#line 1 "test/mini/fused_operations.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0000"
#include <cassert>
#include <climits>
#include <limits>
#include <random>
#include <type_traits>
#line 1 "utility/macro/assert_eq.cpp"
/**
* @brief 等値判定のテスト用マクロ
* @author えびちゃん
*/
#line 10 "utility/macro/assert_eq.cpp"
#include <iomanip>
#include <iostream>
#define assert_eq(expr, expected_) do { \
auto found = (expr); \
auto expected = (expected_); \
std::cerr << std::setw(64) << std::setfill('-') << "\n"; \
std::cerr << "expr: " << #expr << '\n'; \
std::cerr << "expected: " << expected << '\n'; \
std::cerr << "found: "; \
std::cerr << ((found != expected)? "\x1b[1;91m": "\x1b[1;92m"); \
std::cerr << found << "\x1b[m" << '\n'; \
std::cerr << std::setw(64) << std::setfill('-') << "\n"; \
assert(found == expected); \
} while (false)
#line 1 "integer/fused_operations.cpp"
/**
* @brief 乗算との複合演算
* @author えびちゃん
*/
#line 10 "integer/fused_operations.cpp"
#include <algorithm>
#include <type_traits>
#line 1 "integer/overflow.cpp"
/**
* @brief オーバーフロー判定つき演算
* @author えびちゃん
*/
#line 10 "integer/overflow.cpp"
#include <type_traits>
#line 1 "integer/mul_upper.cpp"
/**
* @brief 整数の乗算の上位ワード
* @author えびちゃん
*/
#include <cstdint>
#line 11 "integer/mul_upper.cpp"
#include <type_traits>
#include <utility>
#line 1 "utility/literals.cpp"
/**
* @brief ユーザ定義リテラル
* @author えびちゃん
*/
#include <cstddef>
#line 11 "utility/literals.cpp"
constexpr intmax_t operator ""_jd(unsigned long long n) { return n; }
constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; }
constexpr size_t operator ""_zu(unsigned long long n) { return n; }
constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; }
constexpr int8_t operator ""_i8(unsigned long long n) { return n; }
constexpr int16_t operator ""_i16(unsigned long long n) { return n; }
constexpr int32_t operator ""_i32(unsigned long long n) { return n; }
constexpr int64_t operator ""_i64(unsigned long long n) { return n; }
constexpr uint8_t operator ""_u8(unsigned long long n) { return n; }
constexpr uint16_t operator ""_u16(unsigned long long n) { return n; }
constexpr uint32_t operator ""_u32(unsigned long long n) { return n; }
constexpr uint64_t operator ""_u64(unsigned long long n) { return n; }
#line 15 "integer/mul_upper.cpp"
template <typename Tp>
auto mul_upper(Tp u, Tp v)
-> typename std::enable_if<std::is_integral_v<Tp>, Tp>::type
{
using value_type = Tp;
using unsigned_type = typename std::make_unsigned<Tp>::type;
unsigned_type hi;
int const bits = CHAR_BIT * sizeof(value_type);
if (false && (sizeof u) < sizeof(uintmax_t)) {
uintmax_t mul = uintmax_t(u) * v;
hi = mul >> bits;
// XXX unsigned only
} else {
int const half_bits = bits / 2;
unsigned_type const half_mask = (unsigned_type(1) << half_bits) - 1;
unsigned_type u0 = u & half_mask, v0 = v & half_mask;
unsigned_type u1 = unsigned_type(u) >> half_bits, v1 = unsigned_type(v) >> half_bits;
unsigned_type w0 = u0 * v0;
unsigned_type t = u1 * v0 + (w0 >> half_bits);
unsigned_type w1 = t & half_mask;
unsigned_type w2 = t >> half_bits;
w1 += u0 * v1;
hi = u1 * v1 + w2 + (w1 >> half_bits);
if (u < 0) hi -= v;
if (v < 0) hi -= u;
}
return hi;
}
#line 13 "integer/overflow.cpp"
template <typename Tp>
auto add_overflow(Tp x, Tp y, Tp& z)
-> typename std::enable_if<std::is_integral_v<Tp>, bool>::type
{
using unsigned_type = typename std::make_unsigned<Tp>::type;
unsigned_type ux = x, uy = y;
unsigned_type sign_bit = unsigned_type{1} << ((CHAR_BIT * sizeof(Tp)) - 1);
if ((ux & sign_bit) ^ (uy & sign_bit)) return (z = x + y), false;
if (((ux + uy) & sign_bit) != (ux & sign_bit)) return true;
z = x + y;
return false;
}
template <typename Tp>
auto sub_overflow(Tp x, Tp y, Tp& z)
