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517 lines
13 KiB
517 lines
13 KiB
// SPDX-License-Identifier: GPL-2.0-or-later |
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/* mpihelp-div.c - MPI helper functions |
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* Copyright (C) 1994, 1996 Free Software Foundation, Inc. |
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* Copyright (C) 1998, 1999 Free Software Foundation, Inc. |
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* |
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* This file is part of GnuPG. |
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* |
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* Note: This code is heavily based on the GNU MP Library. |
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* Actually it's the same code with only minor changes in the |
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* way the data is stored; this is to support the abstraction |
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* of an optional secure memory allocation which may be used |
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* to avoid revealing of sensitive data due to paging etc. |
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* The GNU MP Library itself is published under the LGPL; |
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* however I decided to publish this code under the plain GPL. |
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*/ |
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#include "mpi-internal.h" |
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#include "longlong.h" |
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#ifndef UMUL_TIME |
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#define UMUL_TIME 1 |
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#endif |
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#ifndef UDIV_TIME |
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#define UDIV_TIME UMUL_TIME |
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#endif |
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mpi_limb_t |
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mpihelp_mod_1(mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, |
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mpi_limb_t divisor_limb) |
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{ |
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mpi_size_t i; |
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mpi_limb_t n1, n0, r; |
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mpi_limb_t dummy __maybe_unused; |
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|
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/* Botch: Should this be handled at all? Rely on callers? */ |
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if (!dividend_size) |
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return 0; |
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|
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/* If multiplication is much faster than division, and the |
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* dividend is large, pre-invert the divisor, and use |
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* only multiplications in the inner loop. |
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* |
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* This test should be read: |
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* Does it ever help to use udiv_qrnnd_preinv? |
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* && Does what we save compensate for the inversion overhead? |
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*/ |
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if (UDIV_TIME > (2 * UMUL_TIME + 6) |
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&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) { |
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int normalization_steps; |
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normalization_steps = count_leading_zeros(divisor_limb); |
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if (normalization_steps) { |
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mpi_limb_t divisor_limb_inverted; |
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divisor_limb <<= normalization_steps; |
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|
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/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The |
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* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the |
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* most significant bit (with weight 2**N) implicit. |
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* |
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* Special case for DIVISOR_LIMB == 100...000. |
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*/ |
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if (!(divisor_limb << 1)) |
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divisor_limb_inverted = ~(mpi_limb_t)0; |
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else |
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udiv_qrnnd(divisor_limb_inverted, dummy, |
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-divisor_limb, 0, divisor_limb); |
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n1 = dividend_ptr[dividend_size - 1]; |
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r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); |
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|
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/* Possible optimization: |
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* if (r == 0 |
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* && divisor_limb > ((n1 << normalization_steps) |
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* | (dividend_ptr[dividend_size - 2] >> ...))) |
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* ...one division less... |
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*/ |
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for (i = dividend_size - 2; i >= 0; i--) { |
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n0 = dividend_ptr[i]; |
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UDIV_QRNND_PREINV(dummy, r, r, |
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((n1 << normalization_steps) |
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| (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), |
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divisor_limb, divisor_limb_inverted); |
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n1 = n0; |
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} |
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UDIV_QRNND_PREINV(dummy, r, r, |
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n1 << normalization_steps, |
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divisor_limb, divisor_limb_inverted); |
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return r >> normalization_steps; |
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} else { |
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mpi_limb_t divisor_limb_inverted; |
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|
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/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The |
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* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the |
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* most significant bit (with weight 2**N) implicit. |
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* |
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* Special case for DIVISOR_LIMB == 100...000. |
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*/ |
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if (!(divisor_limb << 1)) |
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divisor_limb_inverted = ~(mpi_limb_t)0; |
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else |
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udiv_qrnnd(divisor_limb_inverted, dummy, |
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-divisor_limb, 0, divisor_limb); |
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i = dividend_size - 1; |
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r = dividend_ptr[i]; |
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if (r >= divisor_limb) |
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r = 0; |
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else |
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i--; |
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for ( ; i >= 0; i--) { |
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n0 = dividend_ptr[i]; |
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UDIV_QRNND_PREINV(dummy, r, r, |
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n0, divisor_limb, divisor_limb_inverted); |
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} |
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return r; |
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} |
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} else { |
