1 /* gcd_subdiv_step.c.
2 
3    THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
4    SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
5    GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
6 
7 Copyright 2003-2005, 2008, 2010, 2011 Free Software Foundation, Inc.
8 
9 This file is part of the GNU MP Library.
10 
11 The GNU MP Library is free software; you can redistribute it and/or modify
12 it under the terms of either:
13 
14   * the GNU Lesser General Public License as published by the Free
15     Software Foundation; either version 3 of the License, or (at your
16     option) any later version.
17 
18 or
19 
20   * the GNU General Public License as published by the Free Software
21     Foundation; either version 2 of the License, or (at your option) any
22     later version.
23 
24 or both in parallel, as here.
25 
26 The GNU MP Library is distributed in the hope that it will be useful, but
27 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
28 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
29 for more details.
30 
31 You should have received copies of the GNU General Public License and the
32 GNU Lesser General Public License along with the GNU MP Library.  If not,
33 see https://www.gnu.org/licenses/.  */
34 
35 #include <stdlib.h>		/* for NULL */
36 
37 #include "gmp-impl.h"
38 #include "longlong.h"
39 
40 /* Used when mpn_hgcd or mpn_hgcd2 has failed. Then either one of a or
41    b is small, or the difference is small. Perform one subtraction
42    followed by one division. The normal case is to compute the reduced
43    a and b, and return the new size.
44 
45    If s == 0 (used for gcd and gcdext), returns zero if the gcd is
46    found.
47 
48    If s > 0, don't reduce to size <= s, and return zero if no
49    reduction is possible (if either a, b or |a-b| is of size <= s). */
50 
51 /* The hook function is called as
52 
53      hook(ctx, gp, gn, qp, qn, d)
54 
55    in the following cases:
56 
57    + If A = B at the start, G is the gcd, Q is NULL, d = -1.
58 
59    + If one input is zero at the start, G is the gcd, Q is NULL,
60      d = 0 if A = G and d = 1 if B = G.
61 
62    Otherwise, if d = 0 we have just subtracted a multiple of A from B,
63    and if d = 1 we have subtracted a multiple of B from A.
64 
65    + If A = B after subtraction, G is the gcd, Q is NULL.
66 
67    + If we get a zero remainder after division, G is the gcd, Q is the
68      quotient.
69 
70    + Otherwise, G is NULL, Q is the quotient (often 1).
71 
72  */
73 
74 mp_size_t
mpn_gcd_subdiv_step(mp_ptr ap,mp_ptr bp,mp_size_t n,mp_size_t s,gcd_subdiv_step_hook * hook,void * ctx,mp_ptr tp)75 mpn_gcd_subdiv_step (mp_ptr ap, mp_ptr bp, mp_size_t n, mp_size_t s,
76 		     gcd_subdiv_step_hook *hook, void *ctx,
77 		     mp_ptr tp)
78 {
79   static const mp_limb_t one = CNST_LIMB(1);
80   mp_size_t an, bn, qn;
81 
82   int swapped;
83 
84   ASSERT (n > 0);
85   ASSERT (ap[n-1] > 0 || bp[n-1] > 0);
86 
87   an = bn = n;
88   MPN_NORMALIZE (ap, an);
89   MPN_NORMALIZE (bp, bn);
90 
91   swapped = 0;
92 
93   /* Arrange so that a < b, subtract b -= a, and maintain
94      normalization. */
95   if (an == bn)
96     {
97       int c;
98       MPN_CMP (c, ap, bp, an);
99       if (UNLIKELY (c == 0))
100 	{
101 	  /* For gcdext, return the smallest of the two cofactors, so
102 	     pass d = -1. */
103 	  if (s == 0)
104 	    hook (ctx, ap, an, NULL, 0, -1);
105 	  return 0;
106 	}
107       else if (c > 0)
108 	{
109 	  MP_PTR_SWAP (ap, bp);
110 	  swapped ^= 1;
111 	}
112     }
113   else
114     {
115       if (an > bn)
116 	{
117 	  MPN_PTR_SWAP (ap, an, bp, bn);
118 	  swapped ^= 1;
119 	}
120     }
121   if (an <= s)
122     {
123       if (s == 0)
124 	hook (ctx, bp, bn, NULL, 0, swapped ^ 1);
125       return 0;
126     }
127 
128   ASSERT_NOCARRY (mpn_sub (bp, bp, bn, ap, an));
129   MPN_NORMALIZE (bp, bn);
130   ASSERT (bn > 0);
131 
132   if (bn <= s)
133     {
134       /* Undo subtraction. */
135       mp_limb_t cy = mpn_add (bp, ap, an, bp, bn);
136       if (cy > 0)
137 	bp[an] = cy;
138       return 0;
139     }
140 
141   /* Arrange so that a < b */
142   if (an == bn)
143     {
144       int c;
145       MPN_CMP (c, ap, bp, an);
146       if (UNLIKELY (c == 0))
147 	{
148 	  if (s > 0)
149 	    /* Just record subtraction and return */
150 	    hook (ctx, NULL, 0, &one, 1, swapped);
151 	  else
152 	    /* Found gcd. */
153 	    hook (ctx, bp, bn, NULL, 0, swapped);
154 	  return 0;
155 	}
156 
157       hook (ctx, NULL, 0, &one, 1, swapped);
158 
159       if (c > 0)
160 	{
161 	  MP_PTR_SWAP (ap, bp);
162 	  swapped ^= 1;
163 	}
164     }
165   else
166     {
167       hook (ctx, NULL, 0, &one, 1, swapped);
168 
169       if (an > bn)
170 	{
171 	  MPN_PTR_SWAP (ap, an, bp, bn);
172 	  swapped ^= 1;
173 	}
174     }
175 
176   mpn_tdiv_qr (tp, bp, 0, bp, bn, ap, an);
177   qn = bn - an + 1;
178   bn = an;
179   MPN_NORMALIZE (bp, bn);
180 
181   if (UNLIKELY (bn <= s))
182     {
183       if (s == 0)
184 	{
185 	  hook (ctx, ap, an, tp, qn, swapped);
186 	  return 0;
187 	}
188 
189       /* Quotient is one too large, so decrement it and add back A. */
190       if (bn > 0)
191 	{
192 	  mp_limb_t cy = mpn_add (bp, ap, an, bp, bn);
193 	  if (cy)
194 	    bp[an++] = cy;
195 	}
196       else
197 	MPN_COPY (bp, ap, an);
198 
199       MPN_DECR_U (tp, qn, 1);
200     }
201 
202   hook (ctx, NULL, 0, tp, qn, swapped);
203   return an;
204 }
205