Data update

Task/Legendre-prime-counting-function/Python/legendre-prime-counting-function-1.py

@@ -0,0 +1,30 @@
+from bitarray.util import gen_primes
+from math import isqrt
+from functools import cache
+from time import perf_counter
+
+def countPrimes(limit):
+    if limit < 2: return 0
+
+    rtlmtsz = isqrt(limit) + 1
+    sieve = gen_primes(rtlmtsz)
+    baseprms = [ pi for pi in range(rtlmtsz) if sieve[pi] ]
+    nbps = len(baseprms)
+
+    @cache
+    def phi(x, a): # termination condition means x and a can never be zero
+        rslt = x
+        for na in range(a - 1, -1, -1): # loop takes care of a zero termination!
+            pna = baseprms[na]
+            if pna * pna > x: rslt -= 1; continue # termination before x is zero
+            if na: rslt -= phi(x // pna, na) # lessening recursion depth
+            else: rslt -= x // pna
+        return rslt
+
+    return phi(limit, nbps) + nbps - 1
+
+start = perf_counter()
+for exp in range(10):
+    print(f'10**{exp}: ', countPrimes(10**exp))
+stop = perf_counter()
+print(f"This took {(stop - start) * 1000:.0f} milliseconds.")