685 lines
21 KiB
C++
685 lines
21 KiB
C++
#pragma once
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#include <math.h>
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#include <stdint.h>
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#include <limits.h>
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#include <vector>
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#include <algorithm>
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#include <iostream>
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class Num {
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public:
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typedef uint64_t word;
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std::vector<word> words;
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bool neg;
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static word word_mask(){
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return (word)-1;
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}
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static size_t word_bits(){
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return sizeof(word)*CHAR_BIT;
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}
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static word word_half_mask(){
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return word_mask() >> word_bits()/2;
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}
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static word char_to_word(char c){
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switch (c){
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case '0': return 0;
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case '1': return 1;
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case '2': return 2;
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case '3': return 3;
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case '4': return 4;
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case '5': return 5;
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case '6': return 6;
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case '7': return 7;
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case '8': return 8;
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case '9': return 9;
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case 'a': case 'A': return 10;
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case 'b': case 'B': return 11;
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case 'c': case 'C': return 12;
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case 'd': case 'D': return 13;
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case 'e': case 'E': return 14;
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case 'f': case 'F': return 15;
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case 'g': case 'G': return 16;
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case 'h': case 'H': return 17;
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case 'i': case 'I': return 18;
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case 'j': case 'J': return 19;
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case 'k': case 'K': return 20;
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case 'l': case 'L': return 21;
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case 'm': case 'M': return 22;
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case 'n': case 'N': return 23;
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case 'o': case 'O': return 24;
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case 'p': case 'P': return 25;
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case 'q': case 'Q': return 26;
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case 'r': case 'R': return 27;
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case 's': case 'S': return 28;
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case 't': case 'T': return 29;
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case 'u': case 'U': return 30;
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case 'v': case 'V': return 31;
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case 'w': case 'W': return 32;
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case 'x': case 'X': return 33;
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case 'y': case 'Y': return 34;
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case 'z': case 'Z': return 35;
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default: return word_mask();
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}
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}
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static word word_gcd(word a, word b){
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while (1){
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if (a == 0) return b;
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b %= a;
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if (b == 0) return a;
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a %= b;
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}
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}
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Num(): neg(false){}
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Num(size_t n, word w, bool neg = false): words(n, w), neg(neg){}
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Num(const word *a, const word *b, bool neg = false) : words(a, b), neg(neg){
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truncate();
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}
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Num(const Num &a){
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words = a.words;
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neg = a.neg;
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}
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Num& operator = (const Num &a){
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words = a.words;
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neg = a.neg;
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return *this;
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}
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Num(int i): neg(i < 0){
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unsigned u = (i < 0) ? -(unsigned)i : (unsigned)i;
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if (sizeof(u) <= word_bits()){
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if (u > 0) push_back(u);
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}else{
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for (; u; u >>= word_bits()) push_back(u);
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}
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}
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Num(const char *c, word base = 10, char **endptr = NULL): neg(false){
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// read sign
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if (*c == '-'){
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c++;
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neg = true;
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}
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// read digits
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for (;*c; c++){
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mul_word(base);
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word b = char_to_word(*c);
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if (b >= base) break;
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add_word(b);
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}
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if (endptr) *endptr = (char*)c;
