https://github.com/mit-plv/fiat-crypto
Tip revision: cfaa85b41e93dc84e36ba0cd3328d78748a0cef1 authored by jadep on 07 September 2020, 00:27:24 UTC
Bignum_to_bytes proved; representation working
Bignum_to_bytes proved; representation working
Tip revision: cfaa85b
secp256k1_64.c
/* Autogenerated: src/ExtractionOCaml/word_by_word_montgomery --static --use-value-barrier secp256k1 64 '2^256 - 2^32 - 977' mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes */
/* curve description: secp256k1 */
/* machine_wordsize = 64 (from "64") */
/* requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes */
/* m = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f (from "2^256 - 2^32 - 977") */
/* */
/* 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) */
#include <stdint.h>
typedef unsigned char fiat_secp256k1_uint1;
typedef signed char fiat_secp256k1_int1;
typedef signed __int128 fiat_secp256k1_int128;
typedef unsigned __int128 fiat_secp256k1_uint128;
#if (-1 & 3) != 3
#error "This code only works on a two's complement system"
#endif
#if !defined(FIAT_SECP256K1_NO_ASM) && (defined(__GNUC__) || defined(__clang__))
static __inline__ uint64_t fiat_secp256k1_value_barrier_u64(uint64_t a) {
__asm__("" : "+r"(a) : /* no inputs */);
return a;
}
#else
# define fiat_secp256k1_value_barrier_u64(x) (x)
#endif
/*
* The function fiat_secp256k1_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 void fiat_secp256k1_addcarryx_u64(uint64_t* out1, fiat_secp256k1_uint1* out2, fiat_secp256k1_uint1 arg1, uint64_t arg2, uint64_t arg3) {
fiat_secp256k1_uint128 x1;
uint64_t x2;
fiat_secp256k1_uint1 x3;
x1 = ((arg1 + (fiat_secp256k1_uint128)arg2) + arg3);
x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
x3 = (fiat_secp256k1_uint1)(x1 >> 64);
*out1 = x2;
*out2 = x3;
}
/*
* The function fiat_secp256k1_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 void fiat_secp256k1_subborrowx_u64(uint64_t* out1, fiat_secp256k1_uint1* out2, fiat_secp256k1_uint1 arg1, uint64_t arg2, uint64_t arg3) {
fiat_secp256k1_int128 x1;
fiat_secp256k1_int1 x2;
uint64_t x3;
x1 = ((arg2 - (fiat_secp256k1_int128)arg1) - arg3);
x2 = (fiat_secp256k1_int1)(x1 >> 64);
x3 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
*out1 = x3;
*out2 = (fiat_secp256k1_uint1)(0x0 - x2);
}
/*
* The function fiat_secp256k1_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 void fiat_secp256k1_mulx_u64(uint64_t* out1, uint64_t* out2, uint64_t arg1, uint64_t arg2) {
fiat_secp256k1_uint128 x1;
uint64_t x2;
uint64_t x3;
x1 = ((fiat_secp256k1_uint128)arg1 * arg2);
x2 = (uint64_t)(x1 & UINT64_C(0xffffffffffffffff));
x3 = (uint64_t)(x1 >> 64);
*out1 = x2;
*out2 = x3;
}
/*
* The function fiat_secp256k1_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 void fiat_secp256k1_cmovznz_u64(uint64_t* out1, fiat_secp256k1_uint1 arg1, uint64_t arg2, uint64_t arg3) {
fiat_secp256k1_uint1 x1;
uint64_t x2;
uint64_t x3;
x1 = (!(!arg1));
x2 = ((fiat_secp256k1_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff));
x3 = ((fiat_secp256k1_value_barrier_u64(x2) & arg3) | (fiat_secp256k1_value_barrier_u64((~x2)) & arg2));
*out1 = x3;
}
/*
* The function fiat_secp256k1_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
*
* Input Bounds:
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* Output Bounds:
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
*/
static void fiat_secp256k1_mul(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
uint64_t x6;
uint64_t x7;
uint64_t x8;
uint64_t x9;
uint64_t x10;
uint64_t x11;
uint64_t x12;
uint64_t x13;
fiat_secp256k1_uint1 x14;
uint64_t x15;
fiat_secp256k1_uint1 x16;
uint64_t x17;
fiat_secp256k1_uint1 x18;
uint64_t x19;
uint64_t x20;
uint64_t x21;
uint64_t x22;
uint64_t x23;
uint64_t x24;
uint64_t x25;
uint64_t x26;
uint64_t x27;
uint64_t x28;
uint64_t x29;
uint64_t x30;
fiat_secp256k1_uint1 x31;
uint64_t x32;
fiat_secp256k1_uint1 x33;
uint64_t x34;
fiat_secp256k1_uint1 x35;
uint64_t x36;
uint64_t x37;
fiat_secp256k1_uint1 x38;
uint64_t x39;
fiat_secp256k1_uint1 x40;
uint64_t x41;
fiat_secp256k1_uint1 x42;
uint64_t x43;
fiat_secp256k1_uint1 x44;
uint64_t x45;
fiat_secp256k1_uint1 x46;
uint64_t x47;
uint64_t x48;
uint64_t x49;
uint64_t x50;
uint64_t x51;
uint64_t x52;
uint64_t x53;
uint64_t x54;
uint64_t x55;
fiat_secp256k1_uint1 x56;
uint64_t x57;
fiat_secp256k1_uint1 x58;
uint64_t x59;
fiat_secp256k1_uint1 x60;
uint64_t x61;
uint64_t x62;
fiat_secp256k1_uint1 x63;
uint64_t x64;
fiat_secp256k1_uint1 x65;
uint64_t x66;
fiat_secp256k1_uint1 x67;
uint64_t x68;
fiat_secp256k1_uint1 x69;
uint64_t x70;
fiat_secp256k1_uint1 x71;
uint64_t x72;
uint64_t x73;
uint64_t x74;
uint64_t x75;
uint64_t x76;
uint64_t x77;
uint64_t x78;
uint64_t x79;
uint64_t x80;
uint64_t x81;
uint64_t x82;
fiat_secp256k1_uint1 x83;
uint64_t x84;
fiat_secp256k1_uint1 x85;
uint64_t x86;
fiat_secp256k1_uint1 x87;
uint64_t x88;
uint64_t x89;
fiat_secp256k1_uint1 x90;
uint64_t x91;
fiat_secp256k1_uint1 x92;
uint64_t x93;
fiat_secp256k1_uint1 x94;
uint64_t x95;
fiat_secp256k1_uint1 x96;
uint64_t x97;
fiat_secp256k1_uint1 x98;
uint64_t x99;
uint64_t x100;
uint64_t x101;
uint64_t x102;
uint64_t x103;
uint64_t x104;
uint64_t x105;
uint64_t x106;
uint64_t x107;
uint64_t x108;
fiat_secp256k1_uint1 x109;
uint64_t x110;
fiat_secp256k1_uint1 x111;
uint64_t x112;
fiat_secp256k1_uint1 x113;
uint64_t x114;
uint64_t x115;
fiat_secp256k1_uint1 x116;
uint64_t x117;
fiat_secp256k1_uint1 x118;
uint64_t x119;
fiat_secp256k1_uint1 x120;
uint64_t x121;
fiat_secp256k1_uint1 x122;
uint64_t x123;
fiat_secp256k1_uint1 x124;
uint64_t x125;
uint64_t x126;
uint64_t x127;
uint64_t x128;
uint64_t x129;
uint64_t x130;
uint64_t x131;
uint64_t x132;
uint64_t x133;
uint64_t x134;
uint64_t x135;
fiat_secp256k1_uint1 x136;
uint64_t x137;
fiat_secp256k1_uint1 x138;
uint64_t x139;
fiat_secp256k1_uint1 x140;
uint64_t x141;
uint64_t x142;
fiat_secp256k1_uint1 x143;
uint64_t x144;
fiat_secp256k1_uint1 x145;
uint64_t x146;
fiat_secp256k1_uint1 x147;
uint64_t x148;
fiat_secp256k1_uint1 x149;
uint64_t x150;
fiat_secp256k1_uint1 x151;
uint64_t x152;
uint64_t x153;
uint64_t x154;
uint64_t x155;
uint64_t x156;
uint64_t x157;
uint64_t x158;
uint64_t x159;
uint64_t x160;
uint64_t x161;
fiat_secp256k1_uint1 x162;
uint64_t x163;
fiat_secp256k1_uint1 x164;
uint64_t x165;
fiat_secp256k1_uint1 x166;
uint64_t x167;
uint64_t x168;
fiat_secp256k1_uint1 x169;
uint64_t x170;
fiat_secp256k1_uint1 x171;
uint64_t x172;
fiat_secp256k1_uint1 x173;
uint64_t x174;
fiat_secp256k1_uint1 x175;
uint64_t x176;
