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Merge pull request #193 from jpflori/powm
powmod functions from GMP
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,125 @@ | ||
| /* Compute {up,n}^(-1) mod B^n. | ||
| Contributed to the GNU project by Torbjorn Granlund. | ||
| THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY | ||
| SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST | ||
| GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GMP RELEASE. | ||
| Copyright (C) 2004-2007, 2009, 2012 Free Software Foundation, Inc. | ||
| This file is part of the GNU MP Library. | ||
| The GNU MP Library is free software; you can redistribute it and/or modify | ||
| it under the terms of either: | ||
| * the GNU Lesser General Public License as published by the Free | ||
| Software Foundation; either version 3 of the License, or (at your | ||
| option) any later version. | ||
| or | ||
| * the GNU General Public License as published by the Free Software | ||
| Foundation; either version 2 of the License, or (at your option) any | ||
| later version. | ||
| or both in parallel, as here. | ||
| The GNU MP Library is distributed in the hope that it will be useful, but | ||
| WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY | ||
| or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | ||
| for more details. | ||
| You should have received copies of the GNU General Public License and the | ||
| GNU Lesser General Public License along with the GNU MP Library. If not, | ||
| see https://www.gnu.org/licenses/. */ | ||
|
|
||
| #include "mpir.h" | ||
| #include "gmp-impl.h" | ||
|
|
||
|
|
||
| /* | ||
| r[k+1] = r[k] - r[k] * (u*r[k] - 1) | ||
| r[k+1] = r[k] + r[k] - r[k]*(u*r[k]) | ||
| */ | ||
|
|
||
| #if TUNE_PROGRAM_BUILD | ||
| #define NPOWS \ | ||
| ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t))) | ||
| #else | ||
| #define NPOWS \ | ||
| ((sizeof(mp_size_t) > 6 ? 48 : 8*sizeof(mp_size_t)) - LOG2C (BINV_NEWTON_THRESHOLD)) | ||
| #endif | ||
|
|
||
| mp_size_t | ||
| mpn_binvert_itch (mp_size_t n) | ||
| { | ||
| mp_size_t itch_local = mpn_mulmod_bnm1_next_size (n); | ||
| mp_size_t itch_out = mpn_mulmod_bnm1_itch (itch_local, n, (n + 1) >> 1); | ||
| return itch_local + itch_out; | ||
| } | ||
|
|
||
| void | ||
| mpn_binvert (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_ptr scratch) | ||
| { | ||
| mp_ptr xp; | ||
| mp_size_t rn, newrn; | ||
| mp_size_t sizes[NPOWS], *sizp; | ||
| mp_limb_t di; | ||
|
|
||
| /* Compute the computation precisions from highest to lowest, leaving the | ||
| base case size in 'rn'. */ | ||
| sizp = sizes; | ||
| for (rn = n; ABOVE_THRESHOLD (rn, BINV_NEWTON_THRESHOLD); rn = (rn + 1) >> 1) | ||
| *sizp++ = rn; | ||
|
|
||
| xp = scratch; | ||
|
|
||
| /* Compute a base value of rn limbs. */ | ||
| MPN_ZERO (xp, rn); | ||
| xp[0] = 1; | ||
| /* JPF: GMP goes the other way around and has renamed to binvert_limb */ | ||
| modlimb_invert (di, up[0]); | ||
| /* JPF: GMP vs MPIR diff; MPIR returns a two limbs overflow and use sub rather than add */ | ||
| if (BELOW_THRESHOLD (rn, DC_BDIV_Q_THRESHOLD)) | ||
| mpn_sb_bdiv_q (rp, xp+rn, xp, rn, up, rn, di); | ||
| else | ||
| mpn_dc_bdiv_q (rp, xp, rn, up, rn, di); | ||
|
|
||
| /* Use Newton iterations to get the desired precision. */ | ||
| if (rn == n) | ||
| return; | ||
| newrn = *--sizp; | ||
| for (; newrn < n;) | ||
| { | ||
| mp_size_t m; | ||
|
|
||
| /* X <- UR. */ | ||
| m = mpn_mulmod_bnm1_next_size (newrn); | ||
| mpn_mulmod_bnm1 (xp, m, up, newrn, rp, rn, xp + m); | ||
| mpn_sub_1 (xp + m, xp, rn - (m - newrn), 1); | ||
|
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||
| /* R = R(X/B^rn) */ | ||
| mpn_mullow_n (rp + rn, rp, xp + rn, newrn - rn); | ||
| mpn_neg (rp + rn, rp + rn, newrn - rn); | ||
|
|
||
| rn = newrn; | ||
| newrn = *--sizp; | ||
| } | ||
| /* Last iteration would overflow in the mullow call */ | ||
| { | ||
| mp_size_t m; | ||
|
|
||
| /* X <- UR. */ | ||
| m = mpn_mulmod_bnm1_next_size (newrn); | ||
| mpn_mulmod_bnm1 (xp, m, up, newrn, rp, rn, xp + m); | ||
| mpn_sub_1 (xp + m, xp, rn - (m - newrn), 1); | ||
|
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||
| /* R = R(X/B^rn) */ | ||
| mpn_mullow_n (xp + newrn, rp, xp + rn, newrn - rn); /* JPF: would overflow */ | ||
| /* At most we need 2*(newrn - rn) limbs at xp + newrn, so need 3*newrn - 2*rn */ | ||
| /* As 2rn > newrn, and n == newrn, this gives at max 2*n for xp */ | ||
| /* which we already ensure */ | ||
| mpn_neg (rp + rn, xp + newrn, newrn - rn); | ||
| } | ||
| } |
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