|  | @@ -1,336 +0,0 @@
 | 
		
	
		
			
			| 1 |  | -/*
 | 
		
	
		
			
			| 2 |  | - * Copyright (C) 2007 Michael Brown <mbrown@fensystems.co.uk>.
 | 
		
	
		
			
			| 3 |  | - *
 | 
		
	
		
			
			| 4 |  | - * This program is free software; you can redistribute it and/or
 | 
		
	
		
			
			| 5 |  | - * modify it under the terms of the GNU General Public License as
 | 
		
	
		
			
			| 6 |  | - * published by the Free Software Foundation; either version 2 of the
 | 
		
	
		
			
			| 7 |  | - * License, or any later version.
 | 
		
	
		
			
			| 8 |  | - *
 | 
		
	
		
			
			| 9 |  | - * This program is distributed in the hope that it will be useful, but
 | 
		
	
		
			
			| 10 |  | - * WITHOUT ANY WARRANTY; without even the implied warranty of
 | 
		
	
		
			
			| 11 |  | - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 | 
		
	
		
			
			| 12 |  | - * General Public License for more details.
 | 
		
	
		
			
			| 13 |  | - *
 | 
		
	
		
			
			| 14 |  | - * You should have received a copy of the GNU General Public License
 | 
		
	
		
			
			| 15 |  | - * along with this program; if not, write to the Free Software
 | 
		
	
		
			
			| 16 |  | - * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 | 
		
	
		
			
			| 17 |  | - */
 | 
		
	
		
			
			| 18 |  | -
 | 
		
	
		
			
			| 19 |  | -/** @file
 | 
		
	
		
			
			| 20 |  | - *
 | 
		
	
		
			
			| 21 |  | - * 64-bit division
 | 
		
	
		
			
			| 22 |  | - *
 | 
		
	
		
			
			| 23 |  | - * The x86 CPU (386 upwards) has a divl instruction which will perform
 | 
		
	
		
			
			| 24 |  | - * unsigned division of a 64-bit dividend by a 32-bit divisor.  If the
 | 
		
	
		
			
			| 25 |  | - * resulting quotient does not fit in 32 bits, then a CPU exception
 | 
		
	
		
			
			| 26 |  | - * will occur.
 | 
		
	
		
			
			| 27 |  | - *
 | 
		
	
		
			
			| 28 |  | - * Unsigned integer division is expressed as solving 
 | 
		
	
		
			
			| 29 |  | - *
 | 
		
	
		
			
			| 30 |  | - *   x = d.q + r			0 <= q, 0 <= r < d
 | 
		
	
		
			
			| 31 |  | - *
 | 
		
	
		
			
			| 32 |  | - * given the dividend (x) and divisor (d), to find the quotient (q)
 | 
		
	
		
			
			| 33 |  | - * and remainder (r).
 | 
		
	
		
			
			| 34 |  | - *
 | 
		
	
		
			
			| 35 |  | - * The x86 divl instruction will solve
 | 
		
	
		
			
			| 36 |  | - *
 | 
		
	
		
			
			| 37 |  | - *   x = d.q + r			0 <= q, 0 <= r < d
 | 
		
	
		
			
			| 38 |  | - *
 | 
		
	
		
			
			| 39 |  | - * given x in the range 0 <= x < 2^64 and 1 <= d < 2^32, and causing a
 | 
		
	
		
			
			| 40 |  | - * hardware exception if the resulting q >= 2^32.
 | 
		
	
		
			
			| 41 |  | - *
 | 
		
	
		
			
			| 42 |  | - * We can therefore use divl only if we can prove that the conditions
 | 
		