-> typename std::enable_if<std::is_integral_v<Tp>, bool>::type
{
using unsigned_type = typename std::make_unsigned<Tp>::type;
if (y == 0) return (z = x), false;
unsigned_type uy = y;
if (~(uy | (uy-1)) == 0 && y < 0) return true;
return add_overflow(x, -y, z);
}
template <typename Tp>
auto mul_overflow(Tp x, Tp y, Tp& z)
-> typename std::enable_if<std::is_integral_v<Tp>, bool>::type
{
using unsigned_type = typename std::make_unsigned<Tp>::type;
unsigned_type ux = x, uy = y;
unsigned_type sign_bit = ~(~unsigned_type(0) >> 1);
if (((ux * uy) & sign_bit) != ((ux & sign_bit) ^ (uy & sign_bit))) return true;
z = x * y;
return false;
}
#line 15 "integer/fused_operations.cpp"
template <typename Tp>
Tp fused_mul_add(Tp x, Tp y, Tp z) {
// Return x * y + z without overflow
using unsigned_type = typename std::make_unsigned<Tp>::type;
unsigned_type ux = x, uy = y;
unsigned_type lo = ux * uy;
return lo + z;
}
template <typename Tp>
Tp fused_mul_min(Tp x, Tp y, Tp z) {
// min(x * y, z) without overflow
Tp w;
if (mul_overflow(x, y, w)) return z; // undefined if x*y < minimum
return std::min(w, z);
}
template <typename Tp>
Tp fused_add_mod(Tp x, Tp y, Tp z) {
// (x + y) % z, same sign as z, without overflow
if (std::is_signed_v<Tp>) {
if ((x %= z) != 0 && ((x < 0) != (z < 0))) x += z;
if ((y %= z) != 0 && ((y < 0) != (z < 0))) y += z;
x -= z - y;
if ((x %= z) != 0 && ((x < 0) != (z < 0))) x += z;
} else {
x %= z;
y %= z;
x += ((x < z-y)? y: y-z);
}
return x;
}
template <typename Tp>
Tp fused_mul_mod(Tp x, Tp y, Tp z) {
// (x * y) % z, same sign as z, without overflow
using value_type = Tp;
using unsigned_type = typename std::make_unsigned<Tp>::type;
unsigned_type ux = x, uy = y;
value_type hi = mul_upper(x, y) % z;
int const bits = CHAR_BIT * sizeof(Tp);
for (int i = 0; i < bits; ++i) {
hi = fused_add_mod(hi, hi, z);
}
unsigned_type uxy = ux * uy;
value_type loh = uxy >> (bits/2);
value_type lol = uxy & (~unsigned_type(0) >> (bits/2));
for (int i = 0; i < bits/2; ++i) {
loh = fused_add_mod(loh, loh, z);
}
lol = fused_add_mod(loh, lol, z);
return fused_add_mod(hi, lol, z);
}
#line 11 "test/mini/fused_operations.test.cpp"
#line 1 "test/mini/qq.cpp"
// @ignore
#include <cstdio>
void qq() {
for (int i = 1; i <= 9; ++i)
for (int j = 1; j <= 9; ++j)
printf("%dx%d=%d\n", i, j, i*j);
}
#line 13 "test/mini/fused_operations.test.cpp"
// test_mul_add();
// test_mul_min();
// test_add_mod();
// test_mul_mod();
std::mt19937_64 rng;
template <typename Tp>
static constexpr Tp min_v = std::numeric_limits<Tp>::min();
template <typename Tp>
static constexpr Tp max_v = std::numeric_limits<Tp>::max();
template <typename Tp>
int test_add_mod(int rep) {
using large_type = typename std::conditional<std::is_signed_v<Tp>, __int128, unsigned __int128>::type;
std::uniform_int_distribution<Tp> u(min_v<Tp>, max_v<Tp>);
int neg = 0, pos = 0;
for (int i = 0; i < rep; ++i) {
Tp x = u(rng);
Tp y = u(rng);
Tp z = u(rng);
if (z == 0) continue;
Tp w = (large_type(x) + large_type(y)) % large_type(z);
if (w != 0 && ((w < 0) != (z < 0))) w += z;
std::cerr << __PRETTY_FUNCTION__ << '\n';
std::cerr << "fused_add_mod(" << x << ", " << y << ", " << z << "): " << w << '\n';
assert_eq(fused_add_mod(x, y, z), w);
++((y < 0)? neg: pos);
}
assert(pos > 0 && (std::is_unsigned_v<Tp> || neg > 0));
return neg + pos;
}
void test_add_mod() {
fprintf(stderr, "%d tests passed.\n", test_add_mod<signed int>(10000));
fprintf(stderr, "%d tests passed.\n", test_add_mod<unsigned int>(10000));
fprintf(stderr, "%d tests passed.\n", test_add_mod<signed long>(10000));
fprintf(stderr, "%d tests passed.\n", test_add_mod<unsigned long>(10000));
}
template <typename Tp>
int test_mul_mod(int rep) {
using large_type = typename std::conditional<std::is_signed_v<Tp>, __int128, unsigned __int128>::type;
