From cfba98d2e0b657758748afc251c9624c16c71e5c Mon Sep 17 00:00:00 2001
From: Emile Clark-Boman <eclarkboman@gmail.com>
Date: Tue, 1 Jul 2025 21:08:39 +1000
Subject: [PATCH] Improved eulertotient(n) implementation

---
 imp/math/primes.py | 96 ++++++++++++++--------------------------------
 imp/math/util.py   |  3 +-
 2 files changed, 31 insertions(+), 68 deletions(-)

diff --git a/imp/math/primes.py b/imp/math/primes.py
index eaeebcb..b130a0c 100644
--- a/imp/math/primes.py
+++ b/imp/math/primes.py
@@ -1,5 +1,10 @@
-from math import gcd
-from imp.math.numbers import bigomega
+from math import gcd, inf
+
+from imp.math.numbers import bigomega, factors
+from imp.extern.primefac import (
+    isprime,
+    primegen as Primes,
+)
 
 def coprime(n: int, m: int) -> bool:
     return gcd(n, m) == 1
@@ -18,68 +23,25 @@ def semiprime(n: int) -> bool:
     '''
     return almostprime(n, 2)
     
-'''
-Euler's Totient (Phi) Function
-'''
-def totient(n: int) -> int:
-    phi = int(n > 1 and n)
-    for p in range(2, int(n ** .5) + 1):
-        if not n % p:
-            phi -= phi // p
-            while not n % p:
-                n //= p
-    #if n is > 1 it means it is prime
-    if n > 1: phi -= phi // n 
-    return phi
-
-'''
-Tests the primality of an integer using its totient.
-NOTE: If totient(n) has already been calculated 
-      then pass it as the optional phi parameter. 
-'''
-def is_prime(n: int, phi: int = None) -> bool:
-    return n - 1 == (phi if phi is not None else totient(n))
-
-'''
-Prime number generator function.
-Returns the tuple (p, phi(p)) where p is prime
-    and phi is Euler's totient function.
-'''
-def prime_gen(yield_phi: bool = False) -> int | tuple[int, int]:
-    n = 1
-    while True:
-        n += 1
-        phi = totient(n)
-        if is_prime(n, phi=phi):
-            if yield_phi:
-                yield (n, phi)
-            else:
-                yield n
-
-'''
-Returns the prime factorisation of a number.
-Returns a list of tuples (p, m) where p is
-a prime factor and m is its multiplicity.
-NOTE: uses a trial division algorithm
-'''
-def prime_factors(n: int) -> list[tuple[int, int]]:
-    phi = totient(n)
-    if is_prime(n, phi=phi):
-        return [(n, 1)]
-    factors = []
-    for p in prime_gen(yield_phi=False):
-        if p >= n:
-            break
-        # check if divisor
-        multiplicity = 0
-        while n % p == 0:
-            n //= p
-            multiplicity += 1
-        if multiplicity:
-            factors.append((p, multiplicity))
-            if is_prime(n):
-                break
-    if n != 1:
-        factors.append((n, 1))
-    return factors
-            
+def eulertotient(x: int | list) -> int:
+    '''
+    Evaluates Euler's Totient function.
+    Input: `x: int` is prime factorised by Lucas A. Brown's primefac.py
+           else `x: list` is assumed to the prime factorisation of `x: int`
+    '''
+    pfactors = x if isinstance(x, list) else factors(n)
+    return prod((p-1)*(p**(e-1)) for (p, e) in pfactors)
+# def eulertotient(n: int) -> int:
+#     '''
+#     Uses trial division to compute 
+#     Euler's Totient (Phi) Function.
+#     '''
+#     phi = int(n > 1 and n)
+#     for p in range(2, int(n ** .5) + 1):
+#         if not n % p:
+#             phi -= phi // p
+#             while not n % p:
+#                 n //= p
+#     #if n is > 1 it means it is prime
+#     if n > 1: phi -= phi // n 
+#     return phi
diff --git a/imp/math/util.py b/imp/math/util.py
index 69631c6..4dacda2 100644
--- a/imp/math/util.py
+++ b/imp/math/util.py
@@ -1,8 +1,9 @@
+from collections.abc import Iterable
 from itertools import chain, combinations
 
 def digits(n: int) -> int:
     return len(str(n))
 
-def powerset(iterable):
+def powerset(iterable: Iterable) -> Iterable:
     s = list(iterable)
     return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))