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if (UDIV_NEEDS_NORMALIZATION) { |
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int normalization_steps; |
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normalization_steps = count_leading_zeros(divisor_limb); |
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if (normalization_steps) { |
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divisor_limb <<= normalization_steps; |
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|
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n1 = dividend_ptr[dividend_size - 1]; |
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r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); |
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|
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/* Possible optimization: |
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* if (r == 0 |
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* && divisor_limb > ((n1 << normalization_steps) |
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* | (dividend_ptr[dividend_size - 2] >> ...))) |
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* ...one division less... |
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*/ |
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for (i = dividend_size - 2; i >= 0; i--) { |
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n0 = dividend_ptr[i]; |
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udiv_qrnnd(dummy, r, r, |
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((n1 << normalization_steps) |
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| (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), |
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divisor_limb); |
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n1 = n0; |
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} |
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udiv_qrnnd(dummy, r, r, |
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n1 << normalization_steps, |
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divisor_limb); |
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return r >> normalization_steps; |
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} |
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} |
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/* No normalization needed, either because udiv_qrnnd doesn't require |
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* it, or because DIVISOR_LIMB is already normalized. |
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*/ |
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i = dividend_size - 1; |
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r = dividend_ptr[i]; |
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if (r >= divisor_limb) |
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r = 0; |
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else |
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i--; |
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for (; i >= 0; i--) { |
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n0 = dividend_ptr[i]; |
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udiv_qrnnd(dummy, r, r, n0, divisor_limb); |
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} |
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return r; |
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} |
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} |
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/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write |
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* the NSIZE-DSIZE least significant quotient limbs at QP |
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* and the DSIZE long remainder at NP. If QEXTRA_LIMBS is |
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* non-zero, generate that many fraction bits and append them after the |
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* other quotient limbs. |
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* Return the most significant limb of the quotient, this is always 0 or 1. |
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* |
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* Preconditions: |
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* 0. NSIZE >= DSIZE. |
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* 1. The most significant bit of the divisor must be set. |
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* 2. QP must either not overlap with the input operands at all, or |
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* QP + DSIZE >= NP must hold true. (This means that it's |
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* possible to put the quotient in the high part of NUM, right after the |
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* remainder in NUM. |
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* 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. |
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*/ |
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mpi_limb_t |
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mpihelp_divrem(mpi_ptr_t qp, mpi_size_t qextra_limbs, |
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mpi_ptr_t np, mpi_size_t nsize, mpi_ptr_t dp, mpi_size_t dsize) |
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{ |
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mpi_limb_t most_significant_q_limb = 0; |
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switch (dsize) { |
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case 0: |
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/* We are asked to divide by zero, so go ahead and do it! (To make |
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the compiler not remove this statement, return the value.) */ |
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/* |
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* existing clients of this function have been modified |
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* not to call it with dsize == 0, so this should not happen |
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*/ |
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return 1 / dsize; |
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case 1: |
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{ |
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mpi_size_t i; |
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mpi_limb_t n1; |
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mpi_limb_t d; |
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d = dp[0]; |
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n1 = np[nsize - 1]; |
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if (n1 >= d) { |
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n1 -= d; |
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most_significant_q_limb = 1; |
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} |
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qp += qextra_limbs; |
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for (i = nsize - 2; i >= 0; i--) |
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udiv_qrnnd(qp[i], n1, n1, np[i], d); |
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qp -= qextra_limbs; |
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for (i = qextra_limbs - 1; i >= 0; i--) |
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udiv_qrnnd(qp[i], n1, n1, 0, d); |
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np[0] = n1; |
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} |
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break; |
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case 2: |
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{ |
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mpi_size_t i; |
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mpi_limb_t n1, n0, n2; |
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mpi_limb_t d1, d0; |
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np += nsize - 2; |
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d1 = dp[1]; |
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d0 = dp[0]; |
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n1 = np[1]; |
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n0 = np[0]; |
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if (n1 >= d1 && (n1 > d1 || n0 >= d0)) { |
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sub_ddmmss(n1, n0, n1, n0, d1, d0); |
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most_significant_q_limb = 1; |
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} |
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for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) { |
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mpi_limb_t q; |
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mpi_limb_t r; |
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if (i >= qextra_limbs) |
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np--; |
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else |
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np[0] = 0; |
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if (n1 == d1) { |
