1 /* boost random/detail/polynomial.hpp header file
3 * Copyright Steven Watanabe 2014
4 * Distributed under the Boost Software License, Version 1.0. (See
5 * accompanying file LICENSE_1_0.txt or copy at
6 * http://www.boost.org/LICENSE_1_0.txt)
8 * See http://www.boost.org for most recent version including documentation.
13 #ifndef BOOST_RANDOM_DETAIL_POLYNOMIAL_HPP
14 #define BOOST_RANDOM_DETAIL_POLYNOMIAL_HPP
20 #include <boost/assert.hpp>
21 #include <boost/cstdint.hpp>
27 class polynomial_ops {
29 typedef unsigned long digit_t;
31 static void add(std::size_t size, const digit_t * lhs,
32 const digit_t * rhs, digit_t * output)
34 for(std::size_t i = 0; i < size; ++i) {
35 output[i] = lhs[i] ^ rhs[i];
39 static void add_shifted_inplace(std::size_t size, const digit_t * lhs,
40 digit_t * output, std::size_t shift)
43 add(size, lhs, output, output);
46 std::size_t bits = std::numeric_limits<digit_t>::digits;
48 for(std::size_t i = 0; i < size; ++i) {
50 output[i] ^= (tmp << shift) | (prev >> (bits-shift));
53 output[size] ^= (prev >> (bits-shift));
56 static void multiply_simple(std::size_t size, const digit_t * lhs,
57 const digit_t * rhs, digit_t * output)
59 std::size_t bits = std::numeric_limits<digit_t>::digits;
60 for(std::size_t i = 0; i < 2*size; ++i) {
63 for(std::size_t i = 0; i < size; ++i) {
64 for(std::size_t j = 0; j < bits; ++j) {
65 if((lhs[i] & (digit_t(1) << j)) != 0) {
66 add_shifted_inplace(size, rhs, output + i, j);
72 // memory requirements: (size - cutoff) * 4 + next_smaller
73 static void multiply_karatsuba(std::size_t size,
74 const digit_t * lhs, const digit_t * rhs,
78 multiply_simple(size, lhs, rhs, output);
82 std::size_t cutoff = size/2;
83 multiply_karatsuba(cutoff, lhs, rhs, output);
84 multiply_karatsuba(size - cutoff, lhs + cutoff, rhs + cutoff,
86 std::vector<digit_t> local1(size - cutoff);
87 std::vector<digit_t> local2(size - cutoff);
88 // combine the digits for the inner multiply
89 add(cutoff, lhs, lhs + cutoff, &local1[0]);
90 if(size & 1) local1[cutoff] = lhs[size - 1];
91 add(cutoff, rhs + cutoff, rhs, &local2[0]);
92 if(size & 1) local2[cutoff] = rhs[size - 1];
93 std::vector<digit_t> local3((size - cutoff) * 2);
94 multiply_karatsuba(size - cutoff, &local1[0], &local2[0], &local3[0]);
95 add(cutoff * 2, output, &local3[0], &local3[0]);
96 add((size - cutoff) * 2, output + cutoff*2, &local3[0], &local3[0]);
97 // Finally, add the inner result
98 add((size - cutoff) * 2, output + cutoff, &local3[0], output + cutoff);
101 static void multiply_add_karatsuba(std::size_t size,
102 const digit_t * lhs, const digit_t * rhs,
105 std::vector<digit_t> buf(size * 2);
106 multiply_karatsuba(size, lhs, rhs, &buf[0]);
107 add(size * 2, &buf[0], output, output);
110 static void multiply(const digit_t * lhs, std::size_t lhs_size,
111 const digit_t * rhs, std::size_t rhs_size,
114 std::fill_n(output, lhs_size + rhs_size, digit_t(0));
115 multiply_add(lhs, lhs_size, rhs, rhs_size, output);
118 static void multiply_add(const digit_t * lhs, std::size_t lhs_size,
119 const digit_t * rhs, std::size_t rhs_size,
122 // split into pieces that can be passed to
123 // karatsuba multiply.