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}
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void resize(size_t n){
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words.resize(n);
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}
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void pop_back(){
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words.pop_back();
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}
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void push_back(word b){
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words.push_back(b);
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}
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word& back(){
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return words.back();
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}
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const word& back() const {
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return words.back();
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}
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size_t size() const {
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return words.size();
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}
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word& operator [] (size_t i){
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return words[i];
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}
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const word& operator [] (size_t i) const {
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return words[i];
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}
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Num& set_neg(bool neg){
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this->neg = neg;
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return *this;
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}
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Num& truncate(){
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while (size() > 0 && words.back() == 0) pop_back();
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return *this;
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}
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size_t bitlength() const {
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if (size() == 0) return 0;
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size_t last = size() - 1;
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size_t result = word_bitlength((*this)[last]) + last*word_bits();
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return result;
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}
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size_t count_trailing_zeros() const {
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for (size_t i = 0; i < size(); i++){
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word w = (*this)[i];
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if (w) return word_count_trailing_zeros(w) + i*word_bits();
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}
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return 0;
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}
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static int cmp_abs(const Num &a, const Num &b){
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size_t na = a.size(), nb = b.size();
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if (na != nb){
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return na < nb ? -1 : +1;
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}
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for (size_t i = na; i --> 0;){
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word wa = a[i], wb = b[i];
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if (wa != wb){
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return wa < wb ? -1 : +1;
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}
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}
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return 0;
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}
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static int cmp(const Num &a, const Num &b){
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if (a.size() == 0 && b.size() == 0) return 0;
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if (!a.neg && !b.neg) return +cmp_abs(a, b);
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if ( a.neg && b.neg) return -cmp_abs(a, b);
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return a.neg && !b.neg ? -1 : +1;
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}
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static size_t word_bitlength(word a){
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for (int i = word_bits() - 1; i >= 0; i--) if ((a >> i) & 1) return i+1;
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return 0;
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}
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static size_t word_count_trailing_zeros(word a){
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for (int i = 0; i < (int)word_bits(); i++) if ((a >> i) & 1) return i;
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return word_bits();
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}
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static word add_carry(word *a, word b){
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return (*a += b) < b;
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}
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static word sub_carry(word *a, word b){
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word tmp = *a;
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return (*a = tmp - b) > tmp;
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}
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static word word_mul_hi(word a, word b){
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size_t n = word_bits()/2;
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word a_hi = a >> n;
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word a_lo = a & word_half_mask();
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word b_hi = b >> n;
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word b_lo = b & word_half_mask();
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word tmp = ((a_lo*b_lo) >> n) + a_hi*b_lo;
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tmp = (tmp >> n) + ((a_lo*b_hi + (tmp & word_half_mask())) >> n);
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return tmp + a_hi*b_hi;
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}
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static Num& add_unsigned_overwrite(Num &a, const Num &b){
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size_t i, na = a.size(), nb = b.size(), n = std::max(na, nb);
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a.resize(n);
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word carry = 0;
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for (i = 0; i < nb; i++){
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carry = add_carry(&a[i], carry);
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carry += add_carry(&a[i], b[i]);
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}
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for (; i < n && carry; i++) carry = add_carry(&a[i], carry);
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if (carry) a.push_back(carry);
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return a.truncate();
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}
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static Num& sub_unsigned_overwrite(Num &a, const Num &b){