fiat_secp256k1_uint1 x177;
uint64_t x178;
uint64_t x179;
uint64_t x180;
uint64_t x181;
uint64_t x182;
uint64_t x183;
uint64_t x184;
uint64_t x185;
uint64_t x186;
uint64_t x187;
uint64_t x188;
fiat_secp256k1_uint1 x189;
uint64_t x190;
fiat_secp256k1_uint1 x191;
uint64_t x192;
fiat_secp256k1_uint1 x193;
uint64_t x194;
uint64_t x195;
fiat_secp256k1_uint1 x196;
uint64_t x197;
fiat_secp256k1_uint1 x198;
uint64_t x199;
fiat_secp256k1_uint1 x200;
uint64_t x201;
fiat_secp256k1_uint1 x202;
uint64_t x203;
fiat_secp256k1_uint1 x204;
uint64_t x205;
uint64_t x206;
fiat_secp256k1_uint1 x207;
uint64_t x208;
fiat_secp256k1_uint1 x209;
uint64_t x210;
fiat_secp256k1_uint1 x211;
uint64_t x212;
fiat_secp256k1_uint1 x213;
uint64_t x214;
fiat_secp256k1_uint1 x215;
uint64_t x216;
uint64_t x217;
uint64_t x218;
uint64_t x219;
x1 = (arg1[1]);
x2 = (arg1[2]);
x3 = (arg1[3]);
x4 = (arg1[0]);
fiat_secp256k1_mulx_u64(&x5, &x6, x4, (arg2[3]));
fiat_secp256k1_mulx_u64(&x7, &x8, x4, (arg2[2]));
fiat_secp256k1_mulx_u64(&x9, &x10, x4, (arg2[1]));
fiat_secp256k1_mulx_u64(&x11, &x12, x4, (arg2[0]));
fiat_secp256k1_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
fiat_secp256k1_addcarryx_u64(&x15, &x16, x14, x10, x7);
fiat_secp256k1_addcarryx_u64(&x17, &x18, x16, x8, x5);
x19 = (x18 + x6);
fiat_secp256k1_mulx_u64(&x20, &x21, x11, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x22, &x23, x20, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x24, &x25, x20, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x26, &x27, x20, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x28, &x29, x20, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x30, &x31, 0x0, x29, x26);
fiat_secp256k1_addcarryx_u64(&x32, &x33, x31, x27, x24);
fiat_secp256k1_addcarryx_u64(&x34, &x35, x33, x25, x22);
x36 = (x35 + x23);
fiat_secp256k1_addcarryx_u64(&x37, &x38, 0x0, x11, x28);
fiat_secp256k1_addcarryx_u64(&x39, &x40, x38, x13, x30);
fiat_secp256k1_addcarryx_u64(&x41, &x42, x40, x15, x32);
fiat_secp256k1_addcarryx_u64(&x43, &x44, x42, x17, x34);
fiat_secp256k1_addcarryx_u64(&x45, &x46, x44, x19, x36);
fiat_secp256k1_mulx_u64(&x47, &x48, x1, (arg2[3]));
fiat_secp256k1_mulx_u64(&x49, &x50, x1, (arg2[2]));
fiat_secp256k1_mulx_u64(&x51, &x52, x1, (arg2[1]));
fiat_secp256k1_mulx_u64(&x53, &x54, x1, (arg2[0]));
fiat_secp256k1_addcarryx_u64(&x55, &x56, 0x0, x54, x51);
fiat_secp256k1_addcarryx_u64(&x57, &x58, x56, x52, x49);
fiat_secp256k1_addcarryx_u64(&x59, &x60, x58, x50, x47);
x61 = (x60 + x48);
fiat_secp256k1_addcarryx_u64(&x62, &x63, 0x0, x39, x53);
fiat_secp256k1_addcarryx_u64(&x64, &x65, x63, x41, x55);
fiat_secp256k1_addcarryx_u64(&x66, &x67, x65, x43, x57);
fiat_secp256k1_addcarryx_u64(&x68, &x69, x67, x45, x59);
fiat_secp256k1_addcarryx_u64(&x70, &x71, x69, x46, x61);
fiat_secp256k1_mulx_u64(&x72, &x73, x62, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x74, &x75, x72, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x76, &x77, x72, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x78, &x79, x72, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x80, &x81, x72, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x82, &x83, 0x0, x81, x78);
fiat_secp256k1_addcarryx_u64(&x84, &x85, x83, x79, x76);
fiat_secp256k1_addcarryx_u64(&x86, &x87, x85, x77, x74);
x88 = (x87 + x75);
fiat_secp256k1_addcarryx_u64(&x89, &x90, 0x0, x62, x80);
fiat_secp256k1_addcarryx_u64(&x91, &x92, x90, x64, x82);
fiat_secp256k1_addcarryx_u64(&x93, &x94, x92, x66, x84);
fiat_secp256k1_addcarryx_u64(&x95, &x96, x94, x68, x86);
fiat_secp256k1_addcarryx_u64(&x97, &x98, x96, x70, x88);
x99 = ((uint64_t)x98 + x71);
fiat_secp256k1_mulx_u64(&x100, &x101, x2, (arg2[3]));
fiat_secp256k1_mulx_u64(&x102, &x103, x2, (arg2[2]));
fiat_secp256k1_mulx_u64(&x104, &x105, x2, (arg2[1]));
fiat_secp256k1_mulx_u64(&x106, &x107, x2, (arg2[0]));
fiat_secp256k1_addcarryx_u64(&x108, &x109, 0x0, x107, x104);
fiat_secp256k1_addcarryx_u64(&x110, &x111, x109, x105, x102);
fiat_secp256k1_addcarryx_u64(&x112, &x113, x111, x103, x100);
x114 = (x113 + x101);
fiat_secp256k1_addcarryx_u64(&x115, &x116, 0x0, x91, x106);
fiat_secp256k1_addcarryx_u64(&x117, &x118, x116, x93, x108);
fiat_secp256k1_addcarryx_u64(&x119, &x120, x118, x95, x110);
fiat_secp256k1_addcarryx_u64(&x121, &x122, x120, x97, x112);
fiat_secp256k1_addcarryx_u64(&x123, &x124, x122, x99, x114);
fiat_secp256k1_mulx_u64(&x125, &x126, x115, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x127, &x128, x125, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x129, &x130, x125, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x131, &x132, x125, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x133, &x134, x125, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x135, &x136, 0x0, x134, x131);
fiat_secp256k1_addcarryx_u64(&x137, &x138, x136, x132, x129);
fiat_secp256k1_addcarryx_u64(&x139, &x140, x138, x130, x127);
x141 = (x140 + x128);
fiat_secp256k1_addcarryx_u64(&x142, &x143, 0x0, x115, x133);
fiat_secp256k1_addcarryx_u64(&x144, &x145, x143, x117, x135);
fiat_secp256k1_addcarryx_u64(&x146, &x147, x145, x119, x137);
fiat_secp256k1_addcarryx_u64(&x148, &x149, x147, x121, x139);
fiat_secp256k1_addcarryx_u64(&x150, &x151, x149, x123, x141);
x152 = ((uint64_t)x151 + x124);
fiat_secp256k1_mulx_u64(&x153, &x154, x3, (arg2[3]));
fiat_secp256k1_mulx_u64(&x155, &x156, x3, (arg2[2]));
fiat_secp256k1_mulx_u64(&x157, &x158, x3, (arg2[1]));
fiat_secp256k1_mulx_u64(&x159, &x160, x3, (arg2[0]));
fiat_secp256k1_addcarryx_u64(&x161, &x162, 0x0, x160, x157);
fiat_secp256k1_addcarryx_u64(&x163, &x164, x162, x158, x155);
fiat_secp256k1_addcarryx_u64(&x165, &x166, x164, x156, x153);
x167 = (x166 + x154);
fiat_secp256k1_addcarryx_u64(&x168, &x169, 0x0, x144, x159);
fiat_secp256k1_addcarryx_u64(&x170, &x171, x169, x146, x161);
fiat_secp256k1_addcarryx_u64(&x172, &x173, x171, x148, x163);
fiat_secp256k1_addcarryx_u64(&x174, &x175, x173, x150, x165);
fiat_secp256k1_addcarryx_u64(&x176, &x177, x175, x152, x167);
fiat_secp256k1_mulx_u64(&x178, &x179, x168, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x180, &x181, x178, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x182, &x183, x178, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x184, &x185, x178, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x186, &x187, x178, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x188, &x189, 0x0, x187, x184);
fiat_secp256k1_addcarryx_u64(&x190, &x191, x189, x185, x182);
fiat_secp256k1_addcarryx_u64(&x192, &x193, x191, x183, x180);
