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.
22 UNUSED
23 static 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 
84 static 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 
100 COMPILER_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