std::uniform_int_distribution<Tp> u(min_v<Tp>, max_v<Tp>);
int neg = 0, pos = 0;
for (int i = 0; i < rep; ++i) {
Tp x = u(rng);
Tp y = u(rng);
Tp z = u(rng);
if (z == 0) continue;
Tp w = (large_type(x) * large_type(y)) % large_type(z);
if (w != 0 && ((w < 0) != (z < 0))) w += z;
std::cerr << __PRETTY_FUNCTION__ << '\n';
std::cerr << "fused_mul_mod(" << x << ", " << y << ", " << z << "): " << w << '\n';
assert_eq(fused_mul_mod(x, y, z), w);
++((y < 0)? neg: pos);
}
assert(pos > 0 && (std::is_unsigned_v<Tp> || neg > 0));
return neg + pos;
}
void test_mul_mod() {
fprintf(stderr, "%d tests passed.\n", test_mul_mod<signed int>(10000));
fprintf(stderr, "%d tests passed.\n", test_mul_mod<unsigned int>(10000));
fprintf(stderr, "%d tests passed.\n", test_mul_mod<signed long>(10000));
fprintf(stderr, "%d tests passed.\n", test_mul_mod<unsigned long>(10000));
}
int main() {
assert_eq(fused_mul_add(65536, 32768, -1), 2147483647);
assert_eq(fused_add_mod(1000, 1000, 900), 200);
assert_eq(fused_add_mod(2000000000, 2000000000, 2100000000), 1900000000);
assert_eq(fused_mul_mod(1000000, 1000000, 998244353), 757402647);
assert_eq(fused_mul_add(65536u, 32768u, -1u), 2147483647u);
assert_eq(fused_add_mod(1000u, 1000u, 900u), 200u);
assert_eq(fused_add_mod(2000000000u, 2000000000u, 2100000000u), 1900000000u);
assert_eq(fused_mul_mod(1000000u, 1000000u, 998244353u), 757402647u);
assert_eq(fused_add_mod(1, 3, -3), -2);
assert_eq(fused_add_mod(1, -3, 3), 1);
assert_eq(fused_mul_mod(+1000000000, +1000000000, +1000000007), 49);
assert_eq(fused_mul_mod(+1000000000, +1000000000, -1000000007), -999999958);
assert_eq(fused_mul_mod(+1000000000, -1000000000, +1000000007), 999999958);
assert_eq(fused_mul_mod(+1000000000, -1000000000, -1000000007), -49);
assert_eq(fused_mul_mod(-1000000000, +1000000000, +1000000007), 999999958);
assert_eq(fused_mul_mod(-1000000000, +1000000000, -1000000007), -49);
assert_eq(fused_mul_mod(-1000000000, -1000000000, +1000000007), 49);
assert_eq(fused_mul_mod(-1000000000, -1000000000, -1000000007), -999999958);
assert_eq(fused_mul_mod(+1000000000u, +1000000000u, +1000000007u), 49u);
assert_eq(fused_mul_mod(+1000000000u, +1000000000u, -1000000007u), 1609396939u);
assert_eq(fused_mul_mod(+1000000000u, -1000000000u, +1000000007u), 935229096u);
assert_eq(fused_mul_mod(+1000000000u, -1000000000u, -1000000007u), 410065422u);
assert_eq(fused_mul_mod(-1000000000u, +1000000000u, +1000000007u), 935229096u);
assert_eq(fused_mul_mod(-1000000000u, +1000000000u, -1000000007u), 410065422u);
assert_eq(fused_mul_mod(-1000000000u, -1000000000u, +1000000007u), 711885781u);
assert_eq(fused_mul_mod(-1000000000u, -1000000000u, -1000000007u), 49u);
assert_eq(fused_add_mod(2, 3, +5), 0);
assert_eq(fused_add_mod(2, 3, -5), 0);
assert_eq(fused_mul_mod(+3, +4, +2), 0);
assert_eq(fused_mul_mod(+3, +4, -2), 0);
assert_eq(fused_mul_mod(+3, -4, +2), 0);
assert_eq(fused_mul_mod(+3, -4, -2), 0);
assert_eq(fused_mul_mod(-3, +4, +2), 0);
assert_eq(fused_mul_mod(-3, +4, -2), 0);
assert_eq(fused_mul_mod(-3, -4, +2), 0);
assert_eq(fused_mul_mod(-3, -4, -2), 0);
assert_eq(fused_mul_mod(INT_MIN, -1, -1), 0);
assert_eq(fused_mul_mod(INT_MIN, +1, -1), 0);
assert_eq(fused_mul_mod(INT_MIN, -1, +1), 0);
assert_eq(fused_mul_mod(INT_MIN, +1, +1), 0);
assert_eq(fused_mul_min(1000000000, 1000000000, 2000000000), 2000000000);
assert_eq(fused_mul_min(1000, 1000, 2000000000), 1000000);
assert_eq(fused_mul_min(100, -100, 0), -10000);
assert_eq(fused_mul_min(-100, -100, 0), 0);
assert_eq(fused_mul_mod(1000000000000000000L, 1000000000000000000L, 2305843009213693951L),
1824060670036424877L);
test_add_mod();
test_mul_mod();
qq(); // dummy
}
test/mini/fused_operations.test.cpp