p256_64.h | Explore in Territory

#include <openssl/base.h>
#include "../../crypto/internal.h"
#if !defined(OPENSSL_NO_ASM) && defined(__GNUC__) && defined(__x86_64__)
void fiat_p256_adx_mul(uint64_t*, const uint64_t*, const uint64_t*);
void fiat_p256_adx_sqr(uint64_t*, const uint64_t*);
#endif

/* Autogenerated: 'src/ExtractionOCaml/word_by_word_montgomery' --inline --static --use-value-barrier p256 64 '2^256 - 2^224 + 2^192 + 2^96 - 1' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp */
/* curve description: p256 */
/* machine_wordsize = 64 (from "64") */
/* requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp */
/* m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 2^96 - 1") */
/*                                                                    */
/* NOTE: In addition to the bounds specified above each function, all */
/*   functions synthesized for this Montgomery arithmetic require the */
/*   input to be strictly less than the prime modulus (m), and also   */
/*   require the input to be in the unique saturated representation.  */
/*   All functions also ensure that these two properties are true of  */
/*   return values.                                                   */
/*  */
/* Computed values: */
/*   eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) */
/*   bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) */
/*   twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in */
/*                            if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 */

#include <stdint.h>
fiat_p256_uint1;
fiat_p256_int1;
#if defined(__GNUC__) || defined(__clang__)
#define FIAT_P256_FIAT_EXTENSION …
#define FIAT_P256_FIAT_INLINE …
#else
#define FIAT_P256_FIAT_EXTENSION
#define FIAT_P256_FIAT_INLINE
#endif

FIAT_P256_FIAT_EXTENSION fiat_p256_int128;
FIAT_P256_FIAT_EXTENSION fiat_p256_uint128;

/* The type fiat_p256_montgomery_domain_field_element is a field element in the Montgomery domain. */
/* Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */
fiat_p256_montgomery_domain_field_element;

/* The type fiat_p256_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain. */
/* Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] */
fiat_p256_non_montgomery_domain_field_element;

#if (-1 & 3) != 3
#error "This code only works on a two's complement system"
#endif

#if !defined(FIAT_P256_NO_ASM) && (defined(__GNUC__) || defined(__clang__))
static __inline__ uint64_t fiat_p256_value_barrier_u64(uint64_t a) { … }
#else
#define fiat_p256_value_barrier_u64 …
#endif


/*
 * The function fiat_p256_addcarryx_u64 is an addition with carry.
 *
 * Postconditions:
 *   out1 = (arg1 + arg2 + arg3) mod 2^64
 *   out2 = ⌊(arg1 + arg2 + arg3) / 2^64⌋
 *
 * Input Bounds:
 *   arg1: [0x0 ~> 0x1]
 *   arg2: [0x0 ~> 0xffffffffffffffff]
 *   arg3: [0x0 ~> 0xffffffffffffffff]
 * Output Bounds:
 *   out1: [0x0 ~> 0xffffffffffffffff]
 *   out2: [0x0 ~> 0x1]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_addcarryx_u64(uint64_t* out1, fiat_p256_uint1* out2, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) { … }

/*
 * The function fiat_p256_subborrowx_u64 is a subtraction with borrow.
 *
 * Postconditions:
 *   out1 = (-arg1 + arg2 + -arg3) mod 2^64
 *   out2 = -⌊(-arg1 + arg2 + -arg3) / 2^64⌋
 *
 * Input Bounds:
 *   arg1: [0x0 ~> 0x1]
 *   arg2: [0x0 ~> 0xffffffffffffffff]
 *   arg3: [0x0 ~> 0xffffffffffffffff]
 * Output Bounds:
 *   out1: [0x0 ~> 0xffffffffffffffff]
 *   out2: [0x0 ~> 0x1]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_subborrowx_u64(uint64_t* out1, fiat_p256_uint1* out2, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) { … }

