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1// SPDX-License-Identifier: GPL-2.0-or-later2/* mpihelp-div.c - MPI helper functions3 * Copyright (C) 1994, 1996 Free Software Foundation, Inc.4 * Copyright (C) 1998, 1999 Free Software Foundation, Inc.5 *6 * This file is part of GnuPG.7 *8 * Note: This code is heavily based on the GNU MP Library.9 * Actually it's the same code with only minor changes in the10 * way the data is stored; this is to support the abstraction11 * of an optional secure memory allocation which may be used12 * to avoid revealing of sensitive data due to paging etc.13 * The GNU MP Library itself is published under the LGPL;14 * however I decided to publish this code under the plain GPL.15 */16 17#include "mpi-internal.h"18#include "longlong.h"19 20#ifndef UMUL_TIME21#define UMUL_TIME 122#endif23#ifndef UDIV_TIME24#define UDIV_TIME UMUL_TIME25#endif26 27 28mpi_limb_t29mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,30 mpi_limb_t divisor_limb)31{32 mpi_size_t i;33 mpi_limb_t n1, n0, r;34 mpi_limb_t dummy __maybe_unused;35 36 /* Botch: Should this be handled at all? Rely on callers? */37 if (!dividend_size)38 return 0;39 40 /* If multiplication is much faster than division, and the41 * dividend is large, pre-invert the divisor, and use42 * only multiplications in the inner loop.43 *44 * This test should be read:45 * Does it ever help to use udiv_qrnnd_preinv?46 * && Does what we save compensate for the inversion overhead?47 */48 if (UDIV_TIME > (2 * UMUL_TIME + 6)49 && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {50 int normalization_steps;51 52 normalization_steps = count_leading_zeros(divisor_limb);53 if (normalization_steps) {54 mpi_limb_t divisor_limb_inverted;55 56 divisor_limb <<= normalization_steps;57 58 /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The59 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the60 * most significant bit (with weight 2**N) implicit.61 *62 * Special case for DIVISOR_LIMB == 100...000.63 */64 if (!(divisor_limb << 1))65 divisor_limb_inverted = ~(mpi_limb_t)0;66 else67 udiv_qrnnd(divisor_limb_inverted, dummy,68 -divisor_limb, 0, divisor_limb);69 70 n1 = dividend_ptr[dividend_size - 1];71 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);72 73 /* Possible optimization:74 * if (r == 075 * && divisor_limb > ((n1 << normalization_steps)76 * | (dividend_ptr[dividend_size - 2] >> ...)))77 * ...one division less...78 */79 for (i = dividend_size - 2; i >= 0; i--) {80 n0 = dividend_ptr[i];81 UDIV_QRNND_PREINV(dummy, r, r,82 ((n1 << normalization_steps)83 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),84 divisor_limb, divisor_limb_inverted);85 n1 = n0;86 }87 UDIV_QRNND_PREINV(dummy, r, r,88 n1 << normalization_steps,89 divisor_limb, divisor_limb_inverted);90 return r >> normalization_steps;91 } else {92 mpi_limb_t divisor_limb_inverted;93 94 /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The95 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the96 * most significant bit (with weight 2**N) implicit.97 *98 * Special case for DIVISOR_LIMB == 100...000.99 */100 if (!