124 while(lhs_size != 0) {
125 if(lhs_size < rhs_size) {
127 std::swap(lhs_size, rhs_size);
130 multiply_add_karatsuba(rhs_size, lhs, rhs, output);
133 lhs_size -= rhs_size;
138 static void copy_bits(const digit_t * x, std::size_t low, std::size_t high,
141 const std::size_t bits = std::numeric_limits<digit_t>::digits;
142 std::size_t offset = low/bits;
146 std::size_t n = (high-low)/bits;
148 for(std::size_t i = 0; i < n; ++i) {
152 for(std::size_t i = 0; i < n; ++i) {
153 out[i] = (x[i] >> low) | (x[i+1] << (bits-low));
156 if((high-low)%bits) {
157 digit_t low_mask = (digit_t(1) << ((high-low)%bits)) - 1;
158 digit_t result = (x[n] >> low);
159 if(low != 0 && (n+1)*bits < high) {
160 result |= (x[n+1] << (bits-low));
162 out[n] = (result & low_mask);
166 static void shift_left(digit_t * val, std::size_t size, std::size_t shift)
168 const std::size_t bits = std::numeric_limits<digit_t>::digits;
169 BOOST_ASSERT(shift > 0);
170 BOOST_ASSERT(shift < bits);
172 for(std::size_t i = 0; i < size; ++i) {
173 digit_t tmp = val[i];
174 val[i] = (prev >> (bits - shift)) | (val[i] << shift);
179 static digit_t sqr(digit_t val) {
180 const std::size_t bits = std::numeric_limits<digit_t>::digits;
181 digit_t mask = (digit_t(1) << bits/2) - 1;
182 for(std::size_t i = bits; i > 1; i /= 2) {
183 val = ((val & ~mask) << i/2) | (val & mask);
184 mask = mask & (mask >> i/4);
185 mask = mask | (mask << i/2);
190 static void sqr(digit_t * val, std::size_t size)
192 const std::size_t bits = std::numeric_limits<digit_t>::digits;
193 digit_t mask = (digit_t(1) << bits/2) - 1;
194 for(std::size_t i = 0; i < size; ++i) {
195 digit_t x = val[size - i - 1];
196 val[(size - i - 1) * 2] = sqr(x & mask);
197 val[(size - i - 1) * 2 + 1] = sqr(x >> bits/2);
201 // optimized for the case when the modulus has few bits set.
203 sparse_mod(const digit_t * divisor, std::size_t divisor_bits)
205 const std::size_t bits = std::numeric_limits<digit_t>::digits;
206 _remainder_bits = divisor_bits - 1;
207 for(std::size_t i = 0; i < divisor_bits; ++i) {
208 if(divisor[i/bits] & (digit_t(1) << i%bits)) {
209 _bit_indices.push_back(i);
212 BOOST_ASSERT(_bit_indices.back() == divisor_bits - 1);
213 _bit_indices.pop_back();
214 if(_bit_indices.empty()) {
215 _block_bits = divisor_bits;
218 _block_bits = divisor_bits - _bit_indices.back() - 1;
219 _lower_bits = _bit_indices.back() + 1;
222 _partial_quotient.resize((_block_bits + bits - 1)/bits);
224 void operator()(digit_t * dividend, std::size_t dividend_bits)
226 const std::size_t bits = std::numeric_limits<digit_t>::digits;
227 while(dividend_bits > _remainder_bits) {
228 std::size_t block_start = (std::max)(dividend_bits - _block_bits, _remainder_bits);
229 std::size_t block_size = (dividend_bits - block_start + bits - 1) / bits;
230 copy_bits(dividend, block_start, dividend_bits, &_partial_quotient[0]);
231 for(std::size_t i = 0; i < _bit_indices.size(); ++i) {
232 std::size_t pos = _bit_indices[i] + block_start - _remainder_bits;
233 add_shifted_inplace(block_size, &_partial_quotient[0], dividend + pos/bits, pos%bits);
235 add_shifted_inplace(block_size, &_partial_quotient[0], dividend + block_start/bits, block_start%bits);
236 dividend_bits = block_start;
239 std::vector<digit_t> _partial_quotient;
240 std::size_t _remainder_bits;
241 std::size_t _block_bits;
242 std::size_t _lower_bits;
243 std::vector<std::size_t> _bit_indices;
246 // base should have the same number of bits as mod
247 // base, and mod should both be able to hold a power
248 // of 2 >= mod_bits. out needs to be twice as large.
