libstdc++: Optimise GCD algorithms

The current std::gcd and std::chrono::duration::_S_gcd algorithms are
both recursive. This is potentially expensive to evaluate in constant
expressions, because each level of recursion makes a new copy of the
function to evaluate. The maximum number of steps is bounded
(proportional to the number of decimal digits in the smaller value) and
so unlikely to exceed the limit for constexpr nesting, but the memory
usage is still suboptimal. By using an iterative algorithm we avoid
that compile-time cost. Because looping in constexpr functions is not
allowed until C++14, we need to keep the recursive implementation in
duration::_S_gcd for C++11 mode.

For std::gcd we can also optimise runtime performance by using the
binary GCD algorithm.

libstdc++-v3/ChangeLog:

	* include/std/chrono (duration::_S_gcd): Use iterative algorithm
	for C++14 and later.
	* include/std/numeric (__detail::__gcd): Replace recursive
	Euclidean algorithm with iterative version of binary GCD algorithm.
	* testsuite/26_numerics/gcd/1.cc: Test additional inputs.
	* testsuite/26_numerics/gcd/gcd_neg.cc: Adjust dg-error lines.
	* testsuite/26_numerics/lcm/lcm_neg.cc: Likewise.
	* testsuite/experimental/numeric/gcd.cc: Test additional inputs.
	* testsuite/26_numerics/gcd/2.cc: New test.

7 files changed, 332 insertions, 18 deletions

diff --git a/libstdc++-v3/include/std/chrono b/libstdc++-v3/include/std/chrono
index 1682263..0e2efb2 100644
--- a/libstdc++-v3/include/std/chrono
+++ b/libstdc++-v3/include/std/chrono
@@ -428,8 +428,20 @@ _GLIBCXX_BEGIN_NAMESPACE_VERSION
 	_S_gcd(intmax_t __m, intmax_t __n) noexcept
 	{
 	  // Duration only allows positive periods so we don't need to
-	  // support negative values here (unlike __static_gcd and std::gcd).
+	  // handle negative values here (unlike __static_gcd and std::gcd).
+#if __cplusplus >= 201402L
+	  while (__m != 0 && __n != 0)
+	    {
+	      intmax_t __rem = __m % __n;
+	      __m = __n;
+	      __n = __rem;
+	    }
+	  return __m + __n;
+#else
+	  // C++11 doesn't allow loops in constexpr functions, but this
+	  // recursive version can be more expensive to evaluate.
 	  return (__m == 0) ? __n : (__n == 0) ? __m : _S_gcd(__n, __m % __n);
+#endif
 	}
 
 	// _GLIBCXX_RESOLVE_LIB_DEFECTS
diff --git a/libstdc++-v3/include/std/numeric b/libstdc++-v3/include/std/numeric
index bd70a52..2de6aaf 100644
--- a/libstdc++-v3/include/std/numeric
+++ b/libstdc++-v3/include/std/numeric
@@ -76,6 +76,7 @@
 
 #if __cplusplus >= 201402L
 #include <type_traits>
+#include <bit>
 
 namespace std _GLIBCXX_VISIBILITY(default)
 {
@@ -97,15 +98,40 @@ namespace __detail
 
   template<typename _Up> void __absu(bool) = delete;
 
-  // GCD implementation
+  // GCD implementation, using Stein's algorithm
   template<typename _Tp>
     constexpr _Tp
     __gcd(_Tp __m, _Tp __n)
     {
       static_assert(is_unsigned<_Tp>::value, "type must be unsigned");
-      return __m == 0 ? __n
-	: __n == 0 ? __m
-	: __detail::__gcd(__n, _Tp(__m % __n));
+
+      if (__m == 0)
+	return __n;
+      if (__n == 0)
+	return __m;
+
+      const int __i = std::__countr_zero(__m);
+      __m >>= __i;
+      const int __j = std::__countr_zero(__n);
+      __n >>= __j;
+      const int __k = __i < __j ? __i : __j; // min(i, j)
+
+      while (true)
+	{
+	  if (__m > __n)
+	    {
+	      _Tp __tmp = __m;
+	      __m = __n;
+	      __n = __tmp;
+	    }
+
+	  __n -= __m;
+
+	  if (__n == 0)
+	    return __m << __k;
+
+	  __n >>= std::__countr_zero(__n);
+	}
     }
 
   // LCM implementation
diff --git a/libstdc++-v3/testsuite/26_numerics/gcd/1.cc b/libstdc++-v3/testsuite/26_numerics/gcd/1.cc
index 042f0a9..dc43cda 100644
--- a/libstdc++-v3/testsuite/26_numerics/gcd/1.cc
+++ b/libstdc++-v3/testsuite/26_numerics/gcd/1.cc
@@ -15,7 +15,6 @@
 // with this library; see the file COPYING3.  If not see
 // <http://www.gnu.org/licenses/>.
 
