/usr/include/flint/fft.h is in libflint-dev 2.5.2-17build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 | /* mul_fft -- radix 2 fft routines for MPIR.
Copyright 2009, 2011 William Hart. All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are
permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this list of
conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list
of conditions and the following disclaimer in the documentation and/or other materials
provided with the distribution.
THIS SOFTWARE IS PROVIDED BY William Hart ``AS IS'' AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL William Hart OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
The views and conclusions contained in the software and documentation are those of the
authors and should not be interpreted as representing official policies, either expressed
or implied, of William Hart.
*/
/******************************************************************************
Copyright (C) 2009, 2011 William Hart
******************************************************************************/
#ifndef FFT_H
#define FFT_H
#ifdef FFT_INLINES_C
#define FFT_INLINE FLINT_DLL
#else
#define FFT_INLINE static __inline__
#endif
#undef ulong
#define ulong ulongxx /* interferes with system includes */
#include <stdlib.h>
#include <stdio.h>
#undef ulong
#include <gmp.h>
#define ulong mp_limb_t
#include "flint.h"
#include "mpn_extras.h"
#ifdef __cplusplus
extern "C" {
#endif
#if defined(__MPIR_VERSION)
#if !defined(__MPIR_RELEASE ) || __MPIR_RELEASE < 20600
#define mpn_sumdiff_n __MPN(sumdiff_n)
extern
mp_limb_t mpn_sumdiff_n(mp_ptr, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
#endif
#else
FFT_INLINE
mp_limb_t mpn_sumdiff_n(mp_ptr s, mp_ptr d, mp_srcptr x, mp_srcptr y, mp_size_t n)
{
mp_limb_t ret;
mp_ptr t;
if (n == 0)
return 0;
if ((s == x && d == y) || (s == y && d == x))
{
t = flint_malloc(n * sizeof(mp_limb_t));
ret = mpn_sub_n(t, x, y, n);
ret += 2 * mpn_add_n(s, x, y, n);
flint_mpn_copyi(d, t, n);
flint_free(t);
return ret;
}
if (s == x || s == y)
{
ret = mpn_sub_n(d, x, y, n);
ret += 2 * mpn_add_n(s, x, y, n);
return ret;
}
ret = 2 * mpn_add_n(s, x, y, n);
ret += mpn_sub_n(d, x, y, n);
return ret;
}
#endif
#define fft_sumdiff(t, u, r, s, n) \
(n == 0 ? 0 : mpn_sumdiff_n(t, u, r, s, n))
#define SWAP_PTRS(xx, yy) \
do { \
mp_limb_t * __ptr = xx; \
xx = yy; \
yy = __ptr; \
} while (0)
/* used for generating random values mod p in test code */
#define random_fermat(nn, state, limbs) \
do { \
if (n_randint(state, 10) == 0) { \
flint_mpn_zero(nn, limbs); \
nn[limbs] = 1; \
} else { \
if (n_randint(state, 2) == 0) \
flint_mpn_rrandom(nn, state->gmp_state, limbs); \
else \
flint_mpn_urandomb(nn, state->gmp_state, limbs*FLINT_BITS); \
nn[limbs] = n_randint(state, 1024); \
} \
if (n_randint(state, 2)) \
nn[limbs] = -nn[limbs]; \
} while (0)
FFT_INLINE
void mpn_addmod_2expp1_1(mp_limb_t * r, mp_size_t limbs, mp_limb_signed_t c)
{
mp_limb_t sum = r[0] + c;
/* check if adding c would cause a carry to propagate */
if ((mp_limb_signed_t)(sum ^ r[0]) >= 0)
