1//===-- udivmodti4.c - Implement __udivmodti4 -----------------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8//
9// This file implements __udivmodti4 for the compiler_rt library.
10//
11//===----------------------------------------------------------------------===//
12
13#include "int_lib.h"
14
15#ifdef CRT_HAS_128BIT
16
17// Returns the 128 bit division result by 64 bit. Result must fit in 64 bits.
18// Remainder stored in r.
19// Taken and adjusted from libdivide libdivide_128_div_64_to_64 division
20// fallback. For a correctness proof see the reference for this algorithm
21// in Knuth, Volume 2, section 4.3.1, Algorithm D.
22UNUSED
23static inline du_int udiv128by64to64default(du_int u1, du_int u0, du_int v,
24                                            du_int *r) {
25  const unsigned n_udword_bits = sizeof(du_int) * CHAR_BIT;
26  const du_int b = (1ULL << (n_udword_bits / 2)); // Number base (32 bits)
27  du_int un1, un0;                                // Norm. dividend LSD's
28  du_int vn1, vn0;                                // Norm. divisor digits
29  du_int q1, q0;                                  // Quotient digits
30  du_int un64, un21, un10;                        // Dividend digit pairs
31  du_int rhat;                                    // A remainder
32  si_int s;                                       // Shift amount for normalization
33
34  s = __builtin_clzll(v);
35  if (s > 0) {
36    // Normalize the divisor.
37    v = v << s;
38    un64 = (u1 << s) | (u0 >> (n_udword_bits - s));
39    un10 = u0 << s; // Shift dividend left
40  } else {
41    // Avoid undefined behavior of (u0 >> 64).
42    un64 = u1;
43    un10 = u0;
44  }
45
46  // Break divisor up into two 32-bit digits.
47  vn1 = v >> (n_udword_bits / 2);
48  vn0 = v & 0xFFFFFFFF;
49
50  // Break right half of dividend into two digits.
51  un1 = un10 >> (n_udword_bits / 2);
52  un0 = un10 & 0xFFFFFFFF;
53
54  // Compute the first quotient digit, q1.
55  q1 = un64 / vn1;
56  rhat = un64 - q1 * vn1;
57
58  // q1 has at most error 2. No more than 2 iterations.
59  while (q1 >= b || q1 * vn0 > b * rhat + un1) {
60    q1 = q1 - 1;
61    rhat = rhat + vn1;
62    if (rhat >= b)
63      break;
64  }
65
66  un21 = un64 * b + un1 - q1 * v;
67
68  // Compute the second quotient digit.
69  q0 = un21 / vn1;
70  rhat = un21 - q0 * vn1;
71
72  // q0 has at most error 2. No more than 2 iterations.
73  while (q0 >= b || q0 * vn0 > b * rhat + un0) {
74    q0 = q0 - 1;
75    rhat = rhat + vn1;
76    if (rhat >= b)
77      break;
78  }
79
80  *r = (un21 * b + un0 - q0 * v) >> s;
81  return q1 * b + q0;
82}
83
84static inline du_int udiv128by64to64(du_int u1, du_int u0, du_int v,
85                                     du_int *r) {
86#if defined(__x86_64__)
87  du_int result;
88  __asm__("divq %[v]"
89          : "=a"(result), "=d"(*r)
90          : [ v ] "r"(v), "a"(u0), "d"(u1));
91  return result;
92#else
93  return udiv128by64to64default(u1, u0, v, r);
94#endif
95}
96
97// Effects: if rem != 0, *rem = a % b
98// Returns: a / b
99
100COMPILER_RT_ABI tu_int __udivmodti4(tu_int a, tu_int b, tu_int *rem) {
101  const unsigned n_utword_bits = sizeof(tu_int) * CHAR_BIT;
102  utwords dividend;
103  dividend.all = a;
104  utwords divisor;
105  divisor.all = b;
106  utwords quotient;
107  utwords remainder;
108  if (divisor.all > dividend.all) {
109    if (rem)
110      *rem = dividend.all;
111    return 0;
112  }
113  // When the divisor fits in 64 bits, we can use an optimized path.
114  if (divisor.s.high == 0) {
115    remainder.s.high = 0;
116    if (dividend.s.high < divisor.s.low) {
117      // The result fits in 64 bits.
118      quotient.s.low = udiv128by64to64(dividend.s.high, dividend.s.low,
119                                       divisor.s.low, &remainder.s.low);
120      quotient.s.high = 0;
121    } else {
122      // First, divide with the high part to get the remainder in dividend.s.high.
123      // After that dividend.s.high < divisor.s.low.
124      quotient.s.high = dividend.s.high / divisor.s.low;
125      dividend.s.high = dividend.s.high % divisor.s.low;
126      quotient.s.low = udiv128by64to64(dividend.s.high, dividend.s.low,
127                                       divisor.s.low, &remainder.s.low);
128    }
129    if (rem)
130      *rem = remainder.all;
131    return quotient.all;
132  }
133  // 0 <= shift <= 63.
134  si_int shift =
135      __builtin_clzll(divisor.s.high) - __builtin_clzll(dividend.s.high);
136  divisor.all <<= shift;
137  quotient.s.high = 0;
138  quotient.s.low = 0;
139  for (; shift >= 0; --shift) {
140    quotient.s.low <<= 1;
141    // Branch free version of.
142    // if (dividend.all >= divisor.all)
143    // {
144    //    dividend.all -= divisor.all;
145    //    carry = 1;
146    // }
147    const ti_int s =
148        (ti_int)(divisor.all - dividend.all - 1) >> (n_utword_bits - 1);
149    quotient.s.low |= s & 1;
150    dividend.all -= divisor.all & s;
151    divisor.all >>= 1;
152  }
153  if (rem)
154    *rem = dividend.all;
155  return quotient.all;
156}
157
158#endif // CRT_HAS_128BIT
159