-// { dg-options "-std=gnu++17" }
 // { dg-do compile { target c++17 } }
 
 #include <numeric>
@@ -27,6 +26,7 @@
 #endif
 
 using std::gcd;
+using std::is_same_v;
 
 static_assert( gcd(1071, 462) == 21, "" );
 static_assert( gcd(2000, 20) == 20, "" );
@@ -34,11 +34,20 @@ static_assert( gcd(2011, 17) == 1, "GCD of two primes is 1" );
 static_assert( gcd(200, 200) == 200, "GCD of equal numbers is that number" );
 static_assert( gcd(0, 13) == 13, "GCD of any number and 0 is that number" );
 static_assert( gcd(29, 0) == 29, "GCD of any number and 0 is that number" );
-static_assert( gcd(0, 0) == 0, "" );
+static_assert( gcd(0, 0) == 0, "Zarro Boogs found" );
 
 static_assert(gcd(1u, 2) == 1, "unsigned and signed");
+static_assert(gcd(9, 6u) == 3, "unsigned and signed");
 static_assert(gcd(3, 4u) == 1, "signed and unsigned");
+static_assert(gcd(32u, 24) == 8, "signed and unsigned");
+static_assert(gcd(1u, -2) == 1, "unsigned and negative");
+static_assert(gcd(-21, 28u) == 7, "unsigned and negative");
+static_assert(gcd(-3, 4u) == 1, "negative and unsigned");
+static_assert(gcd(33u, -44) == 11, "negative and unsigned");
 static_assert(gcd(5u, 6u) == 1, "unsigned and unsigned");
+static_assert(gcd(54u, 36u) == 18, "unsigned and unsigned");
+static_assert(gcd(-5, -6) == 1, "negative and negative");
+static_assert(gcd(-50, -60) == 10, "negative and negative");
 