x194 = (x193 + x181);
fiat_secp256k1_addcarryx_u64(&x195, &x196, 0x0, x168, x186);
fiat_secp256k1_addcarryx_u64(&x197, &x198, x196, x170, x188);
fiat_secp256k1_addcarryx_u64(&x199, &x200, x198, x172, x190);
fiat_secp256k1_addcarryx_u64(&x201, &x202, x200, x174, x192);
fiat_secp256k1_addcarryx_u64(&x203, &x204, x202, x176, x194);
x205 = ((uint64_t)x204 + x177);
fiat_secp256k1_subborrowx_u64(&x206, &x207, 0x0, x197, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_subborrowx_u64(&x208, &x209, x207, x199, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x210, &x211, x209, x201, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x212, &x213, x211, x203, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x214, &x215, x213, x205, 0x0);
fiat_secp256k1_cmovznz_u64(&x216, x215, x206, x197);
fiat_secp256k1_cmovznz_u64(&x217, x215, x208, x199);
fiat_secp256k1_cmovznz_u64(&x218, x215, x210, x201);
fiat_secp256k1_cmovznz_u64(&x219, x215, x212, x203);
out1[0] = x216;
out1[1] = x217;
out1[2] = x218;
out1[3] = x219;
}
/*
* The function fiat_secp256k1_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
*
* Input Bounds:
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* Output Bounds:
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
*/
static void fiat_secp256k1_square(uint64_t out1[4], const uint64_t arg1[4]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
uint64_t x6;
uint64_t x7;
uint64_t x8;
uint64_t x9;
uint64_t x10;
uint64_t x11;
uint64_t x12;
uint64_t x13;
fiat_secp256k1_uint1 x14;
uint64_t x15;
fiat_secp256k1_uint1 x16;
uint64_t x17;
fiat_secp256k1_uint1 x18;
uint64_t x19;
uint64_t x20;
uint64_t x21;
uint64_t x22;
uint64_t x23;
uint64_t x24;
uint64_t x25;
uint64_t x26;
uint64_t x27;
uint64_t x28;
uint64_t x29;
uint64_t x30;
fiat_secp256k1_uint1 x31;
uint64_t x32;
fiat_secp256k1_uint1 x33;
uint64_t x34;
fiat_secp256k1_uint1 x35;
uint64_t x36;
uint64_t x37;
fiat_secp256k1_uint1 x38;
uint64_t x39;
fiat_secp256k1_uint1 x40;
uint64_t x41;
fiat_secp256k1_uint1 x42;
uint64_t x43;
fiat_secp256k1_uint1 x44;
uint64_t x45;
fiat_secp256k1_uint1 x46;
uint64_t x47;
uint64_t x48;
uint64_t x49;
uint64_t x50;
uint64_t x51;
uint64_t x52;
uint64_t x53;
uint64_t x54;
uint64_t x55;
fiat_secp256k1_uint1 x56;
uint64_t x57;
fiat_secp256k1_uint1 x58;
uint64_t x59;
fiat_secp256k1_uint1 x60;
uint64_t x61;
uint64_t x62;
fiat_secp256k1_uint1 x63;
uint64_t x64;
fiat_secp256k1_uint1 x65;
uint64_t x66;
fiat_secp256k1_uint1 x67;
uint64_t x68;
fiat_secp256k1_uint1 x69;
uint64_t x70;
fiat_secp256k1_uint1 x71;
uint64_t x72;
uint64_t x73;
uint64_t x74;
uint64_t x75;
uint64_t x76;
uint64_t x77;
uint64_t x78;
uint64_t x79;
uint64_t x80;
uint64_t x81;
uint64_t x82;
fiat_secp256k1_uint1 x83;
uint64_t x84;
fiat_secp256k1_uint1 x85;
uint64_t x86;
fiat_secp256k1_uint1 x87;
uint64_t x88;
uint64_t x89;
fiat_secp256k1_uint1 x90;
uint64_t x91;
fiat_secp256k1_uint1 x92;
uint64_t x93;
fiat_secp256k1_uint1 x94;
uint64_t x95;
fiat_secp256k1_uint1 x96;
uint64_t x97;
fiat_secp256k1_uint1 x98;
uint64_t x99;
uint64_t x100;
uint64_t x101;
uint64_t x102;
uint64_t x103;
uint64_t x104;
uint64_t x105;
uint64_t x106;
uint64_t x107;
uint64_t x108;
fiat_secp256k1_uint1 x109;
uint64_t x110;
fiat_secp256k1_uint1 x111;
uint64_t x112;
fiat_secp256k1_uint1 x113;
uint64_t x114;
uint64_t x115;
fiat_secp256k1_uint1 x116;
uint64_t x117;
fiat_secp256k1_uint1 x118;
uint64_t x119;
fiat_secp256k1_uint1 x120;
uint64_t x121;
fiat_secp256k1_uint1 x122;
uint64_t x123;
fiat_secp256k1_uint1 x124;
uint64_t x125;
uint64_t x126;
uint64_t x127;
uint64_t x128;
uint64_t x129;
uint64_t x130;
uint64_t x131;
uint64_t x132;
uint64_t x133;
uint64_t x134;
uint64_t x135;
fiat_secp256k1_uint1 x136;
uint64_t x137;
fiat_secp256k1_uint1 x138;
uint64_t x139;
fiat_secp256k1_uint1 x140;
uint64_t x141;
uint64_t x142;
fiat_secp256k1_uint1 x143;
uint64_t x144;
fiat_secp256k1_uint1 x145;
uint64_t x146;
fiat_secp256k1_uint1 x147;
uint64_t x148;
fiat_secp256k1_uint1 x149;
uint64_t x150;
fiat_secp256k1_uint1 x151;
uint64_t x152;
uint64_t x153;
uint64_t x154;
uint64_t x155;
uint64_t x156;
uint64_t x157;
uint64_t x158;
uint64_t x159;
uint64_t x160;
uint64_t x161;
fiat_secp256k1_uint1 x162;
uint64_t x163;
fiat_secp256k1_uint1 x164;
uint64_t x165;
fiat_secp256k1_uint1 x166;
uint64_t x167;
uint64_t x168;
fiat_secp256k1_uint1 x169;
uint64_t x170;
fiat_secp256k1_uint1 x171;
uint64_t x172;
fiat_secp256k1_uint1 x173;
uint64_t x174;
fiat_secp256k1_uint1 x175;
uint64_t x176;
fiat_secp256k1_uint1 x177;
uint64_t x178;
uint64_t x179;
uint64_t x180;
uint64_t x181;
uint64_t x182;
uint64_t x183;
uint64_t x184;
uint64_t x185;
uint64_t x186;
uint64_t x187;
uint64_t x188;
fiat_secp256k1_uint1 x189;
uint64_t x190;
fiat_secp256k1_uint1 x191;
uint64_t x192;
fiat_secp256k1_uint1 x193;
uint64_t x194;
uint64_t x195;
fiat_secp256k1_uint1 x196;
uint64_t x197;
fiat_secp256k1_uint1 x198;
uint64_t x199;
fiat_secp256k1_uint1 x200;
uint64_t x201;
fiat_secp256k1_uint1 x202;
uint64_t x203;
fiat_secp256k1_uint1 x204;
uint64_t x205;
uint64_t x206;
fiat_secp256k1_uint1 x207;
uint64_t x208;
fiat_secp256k1_uint1 x209;
uint64_t x210;
fiat_secp256k1_uint1 x211;
uint64_t x212;
fiat_secp256k1_uint1 x213;
uint64_t x214;
fiat_secp256k1_uint1 x215;
uint64_t x216;
uint64_t x217;
uint64_t x218;
uint64_t x219;
x1 = (arg1[1]);
x2 = (arg1[2]);
x3 = (arg1[3]);
x4 = (arg1[0]);
fiat_secp256k1_mulx_u64(&x5, &x6, x4, (arg1[3]));
fiat_secp256k1_mulx_u64(&x7, &x8, x4, (arg1[2]));
fiat_secp256k1_mulx_u64(&x9, &x10, x4, (arg1[1]));
fiat_secp256k1_mulx_u64(&x11, &x12, x4, (arg1[0]));
fiat_secp256k1_addcarryx_u64(&x13, &x14, 0x0, x12, x9);
fiat_secp256k1_addcarryx_u64(&x15, &x16, x14, x10, x7);
fiat_secp256k1_addcarryx_u64(&x17, &x18, x16, x8, x5);
x19 = (x18 + x6);
fiat_secp256k1_mulx_u64(&x20, &x21, x11, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x22, &x23, x20, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x24, &x25, x20, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x26, &x27, x20, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x28, &x29, x20, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x30, &x31, 0x0, x29, x26);
fiat_secp256k1_addcarryx_u64(&x32, &x33, x31, x27, x24);
fiat_secp256k1_addcarryx_u64(&x34, &x35, x33, x25, x22);
x36 = (x35 + x23);
fiat_secp256k1_addcarryx_u64(&x37, &x38, 0x0, x11, x28);
fiat_secp256k1_addcarryx_u64(&x39, &x40, x38, x13, x30);
fiat_secp256k1_addcarryx_u64(&x41, &x42, x40, x15, x32);
fiat_secp256k1_addcarryx_u64(&x43, &x44, x42, x17, x34);
