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glibc/stdlib/divrem.c
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/* mpn_divrem -- Divide natural numbers, producing both remainder and | |
quotient. | |
Copyright (C) 1993-2016 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 the GNU Lesser General Public License as published by | |
the Free Software Foundation; either version 2.1 of the License, or (at your | |
option) any later version. | |
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 Lesser General Public | |
License for more details. | |
You should have received a copy of the GNU Lesser General Public License | |
along with the GNU MP Library; see the file COPYING.LIB. If not, see | |
<http://www.gnu.org/licenses/>. */ | |
#include <gmp.h> | |
#include "gmp-impl.h" | |
#include "longlong.h" | |
/* Divide num (NP/NSIZE) by den (DP/DSIZE) and write | |
the NSIZE-DSIZE least significant quotient limbs at QP | |
and the DSIZE long remainder at NP. If QEXTRA_LIMBS is | |
non-zero, generate that many fraction bits and append them after the | |
other quotient limbs. | |
Return the most significant limb of the quotient, this is always 0 or 1. | |
Preconditions: | |
0. NSIZE >= DSIZE. | |
1. The most significant bit of the divisor must be set. | |
2. QP must either not overlap with the input operands at all, or | |
QP + DSIZE >= NP must hold true. (This means that it's | |
possible to put the quotient in the high part of NUM, right after the | |
remainder in NUM. | |
3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */ | |
mp_limb_t | |
mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs, | |
mp_ptr np, mp_size_t nsize, | |
mp_srcptr dp, mp_size_t dsize) | |
{ | |
mp_limb_t most_significant_q_limb = 0; | |
switch (dsize) | |
{ | |
case 0: | |
/* We are asked to divide by zero, so go ahead and do it! (To make | |
the compiler not remove this statement, return the value.) */ | |
return 1 / dsize; | |
case 1: | |
{ | |
mp_size_t i; | |
mp_limb_t n1; | |
mp_limb_t d; | |
d = dp[0]; | |
n1 = np[nsize - 1]; | |
if (n1 >= d) | |
{ | |
n1 -= d; | |
most_significant_q_limb = 1; | |
} | |
qp += qextra_limbs; | |
for (i = nsize - 2; i >= 0; i--) | |
udiv_qrnnd (qp[i], n1, n1, np[i], d); | |
qp -= qextra_limbs; | |
for (i = qextra_limbs - 1; i >= 0; i--) | |
udiv_qrnnd (qp[i], n1, n1, 0, d); | |
np[0] = n1; | |
} | |
break; | |
case 2: | |
{ | |
mp_size_t i; | |
mp_limb_t n1, n0, n2; | |
mp_limb_t d1, d0; | |
np += nsize - 2; | |
d1 = dp[1]; | |
d0 = dp[0]; | |
n1 = np[1]; | |
n0 = np[0]; | |
if (n1 >= d1 && (n1 > d1 || n0 >= d0)) | |
{ | |
sub_ddmmss (n1, n0, n1, n0, d1, d0); | |
most_significant_q_limb = 1; | |
} | |
for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--) | |
{ | |
mp_limb_t q; | |
mp_limb_t r; | |
if (i >= qextra_limbs) | |
np--; | |
else | |
np[0] = 0; | |
if (n1 == d1) | |
{ | |
/* Q should be either 111..111 or 111..110. Need special | |
treatment of this rare case as normal division would | |
give overflow. */ | |
q = ~(mp_limb_t) 0; | |
r = n0 + d1; | |
if (r < d1) /* Carry in the addition? */ | |
{ | |
add_ssaaaa (n1, n0, r - d0, np[0], 0, d0); | |
qp[i] = q; | |
continue; | |
} | |
n1 = d0 - (d0 != 0); | |
n0 = -d0; | |
} | |
else | |
{ | |
udiv_qrnnd (q, r, n1, n0, d1); | |
umul_ppmm (n1, n0, d0, q); | |
} | |
n2 = np[0]; | |
q_test: | |
if (n1 > r || (n1 == r && n0 > n2)) | |
{ | |
/* The estimated Q was too large. */ | |
q--; | |
sub_ddmmss (n1, n0, n1, n0, 0, d0); | |
r += d1; | |
if (r >= d1) /* If not carry, test Q again. */ | |
goto q_test; | |
} | |
qp[i] = q; | |
sub_ddmmss (n1, n0, r, n2, n1, n0); | |
} | |
np[1] = n1; | |
np[0] = n0; | |
} | |
break; | |
default: | |
{ | |
mp_size_t i; | |
mp_limb_t dX, d1, n0; | |
np += nsize - dsize; | |
dX = dp[dsize - 1]; | |
d1 = dp[dsize - 2]; | |
n0 = np[dsize - 1]; | |
if (n0 >= dX) | |
{ | |
if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0) | |
{ | |
mpn_sub_n (np, np, dp, dsize); | |
n0 = np[dsize - 1]; | |
most_significant_q_limb = 1; | |
} | |
} | |
for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--) | |
{ | |
mp_limb_t q; | |
mp_limb_t n1, n2; | |
mp_limb_t cy_limb; | |
if (i >= qextra_limbs) | |
{ | |
np--; | |
n2 = np[dsize]; | |
} | |
else | |
{ | |
n2 = np[dsize - 1]; | |
MPN_COPY_DECR (np + 1, np, dsize); | |
np[0] = 0; | |
} | |
if (n0 == dX) | |
/* This might over-estimate q, but it's probably not worth | |
the extra code here to find out. */ | |
q = ~(mp_limb_t) 0; | |
else | |
{ | |
mp_limb_t r; | |
udiv_qrnnd (q, r, n0, np[dsize - 1], dX); | |
umul_ppmm (n1, n0, d1, q); | |
while (n1 > r || (n1 == r && n0 > np[dsize - 2])) | |
{ | |
q--; | |
r += dX; | |
if (r < dX) /* I.e. "carry in previous addition?" */ | |
break; | |
n1 -= n0 < d1; | |
n0 -= d1; | |
} | |
} | |
/* Possible optimization: We already have (q * n0) and (1 * n1) | |
after the calculation of q. Taking advantage of that, we | |
could make this loop make two iterations less. */ | |
cy_limb = mpn_submul_1 (np, dp, dsize, q); | |
if (n2 != cy_limb) | |
{ | |
mpn_add_n (np, np, dp, dsize); | |
q--; | |
} | |
qp[i] = q; | |
n0 = np[dsize - 1]; | |
} | |
} | |
} | |
return most_significant_q_limb; | |
} |