/*
 * The function fiat_p256_mulx_u64 is a multiplication, returning the full double-width result.
 *
 * Postconditions:
 *   out1 = (arg1 * arg2) mod 2^64
 *   out2 = ⌊arg1 * arg2 / 2^64⌋
 *
 * Input Bounds:
 *   arg1: [0x0 ~> 0xffffffffffffffff]
 *   arg2: [0x0 ~> 0xffffffffffffffff]
 * Output Bounds:
 *   out1: [0x0 ~> 0xffffffffffffffff]
 *   out2: [0x0 ~> 0xffffffffffffffff]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) { … }

/*
 * The function fiat_p256_cmovznz_u64 is a single-word conditional move.
 *
 * Postconditions:
 *   out1 = (if arg1 = 0 then arg2 else arg3)
 *
 * Input Bounds:
 *   arg1: [0x0 ~> 0x1]
 *   arg2: [0x0 ~> 0xffffffffffffffff]
 *   arg3: [0x0 ~> 0xffffffffffffffff]
 * Output Bounds:
 *   out1: [0x0 ~> 0xffffffffffffffff]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_cmovznz_u64(uint64_t* out1, fiat_p256_uint1 arg1, uint64_t arg2, uint64_t arg3) { … }

/*
 * The function fiat_p256_mul multiplies two field elements in the Montgomery domain.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 *   0 ≤ eval arg2 < m
 * Postconditions:
 *   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m
 *   0 ≤ eval out1 < m
 *
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_mul(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) { … }

/*
 * The function fiat_p256_square squares a field element in the Montgomery domain.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 * Postconditions:
 *   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m
 *   0 ≤ eval out1 < m
 *
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_square(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) { … }

/*
 * The function fiat_p256_add adds two field elements in the Montgomery domain.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 *   0 ≤ eval arg2 < m
 * Postconditions:
 *   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m
 *   0 ≤ eval out1 < m
 *
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_add(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) { … }

/*
 * The function fiat_p256_sub subtracts two field elements in the Montgomery domain.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 *   0 ≤ eval arg2 < m
 * Postconditions:
 *   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m
 *   0 ≤ eval out1 < m
 *
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_sub(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1, const fiat_p256_montgomery_domain_field_element arg2) { … }

/*
 * The function fiat_p256_opp negates a field element in the Montgomery domain.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 * Postconditions:
 *   eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m
 *   0 ≤ eval out1 < m
 *
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_opp(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) { … }

/*
 * The function fiat_p256_from_montgomery translates a field element out of the Montgomery domain.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 * Postconditions:
 *   eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m
 *   0 ≤ eval out1 < m
 *
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_from_montgomery(fiat_p256_non_montgomery_domain_field_element out1, const fiat_p256_montgomery_domain_field_element arg1) { … }

/*
 * The function fiat_p256_to_montgomery translates a field element into the Montgomery domain.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 * Postconditions:
 *   eval (from_montgomery out1) mod m = eval arg1 mod m
 *   0 ≤ eval out1 < m
 *
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_to_montgomery(fiat_p256_montgomery_domain_field_element out1, const fiat_p256_non_montgomery_domain_field_element arg1) { … }

/*
 * The function fiat_p256_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 * Postconditions:
 *   out1 = 0 ↔ eval (from_montgomery arg1) mod m = 0
 *
 * Input Bounds:
 *   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 * Output Bounds:
 *   out1: [0x0 ~> 0xffffffffffffffff]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_nonzero(uint64_t* out1, const uint64_t arg1[4]) { … }

/*
 * The function fiat_p256_selectznz is a multi-limb conditional select.
 *
 * Postconditions:
 *   eval out1 = (if arg1 = 0 then eval arg2 else eval arg3)
 *
 * Input Bounds:
 *   arg1: [0x0 ~> 0x1]
 *   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 *   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 * Output Bounds:
 *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_selectznz(uint64_t out1[4], fiat_p256_uint1 arg1, const uint64_t arg2[4], const uint64_t arg3[4]) { … }