-static_assert( std::is_same_v<decltype(gcd(1l, 1)), long> );
-static_assert( std::is_same_v<decltype(gcd(1ul, 1ull)), unsigned long long> );
+static_assert( is_same_v<decltype(gcd(1l, 1)), long> );
+static_assert( is_same_v<decltype(gcd(1ul, 1ull)), unsigned long long> );
diff --git a/libstdc++-v3/testsuite/26_numerics/gcd/2.cc b/libstdc++-v3/testsuite/26_numerics/gcd/2.cc
new file mode 100644
index 0000000..186dbac
--- /dev/null
+++ b/libstdc++-v3/testsuite/26_numerics/gcd/2.cc
@@ -0,0 +1,133 @@
+// Copyright (C) 2015-2020 Free Software Foundation, Inc.
+//
+// This file is part of the GNU ISO C++ Library.  This library is free
+// software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the
+// Free Software Foundation; either version 3, or (at your option)
+// any later version.
+
+// This library is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+
+// You should have received a copy of the GNU General Public License along
+// with this library; see the file COPYING3.  If not see
+// <http://www.gnu.org/licenses/>.
+
+// { dg-do run { target c++17 } }
+
+#include <numeric>
+#include <climits>
+#include <testsuite_hooks.h>
+
+constexpr struct testcase { unsigned long long p, q, r; } testcases[] = {
+  { 5, 8, 1 },
+  { 6, 35, 1 },
+  { 30, 42, 6 },
+  { 24, 60, 12 },
+  { 55, 144, 1 },
+  { 105, 252, 21 },
+  { 253, 22121, 11 },
+  { 1386, 3213, 63 },
+  { 2028, 2049, 3 },
+  { 46391, 62527, 2017 },
+  { 63245986, 39088169, 1 },
+  { 77160074263, 47687519812, 1 },
+  { 77160074264, 47687519812, 4 },
+};
+
+template<typename P, typename Q>
+constexpr bool
+check(P p, Q q, unsigned long long r)
+{
+  using R = std::common_type_t<P, Q>;
+  static_assert( std::is_same_v<decltype(std::gcd(p, q)), R> );
+  static_assert( std::is_same_v<decltype(std::gcd(q, p)), R> );
+  R r1 = std::gcd(p, q);
+  // Check non-negative, so conversion to unsigned long doesn't alter value.
+  VERIFY( r1 >= 0 );
+  // Check for expected result
+  VERIFY( (unsigned long long)r1 == r );
+  // Check reversing arguments doesn't change result
+  VERIFY( std::gcd(q, p) == r1 );
+
+  P pabs = p < 0 ? -p : p;
+  VERIFY( std::gcd(p, p) == pabs );
+  VERIFY( std::gcd(0, p) == pabs );
+  VERIFY( std::gcd(p, 0) == pabs );
+  VERIFY( std::gcd(1, p) == 1 );
+  VERIFY( std::gcd(p, 1) == 1 );
+  Q qabs = q < 0 ? -q : q;
+  VERIFY( std::gcd(q, q) == qabs );
+  VERIFY( std::gcd(0, q) == qabs );
+  VERIFY( std::gcd(q, 0) == qabs );
+  VERIFY( std::gcd(1, q) == 1 );
+  VERIFY( std::gcd(q, 1) == 1 );
+  VERIFY( std::gcd(r, r) == r );
+  VERIFY( std::gcd(0, r) == r );
+  VERIFY( std::gcd(r, 0) == r );
+  VERIFY( std::gcd(1, r) == 1 );
+  VERIFY( std::gcd(r, 1) == 1 );
+
+  return true;
+}
+
+constexpr bool
+test01()
+{
+  for (auto t : testcases)
+  {
+    check(t.p, t.q, t.r);
+
+    if (t.p <= LONG_MAX && t.q <= LONG_MAX)
+    {
+      check( (long)t.p,  (long)t.p, t.p);
+      check(-(long)t.p,  (long)t.p, t.p);
+      check(-(long)t.p, -(long)t.p, t.p);
+
+      check( (long)t.p, t.q, t.r);
+      check(-(long)t.p, t.q, t.r);
+
+      check(t.p,  (long)t.q, t.r);
+      check(t.p, -(long)t.q, t.r);
+
+      check( (long)t.p,  (long)t.q, t.r);
+      check( (long)t.p, -(long)t.q, t.r);
+      check(-(long)t.p,  (long)t.q, t.r);
+      check(-(long)t.p, -(long)t.q, t.r);
+    }
+
+    if (t.p <= INT_MAX && t.q <= INT_MAX)
+    {
+      check((long)t.p,  (int)t.q, t.r);
+      check(-(int)t.p, (long)t.q, t.r);
+
+      check( (int)t.p, (unsigned)t.q, t.r);
+      check(-(int)t.p, (unsigned)t.q, t.r);
+
+      check(-(int)t.p,  -(int)t.q, t.r);
+      check(-(int)t.p, -(long)t.q, t.r);
+    }
+
+    if (t.p <= SHRT_MAX && t.q <= SHRT_MAX)
+    {
+      check(  (long)t.p, (short)t.q, t.r);
+      check(-(short)t.p,  (long)t.q, t.r);
+
+      check( (short)t.p, (unsigned short)t.q, t.r);
+      check(-(short)t.p, (unsigned short)t.q, t.r);
+
+      check(-(short)t.p, -(short)t.q, t.r);
+      check(-(short)t.p,  -(long)t.q, t.r);
+    }
+  }
+  return true;
+}
+
+
+int main()
+{
+  static_assert( test01() );  // constexpr
+  VERIFY( test01() );	      // non-constexpr
+}
diff --git a/libstdc++-v3/testsuite/26_numerics/gcd/gcd_neg.cc b/libstdc++-v3/testsuite/26_numerics/gcd/gcd_neg.cc
index 2e56bc6..fa559b6 100644
--- a/libstdc++-v3/testsuite/26_numerics/gcd/gcd_neg.cc
+++ b/libstdc++-v3/testsuite/26_numerics/gcd/gcd_neg.cc
@@ -46,9 +46,9 @@ test01()
   std::gcd<const int&, const int&>(0.1, 0.1);   // { dg-error "from here" }
 }
 
