385 lines
13 KiB
Plaintext
385 lines
13 KiB
Plaintext
/* boost random/detail/polynomial.hpp header file
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*
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* Copyright Steven Watanabe 2014
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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* See http://www.boost.org for most recent version including documentation.
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*
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* $Id$
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*/
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#ifndef BOOST_RANDOM_DETAIL_POLYNOMIAL_HPP
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#define BOOST_RANDOM_DETAIL_POLYNOMIAL_HPP
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#include <cstddef>
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#include <limits>
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#include <vector>
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#include <algorithm>
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#include <boost/assert.hpp>
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#include <boost/cstdint.hpp>
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namespace boost {
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namespace random {
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namespace detail {
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class polynomial_ops {
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public:
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typedef unsigned long digit_t;
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static void add(std::size_t size, const digit_t * lhs,
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const digit_t * rhs, digit_t * output)
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{
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for(std::size_t i = 0; i < size; ++i) {
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output[i] = lhs[i] ^ rhs[i];
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}
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}
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static void add_shifted_inplace(std::size_t size, const digit_t * lhs,
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digit_t * output, std::size_t shift)
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{
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if(shift == 0) {
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add(size, lhs, output, output);
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return;
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}
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std::size_t bits = std::numeric_limits<digit_t>::digits;
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digit_t prev = 0;
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for(std::size_t i = 0; i < size; ++i) {
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digit_t tmp = lhs[i];
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output[i] ^= (tmp << shift) | (prev >> (bits-shift));
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prev = tmp;
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}
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output[size] ^= (prev >> (bits-shift));
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}
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static void multiply_simple(std::size_t size, const digit_t * lhs,
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const digit_t * rhs, digit_t * output)
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{
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std::size_t bits = std::numeric_limits<digit_t>::digits;
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for(std::size_t i = 0; i < 2*size; ++i) {
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output[i] = 0;
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}
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for(std::size_t i = 0; i < size; ++i) {
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for(std::size_t j = 0; j < bits; ++j) {
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if((lhs[i] & (digit_t(1) << j)) != 0) {
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add_shifted_inplace(size, rhs, output + i, j);
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}
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}
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}
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}
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// memory requirements: (size - cutoff) * 4 + next_smaller
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static void multiply_karatsuba(std::size_t size,
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const digit_t * lhs, const digit_t * rhs,
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digit_t * output)
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{
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if(size < 64) {
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multiply_simple(size, lhs, rhs, output);
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return;
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}
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// split in half
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std::size_t cutoff = size/2;
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multiply_karatsuba(cutoff, lhs, rhs, output);
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multiply_karatsuba(size - cutoff, lhs + cutoff, rhs + cutoff,
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output + cutoff*2);
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std::vector<digit_t> local1(size - cutoff);
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std::vector<digit_t> local2(size - cutoff);
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// combine the digits for the inner multiply
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add(cutoff, lhs, lhs + cutoff, &local1[0]);
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if(size & 1) local1[cutoff] = lhs[size - 1];
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add(cutoff, rhs + cutoff, rhs, &local2[0]);
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if(size & 1) local2[cutoff] = rhs[size - 1];
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std::vector<digit_t> local3((size - cutoff) * 2);
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multiply_karatsuba(size - cutoff, &local1[0], &local2[0], &local3[0]);
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add(cutoff * 2, output, &local3[0], &local3[0]);
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add((size - cutoff) * 2, output + cutoff*2, &local3[0], &local3[0]);
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// Finally, add the inner result
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add((size - cutoff) * 2, output + cutoff, &local3[0], output + cutoff);
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}
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static void multiply_add_karatsuba(std::size_t size,
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const digit_t * lhs, const digit_t * rhs,
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digit_t * output)
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{
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std::vector<digit_t> buf(size * 2);
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multiply_karatsuba(size, lhs, rhs, &buf[0]);
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add(size * 2, &buf[0], output, output);
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}
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static void multiply(const digit_t * lhs, std::size_t lhs_size,
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const digit_t * rhs, std::size_t rhs_size,
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digit_t * output)
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{
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std::fill_n(output, lhs_size + rhs_size, digit_t(0));
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multiply_add(lhs, lhs_size, rhs, rhs_size, output);
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}
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static void multiply_add(const digit_t * lhs, std::size_t lhs_size,
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const digit_t * rhs, std::size_t rhs_size,
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digit_t * output)
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{
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// split into pieces that can be passed to
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// karatsuba multiply.
