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// --- This file is distributed under the MIT Open Source License, as detailed
// in the file "LICENSE.TXT" in the root of this repository ---
// This file is a trimmed copy of final_bounds.h.
// It contains only the essential assertion results, and omits the proofs.
#ifndef ESSENTIAL_ASSERTS_FINAL
#define ESSENTIAL_ASSERTS_FINAL 1
#ifndef NDEBUG
# include "helpers/assert_helper_gcd.h"
#endif
#include <assert.h>
#include <limits>
#include <algorithm>
template <typename T>
void essential_asserts_final(T a, T b, T* pGcd, T* pX, T* pY)
{
const auto max = static_cast<const T&(*)(const T&, const T&)>(std::max);
static_assert(std::numeric_limits<T>::is_integer, "");
static_assert(std::numeric_limits<T>::is_signed, "");
assert(a >= 0 && b >= 0); // precondition
T x0 = 1, y0 = 0, a0 = a;
T x1 = 0, y1 = 1, a1 = b;
while (a1 != 0) {
T q = a0/a1;
assert(0 <= q && q <= max(a,b));
T a2 = a0 - q*a1;
assert(0 <= (q*a1) && (q*a1) <= max(a,b));
assert(0 <= a2 && a2 < max(a,b));
if (a2 != 0) assert(q <= max(a,b)/2);
T x2 = x0 - q*x1;
assert(abs(q*x1) <= b);
assert(abs(x2) <= b);
if (a2 != 0) assert(abs(q*x1) <= max(1,b/2));
if (a2 != 0) assert(abs(x2) <= max(1,b/2));
T y2 = y0 - q*y1;
assert(abs(q*y1) <= max(1,a));
assert(abs(y2) <= max(1,a));
if (a2 != 0) assert(abs(q*y1) <= max(1,a/2));
if (a2 != 0) assert(abs(y2) <= max(1,a/2));
x0=x1; y0=y1; a0=a1;
x1=x2; y1=y2; a1=a2;
}
assert(a0 == gcd(a,b));
assert(a*x0 + b*y0 == gcd(a,b));
*pX = x0;
*pY = y0;
*pGcd = a0;
}
#endif