-// { dg-error "must be integers" "" { target *-*-* } 134 }
-// { dg-error "must be integers" "" { target *-*-* } 135 }
-// { dg-error "must not be bool" "" { target *-*-* } 136 }
-// { dg-error "must not be bool" "" { target *-*-* } 137 }
+// { dg-error "must be integers" "" { target *-*-* } 160 }
+// { dg-error "must be integers" "" { target *-*-* } 161 }
+// { dg-error "must not be bool" "" { target *-*-* } 162 }
+// { dg-error "must not be bool" "" { target *-*-* } 163 }
 // { dg-prune-output "deleted function" }
 // { dg-prune-output "incomplete type .*make_unsigned" }
diff --git a/libstdc++-v3/testsuite/26_numerics/lcm/lcm_neg.cc b/libstdc++-v3/testsuite/26_numerics/lcm/lcm_neg.cc
index 9e83fdc..7e36c26 100644
--- a/libstdc++-v3/testsuite/26_numerics/lcm/lcm_neg.cc
+++ b/libstdc++-v3/testsuite/26_numerics/lcm/lcm_neg.cc
@@ -46,9 +46,9 @@ test01()
   std::lcm<const int&, const int&>(0.1, 0.1);   // { dg-error "from here" }
 }
 
-// { dg-error "must be integers" "" { target *-*-* } 148 }
-// { dg-error "must be integers" "" { target *-*-* } 149 }
-// { dg-error "must not be bool" "" { target *-*-* } 150 }
-// { dg-error "must not be bool" "" { target *-*-* } 151 }
+// { dg-error "must be integers" "" { target *-*-* } 174 }
+// { dg-error "must be integers" "" { target *-*-* } 175 }
+// { dg-error "must not be bool" "" { target *-*-* } 176 }
+// { dg-error "must not be bool" "" { target *-*-* } 177 }
 // { dg-prune-output "deleted function" }
 // { dg-prune-output "incomplete type .*make_unsigned" }
diff --git a/libstdc++-v3/testsuite/experimental/numeric/gcd.cc b/libstdc++-v3/testsuite/experimental/numeric/gcd.cc
index 33568cb..8555421 100644
--- a/libstdc++-v3/testsuite/experimental/numeric/gcd.cc
+++ b/libstdc++-v3/testsuite/experimental/numeric/gcd.cc
@@ -18,8 +18,16 @@
 // { dg-do compile { target c++14 } }
 
 #include <experimental/numeric>
+#include <experimental/type_traits>
+
+#ifndef __cpp_lib_experimental_gcd_lcm
+# error "Feature-test macro for gcd missing"
+#elif __cpp_lib_experimental_gcd_lcm != 201411
+# error "Feature-test macro for gcd has wrong value"
+#endif
 
 using std::experimental::fundamentals_v2::gcd;
+using std::experimental::is_same_v;
 
 static_assert( gcd(1071, 462) == 21, "" );
 static_assert( gcd(2000, 20) == 20, "" );
@@ -27,8 +35,134 @@ static_assert( gcd(2011, 17) == 1, "GCD of two primes is 1" );
 static_assert( gcd(200, 200) == 200, "GCD of equal numbers is that number" );
 static_assert( gcd(0, 13) == 13, "GCD of any number and 0 is that number" );
 static_assert( gcd(29, 0) == 29, "GCD of any number and 0 is that number" );
-static_assert( gcd(0, 0) == 0, "" );
+static_assert( gcd(0, 0) == 0, "Zarro Boogs found" );
 
