1  /***********************************************************************
 2   * Copyright (c) 2013, 2014 Pieter Wuille                              *
 3   * Distributed under the MIT software license, see the accompanying    *
 4   * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
 5   ***********************************************************************/
 6  
 7  #ifndef SECP256K1_FIELD_REPR_H
 8  #define SECP256K1_FIELD_REPR_H
 9  
10  #include <stdint.h>
11  
12  /** This field implementation represents the value as 5 uint64_t limbs in base
13   *  2^52. */
14  typedef struct {
15     /* A field element f represents the sum(i=0..4, f.n[i] << (i*52)) mod p,
16      * where p is the field modulus, 2^256 - 2^32 - 977.
17      *
18      * The individual limbs f.n[i] can exceed 2^52; the field's magnitude roughly
19      * corresponds to how much excess is allowed. The value
20      * sum(i=0..4, f.n[i] << (i*52)) may exceed p, unless the field element is
21      * normalized. */
22      uint64_t n[5];
23      /*
24       * Magnitude m requires:
25       *     n[i] <= 2 * m * (2^52 - 1) for i=0..3
26       *     n[4] <= 2 * m * (2^48 - 1)
27       *
28       * Normalized requires:
29       *     n[i] <= (2^52 - 1) for i=0..3
30       *     sum(i=0..4, n[i] << (i*52)) < p
31       *     (together these imply n[4] <= 2^48 - 1)
32       */
33      SECP256K1_FE_VERIFY_FIELDS
34  } secp256k1_fe;
35  
36  /* Unpacks a constant into a overlapping multi-limbed FE element. */
37  #define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
38      (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \
39      ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \
40      ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \
41      ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \
42      ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \
43  }
44  
45  typedef struct {
46      uint64_t n[4];
47  } secp256k1_fe_storage;
48  
49  #define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \
50      (d0) | (((uint64_t)(d1)) << 32), \
51      (d2) | (((uint64_t)(d3)) << 32), \
52      (d4) | (((uint64_t)(d5)) << 32), \
53      (d6) | (((uint64_t)(d7)) << 32) \
54  }}
55  
56  #define SECP256K1_FE_STORAGE_CONST_GET(d) \
57      (uint32_t)(d.n[3] >> 32), (uint32_t)d.n[3], \
58      (uint32_t)(d.n[2] >> 32), (uint32_t)d.n[2], \
59      (uint32_t)(d.n[1] >> 32), (uint32_t)d.n[1], \
60      (uint32_t)(d.n[0] >> 32), (uint32_t)d.n[0]
61  
62  #endif /* SECP256K1_FIELD_REPR_H */