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//assert(cmp_abs(a, b) >= 0);
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size_t i, na = a.size(), nb = b.size();
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word carry = 0;
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for (i = 0; i < nb; i++){
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carry = sub_carry(&a[i], carry);
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carry += sub_carry(&a[i], b[i]);
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}
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for (; i < na && carry; i++) carry = sub_carry(&a[i], carry);
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//assert(!carry);
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return a.truncate();
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}
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static Num mul_long(const Num &a, const Num &b){
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size_t na = a.size(), nb = b.size(), nc = na + nb + 1;
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Num c(nc, 0, a.neg ^ b.neg), carries(nc, 0);
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for (size_t ia = 0; ia < na; ia++){
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for (size_t ib = 0; ib < nb; ib++){
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size_t i = ia + ib, j = i + 1;
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// WARNING: Might overflow if word size is chosen too small
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carries[i + 1] += add_carry(&c[i], a[ia] * b[ib]);
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carries[j + 1] += add_carry(&c[j], word_mul_hi(a[ia], b[ib]));
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}
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}
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return add_unsigned_overwrite(c, carries).truncate();
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}
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static Num mul_karatsuba(const Num &a, const Num &b){
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size_t na = a.size(), nb = b.size(), n = std::max(na, nb), m2 = n/2 + (n & 1);
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Num a_parts[2], b_parts[2];
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split(a, a_parts, 2, m2);
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split(b, b_parts, 2, m2);
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m2 *= word_bits();
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Num z0 = a_parts[0] * b_parts[0];
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Num z1 = (a_parts[0] + a_parts[1]) * (b_parts[0] + b_parts[1]);
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Num z2 = a_parts[1] * b_parts[1];
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Num result = z2;
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result <<= m2;
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result += z1 - z2 - z0;
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result <<= m2;
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result += z0;
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return result;
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}
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static Num mul(const Num &a, const Num &b){
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size_t karatsuba_threshold = 20;
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if (a.size() > karatsuba_threshold && b.size() > karatsuba_threshold){
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return mul_karatsuba(a, b);
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}
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return mul_long(a, b);
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}
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static Num add_signed(const Num &a, bool a_neg, const Num &b, bool b_neg){
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if (a_neg == b_neg) return add_unsigned(a, b).set_neg(a_neg);
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if (cmp_abs(a, b) >= 0) return sub_unsigned(a, b).set_neg(a_neg);
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return sub_unsigned(b, a).set_neg(b_neg);
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}
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Num& operator >>= (size_t n_bits){
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if (n_bits == 0) return *this;
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size_t n_words = n_bits / word_bits();
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if (n_words >= size()){
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resize(0);
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return *this;
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}
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n_bits %= word_bits();
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if (n_bits == 0){
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for (size_t i = 0; i < size() - n_words; i++){
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(*this)[i] = (*this)[i + n_words];
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}
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}else{
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word hi, lo = (*this)[n_words];
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for (size_t i = 0; i < size() - n_words - 1; i++){
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hi = (*this)[i + n_words + 1];
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(*this)[i] = (hi << (word_bits() - n_bits)) | (lo >> n_bits);
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lo = hi;
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}
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(*this)[size() - n_words - 1] = lo >> n_bits;
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}
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resize(size() - n_words);
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return truncate();
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}
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Num& operator <<= (size_t n_bits){
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if (n_bits == 0) return *this;
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size_t n_words = n_bits / word_bits();
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n_bits %= word_bits();
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size_t old_size = size();
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size_t n = old_size + n_words + (n_bits != 0);
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resize(n);
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if (n_bits == 0){
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for (size_t i = n; i --> n_words;){
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(*this)[i] = (*this)[i - n_words];
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}
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}else{
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word lo, hi = 0;
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for (size_t i = n - 1; i > n_words; i--){
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lo = (*this)[i - n_words - 1];
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(*this)[i] = (hi << n_bits) | (lo >> (word_bits() - n_bits));
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hi = lo;
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}
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(*this)[n_words] = hi << n_bits;
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}
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for (size_t i = 0; i < n_words; i++) (*this)[i] = 0;