r[0] = sum;
else
{
if (c >= 0) mpn_add_1(r, r, limbs + 1, c);
else mpn_sub_1(r, r, limbs + 1, -c);
}
}
FLINT_DLL void fft_combine_limbs(mp_limb_t * res, mp_limb_t ** poly, slong length,
mp_size_t coeff_limbs, mp_size_t output_limbs, mp_size_t total_limbs);
FLINT_DLL void fft_combine_bits(mp_limb_t * res, mp_limb_t ** poly, slong length,
mp_bitcnt_t bits, mp_size_t output_limbs, mp_size_t total_limbs);
FLINT_DLL mp_size_t fft_split_limbs(mp_limb_t ** poly, mp_srcptr limbs,
mp_size_t total_limbs, mp_size_t coeff_limbs, mp_size_t output_limbs);
FLINT_DLL mp_size_t fft_split_bits(mp_limb_t ** poly, mp_srcptr limbs,
mp_size_t total_limbs, mp_bitcnt_t bits, mp_size_t output_limbs);
FLINT_DLL void fermat_to_mpz(mpz_t m, mp_limb_t * i, mp_size_t limbs);
FLINT_DLL void mpn_normmod_2expp1(mp_limb_t * t, mp_size_t limbs);
FLINT_DLL void butterfly_lshB(mp_limb_t * t, mp_limb_t * u, mp_limb_t * i1,
mp_limb_t * i2, mp_size_t limbs, mp_size_t x, mp_size_t y);
FLINT_DLL void butterfly_rshB(mp_limb_t * t, mp_limb_t * u, mp_limb_t * i1,
mp_limb_t * i2, mp_size_t limbs, mp_size_t x, mp_size_t y);
FLINT_DLL void mpn_mul_2expmod_2expp1(mp_limb_t * t,
mp_limb_t * i1, mp_size_t limbs, mp_bitcnt_t d);
FLINT_DLL void mpn_div_2expmod_2expp1(mp_limb_t * t,
mp_limb_t * i1, mp_size_t limbs, mp_bitcnt_t d);
FLINT_DLL void fft_adjust(mp_limb_t * r, mp_limb_t * i1,
mp_size_t i, mp_size_t limbs, mp_bitcnt_t w);
FLINT_DLL void fft_butterfly(mp_limb_t * s, mp_limb_t * t, mp_limb_t * i1,
mp_limb_t * i2, mp_size_t i, mp_size_t limbs, mp_bitcnt_t w);
FLINT_DLL void ifft_butterfly(mp_limb_t * s, mp_limb_t * t, mp_limb_t * i1,
mp_limb_t * i2, mp_size_t i, mp_size_t limbs, mp_bitcnt_t w);
FLINT_DLL void fft_radix2(mp_limb_t ** ii,
mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2);
FLINT_DLL void fft_truncate1(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w,
mp_limb_t ** t1, mp_limb_t ** t2, mp_size_t trunc);
FLINT_DLL void fft_truncate(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w,
mp_limb_t ** t1, mp_limb_t ** t2, mp_size_t trunc);
FLINT_DLL void ifft_radix2(mp_limb_t ** ii, mp_size_t n,
mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2);
FLINT_DLL void ifft_truncate1(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w,
mp_limb_t ** t1, mp_limb_t ** t2, mp_size_t trunc);
FLINT_DLL void ifft_truncate(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w,
mp_limb_t ** t1, mp_limb_t ** t2, mp_size_t trunc);
FLINT_DLL void fft_butterfly_sqrt2(mp_limb_t * s, mp_limb_t * t,
mp_limb_t * i1, mp_limb_t * i2, mp_size_t i,
mp_size_t limbs, mp_bitcnt_t w, mp_limb_t * temp);
FLINT_DLL void ifft_butterfly_sqrt2(mp_limb_t * s, mp_limb_t * t, mp_limb_t * i1,
mp_limb_t * i2, mp_size_t i, mp_size_t limbs, mp_bitcnt_t w, mp_limb_t * temp);
FLINT_DLL void fft_adjust_sqrt2(mp_limb_t * r, mp_limb_t * i1,
mp_size_t i, mp_size_t limbs, mp_bitcnt_t w, mp_limb_t * temp);
FLINT_DLL void fft_truncate_sqrt2(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w,
mp_limb_t ** t1, mp_limb_t ** t2, mp_limb_t ** temp, mp_size_t trunc);
