xref: /netbsd-src/external/lgpl3/gmp/dist/mpn/generic/mod_1_4.c (revision d909946ca08dceb44d7d0f22ec9488679695d976)
1 /* mpn_mod_1s_4p (ap, n, b, cps)
2    Divide (ap,,n) by b.  Return the single-limb remainder.
3    Requires that d < B / 4.
4 
5    Contributed to the GNU project by Torbjorn Granlund.
6    Based on a suggestion by Peter L. Montgomery.
7 
8    THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
9    SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
10    GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
11 
12 Copyright 2008, 2009, 2010 Free Software Foundation, Inc.
13 
14 This file is part of the GNU MP Library.
15 
16 The GNU MP Library is free software; you can redistribute it and/or modify
17 it under the terms of the GNU Lesser General Public License as published by
18 the Free Software Foundation; either version 3 of the License, or (at your
19 option) any later version.
20 
21 The GNU MP Library is distributed in the hope that it will be useful, but
22 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
23 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
24 License for more details.
25 
26 You should have received a copy of the GNU Lesser General Public License
27 along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
28 
29 #include "gmp.h"
30 #include "gmp-impl.h"
31 #include "longlong.h"
32 
33 void
34 mpn_mod_1s_4p_cps (mp_limb_t cps[7], mp_limb_t b)
35 {
36   mp_limb_t bi;
37   mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb;
38   int cnt;
39 
40   ASSERT (b <= (~(mp_limb_t) 0) / 4);
41 
42   count_leading_zeros (cnt, b);
43 
44   b <<= cnt;
45   invert_limb (bi, b);
46 
47   cps[0] = bi;
48   cps[1] = cnt;
49 
50   B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt));
51   ASSERT (B1modb <= b);		/* NB: not fully reduced mod b */
52   cps[2] = B1modb >> cnt;
53 
54   udiv_rnnd_preinv (B2modb, B1modb, CNST_LIMB(0), b, bi);
55   cps[3] = B2modb >> cnt;
56 
57   udiv_rnnd_preinv (B3modb, B2modb, CNST_LIMB(0), b, bi);
58   cps[4] = B3modb >> cnt;
59 
60   udiv_rnnd_preinv (B4modb, B3modb, CNST_LIMB(0), b, bi);
61   cps[5] = B4modb >> cnt;
62 
63   udiv_rnnd_preinv (B5modb, B4modb, CNST_LIMB(0), b, bi);
64   cps[6] = B5modb >> cnt;
65 
66 #if WANT_ASSERT
67   {
68     int i;
69     b = cps[2];
70     for (i = 3; i <= 6; i++)
71       {
72 	b += cps[i];
73 	ASSERT (b >= cps[i]);
74       }
75   }
76 #endif
77 }
78 
79 mp_limb_t
80 mpn_mod_1s_4p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[7])
81 {
82   mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;
83   mp_limb_t B1modb, B2modb, B3modb, B4modb, B5modb;
84   mp_size_t i;
85   int cnt;
86 
87   ASSERT (n >= 1);
88 
89   B1modb = cps[2];
90   B2modb = cps[3];
91   B3modb = cps[4];
92   B4modb = cps[5];
93   B5modb = cps[6];
94 
95   switch (n & 3)
96     {
97     case 0:
98       umul_ppmm (ph, pl, ap[n - 3], B1modb);
99       add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 4]);
100       umul_ppmm (ch, cl, ap[n - 2], B2modb);
101       add_ssaaaa (ph, pl, ph, pl, ch, cl);
102       umul_ppmm (rh, rl, ap[n - 1], B3modb);
103       add_ssaaaa (rh, rl, rh, rl, ph, pl);
104       n -= 4;
105       break;
106     case 1:
107       rh = 0;
108       rl = ap[n - 1];
109       n -= 1;
110       break;
111     case 2:
112       rh = ap[n - 1];
113       rl = ap[n - 2];
114       n -= 2;
115       break;
116     case 3:
117       umul_ppmm (ph, pl, ap[n - 2], B1modb);
118       add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 3]);
119       umul_ppmm (rh, rl, ap[n - 1], B2modb);
120       add_ssaaaa (rh, rl, rh, rl, ph, pl);
121       n -= 3;
122       break;
123     }
124 
125   for (i = n - 4; i >= 0; i -= 4)
126     {
127       /* rr = ap[i]				< B
128 	    + ap[i+1] * (B mod b)		<= (B-1)(b-1)
129 	    + ap[i+2] * (B^2 mod b)		<= (B-1)(b-1)
130 	    + ap[i+3] * (B^3 mod b)		<= (B-1)(b-1)
131 	    + LO(rr)  * (B^4 mod b)		<= (B-1)(b-1)
132 	    + HI(rr)  * (B^5 mod b)		<= (B-1)(b-1)
133       */
134       umul_ppmm (ph, pl, ap[i + 1], B1modb);
135       add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]);
136 
137       umul_ppmm (ch, cl, ap[i + 2], B2modb);
138       add_ssaaaa (ph, pl, ph, pl, ch, cl);
139 
140       umul_ppmm (ch, cl, ap[i + 3], B3modb);
141       add_ssaaaa (ph, pl, ph, pl, ch, cl);
142 
143       umul_ppmm (ch, cl, rl, B4modb);
144       add_ssaaaa (ph, pl, ph, pl, ch, cl);
145 
146       umul_ppmm (rh, rl, rh, B5modb);
147       add_ssaaaa (rh, rl, rh, rl, ph, pl);
148     }
149 
150   umul_ppmm (rh, cl, rh, B1modb);
151   add_ssaaaa (rh, rl, rh, rl, 0, cl);
152 
153   cnt = cps[1];
154   bi = cps[0];
155 
156   r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
157   udiv_rnnd_preinv (r, r, rl << cnt, b, bi);
158 
159   return r >> cnt;
160 }
161