	
		
			
			| 43 |  | - *
 | 
		
	
		
			
			| 44 |  | - *   0 <= x < 2^64
 | 
		
	
		
			
			| 45 |  | - *   1 <= d < 2^32
 | 
		
	
		
			
			| 46 |  | - *        q < 2^32
 | 
		
	
		
			
			| 47 |  | - *
 | 
		
	
		
			
			| 48 |  | - * are satisfied.
 | 
		
	
		
			
			| 49 |  | - *
 | 
		
	
		
			
			| 50 |  | - *
 | 
		
	
		
			
			| 51 |  | - * Case 1 : 1 <= d < 2^32
 | 
		
	
		
			
			| 52 |  | - * ======================
 | 
		
	
		
			
			| 53 |  | - *
 | 
		
	
		
			
			| 54 |  | - * We express x as
 | 
		
	
		
			
			| 55 |  | - *
 | 
		
	
		
			
			| 56 |  | - *   x = xh.2^32 + xl			0 <= xh < 2^32, 0 <= xl < 2^32	(1)
 | 
		
	
		
			
			| 57 |  | - *
 | 
		
	
		
			
			| 58 |  | - * i.e. split x into low and high dwords.  We then solve
 | 
		
	
		
			
			| 59 |  | - *
 | 
		
	
		
			
			| 60 |  | - *   xh = d.qh + r'			0 <= qh, 0 <= r' < d		(2)
 | 
		
	
		
			
			| 61 |  | - *
 | 
		
	
		
			
			| 62 |  | - * which we can do using a divl instruction since
 | 
		
	
		
			
			| 63 |  | - *
 | 
		
	
		
			
			| 64 |  | - *   0 <= xh < 2^64			since 0 <= xh < 2^32 from (1)	(3)
 | 
		
	
		
			
			| 65 |  | - *
 | 
		
	
		
			
			| 66 |  | - * and
 | 
		
	
		
			
			| 67 |  | - *
 | 
		
	
		
			
			| 68 |  | - *   1 <= d < 2^32			by definition of this Case	(4)
 | 
		
	
		
			
			| 69 |  | - *
 | 
		
	
		
			
			| 70 |  | - * and
 | 
		
	
		
			
			| 71 |  | - *
 | 
		
	
		
			
			| 72 |  | - *   d.qh = xh - r'			from (2)
 | 
		
	
		
			
			| 73 |  | - *   d.qh <= xh				since r' >= 0 from (2)
 | 
		
	
		
			
			| 74 |  | - *   qh <= xh				since d >= 1 from (2)
 | 
		
	
		
			
			| 75 |  | - *   qh < 2^32				since xh < 2^32 from (1)	(5)
 | 
		
	
		
			
			| 76 |  | - *
 | 
		
	
		
			
			| 77 |  | - * Having obtained qh and r', we then solve
 | 
		
	
		
			
			| 78 |  | - *
 | 
		
	
		
			
			| 79 |  | - *   ( r'.2^32 + xl ) = d.ql + r	0 <= ql, 0 <= r < d		(6)
 | 
		
	
		
			
			| 80 |  | - *
 | 
		
	
		
			
			| 81 |  | - * which we can do using another divl instruction since
 | 
		
	
		
			
			| 82 |  | - *
 | 
		
	
		
			
			| 83 |  | - *   xl <= 2^32 - 1			from (1), so
 | 
		
	
		
			
			| 84 |  | - *   r'.2^32 + xl <= ( r' + 1 ).2^32 - 1
 | 
		
	
		
			
			| 85 |  | - *   r'.2^32 + xl <= d.2^32 - 1		since r' < d from (2)
 | 
		
	
		
			
			| 86 |  | - *   r'.2^32 + xl < d.2^32						(7)
 | 
		
	
		
			
			| 87 |  | - *   r'.2^32 + xl < 2^64		since d < 2^32 from (4)		(8)
 | 
		
	
		
			
			| 88 |  | - *
 | 
		
	
		
			
			| 89 |  | - * and
 | 
		
	
		
			
			| 90 |  | - *
 | 
		
	
		
			
			| 91 |  | - *   1 <= d < 2^32			by definition of this Case	(9)
 | 
		
	
		
			
			| 92 |  | - *
 | 
		
	
		