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while(lhs_size != 0) {
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if(lhs_size < rhs_size) {
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std::swap(lhs, rhs);
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std::swap(lhs_size, rhs_size);
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}
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multiply_add_karatsuba(rhs_size, lhs, rhs, output);
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lhs += rhs_size;
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lhs_size -= rhs_size;
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output += rhs_size;
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}
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}
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static void copy_bits(const digit_t * x, std::size_t low, std::size_t high,
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digit_t * out)
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{
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const std::size_t bits = std::numeric_limits<digit_t>::digits;
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std::size_t offset = low/bits;
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x += offset;
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low -= offset*bits;
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high -= offset*bits;
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std::size_t n = (high-low)/bits;
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if(low == 0) {
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for(std::size_t i = 0; i < n; ++i) {
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out[i] = x[i];
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}
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} else {
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for(std::size_t i = 0; i < n; ++i) {
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out[i] = (x[i] >> low) | (x[i+1] << (bits-low));
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}
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}
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if((high-low)%bits) {
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digit_t low_mask = (digit_t(1) << ((high-low)%bits)) - 1;
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digit_t result = (x[n] >> low);
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if(low != 0 && (n+1)*bits < high) {
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result |= (x[n+1] << (bits-low));
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}
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out[n] = (result & low_mask);
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}
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}
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static void shift_left(digit_t * val, std::size_t size, std::size_t shift)
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{
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const std::size_t bits = std::numeric_limits<digit_t>::digits;
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BOOST_ASSERT(shift > 0);
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BOOST_ASSERT(shift < bits);
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digit_t prev = 0;
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for(std::size_t i = 0; i < size; ++i) {
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digit_t tmp = val[i];
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val[i] = (prev >> (bits - shift)) | (val[i] << shift);
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prev = tmp;
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}
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}
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static digit_t sqr(digit_t val) {
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const std::size_t bits = std::numeric_limits<digit_t>::digits;
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digit_t mask = (digit_t(1) << bits/2) - 1;
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for(std::size_t i = bits; i > 1; i /= 2) {
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val = ((val & ~mask) << i/2) | (val & mask);
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mask = mask & (mask >> i/4);
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mask = mask | (mask << i/2);
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}
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return val;
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}
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static void sqr(digit_t * val, std::size_t size)
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{
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const std::size_t bits = std::numeric_limits<digit_t>::digits;
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digit_t mask = (digit_t(1) << bits/2) - 1;
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for(std::size_t i = 0; i < size; ++i) {
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digit_t x = val[size - i - 1];
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val[(size - i - 1) * 2] = sqr(x & mask);
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val[(size - i - 1) * 2 + 1] = sqr(x >> bits/2);
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}
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}
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// optimized for the case when the modulus has few bits set.
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struct sparse_mod {
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sparse_mod(const digit_t * divisor, std::size_t divisor_bits)
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{
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const std::size_t bits = std::numeric_limits<digit_t>::digits;
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_remainder_bits = divisor_bits - 1;
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for(std::size_t i = 0; i < divisor_bits; ++i) {
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if(divisor[i/bits] & (digit_t(1) << i%bits)) {
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_bit_indices.push_back(i);
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}
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}
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BOOST_ASSERT(_bit_indices.back() == divisor_bits - 1);
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_bit_indices.pop_back();
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if(_bit_indices.empty()) {
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_block_bits = divisor_bits;
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_lower_bits = 0;
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} else {
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_block_bits = divisor_bits - _bit_indices.back() - 1;
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_lower_bits = _bit_indices.back() + 1;
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}
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_partial_quotient.resize((_block_bits + bits - 1)/bits);
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}
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void operator()(digit_t * dividend, std::size_t dividend_bits)
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{
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const std::size_t bits = std::numeric_limits<digit_t>::digits;
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while(dividend_bits > _remainder_bits) {
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std::size_t block_start = (std::max)(dividend_bits - _block_bits, _remainder_bits);
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std::size_t block_size = (dividend_bits - block_start + bits - 1) / bits;
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copy_bits(dividend, block_start, dividend_bits, &_partial_quotient[0]);
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for(std::size_t i = 0; i < _bit_indices.size(); ++i) {
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std::size_t pos = _bit_indices[i] + block_start - _remainder_bits;
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add_shifted_inplace(block_size, &_partial_quotient[0], dividend + pos/bits, pos%bits);
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}
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add_shifted_inplace(block_size, &_partial_quotient[0], dividend + block_start/bits, block_start%bits);
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dividend_bits = block_start;
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}
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}
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std::vector<digit_t> _partial_quotient;
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std::size_t _remainder_bits;
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std::size_t _block_bits;
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std::size_t _lower_bits;
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std::vector<std::size_t> _bit_indices;
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};
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// base should have the same number of bits as mod
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// base, and mod should both be able to hold a power
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// of 2 >= mod_bits. out needs to be twice as large.
