From b4c075de96a452fd85f5bb1028b0c111da2177c2 Mon Sep 17 00:00:00 2001
From: Seth Troisi <sethtroisi@google.com>
Date: Sat, 18 May 2019 16:02:49 -0700
Subject: [PATCH] Faster (20-30x) nthprime_ui sieve implementation

---
 mpz/nthprime_ui.c         | 12 ++++++++----
 tests/mpz/t-nthprime_ui.c |  6 +++++-
 2 files changed, 13 insertions(+), 5 deletions(-)

diff --git a/mpz/nthprime_ui.c b/mpz/nthprime_ui.c
index a11cbe4..76d7a60 100644
--- a/mpz/nthprime_ui.c
+++ b/mpz/nthprime_ui.c
@@ -36,7 +36,6 @@ see https://www.gnu.org/licenses/.  */
 
 /* Enhancements:
 
-   - Use sieve for smallish n
    - Use precomputed lookup values as started point
    - Implement a more modern algorithm */
 
@@ -60,9 +59,14 @@ mpz_nthprime_ui (mpz_ptr p, unsigned long n)
       return;
     }
 
-  /* Simple proof of concept implementation, soon to be replaced. */
-  while (n-- > 0)
+  /* Simple sieve implementation. */
+  gmp_primesieve_t ps;
+  gmp_init_primesieve (&ps);
+
+  while (n-- > 1)
     {
-      mpz_nextprime(p, p);
+      gmp_nextprime (&ps);
     }
+
+  PTR (p)[0] = gmp_nextprime (&ps);
 }
diff --git a/tests/mpz/t-nthprime_ui.c b/tests/mpz/t-nthprime_ui.c
index 88fc214..401b6f4 100644
--- a/tests/mpz/t-nthprime_ui.c
+++ b/tests/mpz/t-nthprime_ui.c
@@ -68,6 +68,10 @@ check_data (void)
     { 100,    541 },
     { 1000,   7919 },
     { 3141,   28843 },
+    { 10000,    104729 },
+    { 78499,    1000003 },
+    { 1000000,  15485863 },
+    { 2718281,  45001883 },
   };
 
   for (int i = 0; i < numberof (data); i++)
@@ -103,7 +107,7 @@ check_small (void)
   mpz_t test;
   mpz_init_set_ui(test, 1);
 
-  for (int i = 1; i < 1000; i++)
+  for (int i = 1; i < 5000; i++)
     {
       mpz_nextprime(test, test);