FLINT_DLL void ifft_truncate_sqrt2(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w,
mp_limb_t ** t1, mp_limb_t ** t2, mp_limb_t ** temp, mp_size_t trunc);
FLINT_DLL void mul_truncate_sqrt2(mp_ptr r1, mp_srcptr i1, mp_size_t n1,
mp_srcptr i2, mp_size_t n2, mp_bitcnt_t depth, mp_bitcnt_t w);
FLINT_DLL void fft_butterfly_twiddle(mp_limb_t * u, mp_limb_t * v,
mp_limb_t * s, mp_limb_t * t, mp_size_t limbs, mp_bitcnt_t b1, mp_bitcnt_t b2);
FLINT_DLL void ifft_butterfly_twiddle(mp_limb_t * u, mp_limb_t * v,
mp_limb_t * s, mp_limb_t * t, mp_size_t limbs, mp_bitcnt_t b1, mp_bitcnt_t b2);
FLINT_DLL void fft_radix2_twiddle(mp_limb_t ** ii, mp_size_t is,
mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs);
FLINT_DLL void ifft_radix2_twiddle(mp_limb_t ** ii, mp_size_t is,
mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs);
FLINT_DLL void fft_truncate1_twiddle(mp_limb_t ** ii, mp_size_t is,
mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs, mp_size_t trunc);
FLINT_DLL void ifft_truncate1_twiddle(mp_limb_t ** ii, mp_size_t is,
mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_size_t ws, mp_size_t r, mp_size_t c, mp_size_t rs, mp_size_t trunc);
FLINT_DLL void fft_mfa_truncate_sqrt2(mp_limb_t ** ii, mp_size_t n,
mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc);
FLINT_DLL void ifft_mfa_truncate_sqrt2(mp_limb_t ** ii, mp_size_t n,
mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc);
FLINT_DLL void mul_mfa_truncate_sqrt2(mp_ptr r1, mp_srcptr i1, mp_size_t n1,
mp_srcptr i2, mp_size_t n2, mp_bitcnt_t depth, mp_bitcnt_t w);
FLINT_DLL void fft_mfa_truncate_sqrt2_outer(mp_limb_t ** ii, mp_size_t n,
mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc);
FLINT_DLL void fft_mfa_truncate_sqrt2_inner(mp_limb_t ** ii, mp_limb_t ** jj,
mp_size_t n, mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc, mp_limb_t * tt);
FLINT_DLL void ifft_mfa_truncate_sqrt2_outer(mp_limb_t ** ii, mp_size_t n,
mp_bitcnt_t w, mp_limb_t ** t1, mp_limb_t ** t2,
mp_limb_t ** temp, mp_size_t n1, mp_size_t trunc);
FLINT_DLL void fft_negacyclic(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w,
mp_limb_t ** t1, mp_limb_t ** t2, mp_limb_t ** temp);
FLINT_DLL void ifft_negacyclic(mp_limb_t ** ii, mp_size_t n, mp_bitcnt_t w,
mp_limb_t ** t1, mp_limb_t ** t2, mp_limb_t ** temp);
FLINT_DLL void fft_naive_convolution_1(mp_limb_t * r, mp_limb_t * ii,
mp_limb_t * jj, mp_size_t m);
FLINT_DLL void _fft_mulmod_2expp1(mp_limb_t * r1, mp_limb_t * i1, mp_limb_t * i2,
mp_size_t r_limbs, mp_bitcnt_t depth, mp_bitcnt_t w);
FLINT_DLL slong fft_adjust_limbs(mp_size_t limbs);
FLINT_DLL void fft_mulmod_2expp1(mp_limb_t * r, mp_limb_t * i1, mp_limb_t * i2,
mp_size_t n, mp_size_t w, mp_limb_t * tt);
FLINT_DLL void flint_mpn_mul_fft_main(mp_ptr r1, mp_srcptr i1, mp_size_t n1,
mp_srcptr i2, mp_size_t n2);
FLINT_DLL void fft_convolution(mp_limb_t ** ii, mp_limb_t ** jj, slong depth,
slong limbs, slong trunc, mp_limb_t ** t1,
mp_limb_t ** t2, mp_limb_t ** s1, mp_limb_t * tt);
#ifdef __cplusplus
}
#endif
#endif
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