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/* Q should be either 111..111 or 111..110. Need special |
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* treatment of this rare case as normal division would |
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* give overflow. */ |
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q = ~(mpi_limb_t) 0; |
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r = n0 + d1; |
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if (r < d1) { /* Carry in the addition? */ |
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add_ssaaaa(n1, n0, r - d0, |
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np[0], 0, d0); |
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qp[i] = q; |
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continue; |
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} |
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n1 = d0 - (d0 != 0 ? 1 : 0); |
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n0 = -d0; |
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} else { |
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udiv_qrnnd(q, r, n1, n0, d1); |
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umul_ppmm(n1, n0, d0, q); |
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} |
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n2 = np[0]; |
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q_test: |
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if (n1 > r || (n1 == r && n0 > n2)) { |
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/* The estimated Q was too large. */ |
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q--; |
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sub_ddmmss(n1, n0, n1, n0, 0, d0); |
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r += d1; |
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if (r >= d1) /* If not carry, test Q again. */ |
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goto q_test; |
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} |
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qp[i] = q; |
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sub_ddmmss(n1, n0, r, n2, n1, n0); |
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} |
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np[1] = n1; |
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np[0] = n0; |
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} |
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break; |
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default: |
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{ |
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mpi_size_t i; |
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mpi_limb_t dX, d1, n0; |
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np += nsize - dsize; |
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dX = dp[dsize - 1]; |
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d1 = dp[dsize - 2]; |
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n0 = np[dsize - 1]; |
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if (n0 >= dX) { |
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if (n0 > dX |
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|| mpihelp_cmp(np, dp, dsize - 1) >= 0) { |
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mpihelp_sub_n(np, np, dp, dsize); |
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n0 = np[dsize - 1]; |
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most_significant_q_limb = 1; |
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} |
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} |
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for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) { |
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mpi_limb_t q; |
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mpi_limb_t n1, n2; |
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mpi_limb_t cy_limb; |
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if (i >= qextra_limbs) { |
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np--; |
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n2 = np[dsize]; |
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} else { |
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n2 = np[dsize - 1]; |
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MPN_COPY_DECR(np + 1, np, dsize - 1); |
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np[0] = 0; |
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} |
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if (n0 == dX) { |
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/* This might over-estimate q, but it's probably not worth |
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* the extra code here to find out. */ |
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q = ~(mpi_limb_t) 0; |
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} else { |
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mpi_limb_t r; |
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udiv_qrnnd(q, r, n0, np[dsize - 1], dX); |
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umul_ppmm(n1, n0, d1, q); |
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while (n1 > r |
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|| (n1 == r |
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&& n0 > np[dsize - 2])) { |
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q--; |
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r += dX; |
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if (r < dX) /* I.e. "carry in previous addition?" */ |
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break; |
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n1 -= n0 < d1; |
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n0 -= d1; |
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} |
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} |
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/* Possible optimization: We already have (q * n0) and (1 * n1) |
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* after the calculation of q. Taking advantage of that, we |
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* could make this loop make two iterations less. */ |
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cy_limb = mpihelp_submul_1(np, dp, dsize, q); |
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if (n2 != cy_limb) { |
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mpihelp_add_n(np, np, dp, dsize); |
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q--; |
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} |
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qp[i] = q; |
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n0 = np[dsize - 1]; |
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} |
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} |
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} |
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return most_significant_q_limb; |
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} |
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/**************** |
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* Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB. |
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* Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR. |
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* Return the single-limb remainder. |
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* There are no constraints on the value of the divisor. |
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* |
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* QUOT_PTR and DIVIDEND_PTR might point to the same limb. |
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*/ |
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mpi_limb_t |
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mpihelp_divmod_1(mpi_ptr_t quot_ptr, |
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mpi_ptr_t dividend_ptr, mpi_size_t dividend_size, |
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mpi_limb_t divisor_limb) |
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{ |
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mpi_size_t i; |
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mpi_limb_t n1, n0, r; |
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mpi_limb_t dummy __maybe_unused; |
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|
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if (!dividend_size) |
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return 0; |
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|
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/* If multiplication is much faster than division, and the |
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* dividend is large, pre-invert the divisor, and use |
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* only multiplications in the inner loop. |
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* |
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* This test should be read: |
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* Does it ever help to use udiv_qrnnd_preinv? |