(divisor_limb << 1))101 divisor_limb_inverted = ~(mpi_limb_t)0;102 else103 udiv_qrnnd(divisor_limb_inverted, dummy,104 -divisor_limb, 0, divisor_limb);105 106 i = dividend_size - 1;107 r = dividend_ptr[i];108 109 if (r >= divisor_limb)110 r = 0;111 else112 i--;113 114 for ( ; i >= 0; i--) {115 n0 = dividend_ptr[i];116 UDIV_QRNND_PREINV(dummy, r, r,117 n0, divisor_limb, divisor_limb_inverted);118 }119 return r;120 }121 } else {122 if (UDIV_NEEDS_NORMALIZATION) {123 int normalization_steps;124 125 normalization_steps = count_leading_zeros(divisor_limb);126 if (normalization_steps) {127 divisor_limb <<= normalization_steps;128 129 n1 = dividend_ptr[dividend_size - 1];130 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);131 132 /* Possible optimization:133 * if (r == 0134 * && divisor_limb > ((n1 << normalization_steps)135 * | (dividend_ptr[dividend_size - 2] >> ...)))136 * ...one division less...137 */138 for (i = dividend_size - 2; i >= 0; i--) {139 n0 = dividend_ptr[i];140 udiv_qrnnd(dummy, r, r,141 ((n1 << normalization_steps)142 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),143 divisor_limb);144 n1 = n0;145 }146 udiv_qrnnd(dummy, r, r,147 n1 << normalization_steps,148 divisor_limb);149 return r >> normalization_steps;150 }151 }152 /* No normalization needed, either because udiv_qrnnd doesn't require153 * it, or because DIVISOR_LIMB is already normalized.154 */155 i = dividend_size - 1;156 r = dividend_ptr[i];157 158 if (r >= divisor_limb)159 r = 0;160 else161 i--;162 163 for (; i >= 0; i--) {164 n0 = dividend_ptr[i];165 udiv_qrnnd(dummy, r, r, n0, divisor_limb);166 }167 return r;168 }169}170 171/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write172 * the NSIZE-DSIZE least significant quotient limbs at QP173 * and the DSIZE long remainder at NP. If QEXTRA_LIMBS is174 * non-zero, generate that many fraction bits and append them after the175 * other quotient limbs.176 * Return the most significant limb of the quotient, this is always 0 or 1.177 *178 * Preconditions:179 * 0. NSIZE >= DSIZE.180 * 1. The most significant bit of the divisor must be set.181 * 2. QP must either not overlap with the input operands at all, or182 * QP + DSIZE >= NP must hold true. (This means that it's183 * possible to put the quotient in the high part of NUM, right after the184 * remainder in NUM.185 * 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.186 */187 188mpi_limb_t189mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs,190 mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize)191{192 mpi_limb_t most_significant_q_limb = 0;193 194 switch (dsize) {195 case 0:196 /* We are asked to divide by zero, so go ahead and do it! (To make197 the compiler not remove this statement, return the value.) */198 /*199 * existing clients of this function have been modified200 * not to call it with dsize == 0, so this should not happen201 */202 return 1 / dsize;203 204 case 1:205 {206 mpi_size_t i;207 mpi_limb_t n1;208 mpi_limb_t d;209 210 d = dp[0];211 n1 = np[nsize - 1];212 213 if (n1 >= d) {214 n1 -= d;215 most_significant_q_limb = 1;216 }217 218 qp += qextra_limbs;219 for (i = nsize - 2; i >= 0; i--)220 udiv_qrnnd(qp[i], n1, n1, np[i], d);221 qp -= qextra_limbs;222 223 for (i = qextra_limbs - 1; i >= 0; i--)224 udiv_qrnnd(qp[i], n1, n1, 0, d);225 226 np[0] = n1;227 }228 break;229 230 case 2:231 {232 mpi_size_t i;233 mpi_limb_t n1, n0, n2;234 mpi_limb_t d1, d0;235 236 np += nsize - 2;237 d1 = dp[1];238 d0 = dp[0];239 n1 = np[1];240 n0 = np[0];241 242 if (n1 >= d1 && (n1 > d1 || n0 >= d0)) {243 sub_ddmmss(n1, n0, n1, n0, d1, d0);244 most_significant_q_limb = 1;245 }246 247 for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) {248 mpi_limb_t q;249 mpi_limb_t r;250 251 if (i >= qextra_limbs)252 np--;253 else254 np[0] = 0;255 256 if (n1 == d1) {257 /* Q should be either 111..111 or 111..110. Need special258 * treatment of this rare case as normal division would259 * give overflow. */260 q = ~(mpi_limb_t) 0;261 262 r = n0 + d1;263 if (r < d1) { /* Carry in the addition? */264 add_ssaaaa(n1, n0, r - d0,265 np[0], 0, d0);266 qp[i] = q;267 continue;268 }269 n1 = d0 - (d0 != 0 ? 