Data update
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Ingy döt Net
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2347 changed files with 62432 additions and 16731 deletions
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@ -12,7 +12,7 @@ fastfunc totient n .
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if n > 1 : tot -= tot div n
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return tot
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.
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numfmt 0 3
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numfmt 3 0
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print " N Prim Phi"
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for n = 1 to 25
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tot = totient n
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@ -1,24 +0,0 @@
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/*REXX program calculates the totient numbers for a range of numbers, and count primes. */
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parse arg N . /*obtain optional argument from the CL.*/
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if N=='' | N=="," then N= 25 /*Not specified? Then use the default.*/
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tell= N>0 /*N positive>? Then display them all. */
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N= abs(N) /*use the absolute value of N for loop.*/
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w= length(N) /*W: is used in aligning the output. */
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primes= 0 /*the number of primes found (so far).*/
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/*if N was negative, only count primes.*/
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do j=1 for N; T= phi(j) /*obtain totient number for a number. */
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prime= word('(prime)', 1 + (T \== j-1 ) ) /*determine if J is a prime number. */
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if prime\=='' then primes= primes + 1 /*if a prime, then bump the prime count*/
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if tell then say 'totient number for ' right(j, w) " ──► " right(T, w) ' ' prime
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end /*j*/
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say
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say right(primes, w) ' primes detected for numbers up to and including ' N
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exit 0 /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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gcd: parse arg x,y; do until y==0; parse value x//y y with y x
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end /*until*/; return x
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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phi: procedure; parse arg z; if z==1 then return 1
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#= 1
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do m=2 for z-2; if gcd(m, z)==1 then #= # + 1
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end /*m*/; return #
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@ -1,25 +0,0 @@
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/*REXX program calculates the totient numbers for a range of numbers, and count primes. */
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parse arg N . /*obtain optional argument from the CL.*/
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if N=='' | N=="," then N= 25 /*Not specified? Then use the default.*/
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tell= N>0 /*N positive>? Then display them all. */
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N= abs(N) /*use the absolute value of N for loop.*/
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w= length(N) /*W: is used in aligning the output. */
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primes= 0 /*the number of primes found (so far).*/
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/*if N was negative, only count primes.*/
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do j=1 for N; T= phi(j) /*obtain totient number for a number. */
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prime= word('(prime)', 1 + (T \== j-1 ) ) /*determine if J is a prime number. */
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if prime\=='' then primes= primes + 1 /*if a prime, then bump the prime count*/
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if tell then say 'totient number for ' right(j, w) " ──► " right(T, w) ' ' prime
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end /*j*/
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say
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say right(primes, w) ' primes detected for numbers up to and including ' N
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exit 0 /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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phi: procedure; parse arg z; if z==1 then return 1
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#= 1
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do m=2 for z-2; parse value m z with x y
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do until y==0; parse value x//y y with y x
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end /*until*/
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if x==1 then #= # + 1
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end /*m*/
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return #
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@ -1,137 +0,0 @@
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include Settings
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say version; say 'Totient function (Phi)'; say
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call Time('r')
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numeric digits 10; cycl. = 0; m = 7
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call First25A
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call PrimeCountA m
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say Format(Time('e'),,3) 'seconds'; say
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call Time('r')
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call Totients 10**m
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call First25B
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call PrimeCountB m
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say Format(Time('e'),,3) 'seconds'
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exit
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First25A:
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procedure
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say 'A: using calls to an optimized Totient()'; say
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say ' N Phi(N) Prime?'
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say Copies('-',16)
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n = 0
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do i = 1 to 25
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p = Totient(i)
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if p = i-1 then do
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n = n+1; pr = 'Yes'
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end
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else
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pr = ''
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say Right(i,2) Right(p,6) pr
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end
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say Copies('-',16); say
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say 'Found' Right(n,6) 'primes <' Right(25,8)
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return
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PrimeCountA:
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procedure
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arg x
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n = 0; d = 1
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do i = 1
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p = Totient(i)
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if p = i-1 then
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n = n+1
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e = Xpon(i)
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if e > d then do
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say 'Found' Right(n,6) 'primes <' Right(10**e,8)
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if e > x-1 then
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leave i
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d = e
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end
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end
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say
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return
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First25B:
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procedure expose toti.