/*
 * The function fiat_p256_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
 *
 * Preconditions:
 *   0 ≤ eval arg1 < m
 * Postconditions:
 *   out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
 *
 * Input Bounds:
 *   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 * Output Bounds:
 *   out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_to_bytes(uint8_t out1[32], const uint64_t arg1[4]) { … }

/*
 * The function fiat_p256_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
 *
 * Preconditions:
 *   0 ≤ bytes_eval arg1 < m
 * Postconditions:
 *   eval out1 mod m = bytes_eval arg1 mod m
 *   0 ≤ eval out1 < m
 *
 * Input Bounds:
 *   arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]]
 * Output Bounds:
 *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_from_bytes(uint64_t out1[4], const uint8_t arg1[32]) { … }

/*
 * The function fiat_p256_set_one returns the field element one in the Montgomery domain.
 *
 * Postconditions:
 *   eval (from_montgomery out1) mod m = 1 mod m
 *   0 ≤ eval out1 < m
 *
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_set_one(fiat_p256_montgomery_domain_field_element out1) { … }

/*
 * The function fiat_p256_msat returns the saturated representation of the prime modulus.
 *
 * Postconditions:
 *   twos_complement_eval out1 = m
 *   0 ≤ eval out1 < m
 *
 * Output Bounds:
 *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_msat(uint64_t out1[5]) { … }

/*
 * The function fiat_p256_divstep computes a divstep.
 *
 * Preconditions:
 *   0 ≤ eval arg4 < m
 *   0 ≤ eval arg5 < m
 * Postconditions:
 *   out1 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then 1 - arg1 else 1 + arg1)
 *   twos_complement_eval out2 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then twos_complement_eval arg3 else twos_complement_eval arg2)
 *   twos_complement_eval out3 = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then ⌊(twos_complement_eval arg3 - twos_complement_eval arg2) / 2⌋ else ⌊(twos_complement_eval arg3 + (twos_complement_eval arg3 mod 2) * twos_complement_eval arg2) / 2⌋)
 *   eval (from_montgomery out4) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (2 * eval (from_montgomery arg5)) mod m else (2 * eval (from_montgomery arg4)) mod m)
 *   eval (from_montgomery out5) mod m = (if 0 < arg1 ∧ (twos_complement_eval arg3) is odd then (eval (from_montgomery arg4) - eval (from_montgomery arg4)) mod m else (eval (from_montgomery arg5) + (twos_complement_eval arg3 mod 2) * eval (from_montgomery arg4)) mod m)
 *   0 ≤ eval out5 < m
 *   0 ≤ eval out5 < m
 *   0 ≤ eval out2 < m
 *   0 ≤ eval out3 < m
 *
 * Input Bounds:
 *   arg1: [0x0 ~> 0xffffffffffffffff]
 *   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 *   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 *   arg4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 *   arg5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 * Output Bounds:
 *   out1: [0x0 ~> 0xffffffffffffffff]
 *   out2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 *   out3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 *   out4: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 *   out5: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_divstep(uint64_t* out1, uint64_t out2[5], uint64_t out3[5], uint64_t out4[4], uint64_t out5[4], uint64_t arg1, const uint64_t arg2[5], const uint64_t arg3[5], const uint64_t arg4[4], const uint64_t arg5[4]) { … }

/*
 * The function fiat_p256_divstep_precomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).
 *
 * Postconditions:
 *   eval (from_montgomery out1) = ⌊(m - 1) / 2⌋^(if ⌊log2 m⌋ + 1 < 46 then ⌊(49 * (⌊log2 m⌋ + 1) + 80) / 17⌋ else ⌊(49 * (⌊log2 m⌋ + 1) + 57) / 17⌋)
 *   0 ≤ eval out1 < m
 *
 * Output Bounds:
 *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
 */
static FIAT_P256_FIAT_INLINE void fiat_p256_divstep_precomp(uint64_t out1[4]) { … }
chromium/third_party/boringssl/src/third_party/fiat/p256_64.h