 static_assert(gcd(1u, 2) == 1, "unsigned and signed");
+static_assert(gcd(9, 6u) == 3, "unsigned and signed");
 static_assert(gcd(3, 4u) == 1, "signed and unsigned");
+static_assert(gcd(32u, 24) == 8, "signed and unsigned");
+static_assert(gcd(1u, -2) == 1, "unsigned and negative");
+static_assert(gcd(-21, 28u) == 7, "unsigned and negative");
+static_assert(gcd(-3, 4u) == 1, "negative and unsigned");
+static_assert(gcd(33u, -44) == 11, "negative and unsigned");
 static_assert(gcd(5u, 6u) == 1, "unsigned and unsigned");
+static_assert(gcd(54u, 36u) == 18, "unsigned and unsigned");
+static_assert(gcd(-5, -6) == 1, "negative and negative");
+static_assert(gcd(-50, -60) == 10, "negative and negative");
+
+static_assert( is_same_v<decltype(gcd(1l, 1)), long>, "" );
+static_assert( is_same_v<decltype(gcd(1ul, 1ull)), unsigned long long>, "" );
+
+#include <climits>
+#include <testsuite_hooks.h>
+
+constexpr struct testcase { unsigned long long p, q, r; } testcases[] = {
+  { 5, 8, 1 },
+  { 6, 35, 1 },
+  { 30, 42, 6 },
+  { 24, 60, 12 },
+  { 55, 144, 1 },
+  { 105, 252, 21 },
+  { 253, 22121, 11 },
+  { 1386, 3213, 63 },
+  { 2028, 2049, 3 },
+  { 46391, 62527, 2017 },
+  { 63245986, 39088169, 1 },
+  { 77160074263, 47687519812, 1 },
+  { 77160074264, 47687519812, 4 },
+};
+
+template<typename P, typename Q>
+constexpr bool
+check(P p, Q q, unsigned long long r)
+{
+  using R = std::common_type_t<P, Q>;
+  static_assert( is_same_v<decltype(gcd(p, q)), R>, "" );
+  static_assert( is_same_v<decltype(gcd(q, p)), R>, "" );
+  R r1 = gcd(p, q);
+  // Check non-negative, so conversion to unsigned long doesn't alter value.
+  VERIFY( r1 >= 0 );
+  // Check for expected result
+  VERIFY( (unsigned long long)r1 == r );
+  // Check reversing arguments doesn't change result
+  VERIFY( gcd(q, p) == r1 );
+
+  P pabs = p < 0 ? -p : p;
+  VERIFY( gcd(p, p) == pabs );
+  VERIFY( gcd(0, p) == pabs );
+  VERIFY( gcd(p, 0) == pabs );
+  VERIFY( gcd(1, p) == 1 );
+  VERIFY( gcd(p, 1) == 1 );
+  Q qabs = q < 0 ? -q : q;
+  VERIFY( gcd(q, q) == qabs );
+  VERIFY( gcd(0, q) == qabs );
+  VERIFY( gcd(q, 0) == qabs );
+  VERIFY( gcd(1, q) == 1 );
+  VERIFY( gcd(q, 1) == 1 );
+  VERIFY( gcd(r, r) == r );
+  VERIFY( gcd(0, r) == r );
+  VERIFY( gcd(r, 0) == r );
+  VERIFY( gcd(1, r) == 1 );
+  VERIFY( gcd(r, 1) == 1 );
+
+  return true;
+}
+
+constexpr bool
+test01()
+{
+  for (auto t : testcases)
+  {
+    check(t.p, t.q, t.r);
+
+    if (t.p <= LONG_MAX && t.q <= LONG_MAX)
+    {
+      check( (long)t.p,  (long)t.p, t.p);
+      check(-(long)t.p,  (long)t.p, t.p);
+      check(-(long)t.p, -(long)t.p, t.p);
+
+      check( (long)t.p, t.q, t.r);
+      check(-(long)t.p, t.q, t.r);
+
+      check(t.p,  (long)t.q, t.r);
+      check(t.p, -(long)t.q, t.r);
+
+      check( (long)t.p,  (long)t.q, t.r);
+      check( (long)t.p, -(long)t.q, t.r);
+      check(-(long)t.p,  (long)t.q, t.r);
+      check(-(long)t.p, -(long)t.q, t.r);
+    }
+
+    if (t.p <= INT_MAX && t.q <= INT_MAX)
+    {
+      check((long)t.p,  (int)t.q, t.r);
+      check(-(int)t.p, (long)t.q, t.r);
+
+      check( (int)t.p, (unsigned)t.q, t.r);
+      check(-(int)t.p, (unsigned)t.q, t.r);
+
+      check(-(int)t.p,  -(int)t.q, t.r);
+      check(-(int)t.p, -(long)t.q, t.r);
+    }
+
+    if (t.p <= SHRT_MAX && t.q <= SHRT_MAX)
+    {
+      check(  (long)t.p, (short)t.q, t.r);
+      check(-(short)t.p,  (long)t.q, t.r);
+
+      check( (short)t.p, (unsigned short)t.q, t.r);
+      check(-(short)t.p, (unsigned short)t.q, t.r);
+
+      check(-(short)t.p, -(short)t.q, t.r);
+      check(-(short)t.p,  -(long)t.q, t.r);
+    }
+  }
+  return true;
+}
+
+
+int main()
+{
+  static_assert( test01() );  // constexpr
+  VERIFY( test01() );	      // non-constexpr
+}