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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Test Suite *
* *
* Copyright (c) 1999-2025, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program 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 2 of the *
* License, or (at your option) any later version. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* This program 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 program. If not, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include <limits.h>
#include <numeric> // for std::gcd()
#include "maths/numbertheory.h"
#include "testhelper.h"
// A positive odd integer whose square is a bit less than LONG_MAX:
static constexpr long halfSizeOdd =
(long(1) << (sizeof(long) * 4 - 4)) * 11 + 5;
// An integer type that we can use to safely multiply longs.
using DoubleSize = regina::IntOfSize<sizeof(long) * 2>::type;
static void verifyReducedMod(long k, long modBase) {
SCOPED_TRACE_NUMERIC(k);
SCOPED_TRACE_NUMERIC(modBase);
long ans = regina::reducedMod(k, modBase);
// These tests are written a little awkwardly; the reason is to ensure
// they do the right thing even when pushing up against LONG_MIN / LONG_MAX.
if (ans >= 0)
EXPECT_LE(ans, modBase - ans);
else
EXPECT_GT(ans, -(modBase + ans));
if (k >= 0) {
if (ans >= 0)
EXPECT_EQ((k - ans) % modBase, 0);
else
EXPECT_EQ(((k - modBase) - ans) % modBase, 0);
} else {
if (ans >= 0)
EXPECT_EQ(((k + modBase) - ans) % modBase, 0);
else
EXPECT_EQ((k - ans) % modBase, 0);
}
}
TEST(NumberTheoryTest, reducedMod) {
// 0 mod n:
verifyReducedMod(0, 1);
verifyReducedMod(0, 1000000000);
verifyReducedMod(0, LONG_MAX);
// n mod 1:
verifyReducedMod(1, 1);
verifyReducedMod(-1, 1);
verifyReducedMod(1000000000, 1);
verifyReducedMod(-1000000000, 1);
verifyReducedMod(LONG_MAX, 1);
verifyReducedMod(LONG_MIN, 1);
// Extreme cases:
verifyReducedMod(LONG_MAX - 1, LONG_MAX);
verifyReducedMod(LONG_MAX, LONG_MAX - 1);
verifyReducedMod(LONG_MIN, LONG_MAX);
// Halfway tests:
verifyReducedMod(16, 2);
verifyReducedMod(17, 2);
verifyReducedMod(-16, 2);
verifyReducedMod(-17, 2);
verifyReducedMod(16, 3);
verifyReducedMod(17, 3);
verifyReducedMod(-16, 3);
verifyReducedMod(-17, 3);
verifyReducedMod(LONG_MAX / 2, LONG_MAX);
verifyReducedMod(LONG_MAX / 2 + 1, LONG_MAX);
verifyReducedMod(-(LONG_MAX / 2), LONG_MAX);
verifyReducedMod(-(LONG_MAX / 2 + 1), LONG_MAX);
static constexpr long evenMod = 40000 * 2;
static constexpr long evenHalf = (40000 * 40000) - 40000;
static constexpr long oddMod = 40001;
static constexpr long oddBelowHalf = (40001 * 40001) - ((40001 + 1) / 2);
verifyReducedMod(evenHalf - 1, evenMod);
verifyReducedMod(evenHalf, evenMod);
verifyReducedMod(evenHalf + 1, evenMod);
verifyReducedMod(-(evenHalf - 1), evenMod);
verifyReducedMod(-evenHalf, evenMod);
verifyReducedMod(-(evenHalf + 1), evenMod);
verifyReducedMod(oddBelowHalf, oddMod);
verifyReducedMod(oddBelowHalf + 1, oddMod);
verifyReducedMod(-oddBelowHalf, oddMod);
verifyReducedMod(-(oddBelowHalf + 1), oddMod);