1 : 0);270 n0 = -d0;271 } else {272 udiv_qrnnd(q, r, n1, n0, d1);273 umul_ppmm(n1, n0, d0, q);274 }275 276 n2 = np[0];277q_test:278 if (n1 > r || (n1 == r && n0 > n2)) {279 /* The estimated Q was too large. */280 q--;281 sub_ddmmss(n1, n0, n1, n0, 0, d0);282 r += d1;283 if (r >= d1) /* If not carry, test Q again. */284 goto q_test;285 }286 287 qp[i] = q;288 sub_ddmmss(n1, n0, r, n2, n1, n0);289 }290 np[1] = n1;291 np[0] = n0;292 }293 break;294 295 default:296 {297 mpi_size_t i;298 mpi_limb_t dX, d1, n0;299 300 np += nsize - dsize;301 dX = dp[dsize - 1];302 d1 = dp[dsize - 2];303 n0 = np[dsize - 1];304 305 if (n0 >= dX) {306 if (n0 > dX307 || mpihelp_cmp(np, dp, dsize - 1) >= 0) {308 mpihelp_sub_n(np, np, dp, dsize);309 n0 = np[dsize - 1];310 most_significant_q_limb = 1;311 }312 }313 314 for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) {315 mpi_limb_t q;316 mpi_limb_t n1, n2;317 mpi_limb_t cy_limb;318 319 if (i >= qextra_limbs) {320 np--;321 n2 = np[dsize];322 } else {323 n2 = np[dsize - 1];324 MPN_COPY_DECR(np + 1, np, dsize - 1);325 np[0] = 0;326 }327 328 if (n0 == dX) {329 /* This might over-estimate q, but it's probably not worth330 * the extra code here to find out. */331 q = ~(mpi_limb_t) 0;332 } else {333 mpi_limb_t r;334 335 udiv_qrnnd(q, r, n0, np[dsize - 1], dX);336 umul_ppmm(n1, n0, d1, q);337 338 while (n1 > r339 || (n1 == r340 && n0 > np[dsize - 2])) {341 q--;342 r += dX;343 if (r < dX) /* I.e. "carry in previous addition?" */344 break;345 n1 -= n0 < d1;346 n0 -= d1;347 }348 }349 350 /* Possible optimization: We already have (q * n0) and (1 * n1)351 * after the calculation of q. Taking advantage of that, we352 * could make this loop make two iterations less. */353 cy_limb = mpihelp_submul_1(np, dp, dsize, q);354 355 if (n2 != cy_limb) {356 mpihelp_add_n(np, np, dp, dsize);357 q--;358 }359 360 qp[i] = q;361 n0 = np[dsize - 1];362 }363 }364 }365 366 return most_significant_q_limb;367}368 369/****************370 * Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.371 * Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.372 * Return the single-limb remainder.373 * There are no constraints on the value of the divisor.374 *375 * QUOT_PTR and DIVIDEND_PTR might point to the same limb.376 */377 378mpi_limb_t379mpihelp_divmod_1(mpi_ptr_t quot_ptr,380 mpi_ptr_t dividend_ptr, mpi_size_t dividend_size,381 mpi_limb_t divisor_limb)382{383 mpi_size_t i;384 mpi_limb_t n1, n0, r;385 mpi_limb_t dummy __maybe_unused;386 387 if (!dividend_size)388 return 0;389 390 /* If multiplication is much faster than division, and the391 * dividend is large, pre-invert the divisor, and use392 * only multiplications in the inner loop.393 *394 * This test should be read:395 * Does it ever help to use udiv_qrnnd_preinv?396 * && Does what we save compensate for the inversion overhead?397 */398 if (UDIV_TIME > (2 * UMUL_TIME + 6)399 && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) {400 int normalization_steps;401 402 normalization_steps = count_leading_zeros(divisor_limb);403 if (normalization_steps) {404 mpi_limb_t divisor_limb_inverted;405 406 divisor_limb <<= normalization_steps;407 408 /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The409 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the410 * most significant bit (with weight 2**N) implicit.411 */412 /* Special case for DIVISOR_LIMB == 100...000. */413 if (!