fiat_secp256k1_addcarryx_u64(&x45, &x46, x44, x19, x36);
fiat_secp256k1_mulx_u64(&x47, &x48, x1, (arg1[3]));
fiat_secp256k1_mulx_u64(&x49, &x50, x1, (arg1[2]));
fiat_secp256k1_mulx_u64(&x51, &x52, x1, (arg1[1]));
fiat_secp256k1_mulx_u64(&x53, &x54, x1, (arg1[0]));
fiat_secp256k1_addcarryx_u64(&x55, &x56, 0x0, x54, x51);
fiat_secp256k1_addcarryx_u64(&x57, &x58, x56, x52, x49);
fiat_secp256k1_addcarryx_u64(&x59, &x60, x58, x50, x47);
x61 = (x60 + x48);
fiat_secp256k1_addcarryx_u64(&x62, &x63, 0x0, x39, x53);
fiat_secp256k1_addcarryx_u64(&x64, &x65, x63, x41, x55);
fiat_secp256k1_addcarryx_u64(&x66, &x67, x65, x43, x57);
fiat_secp256k1_addcarryx_u64(&x68, &x69, x67, x45, x59);
fiat_secp256k1_addcarryx_u64(&x70, &x71, x69, x46, x61);
fiat_secp256k1_mulx_u64(&x72, &x73, x62, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x74, &x75, x72, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x76, &x77, x72, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x78, &x79, x72, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x80, &x81, x72, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x82, &x83, 0x0, x81, x78);
fiat_secp256k1_addcarryx_u64(&x84, &x85, x83, x79, x76);
fiat_secp256k1_addcarryx_u64(&x86, &x87, x85, x77, x74);
x88 = (x87 + x75);
fiat_secp256k1_addcarryx_u64(&x89, &x90, 0x0, x62, x80);
fiat_secp256k1_addcarryx_u64(&x91, &x92, x90, x64, x82);
fiat_secp256k1_addcarryx_u64(&x93, &x94, x92, x66, x84);
fiat_secp256k1_addcarryx_u64(&x95, &x96, x94, x68, x86);
fiat_secp256k1_addcarryx_u64(&x97, &x98, x96, x70, x88);
x99 = ((uint64_t)x98 + x71);
fiat_secp256k1_mulx_u64(&x100, &x101, x2, (arg1[3]));
fiat_secp256k1_mulx_u64(&x102, &x103, x2, (arg1[2]));
fiat_secp256k1_mulx_u64(&x104, &x105, x2, (arg1[1]));
fiat_secp256k1_mulx_u64(&x106, &x107, x2, (arg1[0]));
fiat_secp256k1_addcarryx_u64(&x108, &x109, 0x0, x107, x104);
fiat_secp256k1_addcarryx_u64(&x110, &x111, x109, x105, x102);
fiat_secp256k1_addcarryx_u64(&x112, &x113, x111, x103, x100);
x114 = (x113 + x101);
fiat_secp256k1_addcarryx_u64(&x115, &x116, 0x0, x91, x106);
fiat_secp256k1_addcarryx_u64(&x117, &x118, x116, x93, x108);
fiat_secp256k1_addcarryx_u64(&x119, &x120, x118, x95, x110);
fiat_secp256k1_addcarryx_u64(&x121, &x122, x120, x97, x112);
fiat_secp256k1_addcarryx_u64(&x123, &x124, x122, x99, x114);
fiat_secp256k1_mulx_u64(&x125, &x126, x115, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x127, &x128, x125, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x129, &x130, x125, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x131, &x132, x125, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x133, &x134, x125, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x135, &x136, 0x0, x134, x131);
fiat_secp256k1_addcarryx_u64(&x137, &x138, x136, x132, x129);
fiat_secp256k1_addcarryx_u64(&x139, &x140, x138, x130, x127);
x141 = (x140 + x128);
fiat_secp256k1_addcarryx_u64(&x142, &x143, 0x0, x115, x133);
fiat_secp256k1_addcarryx_u64(&x144, &x145, x143, x117, x135);
fiat_secp256k1_addcarryx_u64(&x146, &x147, x145, x119, x137);
fiat_secp256k1_addcarryx_u64(&x148, &x149, x147, x121, x139);
fiat_secp256k1_addcarryx_u64(&x150, &x151, x149, x123, x141);
x152 = ((uint64_t)x151 + x124);
fiat_secp256k1_mulx_u64(&x153, &x154, x3, (arg1[3]));
fiat_secp256k1_mulx_u64(&x155, &x156, x3, (arg1[2]));
fiat_secp256k1_mulx_u64(&x157, &x158, x3, (arg1[1]));
fiat_secp256k1_mulx_u64(&x159, &x160, x3, (arg1[0]));
fiat_secp256k1_addcarryx_u64(&x161, &x162, 0x0, x160, x157);
fiat_secp256k1_addcarryx_u64(&x163, &x164, x162, x158, x155);
fiat_secp256k1_addcarryx_u64(&x165, &x166, x164, x156, x153);
x167 = (x166 + x154);
fiat_secp256k1_addcarryx_u64(&x168, &x169, 0x0, x144, x159);
fiat_secp256k1_addcarryx_u64(&x170, &x171, x169, x146, x161);
fiat_secp256k1_addcarryx_u64(&x172, &x173, x171, x148, x163);
fiat_secp256k1_addcarryx_u64(&x174, &x175, x173, x150, x165);
fiat_secp256k1_addcarryx_u64(&x176, &x177, x175, x152, x167);
fiat_secp256k1_mulx_u64(&x178, &x179, x168, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x180, &x181, x178, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x182, &x183, x178, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x184, &x185, x178, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x186, &x187, x178, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x188, &x189, 0x0, x187, x184);
fiat_secp256k1_addcarryx_u64(&x190, &x191, x189, x185, x182);
fiat_secp256k1_addcarryx_u64(&x192, &x193, x191, x183, x180);
x194 = (x193 + x181);
fiat_secp256k1_addcarryx_u64(&x195, &x196, 0x0, x168, x186);
fiat_secp256k1_addcarryx_u64(&x197, &x198, x196, x170, x188);
fiat_secp256k1_addcarryx_u64(&x199, &x200, x198, x172, x190);
fiat_secp256k1_addcarryx_u64(&x201, &x202, x200, x174, x192);
fiat_secp256k1_addcarryx_u64(&x203, &x204, x202, x176, x194);
x205 = ((uint64_t)x204 + x177);
fiat_secp256k1_subborrowx_u64(&x206, &x207, 0x0, x197, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_subborrowx_u64(&x208, &x209, x207, x199, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x210, &x211, x209, x201, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x212, &x213, x211, x203, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x214, &x215, x213, x205, 0x0);
fiat_secp256k1_cmovznz_u64(&x216, x215, x206, x197);
fiat_secp256k1_cmovznz_u64(&x217, x215, x208, x199);
fiat_secp256k1_cmovznz_u64(&x218, x215, x210, x201);
fiat_secp256k1_cmovznz_u64(&x219, x215, x212, x203);
out1[0] = x216;
out1[1] = x217;
out1[2] = x218;
out1[3] = x219;
}
/*
* The function fiat_secp256k1_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
*
* Input Bounds:
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* Output Bounds:
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
*/
static void fiat_secp256k1_add(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) {
uint64_t x1;
fiat_secp256k1_uint1 x2;
uint64_t x3;
fiat_secp256k1_uint1 x4;
uint64_t x5;
fiat_secp256k1_uint1 x6;
uint64_t x7;
fiat_secp256k1_uint1 x8;
uint64_t x9;
fiat_secp256k1_uint1 x10;
uint64_t x11;
fiat_secp256k1_uint1 x12;
uint64_t x13;
fiat_secp256k1_uint1 x14;
uint64_t x15;
fiat_secp256k1_uint1 x16;
uint64_t x17;
fiat_secp256k1_uint1 x18;
uint64_t x19;
uint64_t x20;
uint64_t x21;
uint64_t x22;
fiat_secp256k1_addcarryx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
fiat_secp256k1_addcarryx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
fiat_secp256k1_addcarryx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
fiat_secp256k1_addcarryx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