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return truncate();
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}
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static void div_mod(const Num &numerator, Num denominator, Num "ient, Num &remainder){
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quotient = 0;
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remainder = numerator;
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if (cmp_abs(remainder, denominator) >= 0){
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int n = numerator.bitlength() - denominator.bitlength();
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denominator <<= n;
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for (; n >= 0; n--){
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if (cmp_abs(remainder, denominator) >= 0){
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sub_unsigned_overwrite(remainder, denominator);
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quotient.set_bit(n);
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}
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denominator >>= 1;
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}
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}
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quotient.set_neg(numerator.neg ^ denominator.neg);
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remainder.set_neg(numerator.neg);
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}
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static void div_mod_half_word(const Num &numerator, word denominator, Num "ient, word &remainder){
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remainder = 0;
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Num dst(numerator.size(), 0);
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for (size_t i = numerator.size(); i --> 0;){
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word dst_word = 0;
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word src_word = numerator[i];
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word parts[2];
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parts[0] = src_word >> word_bits()/2;
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parts[1] = src_word & word_half_mask();
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for (size_t j = 0; j < 2; j++){
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remainder <<= word_bits()/2;
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remainder |= parts[j];
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word div_word = remainder / denominator;
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word mod_word = remainder % denominator;
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remainder = mod_word;
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dst_word <<= word_bits()/2;
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dst_word |= div_word;
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}
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dst[i] = dst_word;
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}
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quotient = dst.truncate().set_neg(numerator.neg);
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}
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static void split(const Num &a, Num *parts, size_t n_parts, size_t n){
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size_t i = 0;
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for (size_t k = 0; k < n_parts; k++){
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Num &part = parts[k];
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part.resize(n);
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for (size_t j = 0; j < n && i < a.size(); j++) part[j] = a[i++];
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part = part.truncate();
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}
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}
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static Num div(const Num &numerator, const Num& denominator){
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Num quotient, remainder;
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div_mod(numerator, denominator, quotient, remainder);
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return quotient;
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}
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static Num mod(const Num &numerator, const Num& denominator){
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Num quotient, remainder;
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div_mod(numerator, denominator, quotient, remainder);
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return remainder;
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}
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static Num add_unsigned(const Num &a, const Num &b){
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Num result(a);
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return add_unsigned_overwrite(result, b);
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}
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static Num sub_unsigned(const Num &a, const Num &b){
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Num result(a);
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return sub_unsigned_overwrite(result, b);
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}
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static Num add(const Num &a, const Num &b){
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Num result = add_signed(a, a.neg, b, b.neg);
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return result;
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}
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static Num sub(const Num &a, const Num &b){
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Num result = add_signed(a, a.neg, b, !b.neg);
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return result;
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}
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static Num gcd(const Num &a0, const Num &b0){
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if (a0.size() == 1 && b0.size() == 1){
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return Num(1, word_gcd(a0[0], b0[0]));
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}
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Num a(a0), b(b0);
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a.neg = b.neg = false;
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if (a.size() == 0) return b0;
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if (b.size() == 0) return a0;
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size_t n = a.count_trailing_zeros();
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size_t m = b.count_trailing_zeros();
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if (n > m) {
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std::swap(n, m);
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a.words.swap(b.words);
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}
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a >>= n;
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b >>= n;
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do {
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b >>= b.count_trailing_zeros();
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if (cmp_abs(a, b) > 0) a.words.swap(b.words);
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sub_unsigned_overwrite(b, a);
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} while (b.size() > 0);
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a <<= n;