249 static void mod_pow_x(boost::uintmax_t exponent, const digit_t * mod, std::size_t mod_bits, digit_t * out)
251 const std::size_t bits = std::numeric_limits<digit_t>::digits;
252 const std::size_t n = (mod_bits + bits - 1) / bits;
253 const std::size_t highbit = mod_bits - 1;
256 std::fill_n(out + 1, n - 1, digit_t(0));
259 boost::uintmax_t i = std::numeric_limits<boost::uintmax_t>::digits - 1;
260 while(((boost::uintmax_t(1) << i) & exponent) == 0) {
264 std::fill_n(out + 1, n - 1, digit_t(0));
265 sparse_mod m(mod, mod_bits);
268 m(out, 2 * mod_bits - 1);
269 if((boost::uintmax_t(1) << i) & exponent) {
270 shift_left(out, n, 1);
271 if(out[highbit / bits] & (digit_t(1) << highbit%bits))
272 add(n, out, mod, out);
280 typedef polynomial_ops::digit_t digit_t;
282 polynomial() : _size(0) {}
285 reference(digit_t &value, int idx)
286 : _value(value), _idx(idx) {}
287 operator bool() const { return (_value & (digit_t(1) << _idx)) != 0; }
288 reference& operator=(bool b)
291 _value |= (digit_t(1) << _idx);
293 _value &= ~(digit_t(1) << _idx);
297 reference &operator^=(bool b)
299 _value ^= (digit_t(b) << _idx);
303 reference &operator=(const reference &other)
305 return *this = static_cast<bool>(other);
311 reference operator[](std::size_t i)
313 static const std::size_t bits = std::numeric_limits<digit_t>::digits;
315 return reference(_storage[i/bits], i%bits);
317 bool operator[](std::size_t i) const
319 static const std::size_t bits = std::numeric_limits<digit_t>::digits;
321 return (_storage[i/bits] & (digit_t(1) << (i%bits))) != 0;
325 std::size_t size() const
329 void resize(std::size_t n)
331 static const std::size_t bits = std::numeric_limits<digit_t>::digits;
332 _storage.resize((n + bits - 1)/bits);
333 // clear the high order bits in case we're shrinking.
335 _storage.back() &= ((digit_t(1) << (n%bits)) - 1);
339 friend polynomial operator*(const polynomial &lhs, const polynomial &rhs);
340 friend polynomial mod_pow_x(boost::uintmax_t exponent, polynomial mod);
342 std::vector<polynomial_ops::digit_t> _storage;
344 void ensure_bit(std::size_t i)
352 while(size() && (*this)[size() - 1] == 0)
357 inline polynomial operator*(const polynomial &lhs, const polynomial &rhs)
360 result._storage.resize(lhs._storage.size() + rhs._storage.size());
361 polynomial_ops::multiply(&lhs._storage[0], lhs._storage.size(),
362 &rhs._storage[0], rhs._storage.size(),
363 &result._storage[0]);
364 result._size = lhs._size + rhs._size;
368 inline polynomial mod_pow_x(boost::uintmax_t exponent, polynomial mod)
372 std::size_t mod_size = mod.size();
373 result._storage.resize(mod._storage.size() * 2);
374 result._size = mod.size() * 2;
375 polynomial_ops::mod_pow_x(exponent, &mod._storage[0], mod_size, &result._storage[0]);
376 result.resize(mod.size() - 1);
384 #endif // BOOST_RANDOM_DETAIL_POLYNOMIAL_HPP