fiat_secp256k1_subborrowx_u64(&x9, &x10, 0x0, x1, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_subborrowx_u64(&x11, &x12, x10, x3, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x13, &x14, x12, x5, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x15, &x16, x14, x7, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x17, &x18, x16, x8, 0x0);
fiat_secp256k1_cmovznz_u64(&x19, x18, x9, x1);
fiat_secp256k1_cmovznz_u64(&x20, x18, x11, x3);
fiat_secp256k1_cmovznz_u64(&x21, x18, x13, x5);
fiat_secp256k1_cmovznz_u64(&x22, x18, x15, x7);
out1[0] = x19;
out1[1] = x20;
out1[2] = x21;
out1[3] = x22;
}
/*
* The function fiat_secp256k1_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
*
* Input Bounds:
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* Output Bounds:
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
*/
static void fiat_secp256k1_sub(uint64_t out1[4], const uint64_t arg1[4], const uint64_t arg2[4]) {
uint64_t x1;
fiat_secp256k1_uint1 x2;
uint64_t x3;
fiat_secp256k1_uint1 x4;
uint64_t x5;
fiat_secp256k1_uint1 x6;
uint64_t x7;
fiat_secp256k1_uint1 x8;
uint64_t x9;
uint64_t x10;
fiat_secp256k1_uint1 x11;
uint64_t x12;
fiat_secp256k1_uint1 x13;
uint64_t x14;
fiat_secp256k1_uint1 x15;
uint64_t x16;
fiat_secp256k1_uint1 x17;
fiat_secp256k1_subborrowx_u64(&x1, &x2, 0x0, (arg1[0]), (arg2[0]));
fiat_secp256k1_subborrowx_u64(&x3, &x4, x2, (arg1[1]), (arg2[1]));
fiat_secp256k1_subborrowx_u64(&x5, &x6, x4, (arg1[2]), (arg2[2]));
fiat_secp256k1_subborrowx_u64(&x7, &x8, x6, (arg1[3]), (arg2[3]));
fiat_secp256k1_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_addcarryx_u64(&x10, &x11, 0x0, x1, (x9 & UINT64_C(0xfffffffefffffc2f)));
fiat_secp256k1_addcarryx_u64(&x12, &x13, x11, x3, x9);
fiat_secp256k1_addcarryx_u64(&x14, &x15, x13, x5, x9);
fiat_secp256k1_addcarryx_u64(&x16, &x17, x15, x7, x9);
out1[0] = x10;
out1[1] = x12;
out1[2] = x14;
out1[3] = x16;
}
/*
* The function fiat_secp256k1_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
*
* Input Bounds:
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* Output Bounds:
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
*/
static void fiat_secp256k1_opp(uint64_t out1[4], const uint64_t arg1[4]) {
uint64_t x1;
fiat_secp256k1_uint1 x2;
uint64_t x3;
fiat_secp256k1_uint1 x4;
uint64_t x5;
fiat_secp256k1_uint1 x6;
uint64_t x7;
fiat_secp256k1_uint1 x8;
uint64_t x9;
uint64_t x10;
fiat_secp256k1_uint1 x11;
uint64_t x12;
fiat_secp256k1_uint1 x13;
uint64_t x14;
fiat_secp256k1_uint1 x15;
uint64_t x16;
fiat_secp256k1_uint1 x17;
fiat_secp256k1_subborrowx_u64(&x1, &x2, 0x0, 0x0, (arg1[0]));
fiat_secp256k1_subborrowx_u64(&x3, &x4, x2, 0x0, (arg1[1]));
fiat_secp256k1_subborrowx_u64(&x5, &x6, x4, 0x0, (arg1[2]));
fiat_secp256k1_subborrowx_u64(&x7, &x8, x6, 0x0, (arg1[3]));
fiat_secp256k1_cmovznz_u64(&x9, x8, 0x0, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_addcarryx_u64(&x10, &x11, 0x0, x1, (x9 & UINT64_C(0xfffffffefffffc2f)));
fiat_secp256k1_addcarryx_u64(&x12, &x13, x11, x3, x9);
fiat_secp256k1_addcarryx_u64(&x14, &x15, x13, x5, x9);
fiat_secp256k1_addcarryx_u64(&x16, &x17, x15, x7, x9);
out1[0] = x10;
out1[1] = x12;
out1[2] = x14;
out1[3] = x16;
}
/*
* The function fiat_secp256k1_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
*
* Input Bounds:
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* Output Bounds:
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
*/
static void fiat_secp256k1_from_montgomery(uint64_t out1[4], const uint64_t arg1[4]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
uint64_t x6;
uint64_t x7;
uint64_t x8;
uint64_t x9;
uint64_t x10;
uint64_t x11;
uint64_t x12;
fiat_secp256k1_uint1 x13;
uint64_t x14;
fiat_secp256k1_uint1 x15;
uint64_t x16;
fiat_secp256k1_uint1 x17;
uint64_t x18;
fiat_secp256k1_uint1 x19;
uint64_t x20;
fiat_secp256k1_uint1 x21;
uint64_t x22;
fiat_secp256k1_uint1 x23;
uint64_t x24;
fiat_secp256k1_uint1 x25;
uint64_t x26;
fiat_secp256k1_uint1 x27;
uint64_t x28;
fiat_secp256k1_uint1 x29;
uint64_t x30;
fiat_secp256k1_uint1 x31;
uint64_t x32;
fiat_secp256k1_uint1 x33;
uint64_t x34;
fiat_secp256k1_uint1 x35;
uint64_t x36;
uint64_t x37;
uint64_t x38;
uint64_t x39;
uint64_t x40;
uint64_t x41;
uint64_t x42;
uint64_t x43;
uint64_t x44;
uint64_t x45;
uint64_t x46;
fiat_secp256k1_uint1 x47;
uint64_t x48;
fiat_secp256k1_uint1 x49;
uint64_t x50;
fiat_secp256k1_uint1 x51;
uint64_t x52;
fiat_secp256k1_uint1 x53;
uint64_t x54;
fiat_secp256k1_uint1 x55;
uint64_t x56;
fiat_secp256k1_uint1 x57;
uint64_t x58;
fiat_secp256k1_uint1 x59;
uint64_t x60;
fiat_secp256k1_uint1 x61;
uint64_t x62;
fiat_secp256k1_uint1 x63;
uint64_t x64;
fiat_secp256k1_uint1 x65;
uint64_t x66;
fiat_secp256k1_uint1 x67;
uint64_t x68;
fiat_secp256k1_uint1 x69;
uint64_t x70;
uint64_t x71;
uint64_t x72;
uint64_t x73;
uint64_t x74;
uint64_t x75;
uint64_t x76;
uint64_t x77;
uint64_t x78;
uint64_t x79;
uint64_t x80;
fiat_secp256k1_uint1 x81;
uint64_t x82;
fiat_secp256k1_uint1 x83;
uint64_t x84;
fiat_secp256k1_uint1 x85;
uint64_t x86;
fiat_secp256k1_uint1 x87;
uint64_t x88;
fiat_secp256k1_uint1 x89;
uint64_t x90;
fiat_secp256k1_uint1 x91;
uint64_t x92;
fiat_secp256k1_uint1 x93;
uint64_t x94;
fiat_secp256k1_uint1 x95;
uint64_t x96;
fiat_secp256k1_uint1 x97;
uint64_t x98;
fiat_secp256k1_uint1 x99;
uint64_t x100;
fiat_secp256k1_uint1 x101;
uint64_t x102;
fiat_secp256k1_uint1 x103;
uint64_t x104;
uint64_t x105;
uint64_t x106;
uint64_t x107;
uint64_t x108;
uint64_t x109;
uint64_t x110;
uint64_t x111;
uint64_t x112;
uint64_t x113;
uint64_t x114;
fiat_secp256k1_uint1 x115;
uint64_t x116;
fiat_secp256k1_uint1 x117;
uint64_t x118;
fiat_secp256k1_uint1 x119;
uint64_t x120;
fiat_secp256k1_uint1 x121;
uint64_t x122;
fiat_secp256k1_uint1 x123;
uint64_t x124;
fiat_secp256k1_uint1 x125;
uint64_t x126;
fiat_secp256k1_uint1 x127;
uint64_t x128;
fiat_secp256k1_uint1 x129;
uint64_t x130;
fiat_secp256k1_uint1 x131;
uint64_t x132;
fiat_secp256k1_uint1 x133;
uint64_t x134;
fiat_secp256k1_uint1 x135;
uint64_t x136;
fiat_secp256k1_uint1 x137;
uint64_t x138;
fiat_secp256k1_uint1 x139;
uint64_t x140;
uint64_t x141;
uint64_t x142;
uint64_t x143;
x1 = (arg1[0]);
fiat_secp256k1_mulx_u64(&x2, &x3, x1, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x4, &x5, x2, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x6, &x7, x2, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x8, &x9, x2, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x10, &x11, x2, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x12, &x13, 0x0, x11, x8);
