1 /* mpn_div_qr_1n_pi2.
2 
3    THIS FILE CONTAINS AN INTERNAL FUNCTION WITH A MUTABLE INTERFACE.  IT IS
4    ONLY SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
5    GUARANTEED THAT IT'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
6 
7 Copyright 2013, 2017 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 /* ISSUES:
36 
37    * Can we really use the high pi2 inverse limb for udiv_qrnnd_preinv?
38 
39    * Are there any problems with generating n quotient limbs in the q area?  It
40      surely simplifies things.
41 
42    * Not yet adequately tested.
43 */
44 
45 #include "gmp-impl.h"
46 #include "longlong.h"
47 
48 /* Define some longlong.h-style macros, but for wider operations.
49    * add_sssaaaa is like longlong.h's add_ssaaaa but propagating carry-out into
50      an additional sum operand.
51 */
52 #if defined (__GNUC__)  && ! defined (__INTEL_COMPILER) && ! defined (NO_ASM)
53 
54 #if HAVE_HOST_CPU_FAMILY_x86 && W_TYPE_SIZE == 32
55 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
56   __asm__ ("add\t%7, %k2\n\tadc\t%5, %k1\n\tadc\t$0, %k0"		\
57 	   : "=r" (s2), "=&r" (s1), "=&r" (s0)				\
58 	   : "0"  ((USItype)(s2)),					\
59 	     "1"  ((USItype)(a1)), "g" ((USItype)(b1)),			\
60 	     "%2" ((USItype)(a0)), "g" ((USItype)(b0)))
61 #endif
62 
63 #if defined (__amd64__) && W_TYPE_SIZE == 64
64 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
65   __asm__ ("add\t%7, %q2\n\tadc\t%5, %q1\n\tadc\t$0, %q0"		\
66 	   : "=r" (s2), "=&r" (s1), "=&r" (s0)				\
67 	   : "0"  ((UDItype)(s2)),					\
68 	     "1"  ((UDItype)(a1)), "rme" ((UDItype)(b1)),		\
69 	     "%2" ((UDItype)(a0)), "rme" ((UDItype)(b0)))
70 #endif
71 
72 #if defined (__aarch64__) && W_TYPE_SIZE == 64
73 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
74   __asm__ ("adds\t%2, %x6, %7\n\tadcs\t%1, %x4, %x5\n\tadc\t%0, %3, xzr"\
75 	   : "=r" (s2), "=&r" (s1), "=&r" (s0)				\
76 	   : "rZ" (s2), "%rZ"  (a1), "rZ" (b1), "%rZ" (a0), "rI" (b0)	\
77 	     __CLOBBER_CC)
78 #endif
79 
80 #if HAVE_HOST_CPU_FAMILY_powerpc && !defined (_LONG_LONG_LIMB)
81 /* This works fine for 32-bit and 64-bit limbs, except for 64-bit limbs with a
82    processor running in 32-bit mode, since the carry flag then gets the 32-bit
83    carry.  */
84 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
85   __asm__ ("add%I7c\t%2,%6,%7\n\tadde\t%1,%4,%5\n\taddze\t%0,%3"	\
86 	   : "=r" (s2), "=&r" (s1), "=&r" (s0)				\
87 	   : "r"  (s2), "r"  (a1), "r" (b1), "%r" (a0), "rI" (b0)	\
88 	     __CLOBBER_CC)
89 #endif
90 
91 #endif /* __GNUC__ */
92 
93 #ifndef add_sssaaaa
94 #define add_sssaaaa(s2, s1, s0, a1, a0, b1, b0)				\
95   do {									\
96     UWtype __s0, __s1, __c0, __c1;					\
97     __s0 = (a0) + (b0);							\
98     __s1 = (a1) + (b1);							\
99     __c0 = __s0 < (a0);							\
100     __c1 = __s1 < (a1);							\
101     (s0) = __s0;							\
102     __s1 = __s1 + __c0;							\
103     (s1) = __s1;							\
104     (s2) += __c1 + (__s1 < __c0);					\
105   } while (0)
106 #endif
107 
108 struct precomp_div_1_pi2
109 {
110   mp_limb_t dip[2];
111   mp_limb_t d;
112   int norm_cnt;
113 };
114 
115 mp_limb_t
mpn_div_qr_1n_pi2(mp_ptr qp,mp_srcptr up,mp_size_t un,struct precomp_div_1_pi2 * pd)116 mpn_div_qr_1n_pi2 (mp_ptr qp,
117 		   mp_srcptr up, mp_size_t un,
118 		   struct precomp_div_1_pi2 *pd)
119 {
120   mp_limb_t most_significant_q_limb;
121   mp_size_t i;
122   mp_limb_t r, u2, u1, u0;
123   mp_limb_t d0, di1, di0;
124   mp_limb_t q3a, q2a, q2b, q1b, q2c, q1c, q1d, q0d;
125   mp_limb_t cnd;
126 
127   ASSERT (un >= 2);
128   ASSERT ((pd->d & GMP_NUMB_HIGHBIT) != 0);
129   ASSERT (! MPN_OVERLAP_P (qp, un-2, up, un) || qp+2 >= up);
130   ASSERT_MPN (up, un);
131 
132 #define q3 q3a
133 #define q2 q2b
134 #define q1 q1b
135 
136   up += un - 3;
137   r = up[2];
138   d0 = pd->d;
139 
140   most_significant_q_limb = (r >= d0);
141   r -= d0 & -most_significant_q_limb;
142 
143   qp += un - 3;
144   qp[2] = most_significant_q_limb;
145 
146   di1 = pd->dip[1];
147   di0 = pd->dip[0];
148 
149   for (i = un - 3; i >= 0; i -= 2)
150     {
151       u2 = r;
152       u1 = up[1];
153       u0 = up[0];
154 
155       /* Dividend in {r,u1,u0} */
156 
157       umul_ppmm (q1d,q0d, u1, di0);
158       umul_ppmm (q2b,q1b, u1, di1);
159       q2b++;				/* cannot spill */
160       add_sssaaaa (r,q2b,q1b, q2b,q1b, u1,u0);
161 
162       umul_ppmm (q2c,q1c, u2,  di0);
163       add_sssaaaa (r,q2b,q1b, q2b,q1b, q2c,q1c);
164       umul_ppmm (q3a,q2a, u2, di1);
165 
166       add_sssaaaa (r,q2b,q1b, q2b,q1b, q2a,q1d);
167 
168       q3 += r;
169 
170       r = u0 - q2 * d0;
171 
172       cnd = (r >= q1);
173       r += d0 & -cnd;
174       sub_ddmmss (q3,q2,  q3,q2,  0,cnd);
175 
176       if (UNLIKELY (r >= d0))
177 	{
178 	  r -= d0;
179 	  add_ssaaaa (q3,q2,  q3,q2,  0,1);
180 	}
181 
182       qp[0] = q2;
183       qp[1] = q3;
184 
185       up -= 2;
186       qp -= 2;
187     }
188 
189   if ((un & 1) == 0)
190     {
191       u2 = r;
192       u1 = up[1];
193 
194       udiv_qrnnd_preinv (q3, r, u2, u1, d0, di1);
195       qp[1] = q3;
196     }
197 
198   return r;
199 
200 #undef q3
201 #undef q2
202 #undef q1
203 }
204