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static void mod_pow_x(boost::uintmax_t exponent, const digit_t * mod, std::size_t mod_bits, digit_t * out)
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{
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const std::size_t bits = std::numeric_limits<digit_t>::digits;
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const std::size_t n = (mod_bits + bits - 1) / bits;
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const std::size_t highbit = mod_bits - 1;
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if(exponent == 0) {
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out[0] = 1;
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std::fill_n(out + 1, n - 1, digit_t(0));
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return;
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}
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boost::uintmax_t i = std::numeric_limits<boost::uintmax_t>::digits - 1;
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while(((boost::uintmax_t(1) << i) & exponent) == 0) {
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--i;
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}
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out[0] = 2;
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std::fill_n(out + 1, n - 1, digit_t(0));
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sparse_mod m(mod, mod_bits);
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while(i--) {
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sqr(out, n);
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m(out, 2 * mod_bits - 1);
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if((boost::uintmax_t(1) << i) & exponent) {
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shift_left(out, n, 1);
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if(out[highbit / bits] & (digit_t(1) << highbit%bits))
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add(n, out, mod, out);
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}
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}
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}
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};
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class polynomial
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{
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typedef polynomial_ops::digit_t digit_t;
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public:
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polynomial() : _size(0) {}
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class reference {
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public:
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reference(digit_t &value, int idx)
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: _value(value), _idx(idx) {}
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operator bool() const { return (_value & (digit_t(1) << _idx)) != 0; }
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reference& operator=(bool b)
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{
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if(b) {
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_value |= (digit_t(1) << _idx);
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} else {
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_value &= ~(digit_t(1) << _idx);
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}
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return *this;
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}
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reference &operator^=(bool b)
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{
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_value ^= (digit_t(b) << _idx);
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return *this;
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}
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reference &operator=(const reference &other)
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{
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return *this = static_cast<bool>(other);
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}
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private:
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digit_t &_value;
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int _idx;
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};
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reference operator[](std::size_t i)
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{
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static const std::size_t bits = std::numeric_limits<digit_t>::digits;
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ensure_bit(i);
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return reference(_storage[i/bits], i%bits);
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}
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bool operator[](std::size_t i) const
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{
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static const std::size_t bits = std::numeric_limits<digit_t>::digits;
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if(i < size())
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return (_storage[i/bits] & (digit_t(1) << (i%bits))) != 0;
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else
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return false;
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}
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std::size_t size() const
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{
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return _size;
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}
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void resize(std::size_t n)
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{
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static const std::size_t bits = std::numeric_limits<digit_t>::digits;
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_storage.resize((n + bits - 1)/bits);
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// clear the high order bits in case we're shrinking.
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if(n%bits) {
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_storage.back() &= ((digit_t(1) << (n%bits)) - 1);
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}
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_size = n;
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}
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friend polynomial operator*(const polynomial &lhs, const polynomial &rhs);
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friend polynomial mod_pow_x(boost::uintmax_t exponent, polynomial mod);
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private:
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std::vector<polynomial_ops::digit_t> _storage;
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std::size_t _size;
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void ensure_bit(std::size_t i)
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{
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if(i >= size()) {
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resize(i + 1);
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}
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}
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void normalize()
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{
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while(size() && (*this)[size() - 1] == 0)
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resize(size() - 1);
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}
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};
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inline polynomial operator*(const polynomial &lhs, const polynomial &rhs)
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{
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polynomial result;
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result._storage.resize(lhs._storage.size() + rhs._storage.size());
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polynomial_ops::multiply(&lhs._storage[0], lhs._storage.size(),
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&rhs._storage[0], rhs._storage.size(),
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&result._storage[0]);
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result._size = lhs._size + rhs._size;
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return result;
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}
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inline polynomial mod_pow_x(boost::uintmax_t exponent, polynomial mod)
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{
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polynomial result;
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mod.normalize();
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std::size_t mod_size = mod.size();
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result._storage.resize(mod._storage.size() * 2);
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result._size = mod.size() * 2;
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polynomial_ops::mod_pow_x(exponent, &mod._storage[0], mod_size, &result._storage[0]);
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result.resize(mod.size() - 1);
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return result;
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}
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}
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}
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}
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#endif // BOOST_RANDOM_DETAIL_POLYNOMIAL_HPP
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