fiat_secp256k1_addcarryx_u64(&x14, &x15, x13, x9, x6);
fiat_secp256k1_addcarryx_u64(&x16, &x17, x15, x7, x4);
fiat_secp256k1_addcarryx_u64(&x18, &x19, 0x0, x1, x10);
fiat_secp256k1_addcarryx_u64(&x20, &x21, x19, 0x0, x12);
fiat_secp256k1_addcarryx_u64(&x22, &x23, x21, 0x0, x14);
fiat_secp256k1_addcarryx_u64(&x24, &x25, x23, 0x0, x16);
fiat_secp256k1_addcarryx_u64(&x26, &x27, x25, 0x0, (x17 + x5));
fiat_secp256k1_addcarryx_u64(&x28, &x29, 0x0, x20, (arg1[1]));
fiat_secp256k1_addcarryx_u64(&x30, &x31, x29, x22, 0x0);
fiat_secp256k1_addcarryx_u64(&x32, &x33, x31, x24, 0x0);
fiat_secp256k1_addcarryx_u64(&x34, &x35, x33, x26, 0x0);
fiat_secp256k1_mulx_u64(&x36, &x37, x28, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x38, &x39, x36, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x40, &x41, x36, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x42, &x43, x36, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x44, &x45, x36, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x46, &x47, 0x0, x45, x42);
fiat_secp256k1_addcarryx_u64(&x48, &x49, x47, x43, x40);
fiat_secp256k1_addcarryx_u64(&x50, &x51, x49, x41, x38);
fiat_secp256k1_addcarryx_u64(&x52, &x53, 0x0, x28, x44);
fiat_secp256k1_addcarryx_u64(&x54, &x55, x53, x30, x46);
fiat_secp256k1_addcarryx_u64(&x56, &x57, x55, x32, x48);
fiat_secp256k1_addcarryx_u64(&x58, &x59, x57, x34, x50);
fiat_secp256k1_addcarryx_u64(&x60, &x61, x59, ((uint64_t)x35 + x27), (x51 + x39));
fiat_secp256k1_addcarryx_u64(&x62, &x63, 0x0, x54, (arg1[2]));
fiat_secp256k1_addcarryx_u64(&x64, &x65, x63, x56, 0x0);
fiat_secp256k1_addcarryx_u64(&x66, &x67, x65, x58, 0x0);
fiat_secp256k1_addcarryx_u64(&x68, &x69, x67, x60, 0x0);
fiat_secp256k1_mulx_u64(&x70, &x71, x62, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x72, &x73, x70, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x74, &x75, x70, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x76, &x77, x70, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x78, &x79, x70, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x80, &x81, 0x0, x79, x76);
fiat_secp256k1_addcarryx_u64(&x82, &x83, x81, x77, x74);
fiat_secp256k1_addcarryx_u64(&x84, &x85, x83, x75, x72);
fiat_secp256k1_addcarryx_u64(&x86, &x87, 0x0, x62, x78);
fiat_secp256k1_addcarryx_u64(&x88, &x89, x87, x64, x80);
fiat_secp256k1_addcarryx_u64(&x90, &x91, x89, x66, x82);
fiat_secp256k1_addcarryx_u64(&x92, &x93, x91, x68, x84);
fiat_secp256k1_addcarryx_u64(&x94, &x95, x93, ((uint64_t)x69 + x61), (x85 + x73));
fiat_secp256k1_addcarryx_u64(&x96, &x97, 0x0, x88, (arg1[3]));
fiat_secp256k1_addcarryx_u64(&x98, &x99, x97, x90, 0x0);
fiat_secp256k1_addcarryx_u64(&x100, &x101, x99, x92, 0x0);
fiat_secp256k1_addcarryx_u64(&x102, &x103, x101, x94, 0x0);
fiat_secp256k1_mulx_u64(&x104, &x105, x96, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x106, &x107, x104, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x108, &x109, x104, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x110, &x111, x104, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x112, &x113, x104, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x114, &x115, 0x0, x113, x110);
fiat_secp256k1_addcarryx_u64(&x116, &x117, x115, x111, x108);
fiat_secp256k1_addcarryx_u64(&x118, &x119, x117, x109, x106);
fiat_secp256k1_addcarryx_u64(&x120, &x121, 0x0, x96, x112);
fiat_secp256k1_addcarryx_u64(&x122, &x123, x121, x98, x114);
fiat_secp256k1_addcarryx_u64(&x124, &x125, x123, x100, x116);
fiat_secp256k1_addcarryx_u64(&x126, &x127, x125, x102, x118);
fiat_secp256k1_addcarryx_u64(&x128, &x129, x127, ((uint64_t)x103 + x95), (x119 + x107));
fiat_secp256k1_subborrowx_u64(&x130, &x131, 0x0, x122, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_subborrowx_u64(&x132, &x133, x131, x124, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x134, &x135, x133, x126, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x136, &x137, x135, x128, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x138, &x139, x137, x129, 0x0);
fiat_secp256k1_cmovznz_u64(&x140, x139, x130, x122);
fiat_secp256k1_cmovznz_u64(&x141, x139, x132, x124);
fiat_secp256k1_cmovznz_u64(&x142, x139, x134, x126);
fiat_secp256k1_cmovznz_u64(&x143, x139, x136, x128);
out1[0] = x140;
out1[1] = x141;
out1[2] = x142;
out1[3] = x143;
}
/*
* The function fiat_secp256k1_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
*
* Input Bounds:
* arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
* Output Bounds:
* out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
*/
static void fiat_secp256k1_to_montgomery(uint64_t out1[4], const uint64_t arg1[4]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
uint64_t x6;
uint64_t x7;
fiat_secp256k1_uint1 x8;
uint64_t x9;
uint64_t x10;
uint64_t x11;
uint64_t x12;
uint64_t x13;
uint64_t x14;
uint64_t x15;
uint64_t x16;
uint64_t x17;
uint64_t x18;
uint64_t x19;
fiat_secp256k1_uint1 x20;
uint64_t x21;
fiat_secp256k1_uint1 x22;
uint64_t x23;
fiat_secp256k1_uint1 x24;
uint64_t x25;
fiat_secp256k1_uint1 x26;
uint64_t x27;
fiat_secp256k1_uint1 x28;
uint64_t x29;
fiat_secp256k1_uint1 x30;
uint64_t x31;
fiat_secp256k1_uint1 x32;
uint64_t x33;
fiat_secp256k1_uint1 x34;
uint64_t x35;
uint64_t x36;
uint64_t x37;
fiat_secp256k1_uint1 x38;
uint64_t x39;
fiat_secp256k1_uint1 x40;
uint64_t x41;
fiat_secp256k1_uint1 x42;
uint64_t x43;
fiat_secp256k1_uint1 x44;
uint64_t x45;
fiat_secp256k1_uint1 x46;
uint64_t x47;
uint64_t x48;
uint64_t x49;
uint64_t x50;
uint64_t x51;
uint64_t x52;
uint64_t x53;
uint64_t x54;
uint64_t x55;
uint64_t x56;
uint64_t x57;
fiat_secp256k1_uint1 x58;
uint64_t x59;
fiat_secp256k1_uint1 x60;
uint64_t x61;
fiat_secp256k1_uint1 x62;
uint64_t x63;
fiat_secp256k1_uint1 x64;
uint64_t x65;
fiat_secp256k1_uint1 x66;
uint64_t x67;
fiat_secp256k1_uint1 x68;
uint64_t x69;
fiat_secp256k1_uint1 x70;
uint64_t x71;
fiat_secp256k1_uint1 x72;
uint64_t x73;
uint64_t x74;
uint64_t x75;
fiat_secp256k1_uint1 x76;
uint64_t x77;
fiat_secp256k1_uint1 x78;
uint64_t x79;
fiat_secp256k1_uint1 x80;
uint64_t x81;
fiat_secp256k1_uint1 x82;
uint64_t x83;
fiat_secp256k1_uint1 x84;
uint64_t x85;
uint64_t x86;
uint64_t x87;
uint64_t x88;
uint64_t x89;
uint64_t x90;
uint64_t x91;
uint64_t x92;
uint64_t x93;
uint64_t x94;
uint64_t x95;
fiat_secp256k1_uint1 x96;
uint64_t x97;
fiat_secp256k1_uint1 x98;
uint64_t x99;
fiat_secp256k1_uint1 x100;
uint64_t x101;
fiat_secp256k1_uint1 x102;
uint64_t x103;
fiat_secp256k1_uint1 x104;
uint64_t x105;
fiat_secp256k1_uint1 x106;