// Examples from documentation:
verifyReducedMod(4, 10);
verifyReducedMod(6, 10);
// Invalid cases:
EXPECT_THROW({ regina::reducedMod(0, 0); }, regina::InvalidArgument);
EXPECT_THROW({ regina::reducedMod(3, 0); }, regina::InvalidArgument);
EXPECT_THROW({ regina::reducedMod(3, -7); }, regina::InvalidArgument);
EXPECT_THROW({ regina::reducedMod(3, LONG_MIN); }, regina::InvalidArgument);
EXPECT_THROW({ regina::reducedMod(LONG_MAX, LONG_MIN); },
regina::InvalidArgument);
}
static void verifyGcdWithCoeffs(long a, long b, long gcd) {
SCOPED_TRACE_NUMERIC(a);
SCOPED_TRACE_NUMERIC(b);
auto [d, u, v] = regina::gcdWithCoeffs(a, b);
EXPECT_EQ(d, gcd);
EXPECT_GE(d, 0);
EXPECT_EQ(static_cast<DoubleSize>(u) * a + static_cast<DoubleSize>(v) * b,
static_cast<DoubleSize>(d));
if (a == 0 && b == 0) {
EXPECT_EQ(d, 0);
EXPECT_EQ(u, 0);
EXPECT_EQ(v, 0);
} else if (a == 0) {
EXPECT_EQ(d, std::abs(b));
EXPECT_EQ(u, 0);
EXPECT_EQ(v, (b < 0 ? -1 : 1));
} else if (b == 0) {
EXPECT_EQ(d, std::abs(a));
EXPECT_EQ(u, (a < 0 ? -1 : 1));
EXPECT_EQ(v, 0);
} else {
ASSERT_NE(d, 0);
EXPECT_EQ(a % d, 0);
EXPECT_EQ(b % d, 0);
long aMult = (a >= 0 ? a / d : (-a) / d);
long bMult = (b >= 0 ? b / d : (-b) / d);
long uSigned = (a >= 0 ? u : -u);
long vSigned = (b >= 0 ? v : -v);
EXPECT_LT(-aMult, vSigned);
EXPECT_LE(vSigned, 0);
EXPECT_LE(1, uSigned);
EXPECT_LE(uSigned, bMult);
}
// While we're here, verify that std::gcd() does the right thing also.
EXPECT_EQ(std::gcd(a, b), gcd);
}
static void verifyGcdWithCoeffsAllCombs(long a, long b, long gcd) {
verifyGcdWithCoeffs(a, b, gcd);
verifyGcdWithCoeffs(a, -b, gcd);
verifyGcdWithCoeffs(-a, b, gcd);
verifyGcdWithCoeffs(-a, -b, gcd);
verifyGcdWithCoeffs(b, a, gcd);
verifyGcdWithCoeffs(b, -a, gcd);
verifyGcdWithCoeffs(-b, a, gcd);
verifyGcdWithCoeffs(-b, -a, gcd);
}
TEST(NumberTheoryTest, gcdWithCoeffs) {
// All of these cases are designed so that the arguments fit within
// 32-bit integers.
// Small cases:
verifyGcdWithCoeffsAllCombs(0, 0, 0);
verifyGcdWithCoeffsAllCombs(0, 1, 1);
verifyGcdWithCoeffsAllCombs(0, 40000, 40000);
verifyGcdWithCoeffsAllCombs(0, 1000000001, 1000000001);
verifyGcdWithCoeffsAllCombs(0, LONG_MAX, LONG_MAX);
verifyGcdWithCoeffsAllCombs(1, 40000, 1);
verifyGcdWithCoeffsAllCombs(1, 1000000001, 1);
verifyGcdWithCoeffsAllCombs(1, LONG_MAX, 1);
// Equal / multiple of:
verifyGcdWithCoeffsAllCombs(1000, 1000 * 999, 1000);
verifyGcdWithCoeffsAllCombs(1000, 1000 * 1000, 1000);
verifyGcdWithCoeffsAllCombs(40000, 40000, 40000);
verifyGcdWithCoeffsAllCombs(40000, 40000 * 40000, 40000);
verifyGcdWithCoeffsAllCombs(halfSizeOdd, halfSizeOdd, halfSizeOdd);
verifyGcdWithCoeffsAllCombs(halfSizeOdd, halfSizeOdd * (halfSizeOdd - 1),
halfSizeOdd);
verifyGcdWithCoeffsAllCombs(halfSizeOdd, halfSizeOdd * halfSizeOdd,
halfSizeOdd);
// Large cases:
verifyGcdWithCoeffsAllCombs(200 * 197, 200 * 199, 200);
verifyGcdWithCoeffsAllCombs(200 * 196, 200 * 198, 200 * 2);
verifyGcdWithCoeffsAllCombs(1000 * 3, 1000 * 1000, 1000);
verifyGcdWithCoeffsAllCombs(1000 * 3, 1000 * 999, 1000 * 3);
