1 /* mpn_divrem -- Divide natural numbers, producing both remainder and
4 Copyright (C) 1993-2017 Free Software Foundation, Inc.
6 This file is part of the GNU MP Library.
8 The GNU MP Library is free software; you can redistribute it and/or modify
9 it under the terms of the GNU Lesser General Public License as published by
10 the Free Software Foundation; either version 2.1 of the License, or (at your
11 option) any later version.
13 The GNU MP Library is distributed in the hope that it will be useful, but
14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
16 License for more details.
18 You should have received a copy of the GNU Lesser General Public License
19 along with the GNU MP Library; see the file COPYING.LIB. If not, see
20 <http://www.gnu.org/licenses/>. */
26 /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
27 the NSIZE-DSIZE least significant quotient limbs at QP
28 and the DSIZE long remainder at NP. If QEXTRA_LIMBS is
29 non-zero, generate that many fraction bits and append them after the
31 Return the most significant limb of the quotient, this is always 0 or 1.
35 1. The most significant bit of the divisor must be set.
36 2. QP must either not overlap with the input operands at all, or
37 QP + DSIZE >= NP must hold true. (This means that it's
38 possible to put the quotient in the high part of NUM, right after the
40 3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero. */
43 mpn_divrem (mp_ptr qp
, mp_size_t qextra_limbs
,
44 mp_ptr np
, mp_size_t nsize
,
45 mp_srcptr dp
, mp_size_t dsize
)
47 mp_limb_t most_significant_q_limb
= 0;
52 /* We are asked to divide by zero, so go ahead and do it! (To make
53 the compiler not remove this statement, return the value.) */
68 most_significant_q_limb
= 1;
72 for (i
= nsize
- 2; i
>= 0; i
--)
73 udiv_qrnnd (qp
[i
], n1
, n1
, np
[i
], d
);
76 for (i
= qextra_limbs
- 1; i
>= 0; i
--)
77 udiv_qrnnd (qp
[i
], n1
, n1
, 0, d
);
95 if (n1
>= d1
&& (n1
> d1
|| n0
>= d0
))
97 sub_ddmmss (n1
, n0
, n1
, n0
, d1
, d0
);
98 most_significant_q_limb
= 1;
101 for (i
= qextra_limbs
+ nsize
- 2 - 1; i
>= 0; i
--)
106 if (i
>= qextra_limbs
)
113 /* Q should be either 111..111 or 111..110. Need special
114 treatment of this rare case as normal division would
119 if (r
< d1
) /* Carry in the addition? */
121 add_ssaaaa (n1
, n0
, r
- d0
, np
[0], 0, d0
);
130 udiv_qrnnd (q
, r
, n1
, n0
, d1
);
131 umul_ppmm (n1
, n0
, d0
, q
);
136 if (n1
> r
|| (n1
== r
&& n0
> n2
))
138 /* The estimated Q was too large. */
141 sub_ddmmss (n1
, n0
, n1
, n0
, 0, d0
);
143 if (r
>= d1
) /* If not carry, test Q again. */
148 sub_ddmmss (n1
, n0
, r
, n2
, n1
, n0
);
158 mp_limb_t dX
, d1
, n0
;
167 if (n0
> dX
|| mpn_cmp (np
, dp
, dsize
- 1) >= 0)
169 mpn_sub_n (np
, np
, dp
, dsize
);
171 most_significant_q_limb
= 1;
175 for (i
= qextra_limbs
+ nsize
- dsize
- 1; i
>= 0; i
--)
181 if (i
>= qextra_limbs
)
189 MPN_COPY_DECR (np
+ 1, np
, dsize
);
194 /* This might over-estimate q, but it's probably not worth
195 the extra code here to find out. */
201 udiv_qrnnd (q
, r
, n0
, np
[dsize
- 1], dX
);
202 umul_ppmm (n1
, n0
, d1
, q
);
204 while (n1
> r
|| (n1
== r
&& n0
> np
[dsize
- 2]))
208 if (r
< dX
) /* I.e. "carry in previous addition?" */
215 /* Possible optimization: We already have (q * n0) and (1 * n1)
216 after the calculation of q. Taking advantage of that, we
217 could make this loop make two iterations less. */
219 cy_limb
= mpn_submul_1 (np
, dp
, dsize
, q
);
223 mpn_add_n (np
, np
, dp
, dsize
);
233 return most_significant_q_limb
;