1+ /**
2+ * detect_product_overflow.c
3+ * detect_product_overflow_u64 detects numeric overflow in the multiplication
4+ * of two uint64_t numbers without relying on potentially non-portable
5+ * 128-bit integer types.
6+ *
7+ * Written in 2019 by Ben Tesch.
8+ * Originally distributed at https://github.com/slugrustle/numerical_routines
9+ *
10+ * To the extent possible under law, the author has dedicated all copyright
11+ * and related and neighboring rights to this software to the public domain
12+ * worldwide.This software is distributed without any warranty.
13+ * The text of the CC0 Public Domain Dedication should be reproduced at the
14+ * end of this file. If not, see http ://creativecommons.org/publicdomain/zero/1.0/
15+ */
16+
17+ #include "detect_product_overflow.h"
18+
19+ /**
20+ * Returns true if the product a * b would overflow the range
21+ * of a uin64_t and false otherwise.
22+ */
23+ bool detect_product_overflow_u64 (const uint64_t a , const uint64_t b ) {
24+ /**
25+ * a * b = 2^64 * (a_hi * b_hi) +
26+ * 2^32 * (a_hi * b_lo + a_lo * b_hi) +
27+ * a_lo * b_lo
28+ * All of the products a_hi*b_hi, a_hi*b_lo,
29+ * a_lo*b_hi, and a_lo*b_lo will be on the range
30+ * [0,2^64-2^33+1].
31+ */
32+ uint64_t a_hi = (a & 0xFFFFFFFF00000000ull ) >> 32 ;
33+ uint64_t a_lo = a & 0x00000000FFFFFFFFull ;
34+ uint64_t b_hi = (b & 0xFFFFFFFF00000000ull ) >> 32 ;
35+ uint64_t b_lo = b & 0x00000000FFFFFFFFull ;
36+
37+ if (a_hi * b_hi > 0ull ) return true;
38+ /**
39+ * Now we know that a_hi * b_hi == 0.
40+ * Consequently,
41+ * a * b = 2^32 * (a_hi * b_lo + a_lo * b_hi) +
42+ * a_lo * b_lo
43+ */
44+
45+ uint64_t mid_prod_1 = a_hi * b_lo ;
46+ uint64_t mid_prod_2 = a_lo * b_hi ;
47+
48+ if (UINT64_MAX - mid_prod_2 < mid_prod_1 ) return true;
49+ /* Now we know that mid_prod_1 + mid_prod_2 <= UINT64_MAX. */
50+ uint64_t mid_prod = mid_prod_1 + mid_prod_2 ;
51+
52+ if (mid_prod >= (1ull << 32 )) return true;
53+ /* Now we know that 2^32 * mid_prod < UINT64_MAX. */
54+ if (UINT64_MAX - a_lo * b_lo < mid_prod << 32 ) return true;
55+
56+ return false;
57+ }
58+
59+ /*
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