verifyGcdWithCoeffsAllCombs(40000 * 39997, 40000 * 39999, 40000);
verifyGcdWithCoeffsAllCombs(40000 * 39996, 40000 * 39998, 40000 * 2);
verifyGcdWithCoeffsAllCombs(halfSizeOdd * (halfSizeOdd - 3),
halfSizeOdd * (halfSizeOdd - 1), halfSizeOdd * 2);
verifyGcdWithCoeffsAllCombs(halfSizeOdd * (halfSizeOdd - 4),
halfSizeOdd * (halfSizeOdd - 2), halfSizeOdd);
// Miscellaneous cases:
verifyGcdWithCoeffsAllCombs(96, 324, 12);
// Extreme cases:
verifyGcdWithCoeffsAllCombs(LONG_MAX / 2, LONG_MAX, 1);
verifyGcdWithCoeffsAllCombs(LONG_MAX - 1, LONG_MAX, 1);
verifyGcdWithCoeffsAllCombs(LONG_MAX, LONG_MAX, LONG_MAX);
}
static void verifyModularInverse(long n, long k) {
SCOPED_TRACE_NUMERIC(n);
SCOPED_TRACE_NUMERIC(k);
long ans = regina::modularInverse(n, k);
EXPECT_GE(ans, 0);
EXPECT_LT(ans, n);
EXPECT_EQ((static_cast<DoubleSize>(ans) * (k % n) - 1) % n, 0);
}
static void verifyModularInverseAllCombs(long n, long k) {
verifyModularInverse(n, k);
verifyModularInverse(n, -k);
}
static void verifyModularInverseExhaustive(long n) {
SCOPED_TRACE_NUMERIC(n);
for (long k = 1; k < n; ++k) {
if (std::gcd(k, n) != 1)
continue;
SCOPED_TRACE_NUMERIC(k);
// Element to invert within standard range.
long ans = regina::modularInverse(n, k);
EXPECT_GE(ans, 0);
EXPECT_LT(ans, n);
EXPECT_EQ((static_cast<DoubleSize>(ans) * k - 1) % n, 0);
// Element to invert not within standard range.
DoubleSize large = static_cast<DoubleSize>(n) * (n - 1) + k;
if (large <= LONG_MAX)
EXPECT_EQ(regina::modularInverse(n, static_cast<long>(large)), ans);
}
}
TEST(NumberTheoryTest, modularInverse) {
// Small cases:
verifyModularInverseAllCombs(1, 0);
verifyModularInverseAllCombs(1, 1);
verifyModularInverseAllCombs(1, 40000);
verifyModularInverseAllCombs(2, 1);
verifyModularInverseAllCombs(2, 40001);
// Boundary cases:
verifyModularInverseAllCombs(40000, 1);
verifyModularInverseAllCombs(40000, 39999);
verifyModularInverseAllCombs(40000, 40001);
verifyModularInverseAllCombs(40001, 1);
verifyModularInverseAllCombs(40001, 40000);
verifyModularInverseAllCombs(40001, 40002);
// All cases for a particular modular base:
verifyModularInverseExhaustive(40000);
verifyModularInverseExhaustive(40001);
// Extreme cases:
verifyModularInverseAllCombs(2, LONG_MAX);
verifyModularInverseAllCombs(LONG_MAX - 2, LONG_MAX);
verifyModularInverseAllCombs(LONG_MAX / 2, LONG_MAX);
// Invalid cases:
EXPECT_THROW({ regina::modularInverse(0, 0); }, regina::InvalidArgument);
EXPECT_THROW({ regina::modularInverse(0, 1); }, regina::InvalidArgument);
EXPECT_THROW({ regina::modularInverse(0, 2); }, regina::InvalidArgument);
EXPECT_THROW({ regina::modularInverse(2, 0); }, regina::InvalidArgument);
EXPECT_THROW({ regina::modularInverse(2, 2); }, regina::InvalidArgument);
EXPECT_THROW({ regina::modularInverse(2, 10); }, regina::InvalidArgument);
EXPECT_THROW({ regina::modularInverse(101 * 7, 101 * 5); },
regina::InvalidArgument);
EXPECT_THROW({ regina::modularInverse(101 * 5, 101 * 7); },
regina::InvalidArgument);
}
|