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return a;
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}
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typedef void (*random_func)(uint8_t *bytes, size_t n_bytes);
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static Num random_bits(size_t n_bits, random_func func){
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if (n_bits == 0) return 0;
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size_t partial_bits = n_bits % word_bits();
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size_t n_words = n_bits / word_bits() + (partial_bits > 0);
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size_t n_bytes = n_words*sizeof(word);
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Num result(n_words, 0);
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uint8_t *bytes = (uint8_t*)&result[0];
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func(bytes, n_bytes);
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if (partial_bits){
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size_t too_many_bits = word_bits() - partial_bits;
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result.back() >>= too_many_bits;
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}
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return result;
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}
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static Num random_inclusive(const Num &inclusive, random_func func){
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size_t n_bits = inclusive.bitlength();
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while (true){
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Num result = random_bits(n_bits, func);
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if (result <= inclusive) return result;
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}
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}
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static Num random_exclusive(const Num &exclusive, random_func func){
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size_t n_bits = exclusive.bitlength();
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while (true){
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Num result = random_bits(n_bits, func);
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if (result < exclusive) return result;
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}
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}
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static Num random_second_exclusive(const Num &inclusive_min_val, const Num &exclusive_max_val, random_func func){
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return inclusive_min_val + random_exclusive(exclusive_max_val - inclusive_min_val, func);
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}
|
|
|
|
static Num random_both_inclusive(const Num &inclusive_min_val, const Num &inclusive_max_val, random_func func){
|
|
return inclusive_min_val + random_inclusive(inclusive_max_val - inclusive_min_val, func);
|
|
}
|
|
|
|
Num& set_bit(size_t i){
|
|
size_t i_word = i / word_bits();
|
|
size_t i_bit = i % word_bits();
|
|
if (size() <= i_word) resize(i_word + 1);
|
|
(*this)[i_word] |= ((word)1) << i_bit;
|
|
return *this;
|
|
}
|
|
|
|
word get_bit(size_t i) const {
|
|
size_t i_word = i / word_bits();
|
|
size_t i_bit = i % word_bits();
|
|
if (i_word >= size()) return 0;
|
|
return ((*this)[i_word] >> i_bit) & 1;
|
|
}
|
|
|
|
void clr_bit(size_t i){
|
|
size_t i_word = i / word_bits();
|
|
size_t i_bit = i % word_bits();
|
|
if (i_word >= size()) return;
|
|
word mask = 1;
|
|
mask <<= i_bit;
|
|
(*this)[i_word] &= ~mask;
|
|
}
|
|
|
|
Num& mul_word(word b){
|
|
word carry = 0;
|
|
for (size_t i = 0; i < size(); i++){
|
|
word a = (*this)[i];
|
|
word tmp = a * b;
|
|
carry = add_carry(&tmp, carry);
|
|
carry += word_mul_hi(a, b);
|
|
(*this)[i] = tmp;
|
|
}
|
|
if (carry) push_back(carry);
|
|
return truncate();
|
|
}
|
|
|
|
Num& add_word(word carry, size_t i0 = 0){
|
|
if (i0 >= size()) resize(i0 + 1);
|
|
for (size_t i = i0; i < size() && carry; i++){
|
|
carry = add_carry(&(*this)[i], carry);
|
|
}
|
|
if (carry) push_back(carry);
|
|
return truncate();
|
|
}
|
|
|
|
void print(
|
|
std::vector<char> &text,
|
|
word base = 10,
|
|
const char *alphabet = "0123456789abcdefghijklmnopqrstuvwxyz"
|
|
) const {
|
|
if (size() == 0){
|
|
text.push_back('0');
|
|
}else{
|
|
Num tmp(*this);
|
|
while (tmp.size() > 0){
|
|
word remainder;
|
|
div_mod_half_word(tmp, base, tmp, remainder);
|
|
text.push_back(alphabet[remainder]);
|
|
}
|
|
if (neg) text.push_back('-');
|
|
std::reverse(text.begin(), text.end());
|
|
}
|
|
text.push_back('\0');
|
|
}
|
|
|
|
friend std::ostream& operator << (std::ostream& out, const Num &num){
|
|
std::vector<char> tmp;
|
|
num.print(tmp);
|
|
out << &tmp[0];
|
|
return out;
|
|
}
|
|
|
|
double to_double() const {
|
|
if (size() == 0) return 0.0;
|
|
double d = 0.0, base = ::pow(2.0, word_bits());
|
|
for (size_t i = size(); i --> 0;) d = d * base + (*this)[i];
|
|
return neg ? -d : d;
|
|
}
|
|
|
|
bool can_convert_to_int(int *result){
|
|
if (*this < Num(INT_MIN) || *this > Num(INT_MAX)) return false;
|
|
|
|
unsigned temp = 0;
|
|
|
|
if (word_bits() >= sizeof(temp)*CHAR_BIT){
|
|
if (words.size() > 0){
|
|
temp = (*this)[0];
|
|
}
|
|
}else{
|
|
for (size_t i = words.size(); i --> 0;){
|
|
temp <<= word_bits();
|
|
temp += (*this)[i];
|
|
}
|
|
}
|
|
|
|
*result = neg ? -temp : temp;
|
|
|
|
return true;
|
|
}
|
|
|
|
Num pow(size_t exponent) const {
|
|
Num result(1), p(*this);
|
|
for (; exponent; exponent >>= 1){
|
|
if (exponent & 1){
|
|
result = result * p;
|
|
exponent--;
|
|
}
|
|
p = p*p;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
Num mod_pow(Num exponent, const Num &modulus) const {
|
|
Num result(1), base = (*this) % modulus;
|
|
for (; exponent.size() > 0; exponent >>= 1){
|
|
if (exponent.get_bit(0)){
|
|
result = (result * base) % modulus;
|
|
}
|
|
base = (base * base) % modulus;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
Num sqrt() const {
|
|
Num n = *this;
|
|
int bit = bitlength();
|
|
if (bit & 1) bit ^= 1;
|
|
Num result = 0;
|
|
for (; bit >= 0; bit -= 2){
|
|
Num tmp = result;
|
|
tmp.set_bit(bit);
|
|
if (n >= tmp){
|
|
n -= tmp;
|
|
result.set_bit(bit + 1);
|
|
}
|
|
result >>= 1;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
Num& operator ++(){
|
|
add_word(1);
|
|
return *this;
|
|
}
|
|
|
|
Num& operator += (const Num &b){ return *this = add(*this, b); }
|
|
Num& operator -= (const Num &b){ return *this = sub(*this, b); }
|
|
Num& operator *= (const Num &b){ return *this = mul(*this, b); }
|
|
Num& operator /= (const Num &b){ return *this = div(*this, b); }
|
|
Num& operator %= (const Num &b){ return *this = mod(*this, b); }
|
|
|
|
bool operator == (const Num &b) const { return cmp(*this, b) == 0; }
|
|
bool operator != (const Num &b) const { return cmp(*this, b) != 0; }
|
|
bool operator <= (const Num &b) const { return cmp(*this, b) <= 0; }
|
|
bool operator >= (const Num &b) const { return cmp(*this, b) >= 0; }
|
|
bool operator < (const Num &b) const { return cmp(*this, b) < 0; }
|
|
bool operator > (const Num &b) const { return cmp(*this, b) > 0; }
|
|
|
|
Num operator + (const Num &b) const { return add(*this, b); }
|
|
Num operator - (const Num &b) const { return sub(*this, b); }
|
|
Num operator * (const Num &b) const { return mul(*this, b); }
|
|
Num operator / (const Num &b) const { return div(*this, b); }
|
|
Num operator % (const Num &b) const { return mod(*this, b); }
|
|
Num operator - ( ) const { return Num(*this).set_neg(!neg); }
|
|
|
|
Num operator >> (size_t n_bits) const { return Num(*this) >>= n_bits; }
|
|
Num operator << (size_t n_bits) const { return Num(*this) <<= n_bits; }
|
|
};
|