1 /* original source code from Hackers-Delight
2 https://github.com/hcs0/Hackers-Delight
4 /* This divides an n-word dividend by an m-word divisor, giving an
5 n-m+1-word quotient and m-word remainder. The bignums are in arrays of
6 words. Here a "word" is 32 bits. This routine is designed for a 64-bit
7 machine which has a 64/64 division instruction. */
10 #include <stdlib.h> //To define "exit", req'd by XLC.
12 #define max(x, y) ((x) > (y) ? (x) : (y))
17 if (x
== 0) return(32);
19 if (x
<= 0x0000FFFF) {n
= n
+16; x
= x
<<16;}
20 if (x
<= 0x00FFFFFF) {n
= n
+ 8; x
= x
<< 8;}
21 if (x
<= 0x0FFFFFFF) {n
= n
+ 4; x
= x
<< 4;}
22 if (x
<= 0x3FFFFFFF) {n
= n
+ 2; x
= x
<< 2;}
23 if (x
<= 0x7FFFFFFF) {n
= n
+ 1;}
27 void dumpit(char *msg
, int n
, unsigned v
[]) {
30 for (i
= n
-1; i
>= 0; i
--) printf(" %08x", v
[i
]);
34 /* q[0], r[0], u[0], and v[0] contain the LEAST significant words.
35 (The sequence is in little-endian order).
37 This is a fairly precise implementation of Knuth's Algorithm D, for a
38 binary computer with base b = 2**32. The caller supplies:
39 1. Space q for the quotient, m - n + 1 words (at least one).
40 2. Space r for the remainder (optional), n words.
41 3. The dividend u, m words, m >= 1.
42 4. The divisor v, n words, n >= 2.
43 The most significant digit of the divisor, v[n-1], must be nonzero. The
44 dividend u may have leading zeros; this just makes the algorithm take
45 longer and makes the quotient contain more leading zeros. A value of
46 NULL may be given for the address of the remainder to signify that the
47 caller does not want the remainder.
48 The program does not alter the input parameters u and v.
49 The quotient and remainder returned may have leading zeros. The
50 function itself returns a value of 0 for success and 1 for invalid
51 parameters (e.g., division by 0).
52 For now, we must have m >= n. Knuth's Algorithm D also requires
53 that the dividend be at least as long as the divisor. (In his terms,
54 m >= 0 (unstated). Therefore m+n >= n.) */
56 int divmnu(unsigned q
[], unsigned r
[],
57 const unsigned u
[], const unsigned v
[],
60 const unsigned long long b
= 4294967296LL; // Number base (2**32).
61 unsigned *un
, *vn
; // Normalized form of u, v.
62 unsigned long long qhat
; // Estimated quotient digit.
63 unsigned long long rhat
; // A remainder.
64 unsigned long long p
; // Product of two digits.
68 if (m
< n
|| n
<= 0 || v
[n
-1] == 0)
69 return 1; // Return if invalid param.
71 if (n
== 1) { // Take care of
72 k
= 0; // the case of a
73 for (j
= m
- 1; j
>= 0; j
--) { // single-digit
74 q
[j
] = (k
*b
+ u
[j
])/v
[0]; // divisor here.
75 k
= (k
*b
+ u
[j
]) - q
[j
]*v
[0];
77 if (r
!= NULL
) r
[0] = k
;
81 /* Normalize by shifting v left just enough so that its high-order
82 bit is on, and shift u left the same amount. We may have to append a
83 high-order digit on the dividend; we do that unconditionally. */
85 s
= nlz(v
[n
-1]); // 0 <= s <= 31.
