github.com/ethereum/go-ethereum@v1.16.1/crypto/secp256k1/libsecp256k1/src/field_5x52.h (about)

     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 */