			
			| 93 |  | - * and
 | 
		
	
		
			
			| 94 |  | - *
 | 
		
	
		
			
			| 95 |  | - *   d.ql = ( r'.2^32 + xl ) - r	from (6)
 | 
		
	
		
			
			| 96 |  | - *   d.ql <= r'.2^32 + xl		since r >= 0 from (6)
 | 
		
	
		
			
			| 97 |  | - *   d.ql < d.2^32			from (7)
 | 
		
	
		
			
			| 98 |  | - *   ql < 2^32				since d >= 1 from (2)		(10)
 | 
		
	
		
			
			| 99 |  | - *
 | 
		
	
		
			
			| 100 |  | - * This then gives us
 | 
		
	
		
			
			| 101 |  | - *
 | 
		
	
		
			
			| 102 |  | - *   x = xh.2^32 + xl			from (1)
 | 
		
	
		
			
			| 103 |  | - *   x = ( d.qh + r' ).2^32 + xl	from (2)
 | 
		
	
		
			
			| 104 |  | - *   x = d.qh.2^32 + ( r'.2^32 + xl )
 | 
		
	
		
			
			| 105 |  | - *   x = d.qh.2^32 + d.ql + r		from (3)
 | 
		
	
		
			
			| 106 |  | - *   x = d.( qh.2^32 + ql ) + r						(11)
 | 
		
	
		
			
			| 107 |  | - *
 | 
		
	
		
			
			| 108 |  | - * Letting
 | 
		
	
		
			
			| 109 |  | - *
 | 
		
	
		
			
			| 110 |  | - *   q = qh.2^32 + ql							(12)
 | 
		
	
		
			
			| 111 |  | - *
 | 
		
	
		
			
			| 112 |  | - * gives
 | 
		
	
		
			
			| 113 |  | - *
 | 
		
	
		
			
			| 114 |  | - *   x = d.q + r			from (11) and (12)
 | 
		
	
		
			
			| 115 |  | - *
 | 
		
	
		
			
			| 116 |  | - * which is the solution.
 | 
		
	
		
			
			| 117 |  | - *
 | 
		
	
		
			
			| 118 |  | - *
 | 
		
	
		
			
			| 119 |  | - * This therefore gives us a two-step algorithm:
 | 
		
	
		
			
			| 120 |  | - *
 | 
		
	
		
			
			| 121 |  | - *   xh = d.qh + r'			0 <= qh, 0 <= r' < d		(2)
 | 
		
	
		
			
			| 122 |  | - *   ( r'.2^32 + xl ) = d.ql + r	0 <= ql, 0 <= r < d		(6)
 | 
		
	
		
			
			| 123 |  | - *
 | 
		
	
		
			
			| 124 |  | - * which translates to
 | 
		
	
		
			
			| 125 |  | - *
 | 
		
	
		
			
			| 126 |  | - *   %edx:%eax = 0:xh
 | 
		
	
		
			
			| 127 |  | - *   divl d
 | 
		
	
		
			
			| 128 |  | - *   qh = %eax
 | 
		
	
		
			
			| 129 |  | - *   r' = %edx
 | 
		
	
		
			
			| 130 |  | - *
 | 
		
	
		
			
			| 131 |  | - *   %edx:%eax = r':xl
 | 
		
	
		
			
			| 132 |  | - *   divl d
 | 
		
	
		
			
			| 133 |  | - *   ql = %eax
 | 
		
	
		
			
			| 134 |  | - *   r = %edx
 | 
		
	
		
			
			| 135 |  | - *
 | 
		
	
		
			
			| 136 |  | - * Note that if
 | 
		
	
		
			
			| 137 |  | - *
 | 
		
	
		
			
			| 138 |  | - *   xh < d
 | 
		
	
		
			
			| 139 |  | - *
 | 
		
	
		
			
			| 140 |  | - * (which is a fast dword comparison) then the first divl instruction
 | 
		
