Data update

Task/Totient-function/REXX/totient-function-3.rexx

@@ -0,0 +1,136 @@
+include Settings
+
+say version; say 'Totient function (Phi)'; say
+call Time('r')
+numeric digits 10; cycl. = 0; m = 7
+call First25A
+call PrimeCountA m
+say Format(Time('e'),,3) 'seconds'; say
+call Time('r')
+call Totients 10**m
+call First25B
+call PrimeCountB m
+say Format(Time('e'),,3) 'seconds'
+exit
+
+First25A:
+procedure
+say 'A: using calls to an optimized Totient()'; say
+say ' N Phi(N) Prime?'
+say Copies('-',16)
+n = 0
+do i = 1 to 25
+   p = Totient(i)
+   if p = i-1 then do
+      n = n+1; pr = 'Yes'
+   end
+   else
+      pr = ''
+   say Right(i,2) Right(p,6) pr
+end
+say Copies('-',16); say
+say 'Found' Right(n,6) 'primes <' Right(25,8)
+return
+
+PrimeCountA:
+procedure
+arg x
+n = 0; d = 1
+do i = 1
+   p = Totient(i)
+   if p = i-1 then
+      n = n+1
+   e = Xpon(i)
+   if e > d then do
+      say 'Found' Right(n,6) 'primes <' Right(10**e,8)
+      if e > x-1 then
+         leave i
+      d = e
+   end
+end
+say
+return
+
+First25B:
+procedure expose toti.
+say 'B: generate and save all Totients, and use the stored values'; say
+say ' N Phi(N) Prime?'
+say Copies('-',16)
+n = 0
+do i = 1 to 25
+   p = toti.totient.i
+   if p = i-1 then do
+      n = n+1; pr = 'Yes'
+   end
+   else
+      pr = ''
+   say Right(i,2) Right(p,6) pr
+end
+say Copies('-',16)
+say
+say 'Found' Right(n,6) 'primes <' Right(25,8)
+return
+
+PrimeCountB:
+procedure expose toti.
+arg x
+n = 0; d = 1
+do i = 1
+   p = toti.totient.i
+   if p = i-1 then
+      n = n+1
+   e = Xpon(i)
+   if e > d then do
+      say 'Found' Right(n,6) 'primes <' Right(10**e,8)
+      if e > x-1 then
+         leave i
+      d = e
+   end
+end
+say
+return
+
+Totient:
+/* Euler's totient function */
+procedure expose toti.
+arg x
+/* Fast values */
+if x < 3 then
+   return 1
+if x < 5 then
+   return 2
+/* Multiplicative property using Factors */
+f = Factors(x)+1; fact.factor.f = 0
+y = 1; v = fact.factor.1; n = 1
+do i = 2 to f
+   a = fact.factor.i
+   if a = v then
+      n = n+1
+   else do
+      y = y*v**(n-1)*(v-1)
+      v = a; n = 1
+   end
+end
+return y
+
+Totients:
+/* Euler's totient numbers */
+procedure expose toti.
+arg x
+/* Recurring sequence */
+do i = 1 to x
+   toti.totient.i = i
+end
+do i = 2 to x
+   if toti.totient.i < i then
+      iterate i
+   do j = i by i to x
+      toti.totient.j = toti.totient.j-toti.totient.j/i
+   end
+end
+toti.0 = x
+return x
+
+include Functions
+include Numbers
+include Abend