uint64_t x107;
fiat_secp256k1_uint1 x108;
uint64_t x109;
fiat_secp256k1_uint1 x110;
uint64_t x111;
uint64_t x112;
uint64_t x113;
fiat_secp256k1_uint1 x114;
uint64_t x115;
fiat_secp256k1_uint1 x116;
uint64_t x117;
fiat_secp256k1_uint1 x118;
uint64_t x119;
fiat_secp256k1_uint1 x120;
uint64_t x121;
fiat_secp256k1_uint1 x122;
uint64_t x123;
uint64_t x124;
uint64_t x125;
uint64_t x126;
uint64_t x127;
uint64_t x128;
uint64_t x129;
uint64_t x130;
uint64_t x131;
uint64_t x132;
uint64_t x133;
fiat_secp256k1_uint1 x134;
uint64_t x135;
fiat_secp256k1_uint1 x136;
uint64_t x137;
fiat_secp256k1_uint1 x138;
uint64_t x139;
fiat_secp256k1_uint1 x140;
uint64_t x141;
fiat_secp256k1_uint1 x142;
uint64_t x143;
fiat_secp256k1_uint1 x144;
uint64_t x145;
fiat_secp256k1_uint1 x146;
uint64_t x147;
fiat_secp256k1_uint1 x148;
uint64_t x149;
fiat_secp256k1_uint1 x150;
uint64_t x151;
fiat_secp256k1_uint1 x152;
uint64_t x153;
fiat_secp256k1_uint1 x154;
uint64_t x155;
fiat_secp256k1_uint1 x156;
uint64_t x157;
fiat_secp256k1_uint1 x158;
uint64_t x159;
uint64_t x160;
uint64_t x161;
uint64_t x162;
x1 = (arg1[1]);
x2 = (arg1[2]);
x3 = (arg1[3]);
x4 = (arg1[0]);
fiat_secp256k1_mulx_u64(&x5, &x6, x4, UINT64_C(0x7a2000e90a1));
fiat_secp256k1_addcarryx_u64(&x7, &x8, 0x0, x6, x4);
fiat_secp256k1_mulx_u64(&x9, &x10, x5, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x11, &x12, x9, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x13, &x14, x9, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x15, &x16, x9, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x17, &x18, x9, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x19, &x20, 0x0, x18, x15);
fiat_secp256k1_addcarryx_u64(&x21, &x22, x20, x16, x13);
fiat_secp256k1_addcarryx_u64(&x23, &x24, x22, x14, x11);
fiat_secp256k1_addcarryx_u64(&x25, &x26, 0x0, x5, x17);
fiat_secp256k1_addcarryx_u64(&x27, &x28, x26, x7, x19);
fiat_secp256k1_addcarryx_u64(&x29, &x30, x28, x8, x21);
fiat_secp256k1_addcarryx_u64(&x31, &x32, x30, 0x0, x23);
fiat_secp256k1_addcarryx_u64(&x33, &x34, x32, 0x0, (x24 + x12));
fiat_secp256k1_mulx_u64(&x35, &x36, x1, UINT64_C(0x7a2000e90a1));
fiat_secp256k1_addcarryx_u64(&x37, &x38, 0x0, x36, x1);
fiat_secp256k1_addcarryx_u64(&x39, &x40, 0x0, x27, x35);
fiat_secp256k1_addcarryx_u64(&x41, &x42, x40, x29, x37);
fiat_secp256k1_addcarryx_u64(&x43, &x44, x42, x31, x38);
fiat_secp256k1_addcarryx_u64(&x45, &x46, x44, x33, 0x0);
fiat_secp256k1_mulx_u64(&x47, &x48, x39, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x49, &x50, x47, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x51, &x52, x47, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x53, &x54, x47, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x55, &x56, x47, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x57, &x58, 0x0, x56, x53);
fiat_secp256k1_addcarryx_u64(&x59, &x60, x58, x54, x51);
fiat_secp256k1_addcarryx_u64(&x61, &x62, x60, x52, x49);
fiat_secp256k1_addcarryx_u64(&x63, &x64, 0x0, x39, x55);
fiat_secp256k1_addcarryx_u64(&x65, &x66, x64, x41, x57);
fiat_secp256k1_addcarryx_u64(&x67, &x68, x66, x43, x59);
fiat_secp256k1_addcarryx_u64(&x69, &x70, x68, x45, x61);
fiat_secp256k1_addcarryx_u64(&x71, &x72, x70, ((uint64_t)x46 + x34), (x62 + x50));
fiat_secp256k1_mulx_u64(&x73, &x74, x2, UINT64_C(0x7a2000e90a1));
fiat_secp256k1_addcarryx_u64(&x75, &x76, 0x0, x74, x2);
fiat_secp256k1_addcarryx_u64(&x77, &x78, 0x0, x65, x73);
fiat_secp256k1_addcarryx_u64(&x79, &x80, x78, x67, x75);
fiat_secp256k1_addcarryx_u64(&x81, &x82, x80, x69, x76);
fiat_secp256k1_addcarryx_u64(&x83, &x84, x82, x71, 0x0);
fiat_secp256k1_mulx_u64(&x85, &x86, x77, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x87, &x88, x85, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x89, &x90, x85, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x91, &x92, x85, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x93, &x94, x85, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x95, &x96, 0x0, x94, x91);
fiat_secp256k1_addcarryx_u64(&x97, &x98, x96, x92, x89);
fiat_secp256k1_addcarryx_u64(&x99, &x100, x98, x90, x87);
fiat_secp256k1_addcarryx_u64(&x101, &x102, 0x0, x77, x93);
fiat_secp256k1_addcarryx_u64(&x103, &x104, x102, x79, x95);
fiat_secp256k1_addcarryx_u64(&x105, &x106, x104, x81, x97);
fiat_secp256k1_addcarryx_u64(&x107, &x108, x106, x83, x99);
fiat_secp256k1_addcarryx_u64(&x109, &x110, x108, ((uint64_t)x84 + x72), (x100 + x88));
fiat_secp256k1_mulx_u64(&x111, &x112, x3, UINT64_C(0x7a2000e90a1));
fiat_secp256k1_addcarryx_u64(&x113, &x114, 0x0, x112, x3);
fiat_secp256k1_addcarryx_u64(&x115, &x116, 0x0, x103, x111);
fiat_secp256k1_addcarryx_u64(&x117, &x118, x116, x105, x113);
fiat_secp256k1_addcarryx_u64(&x119, &x120, x118, x107, x114);
fiat_secp256k1_addcarryx_u64(&x121, &x122, x120, x109, 0x0);
fiat_secp256k1_mulx_u64(&x123, &x124, x115, UINT64_C(0xd838091dd2253531));
fiat_secp256k1_mulx_u64(&x125, &x126, x123, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x127, &x128, x123, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x129, &x130, x123, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_mulx_u64(&x131, &x132, x123, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_addcarryx_u64(&x133, &x134, 0x0, x132, x129);
fiat_secp256k1_addcarryx_u64(&x135, &x136, x134, x130, x127);
fiat_secp256k1_addcarryx_u64(&x137, &x138, x136, x128, x125);
fiat_secp256k1_addcarryx_u64(&x139, &x140, 0x0, x115, x131);
fiat_secp256k1_addcarryx_u64(&x141, &x142, x140, x117, x133);
fiat_secp256k1_addcarryx_u64(&x143, &x144, x142, x119, x135);
fiat_secp256k1_addcarryx_u64(&x145, &x146, x144, x121, x137);
fiat_secp256k1_addcarryx_u64(&x147, &x148, x146, ((uint64_t)x122 + x110), (x138 + x126));
fiat_secp256k1_subborrowx_u64(&x149, &x150, 0x0, x141, UINT64_C(0xfffffffefffffc2f));
fiat_secp256k1_subborrowx_u64(&x151, &x152, x150, x143, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x153, &x154, x152, x145, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x155, &x156, x154, x147, UINT64_C(0xffffffffffffffff));
fiat_secp256k1_subborrowx_u64(&x157, &x158, x156, x148, 0x0);
fiat_secp256k1_cmovznz_u64(&x159, x158, x149, x141);
fiat_secp256k1_cmovznz_u64(&x160, x158, x151, x143);
fiat_secp256k1_cmovznz_u64(&x161, x158, x153, x145);
fiat_secp256k1_cmovznz_u64(&x162, x158, x155, x147);
out1[0] = x159;
out1[1] = x160;
out1[2] = x161;
out1[3] = x162;
}
/*
* The function fiat_secp256k1_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 void fiat_secp256k1_nonzero(uint64_t* out1, const uint64_t arg1[4]) {