	
		
			
			| 141 |  | - * can be omitted, since the answer will be
 | 
		
	
		
			
			| 142 |  | - *
 | 
		
	
		
			
			| 143 |  | - *   qh = 0
 | 
		
	
		
			
			| 144 |  | - *   r = xh
 | 
		
	
		
			
			| 145 |  | - *
 | 
		
	
		
			
			| 146 |  | - *
 | 
		
	
		
			
			| 147 |  | - * Case 2 : 2^32 <= d < 2^64
 | 
		
	
		
			
			| 148 |  | - * =========================
 | 
		
	
		
			
			| 149 |  | - *
 | 
		
	
		
			
			| 150 |  | - * We first express d as
 | 
		
	
		
			
			| 151 |  | - *
 | 
		
	
		
			
			| 152 |  | - *   d = dh.2^k + dl			2^31 <= dh < 2^32,
 | 
		
	
		
			
			| 153 |  | - *					0 <= dl < 2^k, 1 <= k <= 32	(1)
 | 
		
	
		
			
			| 154 |  | - *
 | 
		
	
		
			
			| 155 |  | - * i.e. find the highest bit set in d, subtract 32, and split d into
 | 
		
	
		
			
			| 156 |  | - * dh and dl at that point.
 | 
		
	
		
			
			| 157 |  | - *
 | 
		
	
		
			
			| 158 |  | - * We then express x as
 | 
		
	
		
			
			| 159 |  | - *
 | 
		
	
		
			
			| 160 |  | - *   x = xh.2^k + xl			0 <= xl < 2^k			(2)
 | 
		
	
		
			
			| 161 |  | - *
 | 
		
	
		
			
			| 162 |  | - * giving
 | 
		
	
		
			
			| 163 |  | - *
 | 
		
	
		
			
			| 164 |  | - *   xh.2^k = x - xl			from (2)
 | 
		
	
		
			
			| 165 |  | - *   xh.2^k <= x			since xl >= 0 from (1)
 | 
		
	
		
			
			| 166 |  | - *   xh.2^k < 2^64			since xh < 2^64 from (1)
 | 
		
	
		
			
			| 167 |  | - *   xh < 2^(64-k)							(3)
 | 
		
	
		
			
			| 168 |  | - *
 | 
		
	
		
			
			| 169 |  | - * We then solve the division
 | 
		
	
		
			
			| 170 |  | - *
 | 
		
	
		
			
			| 171 |  | - *   xh = dh.q' + r'	            		0 <= r' < dh		(4)
 | 
		
	
		
			
			| 172 |  | - *
 | 
		
	
		
			
			| 173 |  | - * which we can do using a divl instruction since
 | 
		
	
		
			
			| 174 |  | - *
 | 
		
	
		
			
			| 175 |  | - *   0 <= xh < 2^64			since x < 2^64 and xh < x
 | 
		
	
		
			
			| 176 |  | - *
 | 
		
	
		
			
			| 177 |  | - * and
 | 
		
	
		
			
			| 178 |  | - *
 | 
		
	
		
			
			| 179 |  | - *   1 <= dh < 2^32			from (1)
 | 
		
	
		
			
			| 180 |  | - *
 | 
		
	
		
			
			| 181 |  | - * and
 | 
		
	
		
			
			| 182 |  | - *
 | 
		
	
		
			
			| 183 |  | - *   dh.q' = xh - r'			from (4)
 | 
		
	
		
			
			| 184 |  | - *   dh.q' <= xh			since r' >= 0 from (4)
 | 
		
	
		
			
			| 185 |  | - *   dh.q' < 2^(64-k)			from (3)			(5)
 | 
		
	
		
			
			| 186 |  | - *   q'.2^31 <= dh.q'			since dh >= 2^31 from (1)	(6)
 | 
		
	
		
			
			| 187 |  | - *   q'.2^31 < 2^(64-k)			from (5) and (6)
 | 
		
	
		
			
			| 188 |  | - *   q' < 2^(33-k)
 | 
		
	
		
