Data update

Task/Legendre-prime-counting-function/REXX/legendre-prime-counting-function-1.rexx

@@ -0,0 +1,32 @@
+Main:
+include Settings
+say version; say 'Legendre Prime counter (no memoization)'; say
+numeric digits 10
+do n = 0 to 9
+   call Time('r')
+   a = 10**n; p = pi(a)
+   say '10^'n Right(p,9) Format(Time('e'),3,3)'s'
+end
+exit
+
+Pi:
+procedure expose prim.
+arg xx
+if xx < 3 then
+   return 0+(xx=2)
+n = Primes(Isqrt(xx))
+return Phi(xx,n)+n-1
+
+Phi:
+procedure expose prim.
+arg xx,yy
+if yy < 2 then
+   return xx-(xx%2)*(yy=1)
+p = prim.prime.yy
+if xx <= p then
+   return 1
+return Phi(xx,yy-1)-Phi(xx%p,yy-1)
+
+include Abend
+include Functions
+include Sequences

Task/Legendre-prime-counting-function/REXX/legendre-prime-counting-function-2.rexx

@@ -0,0 +1,36 @@
+Main:
+include Settings
+say version; say 'Legendre Prime counter (with memoization)'; say
+numeric digits 10
+do n = 0 to 9
+   call Time('r')
+   a = 10**n; p = Pi(a)
+   say '10^'n Right(p,9) Format(Time('e'),3,3)'s'
+end
+exit
+
+Pi:
+procedure expose prim. work.
+arg xx
+if xx < 3 then
+   return 0+(xx=2)
+n = Primes(Isqrt(xx))
+work. = 0
+return Phi(xx,n)+n-1
+
+Phi:
+procedure expose prim. work.
+arg xx,yy
+if yy < 2 then
+   return xx-(xx%2)*(yy=1)
+p = prim.prime.yy
+if xx <= p then
+   return 1
+if work.xx.yy > 0 then
+   return work.xx.yy
+work.xx.yy = Phi(xx,yy-1)-Phi(xx%p,yy-1)
+return work.xx.yy
+
+include Abend
+include Functions
+include Sequences

Task/Legendre-prime-counting-function/REXX/legendre-prime-counting-function-3.rexx

@@ -0,0 +1,14 @@
+Main:
+include Settings
+say version; say 'Legendre Prime counter (sieving)'; say
+numeric digits 10
+do n = 0 to 8
+   call Time('r')
+   a = 10**n; p = Primes(a)
+   say '10^'n Right(p,9) Format(Time('e'),3,3)'s'
+end
+exit
+
+include Abend
+include Functions
+include Sequences