86 vn
= (unsigned *)alloca(4*n
);
87 for (i
= n
- 1; i
> 0; i
--)
88 vn
[i
] = (v
[i
] << s
) | ((unsigned long long)v
[i
-1] >> (32-s
));
91 un
= (unsigned *)alloca(4*(m
+ 1));
92 un
[m
] = (unsigned long long)u
[m
-1] >> (32-s
);
93 for (i
= m
- 1; i
> 0; i
--)
94 un
[i
] = (u
[i
] << s
) | ((unsigned long long)u
[i
-1] >> (32-s
));
97 for (j
= m
- n
; j
>= 0; j
--) { // Main loop.
98 // Compute estimate qhat of q[j].
99 qhat
= (un
[j
+n
]*b
+ un
[j
+n
-1])/vn
[n
-1];
100 rhat
= (un
[j
+n
]*b
+ un
[j
+n
-1]) - qhat
*vn
[n
-1];
102 if (qhat
>= b
|| qhat
*vn
[n
-2] > b
*rhat
+ un
[j
+n
-2])
104 rhat
= rhat
+ vn
[n
-1];
105 if (rhat
< b
) goto again
;
108 // Multiply and subtract.
111 for (i
= 0; i
< n
; i
++) {
113 t
= un
[i
+j
] - k
- (p
& 0xFFFFFFFFLL
);
115 k
= (p
>> 32) - (t
>> 32);
118 for (i
= 0; i
< n
; i
++) {
120 unsigned long long sum
;
121 p
= ((unsigned long long)un
[i
+j
])+ ~(qhat
*vn
[i
]) + k
;
123 if (((unsigned long long)k
) <= 1) rhi
+= 1;
125 un
[i
+j
] = sum
& 0xffffffff;
131 q
[j
] = qhat
; // Store quotient digit.
132 if (t
< 0) { // If we subtracted too
133 q
[j
] = q
[j
] - 1; // much, add back.
135 for (i
= 0; i
< n
; i
++) {
136 t
= (unsigned long long)un
[i
+j
] + vn
[i
] + k
;
140 un
[j
+n
] = un
[j
+n
] + k
;
143 // If the caller wants the remainder, unnormalize
144 // it and pass it back.
146 for (i
= 0; i
< n
-1; i
++)
147 r
[i
] = (un
[i
] >> s
) | ((unsigned long long)un
[i
+1] << (32-s
));
148 r
[n
-1] = un
[n
-1] >> s
;
155 void check(unsigned q
[], unsigned r
[],
156 unsigned u
[], unsigned v
[],
158 unsigned cq
[], unsigned cr
[]) {
161 szq
= max(m
- n
+ 1, 1);
162 for (i
= 0; i
< szq
; i
++) {
165 dumpit("Error, dividend u =", m
, u
);
166 dumpit(" divisor v =", n
, v
);
167 dumpit("For quotient, got:", m
-n
+1, q
);
168 dumpit(" Should get:", m
-n
+1, cq
);
172 for (i
= 0; i
< n
; i
++) {
175 dumpit("Error, dividend u =", m
, u
);
176 dumpit(" divisor v =", n
, v
);
177 dumpit("For remainder, got:", n
, r
);
178 dumpit(" Should get:", n
, cr
);
186 static unsigned test
[] = {
187 // m, n, u..., v..., cq..., cr....
188 1, 1, 3, 0, 1, 1, // Error, divide by 0.
189 1, 2, 7, 1,3, 0, 7,0, // Error, n > m.
190 2, 2, 0,0, 1,0, 0, 0,0, // Error, incorrect remainder cr.