			
			| 189 |  | - *   q' < 2^32				since k >= 1 from (1)		(7)
 | 
		
	
		
			
			| 190 |  | - *
 | 
		
	
		
			
			| 191 |  | - * This gives us
 | 
		
	
		
			
			| 192 |  | - *
 | 
		
	
		
			
			| 193 |  | - *   xh.2^k = dh.q'.2^k + r'.2^k	from (4)
 | 
		
	
		
			
			| 194 |  | - *   x - xl = ( d - dl ).q' + r'.2^k	from (1) and (2)
 | 
		
	
		
			
			| 195 |  | - *   x = d.q' + ( r'.2^k + xl ) - dl.q'					(8)
 | 
		
	
		
			
			| 196 |  | - *
 | 
		
	
		
			
			| 197 |  | - * Now
 | 
		
	
		
			
			| 198 |  | - *
 | 
		
	
		
			
			| 199 |  | - *  r'.2^k + xl < r'.2^k + 2^k		since xl < 2^k from (2)
 | 
		
	
		
			
			| 200 |  | - *  r'.2^k + xl < ( r' + 1 ).2^k
 | 
		
	
		
			
			| 201 |  | - *  r'.2^k + xl < dh.2^k		since r' < dh from (4)
 | 
		
	
		
			
			| 202 |  | - *  r'.2^k + xl < ( d - dl )		from (1)			(9)
 | 
		
	
		
			
			| 203 |  | - *
 | 
		
	
		
			
			| 204 |  | - *
 | 
		
	
		
			
			| 205 |  | - * (missing)
 | 
		
	
		
			
			| 206 |  | - *
 | 
		
	
		
			
			| 207 |  | - *
 | 
		
	
		
			
			| 208 |  | - * This gives us two cases to consider:
 | 
		
	
		
			
			| 209 |  | - *
 | 
		
	
		
			
			| 210 |  | - * case (a):
 | 
		
	
		
			
			| 211 |  | - *
 | 
		
	
		
			
			| 212 |  | - *   dl.q' <= ( r'.2^k + xl )						(15a)
 | 
		
	
		
			
			| 213 |  | - *
 | 
		
	
		
			
			| 214 |  | - * in which case
 | 
		
	
		
			
			| 215 |  | - *
 | 
		
	
		
			
			| 216 |  | - *   x = d.q' + ( r'.2^k + xl - dl.q' )
 | 
		
	
		
			
			| 217 |  | - *
 | 
		
	
		
			
			| 218 |  | - * is a direct solution to the division, since
 | 
		
	
		
			
			| 219 |  | - *
 | 
		
	
		
			
			| 220 |  | - *   r'.2^k + xl < d			from (9)
 | 
		
	
		
			
			| 221 |  | - *   ( r'.2^k + xl - dl.q' ) < d	since dl >= 0 and q' >= 0
 | 
		
	
		
			
			| 222 |  | - *
 | 
		
	
		
			
			| 223 |  | - * and
 | 
		
	
		
			
			| 224 |  | - *
 | 
		
	
		
			
			| 225 |  | - *   0 <= ( r'.2^k + xl - dl.q' )	from (15a)
 | 
		
	
		
			
			| 226 |  | - *
 | 
		
	
		
			
			| 227 |  | - * case (b):
 | 
		
	
		
			
			| 228 |  | - *
 | 
		
	
		
			
			| 229 |  | - *   dl.q' > ( r'.2^k + xl )						(15b)
 | 
		
	
		
			
			| 230 |  | - *   
 | 
		
	
		
			
			| 231 |  | - * Express
 | 
		
	
		
			
			| 232 |  | - *
 | 
		
	
		
			
			| 233 |  | - *  x = d.(q'-1) + ( r'.2^k + xl ) + ( d - dl.q' )
 | 
		
	
		
			
			| 234 |  | - *  
 | 
		
	
		
			
			| 235 |  | - *   
 | 
		
	
		