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* && Does what we save compensate for the inversion overhead? |
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*/ |
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if (UDIV_TIME > (2 * UMUL_TIME + 6) |
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&& (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) { |
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int normalization_steps; |
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normalization_steps = count_leading_zeros(divisor_limb); |
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if (normalization_steps) { |
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mpi_limb_t divisor_limb_inverted; |
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divisor_limb <<= normalization_steps; |
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|
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/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The |
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* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the |
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* most significant bit (with weight 2**N) implicit. |
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*/ |
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/* Special case for DIVISOR_LIMB == 100...000. */ |
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if (!(divisor_limb << 1)) |
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divisor_limb_inverted = ~(mpi_limb_t)0; |
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else |
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udiv_qrnnd(divisor_limb_inverted, dummy, |
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-divisor_limb, 0, divisor_limb); |
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n1 = dividend_ptr[dividend_size - 1]; |
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r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); |
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|
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/* Possible optimization: |
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* if (r == 0 |
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* && divisor_limb > ((n1 << normalization_steps) |
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* | (dividend_ptr[dividend_size - 2] >> ...))) |
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* ...one division less... |
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*/ |
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for (i = dividend_size - 2; i >= 0; i--) { |
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n0 = dividend_ptr[i]; |
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UDIV_QRNND_PREINV(quot_ptr[i + 1], r, r, |
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((n1 << normalization_steps) |
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| (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), |
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divisor_limb, divisor_limb_inverted); |
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n1 = n0; |
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} |
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UDIV_QRNND_PREINV(quot_ptr[0], r, r, |
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n1 << normalization_steps, |
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divisor_limb, divisor_limb_inverted); |
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return r >> normalization_steps; |
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} else { |
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mpi_limb_t divisor_limb_inverted; |
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|
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/* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The |
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* result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the |
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* most significant bit (with weight 2**N) implicit. |
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*/ |
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/* Special case for DIVISOR_LIMB == 100...000. */ |
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if (!(divisor_limb << 1)) |
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divisor_limb_inverted = ~(mpi_limb_t) 0; |
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else |
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udiv_qrnnd(divisor_limb_inverted, dummy, |
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-divisor_limb, 0, divisor_limb); |
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i = dividend_size - 1; |
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r = dividend_ptr[i]; |
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if (r >= divisor_limb) |
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r = 0; |
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else |
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quot_ptr[i--] = 0; |
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for ( ; i >= 0; i--) { |
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n0 = dividend_ptr[i]; |
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UDIV_QRNND_PREINV(quot_ptr[i], r, r, |
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n0, divisor_limb, divisor_limb_inverted); |
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} |
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return r; |
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} |
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} else { |
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if (UDIV_NEEDS_NORMALIZATION) { |
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int normalization_steps; |
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|
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normalization_steps = count_leading_zeros(divisor_limb); |
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if (normalization_steps) { |
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divisor_limb <<= normalization_steps; |
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|
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n1 = dividend_ptr[dividend_size - 1]; |
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r = n1 >> (BITS_PER_MPI_LIMB - normalization_steps); |
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|
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/* Possible optimization: |
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* if (r == 0 |
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* && divisor_limb > ((n1 << normalization_steps) |
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* | (dividend_ptr[dividend_size - 2] >> ...))) |
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* ...one division less... |
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*/ |
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for (i = dividend_size - 2; i >= 0; i--) { |
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n0 = dividend_ptr[i]; |
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udiv_qrnnd(quot_ptr[i + 1], r, r, |
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((n1 << normalization_steps) |
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| (n0 >> (BITS_PER_MPI_LIMB - normalization_steps))), |
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divisor_limb); |
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n1 = n0; |
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} |
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udiv_qrnnd(quot_ptr[0], r, r, |
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n1 << normalization_steps, |
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divisor_limb); |
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return r >> normalization_steps; |
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} |
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} |
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/* No normalization needed, either because udiv_qrnnd doesn't require |
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* it, or because DIVISOR_LIMB is already normalized. |
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*/ |
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i = dividend_size - 1; |
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r = dividend_ptr[i]; |
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|
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if (r >= divisor_limb) |
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r = 0; |
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else |
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quot_ptr[i--] = 0; |
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for (; i >= 0; i--) { |
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n0 = dividend_ptr[i]; |
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udiv_qrnnd(quot_ptr[i], r, r, n0, divisor_limb); |
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} |
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return r; |
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} |
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}
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