' | b==',' then b=2351399303373464486466122544523690094744975233415544072992656881240319
if mm='' | mm=',' then mm=40 /*MM specified? Use default.*/
say 'a=' a; say ' ('length(a) "digits)" /*show value of A.*/
say 'b=' b; say ' ('length(b) "digits)" /* " " " B.*/
/*REXX program displays modular exponentiation of: a**b mod M */
parse arg a b mm /*obtain optional args from the CL*/
if a=='' | a=="," then a=2988348162058574136915891421498819466320163312926952423791023078876139
if b=='' | b=="," then b=2351399303373464486466122544523690094744975233415544072992656881240319
if mm='' | mm="," then mm=40 /*MM not specified? Use default.*/
say 'a=' a; say " ("length(a) 'digits)' /*display the value of A. */
say 'b=' b; say " ("length(b) 'digits)' /* " " " " B. */
do j=1 for words(mm); m=word(mm,j) /*use one of the MM powers.*/
say copies('─',linesize()-1) /*show a nice separator line*/
say 'a**b (mod 10**'m")=" powerModulated(a,b,10**m) /*show ans*/
do j=1 for words(mm); m=word(mm,j) /*use one of the MM powers (list).*/
say copies('─', linesize()-1) /*show a nice separator fence line*/
say 'a**b (mod 10**'m")=" powerMod(a,b,10**m) /*display the answer ───► console.*/
end /*j*/
exit /*stick a fork in it; done.*/
/*──────────────────────────────────────POWERMODULATED subroutine───────*/
powerModulated: procedure; parse arg x,p,n /*fast modular exponentation*/
if p==0 then return 1 /*special case of P = zero. */
if p==1 then return x /* " " " " = unity.*/
if p<0 then do; say '***error!*** power is negative:' p; exit 13; end
parse value max(x**2,p,n)'E0' with "E" e /*pick biggest of the three.*/
numeric digits max(20,e*2) /*big enough to handle A² */
_=1 /*use this for the 1st value*/
do while p\==0; if p//2==1 then _=_*x//n /*is P odd? */
p=p%2; x=x*x//n /*halve P; calc x² mod n */
end /*while*/ /* [↑] keep moding 'til =0.*/
return _
exit /*stick a fork in it, we're done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
powerMod: procedure; parse arg x,p,n /*fast modular exponentiation code*/
if p==0 then return 1 /*special case of P being zero. */
if p==1 then return x /* " " " " " unity.*/
if p<0 then do; say '***error*** power is negative:' p; exit 13; end
parse value max(x**2,p,n)'E0' with "E" e /*obtain the biggest of the three.*/
numeric digits max(20, e*2) /*big enough to handle A². */
_=1 /*use this for the first value. */
do while p\==0 /*perform while P isn't zero.*/
if p//2 then _=_*x//n /*is P odd? (is ÷ remainder≡1).*/
p=p%2; x=x*x//n /*halve P; calculate x² mod n */
end /*while*/ /* [↑] keep mod'ing 'til equal 0.*/
return _