			
			| 236 |  | - * (missing)
 | 
		
	
		
			
			| 237 |  | - *
 | 
		
	
		
			
			| 238 |  | - *
 | 
		
	
		
			
			| 239 |  | - * special case: k = 32 cannot be handled with shifts
 | 
		
	
		
			
			| 240 |  | - *
 | 
		
	
		
			
			| 241 |  | - * (missing)
 | 
		
	
		
			
			| 242 |  | - * 
 | 
		
	
		
			
			| 243 |  | - */
 | 
		
	
		
			
			| 244 |  | -
 | 
		
	
		
			
			| 245 |  | -#include <stdint.h>
 | 
		
	
		
			
			| 246 |  | -#include <assert.h>
 | 
		
	
		
			
			| 247 |  | -
 | 
		
	
		
			
			| 248 |  | -typedef uint64_t UDItype;
 | 
		
	
		
			
			| 249 |  | -
 | 
		
	
		
			
			| 250 |  | -struct uint64 {
 | 
		
	
		
			
			| 251 |  | -	uint32_t l;
 | 
		
	
		
			
			| 252 |  | -	uint32_t h;
 | 
		
	
		
			
			| 253 |  | -};
 | 
		
	
		
			
			| 254 |  | -
 | 
		
	
		
			
			| 255 |  | -static inline void udivmod64_lo ( const struct uint64 *x,
 | 
		
	
		
			
			| 256 |  | -				  const struct uint64 *d,
 | 
		
	
		
			
			| 257 |  | -				  struct uint64 *q,
 | 
		
	
		
			
			| 258 |  | -				  struct uint64 *r ) {
 | 
		
	
		
			
			| 259 |  | -	uint32_t r_dash;
 | 
		
	
		
			
			| 260 |  | -
 | 
		
	
		
			
			| 261 |  | -	q->h = 0;
 | 
		
	
		
			
			| 262 |  | -	r->h = 0;
 | 
		
	
		
			
			| 263 |  | -	r_dash = x->h;
 | 
		
	
		
			
			| 264 |  | -
 | 
		
	
		
			
			| 265 |  | -	if ( x->h >= d->l ) {
 | 
		
	
		
			
			| 266 |  | -		__asm__ ( "divl %2"
 | 
		
	
		
			
			| 267 |  | -			  : "=&a" ( q->h ), "=&d" ( r_dash )
 | 
		
	
		
			
			| 268 |  | -			  : "g" ( d->l ), "0" ( x->h ), "1" ( 0 ) );
 | 
		
	
		
			
			| 269 |  | -	}
 | 
		
	
		
			
			| 270 |  | -
 | 
		
	
		
			
			| 271 |  | -	__asm__ ( "divl %2"
 | 
		
	
		
			
			| 272 |  | -		  : "=&a" ( q->l ), "=&d" ( r->l )
 | 
		
	
		
			
			| 273 |  | -		  : "g" ( d->l ), "0" ( x->l ), "1" ( r_dash ) );
 | 
		
	
		
			
			| 274 |  | -}
 | 
		
	
		
			
			| 275 |  | -
 | 
		
	
		
			
			| 276 |  | -void udivmod64 ( const struct uint64 *x,
 | 
		
	
		
			
			| 277 |  | -			const struct uint64 *d,
 | 
		
	
		
			
			| 278 |  | -			struct uint64 *q,
 | 
		
	
		
			
			| 279 |  | -			struct uint64 *r ) {
 | 
		
	
		
			
			| 280 |  | -
 | 
		
	
		
			
			| 281 |  | -	if ( d->h == 0 ) {
 | 
		
	
		
			
			| 282 |  | -		udivmod64_lo ( x, d, q, r );
 | 
		
	
		
			
			| 283 |  | -	} else {
 | 
		
	
		
			
			| 284 |  | -		assert ( 0 );
 | 
		
	
		
			
			| 285 |  | -		while ( 1 ) {};
 | 
		
	
		