194 1, 1, 0, 0xffffffff, 0, 0,
195 1, 1, 0xffffffff, 1, 0xffffffff, 0,
196 1, 1, 0xffffffff, 0xffffffff, 1, 0,
197 1, 1, 0xffffffff, 3, 0x55555555, 0,
198 2, 1, 0xffffffff,0xffffffff, 1, 0xffffffff,0xffffffff, 0,
199 2, 1, 0xffffffff,0xffffffff, 0xffffffff, 1,1, 0,
200 2, 1, 0xffffffff,0xfffffffe, 0xffffffff, 0xffffffff,0, 0xfffffffe,
201 2, 1, 0x00005678,0x00001234, 0x00009abc, 0x1e1dba76,0, 0x6bd0,
202 2, 2, 0,0, 0,1, 0, 0,0,
203 2, 2, 0,7, 0,3, 2, 0,1,
204 2, 2, 5,7, 0,3, 2, 5,1,
205 2, 2, 0,6, 0,2, 3, 0,0,
206 1, 1, 0x80000000, 0x40000001, 0x00000001, 0x3fffffff,
207 2, 1, 0x00000000,0x80000000, 0x40000001, 0xfffffff8,0x00000001, 0x00000008,
208 2, 2, 0x00000000,0x80000000, 0x00000001,0x40000000, 0x00000001, 0xffffffff,0x3fffffff,
209 2, 2, 0x0000789a,0x0000bcde, 0x0000789a,0x0000bcde, 1, 0,0,
210 2, 2, 0x0000789b,0x0000bcde, 0x0000789a,0x0000bcde, 1, 1,0,
211 2, 2, 0x00007899,0x0000bcde, 0x0000789a,0x0000bcde, 0, 0x00007899,0x0000bcde,
212 2, 2, 0x0000ffff,0x0000ffff, 0x0000ffff,0x0000ffff, 1, 0,0,
213 2, 2, 0x0000ffff,0x0000ffff, 0x00000000,0x00000001, 0x0000ffff, 0x0000ffff,0,
214 3, 2, 0x000089ab,0x00004567,0x00000123, 0x00000000,0x00000001, 0x00004567,0x00000123, 0x000089ab,0,
215 3, 2, 0x00000000,0x0000fffe,0x00008000, 0x0000ffff,0x00008000, 0xffffffff,0x00000000, 0x0000ffff,0x00007fff, // Shows that first qhat can = b + 1.
216 3, 3, 0x00000003,0x00000000,0x80000000, 0x00000001,0x00000000,0x20000000, 0x00000003, 0,0,0x20000000, // Adding back step req'd.
217 3, 3, 0x00000003,0x00000000,0x00008000, 0x00000001,0x00000000,0x00002000, 0x00000003, 0,0,0x00002000, // Adding back step req'd.
218 4, 3, 0,0,0x00008000,0x00007fff, 1,0,0x00008000, 0xfffe0000,0, 0x00020000,0xffffffff,0x00007fff, // Add back req'd.
219 4, 3, 0,0x0000fffe,0,0x00008000, 0x0000ffff,0,0x00008000, 0xffffffff,0, 0x0000ffff,0xffffffff,0x00007fff, // Shows that mult-sub quantity cannot be treated as signed.
220 4, 3, 0,0xfffffffe,0,0x80000000, 0x0000ffff,0,0x80000000, 0x00000000,1, 0x00000000,0xfffeffff,0x00000000, // Shows that mult-sub quantity cannot be treated as signed.
221 4, 3, 0,0xfffffffe,0,0x80000000, 0xffffffff,0,0x80000000, 0xffffffff,0, 0xffffffff,0xffffffff,0x7fffffff, // Shows that mult-sub quantity cannot be treated as signed.
223 int i
, n
, m
, ncases
, f
;
224 unsigned q
[10], r
[10];
225 unsigned *u
, *v
, *cq
, *cr
;
230 while (i
< sizeof(test
)/4) {
236 cr
= &test
[i
+2+m
+n
+max(m
-n
+1, 1)];
238 f
= divmnu(q
, r
, u
, v
, m
, n
);
240 dumpit("Error return code for dividend u =", m
, u
);
241 dumpit(" divisor v =", n
, v
);
245 check(q
, r
, u
, v
, m
, n
, cq
, cr
);
246 i
= i
+ 2 + m
+ n
+ max(m
-n
+1, 1) + n
;
250 printf("%d errors out of %d cases; there should be 3.\n", errors
, ncases
);