/* 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 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; }