			
			| 286 |  | -	}	
 | 
		
	
		
			
			| 287 |  | -}
 | 
		
	
		
			
			| 288 |  | -
 | 
		
	
		
			
			| 289 |  | -/**
 | 
		
	
		
			
			| 290 |  | - * 64-bit division with remainder
 | 
		
	
		
			
			| 291 |  | - *
 | 
		
	
		
			
			| 292 |  | - * @v x			Dividend
 | 
		
	
		
			
			| 293 |  | - * @v d			Divisor
 | 
		
	
		
			
			| 294 |  | - * @ret r		Remainder
 | 
		
	
		
			
			| 295 |  | - * @ret q		Quotient
 | 
		
	
		
			
			| 296 |  | - */
 | 
		
	
		
			
			| 297 |  | -UDItype __udivmoddi4 ( UDItype x, UDItype d, UDItype *r ) {
 | 
		
	
		
			
			| 298 |  | -	UDItype q;
 | 
		
	
		
			
			| 299 |  | -	UDItype *_x = &x;
 | 
		
	
		
			
			| 300 |  | -	UDItype *_d = &d;
 | 
		
	
		
			
			| 301 |  | -	UDItype *_q = &q;
 | 
		
	
		
			
			| 302 |  | -	UDItype *_r = r;
 | 
		
	
		
			
			| 303 |  | -
 | 
		
	
		
			
			| 304 |  | -	udivmod64 ( ( struct uint64 * ) _x, ( struct uint64 * ) _d,
 | 
		
	
		
			
			| 305 |  | -		    ( struct uint64 * ) _q, ( struct uint64 * ) _r );
 | 
		
	
		
			
			| 306 |  | -
 | 
		
	
		
			
			| 307 |  | -	assert ( ( x == ( ( d * q ) + (*r) ) ) );
 | 
		
	
		
			
			| 308 |  | -	assert ( (*r) < d );
 | 
		
	
		
			
			| 309 |  | -
 | 
		
	
		
			
			| 310 |  | -	return q;
 | 
		
	
		
			
			| 311 |  | -}
 | 
		
	
		
			
			| 312 |  | -
 | 
		
	
		
			
			| 313 |  | -/**
 | 
		
	
		
			
			| 314 |  | - * 64-bit division
 | 
		
	
		
			
			| 315 |  | - *
 | 
		
	
		
			
			| 316 |  | - * @v x			Dividend
 | 
		
	
		
			
			| 317 |  | - * @v d			Divisor
 | 
		
	
		
			
			| 318 |  | - * @ret q		Quotient
 | 
		
	
		
			
			| 319 |  | - */
 | 
		
	
		
			
			| 320 |  | -UDItype __udivdi3 ( UDItype x, UDItype d ) {
 | 
		
	
		
			
			| 321 |  | -	UDItype r;
 | 
		
	
		
			
			| 322 |  | -	return __udivmoddi4 ( x, d, &r );
 | 
		
	
		
			
			| 323 |  | -}
 | 
		
	
		
			
			| 324 |  | -
 | 
		
	
		
			
			| 325 |  | -/**
 | 
		
	
		
			
			| 326 |  | - * 64-bit modulus
 | 
		
	
		
			
			| 327 |  | - *
 | 
		
	
		
			
			| 328 |  | - * @v x			Dividend
 | 
		
	
		
			
			| 329 |  | - * @v d			Divisor
 | 
		
	
		
			
			| 330 |  | - * @ret q		Quotient
 | 
		
	
		
			
			| 331 |  | - */
 | 
		
	
		
			
			| 332 |  | -UDItype __umoddi3 ( UDItype x, UDItype d ) {
 | 
		
	
		
			
			| 333 |  | -	UDItype r;
 | 
		
	
		
			
			| 334 |  | -	__udivmoddi4 ( x, d, &r );
 | 
		
	
		
			
			| 335 |  | -	return r;
 | 
		
	
		
			
			| 336 |  | -}
 |