(divisor_limb << 1))414 divisor_limb_inverted = ~(mpi_limb_t)0;415 else416 udiv_qrnnd(divisor_limb_inverted, dummy,417 -divisor_limb, 0, divisor_limb);418 419 n1 = dividend_ptr[dividend_size - 1];420 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);421 422 /* Possible optimization:423 * if (r == 0424 * && divisor_limb > ((n1 << normalization_steps)425 * | (dividend_ptr[dividend_size - 2] >> ...)))426 * ...one division less...427 */428 for (i = dividend_size - 2; i >= 0; i--) {429 n0 = dividend_ptr[i];430 UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r,431 ((n1 << normalization_steps)432 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),433 divisor_limb, divisor_limb_inverted);434 n1 = n0;435 }436 UDIV_QRNND_PREINV(quot_ptr[0], r, r,437 n1 << normalization_steps,438 divisor_limb, divisor_limb_inverted);439 return r >> normalization_steps;440 } else {441 mpi_limb_t divisor_limb_inverted;442 443 /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The444 * result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the445 * most significant bit (with weight 2**N) implicit.446 */447 /* Special case for DIVISOR_LIMB == 100...000. */448 if (!(divisor_limb << 1))449 divisor_limb_inverted = ~(mpi_limb_t) 0;450 else451 udiv_qrnnd(divisor_limb_inverted, dummy,452 -divisor_limb, 0, divisor_limb);453 454 i = dividend_size - 1;455 r = dividend_ptr[i];456 457 if (r >= divisor_limb)458 r = 0;459 else460 quot_ptr[i--] = 0;461 462 for ( ; i >= 0; i--) {463 n0 = dividend_ptr[i];464 UDIV_QRNND_PREINV(quot_ptr[i], r, r,465 n0, divisor_limb, divisor_limb_inverted);466 }467 return r;468 }469 } else {470 if (UDIV_NEEDS_NORMALIZATION) {471 int normalization_steps;472 473 normalization_steps = count_leading_zeros(divisor_limb);474 if (normalization_steps) {475 divisor_limb <<= normalization_steps;476 477 n1 = dividend_ptr[dividend_size - 1];478 r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps);479 480 /* Possible optimization:481 * if (r == 0482 * && divisor_limb > ((n1 << normalization_steps)483 * | (dividend_ptr[dividend_size - 2] >> ...)))484 * ...one division less...485 */486 for (i = dividend_size - 2; i >= 0; i--) {487 n0 = dividend_ptr[i];488 udiv_qrnnd(quot_ptr[i + 1], r, r,489 ((n1 << normalization_steps)490 | (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))),491 divisor_limb);492 n1 = n0;493 }494 udiv_qrnnd(quot_ptr[0], r, r,495 n1 << normalization_steps,496 divisor_limb);497 return r >> normalization_steps;498 }499 }500 /* No normalization needed, either because udiv_qrnnd doesn't require501 * it, or because DIVISOR_LIMB is already normalized.502 */503 i = dividend_size - 1;504 r = dividend_ptr[i];505 506 if (r >= divisor_limb)507 r = 0;508 else509 quot_ptr[i--] = 0;510 511 for (; i >= 0; i--) {512 n0 = dividend_ptr[i];513 udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb);514 }515 return r;516 }517}518