uint64_t x1;
x1 = ((arg1[0]) | ((arg1[1]) | ((arg1[2]) | (arg1[3]))));
*out1 = x1;
}
/*
* The function fiat_secp256k1_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 void fiat_secp256k1_selectznz(uint64_t out1[4], fiat_secp256k1_uint1 arg1, const uint64_t arg2[4], const uint64_t arg3[4]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
fiat_secp256k1_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0]));
fiat_secp256k1_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1]));
fiat_secp256k1_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2]));
fiat_secp256k1_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3]));
out1[0] = x1;
out1[1] = x2;
out1[2] = x3;
out1[3] = x4;
}
/*
* The function fiat_secp256k1_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 void fiat_secp256k1_to_bytes(uint8_t out1[32], const uint64_t arg1[4]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint8_t x5;
uint64_t x6;
uint8_t x7;
uint64_t x8;
uint8_t x9;
uint64_t x10;
uint8_t x11;
uint64_t x12;
uint8_t x13;
uint64_t x14;
uint8_t x15;
uint64_t x16;
uint8_t x17;
uint8_t x18;
uint8_t x19;
uint64_t x20;
uint8_t x21;
uint64_t x22;
uint8_t x23;
uint64_t x24;
uint8_t x25;
uint64_t x26;
uint8_t x27;
uint64_t x28;
uint8_t x29;
uint64_t x30;
uint8_t x31;
uint8_t x32;
uint8_t x33;
uint64_t x34;
uint8_t x35;
uint64_t x36;
uint8_t x37;
uint64_t x38;
uint8_t x39;
uint64_t x40;
uint8_t x41;
uint64_t x42;
uint8_t x43;
uint64_t x44;
uint8_t x45;
uint8_t x46;
uint8_t x47;
uint64_t x48;
uint8_t x49;
uint64_t x50;
uint8_t x51;
uint64_t x52;
uint8_t x53;
uint64_t x54;
uint8_t x55;
uint64_t x56;
uint8_t x57;
uint64_t x58;
uint8_t x59;
uint8_t x60;
x1 = (arg1[3]);
x2 = (arg1[2]);
x3 = (arg1[1]);
x4 = (arg1[0]);
x5 = (uint8_t)(x4 & UINT8_C(0xff));
x6 = (x4 >> 8);
x7 = (uint8_t)(x6 & UINT8_C(0xff));
x8 = (x6 >> 8);
x9 = (uint8_t)(x8 & UINT8_C(0xff));
x10 = (x8 >> 8);
x11 = (uint8_t)(x10 & UINT8_C(0xff));
x12 = (x10 >> 8);
x13 = (uint8_t)(x12 & UINT8_C(0xff));
x14 = (x12 >> 8);
x15 = (uint8_t)(x14 & UINT8_C(0xff));
x16 = (x14 >> 8);
x17 = (uint8_t)(x16 & UINT8_C(0xff));
x18 = (uint8_t)(x16 >> 8);
x19 = (uint8_t)(x3 & UINT8_C(0xff));
x20 = (x3 >> 8);
x21 = (uint8_t)(x20 & UINT8_C(0xff));
x22 = (x20 >> 8);
x23 = (uint8_t)(x22 & UINT8_C(0xff));
x24 = (x22 >> 8);
x25 = (uint8_t)(x24 & UINT8_C(0xff));
x26 = (x24 >> 8);
x27 = (uint8_t)(x26 & UINT8_C(0xff));
x28 = (x26 >> 8);
x29 = (uint8_t)(x28 & UINT8_C(0xff));
x30 = (x28 >> 8);
x31 = (uint8_t)(x30 & UINT8_C(0xff));
x32 = (uint8_t)(x30 >> 8);
x33 = (uint8_t)(x2 & UINT8_C(0xff));
x34 = (x2 >> 8);
x35 = (uint8_t)(x34 & UINT8_C(0xff));
x36 = (x34 >> 8);
x37 = (uint8_t)(x36 & UINT8_C(0xff));
x38 = (x36 >> 8);
x39 = (uint8_t)(x38 & UINT8_C(0xff));
x40 = (x38 >> 8);
x41 = (uint8_t)(x40 & UINT8_C(0xff));
x42 = (x40 >> 8);
x43 = (uint8_t)(x42 & UINT8_C(0xff));
x44 = (x42 >> 8);
x45 = (uint8_t)(x44 & UINT8_C(0xff));
x46 = (uint8_t)(x44 >> 8);
x47 = (uint8_t)(x1 & UINT8_C(0xff));
x48 = (x1 >> 8);
x49 = (uint8_t)(x48 & UINT8_C(0xff));
x50 = (x48 >> 8);
x51 = (uint8_t)(x50 & UINT8_C(0xff));
x52 = (x50 >> 8);
x53 = (uint8_t)(x52 & UINT8_C(0xff));
x54 = (x52 >> 8);
x55 = (uint8_t)(x54 & UINT8_C(0xff));
x56 = (x54 >> 8);
x57 = (uint8_t)(x56 & UINT8_C(0xff));
x58 = (x56 >> 8);
x59 = (uint8_t)(x58 & UINT8_C(0xff));
x60 = (uint8_t)(x58 >> 8);
out1[0] = x5;
out1[1] = x7;
out1[2] = x9;
out1[3] = x11;
out1[4] = x13;
out1[5] = x15;
out1[6] = x17;
out1[7] = x18;
out1[8] = x19;
out1[9] = x21;
out1[10] = x23;
out1[11] = x25;
out1[12] = x27;
out1[13] = x29;
out1[14] = x31;
out1[15] = x32;
out1[16] = x33;
out1[17] = x35;
out1[18] = x37;
out1[19] = x39;
out1[20] = x41;
out1[21] = x43;
out1[22] = x45;
out1[23] = x46;
out1[24] = x47;
out1[25] = x49;
out1[26] = x51;
out1[27] = x53;
out1[28] = x55;
out1[29] = x57;
out1[30] = x59;
out1[31] = x60;
}
/*
* The function fiat_secp256k1_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 void fiat_secp256k1_from_bytes(uint64_t out1[4], const uint8_t arg1[32]) {
uint64_t x1;
uint64_t x2;
uint64_t x3;
uint64_t x4;
uint64_t x5;
uint64_t x6;
uint64_t x7;
uint8_t x8;
uint64_t x9;
uint64_t x10;
uint64_t x11;
uint64_t x12;
uint64_t x13;
uint64_t x14;
uint64_t x15;
uint8_t x16;
uint64_t x17;
uint64_t x18;
uint64_t x19;
uint64_t x20;
uint64_t x21;
uint64_t x22;
uint64_t x23;
uint8_t x24;
uint64_t x25;
uint64_t x26;
uint64_t x27;
uint64_t x28;
uint64_t x29;
uint64_t x30;
uint64_t x31;
uint8_t x32;
uint64_t x33;
uint64_t x34;
uint64_t x35;
uint64_t x36;
uint64_t x37;
uint64_t x38;
uint64_t x39;
uint64_t x40;
uint64_t x41;
uint64_t x42;
uint64_t x43;
uint64_t x44;
uint64_t x45;
uint64_t x46;
uint64_t x47;
uint64_t x48;
uint64_t x49;
uint64_t x50;
uint64_t x51;
uint64_t x52;
uint64_t x53;
uint64_t x54;
uint64_t x55;
uint64_t x56;
uint64_t x57;
uint64_t x58;
uint64_t x59;
uint64_t x60;
x1 = ((uint64_t)(arg1[31]) << 56);
x2 = ((uint64_t)(arg1[30]) << 48);
x3 = ((uint64_t)(arg1[29]) << 40);
x4 = ((uint64_t)(arg1[28]) << 32);
x5 = ((uint64_t)(arg1[27]) << 24);
x6 = ((uint64_t)(arg1[26]) << 16);
x7 = ((uint64_t)(arg1[25]) << 8);
x8 = (arg1[24]);
x9 = ((uint64_t)(arg1[23]) << 56);
x10 = ((uint64_t)(arg1[22]) << 48);
x11 = ((uint64_t)(arg1[21]) << 40);
x12 = ((uint64_t)(arg1[20]) << 32);
x13 = ((uint64_t)(arg1[19]) << 24);
x14 = ((uint64_t)(arg1[18]) << 16);
x15 = ((uint64_t)(arg1[17]) << 8);
x16 = (arg1[16]);
x17 = ((uint64_t)(arg1[15]) << 56);
x18 = ((uint64_t)(arg1[14]) << 48);
x19 = ((uint64_t)(arg1[13]) << 40);
x20 = ((uint64_t)(arg1[12]) << 32);
x21 = ((uint64_t)(arg1[11]) << 24);
x22 = ((uint64_t)(arg1[10]) << 16);
x23 = ((uint64_t)(arg1[9]) << 8);
x24 = (arg1[8]);
x25 = ((uint64_t)(arg1[7]) << 56);
x26 = ((uint64_t)(arg1[6]) << 48);
x27 = ((uint64_t)(arg1[5]) << 40);
x28 = ((uint64_t)(arg1[4]) << 32);
x29 = ((uint64_t)(arg1[3]) << 24);
x30 = ((uint64_t)(arg1[2]) << 16);
x31 = ((uint64_t)(arg1[1]) << 8);
x32 = (arg1[0]);
x33 = (x31 + (uint64_t)x32);
x34 = (x30 + x33);
x35 = (x29 + x34);
x36 = (x28 + x35);
x37 = (x27 + x36);
x38 = (x26 + x37);
x39 = (x25 + x38);
x40 = (x23 + (uint64_t)x24);
x41 = (x22 + x40);
x42 = (x21 + x41);
x43 = (x20 + x42);
x44 = (x19 + x43);
x45 = (x18 + x44);
x46 = (x17 + x45);
x47 = (x15 + (uint64_t)x16);
x48 = (x14 + x47);
x49 = (x13 + x48);
x50 = (x12 + x49);
x51 = (x11 + x50);
x52 = (x10 + x51);
x53 = (x9 + x52);
x54 = (x7 + (uint64_t)x8);
x55 = (x6 + x54);
x56 = (x5 + x55);
x57 = (x4 + x56);
x58 = (x3 + x57);
x59 = (x2 + x58);
x60 = (x1 + x59);
out1[0] = x39;
out1[1] = x46;
out1[2] = x53;
out1[3] = x60;
}