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say 'B: generate and save all Totients, and use the stored values'; say
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say ' N Phi(N) Prime?'
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say Copies('-',16)
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n = 0
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do i = 1 to 25
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p = toti.totient.i
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if p = i-1 then do
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n = n+1; pr = 'Yes'
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end
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else
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pr = ''
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say Right(i,2) Right(p,6) pr
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end
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say Copies('-',16)
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say
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say 'Found' Right(n,6) 'primes <' Right(25,8)
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return
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PrimeCountB:
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procedure expose toti.
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arg x
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n = 0; d = 1
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do i = 1
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p = toti.totient.i
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if p = i-1 then
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n = n+1
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e = Xpon(i)
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if e > d then do
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say 'Found' Right(n,6) 'primes <' Right(10**e,8)
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if e > x-1 then
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leave i
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d = e
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end
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end
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say
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return
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Totient:
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/* Euler's totient function */
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procedure expose toti.
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arg x
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/* Fast values */
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if x < 3 then
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return 1
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if x < 5 then
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return 2
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/* Multiplicative property using Factors */
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f = Factors(x)+1; fact.factor.f = 0
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y = 1; v = fact.factor.1; n = 1
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do i = 2 to f
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a = fact.factor.i
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if a = v then
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n = n+1
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else do
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y = y*v**(n-1)*(v-1)
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v = a; n = 1
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end
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end
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return y
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Totients:
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/* Euler's totient numbers */
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procedure expose toti.
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arg x
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/* Recurring sequence */
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do i = 1 to x
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toti.totient.i = i
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end
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do i = 2 to x
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if toti.totient.i < i then
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iterate i
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do j = i by i to x
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toti.totient.j = toti.totient.j-toti.totient.j/i
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end
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end
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toti.0 = x
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return x
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include Functions
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include Numbers
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include Sequences
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include Abend
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99
Task/Totient-function/REXX/totient-function.rexx
Normal file
99
Task/Totient-function/REXX/totient-function.rexx
Normal file
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@ -0,0 +1,99 @@
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-- 8 May 2025
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include Settings
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say 'TOTIENT FUNCTION (PHI)'
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say version
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numeric digits 10; m = 6
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call First25A
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call PrimeCountA m
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say Format(Time('e'),,3) 'seconds'; say
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call Time('r')
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call First25B m
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call PrimeCountB m
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say Format(Time('e'),,3) 'seconds'
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exit
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First25A:
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procedure
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say 'A: using calls to function Totient()'; say
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say ' N Phi(N) Prime?'
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say Copies('-',16)
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n = 0
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do i = 1 to 25
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p = Totient(i)
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if p = i-1 then do
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n = n+1; pr = 'Yes'
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end
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else
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pr = ''
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say Right(i,2) Right(p,6) pr
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end
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say Copies('-',16); say
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say 'Found' Right(n,6) 'PrimeS <' Right(25,8)
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return
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PrimeCountA:
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procedure
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arg x
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n = 0; d = 1
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do i = 1
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p = Totient(i)
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if p = i-1 then
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n = n+1
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e = Xpon(i)
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if e > d then do
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say 'Found' Right(n,6) 'PrimeS <' Right(10**e,8)
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if e > x-1 then
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leave i
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d = e
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end
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end
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say
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return
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First25B:
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procedure expose toti.
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arg m
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say 'B: generate and save all TotientS, use the stored values'; say
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call TotientS 10**m
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say ' N Phi(N) Prime?'
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say Copies('-',16)
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n = 0
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do i = 1 to 25
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p = toti.i
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if p = i-1 then do
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n = n+1; pr = 'Yes'
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end
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else
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pr = ''
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say Right(i,2) Right(p,6) pr
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end
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say Copies('-',16)
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say
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say 'Found' Right(n,6) 'PrimeS <' Right(25,8)
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return
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PrimeCountB:
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procedure expose toti.
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arg x
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n = 0; d = 1
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do i = 1
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p = toti.i
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if p = i-1 then
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n = n+1
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e = Xpon(i)
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if e > d then do
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say 'Found' Right(n,6) 'PrimeS <' Right(10**e,8)
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if e > x-1 then
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leave i
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d = e
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end
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end
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say
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return
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include Functions
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include Special
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include Numbers
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include Sequences
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include Abend
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