/* mpi-div.c - MPI functions * Copyright (C) 1994, 1996, 1998, 2001, 2002, * 2003 Free Software Foundation, Inc. * * This file is part of Libgcrypt. * * Note: This code is heavily based on the GNU MP Library. * Actually it's the same code with only minor changes in the * way the data is stored; this is to support the abstraction * of an optional secure memory allocation which may be used * to avoid revealing of sensitive data due to paging etc. */ #include "mpi-internal.h" #include "longlong.h" void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den); void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor); void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor) { int divisor_sign = divisor->sign; MPI temp_divisor = NULL; /* We need the original value of the divisor after the remainder has been * preliminary calculated. We have to copy it to temporary space if it's * the same variable as REM. */ if (rem == divisor) { temp_divisor = mpi_copy(divisor); divisor = temp_divisor; } mpi_tdiv_r(rem, dividend, divisor); if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs) mpi_add(rem, rem, divisor); if (temp_divisor) mpi_free(temp_divisor); } void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor) { MPI tmp = mpi_alloc(mpi_get_nlimbs(quot)); mpi_fdiv_qr(quot, tmp, dividend, divisor); mpi_free(tmp); } void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor) { int divisor_sign = divisor->sign; MPI temp_divisor = NULL; if (quot == divisor || rem == divisor) { temp_divisor = mpi_copy(divisor); divisor = temp_divisor; } mpi_tdiv_qr(quot, rem, dividend, divisor); if ((divisor_sign ^ dividend->sign) && rem->nlimbs) { mpi_sub_ui(quot, quot, 1); mpi_add(rem, rem, divisor); } if (temp_divisor) mpi_free(temp_divisor); } /* If den == quot, den needs temporary storage. * If den == rem, den needs temporary storage. * If num == quot, num needs temporary storage. * If den has temporary storage, it can be normalized while being copied, * i.e no extra storage should be allocated. */ void mpi_tdiv_r(MPI rem, MPI num, MPI den) { mpi_tdiv_qr(NULL, rem, num, den); } void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den) { mpi_ptr_t np, dp; mpi_ptr_t qp, rp; mpi_size_t nsize = num->nlimbs; mpi_size_t dsize = den->nlimbs; mpi_size_t qsize, rsize; mpi_size_t sign_remainder = num->sign; mpi_size_t sign_quotient = num->sign ^ den->sign; unsigned int normalization_steps; mpi_limb_t q_limb; mpi_ptr_t marker[5]; int markidx = 0; /* Ensure space is enough for quotient and remainder. * We need space for an extra limb in the remainder, because it's * up-shifted (normalized) below. */ rsize = nsize + 1; mpi_resize(rem, rsize); qsize = rsize - dsize; /* qsize cannot be bigger than this. */ if (qsize <= 0) { if (num != rem) { rem->nlimbs = num->nlimbs; rem->sign = num->sign; MPN_COPY(rem->d, num->d, nsize); } if (quot) { /* This needs to follow the assignment to rem, in case the * numerator and quotient are the same. */ quot->nlimbs = 0; quot->sign = 0; } return; } if (quot) mpi_resize(quot, qsize); /* Read pointers here, when reallocation is finished. */ np = num->d; dp = den->d; rp = rem->d; /* Optimize division by a single-limb divisor. */ if (dsize == 1) { mpi_limb_t rlimb; if (quot) { qp = quot->d; rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]); qsize -= qp[qsize - 1] == 0; quot->nlimbs = qsize; quot->sign = sign_quotient; } else rlimb = mpihelp_mod_1(np, nsize, dp[0]); rp[0] = rlimb; rsize = rlimb != 0?1:0; rem->nlimbs = rsize; rem->sign = sign_remainder; return; } if (quot) { qp = quot->d; /* Make sure QP and NP point to different objects. Otherwise the * numerator would be gradually overwritten by the quotient limbs. */ if (qp == np) { /* Copy NP object to temporary space. */ np = marker[markidx++] = mpi_alloc_limb_space(nsize); MPN_COPY(np, qp, nsize); } } else /* Put quotient at top of remainder. */ qp = rp + dsize; normalization_steps = count_leading_zeros(dp[dsize - 1]); /* Normalize the denominator, i.e. make its most significant bit set by * shifting it NORMALIZATION_STEPS bits to the left. Also shift the * numerator the same number of steps (to keep the quotient the same!). */ if (normalization_steps) { mpi_ptr_t tp; mpi_limb_t nlimb; /* Shift up the denominator setting the most significant bit of * the most significant word. Use temporary storage not to clobber * the original contents of the denominator. */ tp = marker[markidx++] = mpi_alloc_limb_space(dsize); mpihelp_lshift(tp, dp, dsize, normalization_steps); dp = tp; /* Shift up the numerator, possibly introducing a new most * significant word. Move the shifted numerator in the remainder * meanwhile. */ nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps); if (nlimb) { rp[nsize] = nlimb; rsize = nsize + 1; } else rsize = nsize; } else { /* The denominator is already normalized, as required. Copy it to * temporary space if it overlaps with the quotient or remainder. */ if (dp == rp || (quot && (dp == qp))) { mpi_ptr_t tp; tp = marker[markidx++] = mpi_alloc_limb_space(dsize); MPN_COPY(tp, dp, dsize); dp = tp; } /* Move the numerator to the remainder. */ if (rp != np) MPN_COPY(rp, np, nsize); rsize = nsize; } q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize); if (quot) { qsize = rsize - dsize; if (q_limb) { qp[qsize] = q_limb; qsize += 1; } quot->nlimbs = qsize; quot->sign = sign_quotient; } rsize = dsize; MPN_NORMALIZE(rp, rsize); if (normalization_steps && rsize) { mpihelp_rshift(rp, rp, rsize, normalization_steps); rsize -= rp[rsize - 1] == 0?1:0; } rem->nlimbs = rsize; rem->sign = sign_remainder; while (markidx) { markidx--; mpi_free_limb_space(marker[markidx]); } }