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/*****************************************************************
*
* The Compcert verified compiler
*
* Xavier Leroy, INRIA Paris-Rocquencourt
*
* Copyright (c) 2013 Institut National de Recherche en Informatique et
* en Automatique.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* * Neither the name of the <organization> nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT
* HOLDER> BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
**********************************************************************/
/* Helper functions for 64-bit integer arithmetic. Reference C implementation */
#include <stddef.h>
#include "i64.h"
static unsigned i64_udiv6432(unsigned u1, unsigned u0,
unsigned v, unsigned *r);
static int i64_nlz(unsigned x);
/* Unsigned division and remainder */
unsigned long long i64_udivmod(unsigned long long n,
unsigned long long d,
unsigned long long * rp)
{
unsigned dh = d >> 32;
if (dh == 0) {
unsigned nh = n >> 32;
if (nh == 0) {
/* Special case 32 / 32 */
unsigned nl = n;
unsigned dl = d;
*rp = (unsigned long long) (nl % dl);
return (unsigned long long) (nl / dl);
} else {
/* Special case 64 / 32 */
unsigned nl = n;
unsigned dl = d;
unsigned qh = nh / dl;
unsigned rl;
unsigned ql = i64_udiv6432(nh % dl, nl, dl, &rl);
*rp = (unsigned long long) rl; /* high word of remainder is 0 */
return ((unsigned long long) qh) << 32 | ql;
}
} else {
/* General case 64 / 64 */
unsigned dl = d;
/* Scale N and D down, giving N' and D' such that 2^31 <= D' < 2^32 */
int s = 32 - i64_nlz(dh); /* shift amount, between 1 and 32 */
unsigned long long np = i64_shr(n, s);
unsigned dp = (unsigned) i64_shr(d, s);
/* Divide N' by D' to get an approximate quotient Q */
unsigned q = i64_udiv6432(np >> 32, np, dp, NULL);
again: ;
/* Tentative quotient Q is either correct or one too high */
/* Compute Q * D, checking for overflow */
unsigned long long p1 = (unsigned long long) dl * q;
unsigned long long p2 = (unsigned long long) (dh * q) << 32;
unsigned long long p = p1 + p2;
if (p < p1) {
/* Overflow occurred: adjust Q down by 1 and redo check */
q = q - 1; goto again;
}
/* Compute remainder R */
unsigned long long r = n - p;
if (n < p) {
/* Q is one too high, adjust Q down by 1 and R up by D */
q = q - 1; r = r + d;
}
*rp = r;
return (unsigned long long) q;
}
}
/* Unsigned division and remainder for 64 bits divided by 32 bits. */
/* This is algorithm "divlu" from _Hacker's Delight_, fig 9.3 */
static unsigned i64_udiv6432(unsigned u1, unsigned u0,
unsigned v, unsigned *r)
{
const unsigned b = 65536; // Number base (16 bits).
unsigned un1, un0, // Norm. dividend LSD's.
vn1, vn0, // Norm. divisor digits.
q1, q0, // Quotient digits.
un32, un21, un10,// Divided digit pairs.
rhat; // A remainder.
int s; // Shift amount for norm.
if (u1 >= v) { // If overflow,
if (r != NULL) *r = 0xFFFFFFFFU; // set rem to an impossible value,
return 0xFFFFFFFFU; // and return largest possible quotient.
}
s = i64_nlz(v); // 0 <= s <= 31.
v = v << s; // Normalize divisor.
vn1 = v >> 16; // Break divisor up into
vn0 = v & 0xFFFF; // two 16-bit digits.
un32 = (u1 << s) | ((u0 >> (32 - s)) & (-s >> 31));
un10 = u0 << s; // Shift dividend left.
un1 = un10 >> 16; // Break right half of
un0 = un10 & 0xFFFF; // dividend into two digits.
q1 = un32/vn1; // Compute the first quotient digit, q1.
rhat = un32 - q1*vn1;
again1:
if (q1 >= b || q1*vn0 > b*rhat + un1) {
q1 = q1 - 1;
rhat = rhat + vn1;
if (rhat < b) goto again1;
}
un21 = un32*b + un1 - q1*v; // Multiply and subtract.
q0 = un21/vn1; // Compute the second quotient digit, q0
rhat = un21 - q0*vn1;
again2:
if (q0 >= b || q0*vn0 > b*rhat + un0) {
q0 = q0 - 1;
rhat = rhat + vn1;
if (rhat < b) goto again2;
}
if (r != NULL) *r = (un21*b + un0 - q0*v) >> s;
return q1*b + q0;
}
/* Number of leading zeroes */
static int i64_nlz(unsigned x)
{
if (x == 0) return 32;
int n = 0;
if (x <= 0x0000FFFF) { n += 16; x <<= 16; }
if (x <= 0x00FFFFFF) { n += 8; x <<= 8; }
if (x <= 0x0FFFFFFF) { n += 4; x <<= 4; }
if (x <= 0x3FFFFFFF) { n += 2; x <<= 2; }
if (x <= 0x7FFFFFFF) { n += 1; x <<= 1; }
return n;
}
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