758f8f42a33b7946beb4cdd103c5ec013285a0ee
2 * Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
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9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
12 * The above copyright notice and this permission notice shall be
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15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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29 br_i31_montymul(uint32_t *d
, const uint32_t *x
, const uint32_t *y
,
30 const uint32_t *m
, uint32_t m0i
)
33 * Each outer loop iteration computes:
34 * d <- (d + xu*y + f*m) / 2^31
35 * We have xu <= 2^31-1 and f <= 2^31-1.
36 * Thus, if d <= 2*m-1 on input, then:
37 * 2*m-1 + 2*(2^31-1)*m <= (2^32)*m-1
38 * and the new d value is less than 2*m.
40 * We represent d over 31-bit words, with an extra word 'dh'
41 * which can thus be only 0 or 1.
43 size_t len
, len4
, u
, v
;
46 len
= (m
[0] + 31) >> 5;
47 len4
= len
& ~(size_t)3;
50 for (u
= 0; u
< len
; u
++) {
52 * The carry for each operation fits on 32 bits:
54 * xu*y[v+1] <= (2^31-1)*(2^31-1)
55 * f*m[v+1] <= (2^31-1)*(2^31-1)
57 * (2^31-1) + 2*(2^31-1)*(2^31-1) + (2^32-1) = 2^63 - 2^31
58 * After division by 2^31, the new r is then at most 2^32-1
60 * Using a 32-bit carry has performance benefits on 32-bit
61 * systems; however, on 64-bit architectures, we prefer to
62 * keep the carry (r) in a 64-bit register, thus avoiding some
63 * "clear high bits" operations.
73 f
= MUL31_lo((d
[1] + MUL31_lo(x
[u
+ 1], y
[1])), m0i
);
76 for (v
= 0; v
< len4
; v
+= 4) {
79 z
= (uint64_t)d
[v
+ 1] + MUL31(xu
, y
[v
+ 1])
80 + MUL31(f
, m
[v
+ 1]) + r
;
82 d
[v
+ 0] = (uint32_t)z
& 0x7FFFFFFF;
83 z
= (uint64_t)d
[v
+ 2] + MUL31(xu
, y
[v
+ 2])
84 + MUL31(f
, m
[v
+ 2]) + r
;
86 d
[v
+ 1] = (uint32_t)z
& 0x7FFFFFFF;
87 z
= (uint64_t)d
[v
+ 3] + MUL31(xu
, y
[v
+ 3])
88 + MUL31(f
, m
[v
+ 3]) + r
;
90 d
[v
+ 2] = (uint32_t)z
& 0x7FFFFFFF;
91 z
= (uint64_t)d
[v
+ 4] + MUL31(xu
, y
[v
+ 4])
92 + MUL31(f
, m
[v
+ 4]) + r
;
94 d
[v
+ 3] = (uint32_t)z
& 0x7FFFFFFF;
96 for (; v
< len
; v
++) {
99 z
= (uint64_t)d
[v
+ 1] + MUL31(xu
, y
[v
+ 1])
100 + MUL31(f
, m
[v
+ 1]) + r
;
102 d
[v
] = (uint32_t)z
& 0x7FFFFFFF;
106 * Since the new dh can only be 0 or 1, the addition of
107 * the old dh with the carry MUST fit on 32 bits, and
108 * thus can be done into dh itself.
111 d
[len
] = dh
& 0x7FFFFFFF;
116 * We must write back the bit length because it was overwritten in
117 * the loop (not overwriting it would require a test in the loop,
118 * which would yield bigger and slower code).
123 * d[] may still be greater than m[] at that point; notably, the
124 * 'dh' word may be non-zero.
126 br_i31_sub(d
, m
, NEQ(dh
, 0) | NOT(br_i31_sub(d
, m
, 0)));