diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..becd7f9 --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ +* +!*/ +!*.* diff --git a/LICENSE.md b/LICENSE.md new file mode 100644 index 0000000..966d4c4 --- /dev/null +++ b/LICENSE.md @@ -0,0 +1,5 @@ +Licensed and distributed under either of +[MIT license](http://opensource.org/licenses/MIT) or +[Apache License, Version 2.0](http://www.apache.org/licenses/LICENSE-2.0) +at your option. These files may not be copied, modified, or distributed except +according to those terms. diff --git a/README.md b/README.md new file mode 100644 index 0000000..518d476 --- /dev/null +++ b/README.md @@ -0,0 +1,42 @@ +Nim/C implementation of Poseidon2 over the Goldilocks field +=========================================================== + +Experimental implementation of the [Poseidon2][1] cryptographic hash function, +specialized to the Goldilocks field `p=2^64-2^32+1` and `t=12`. +Uses a C implementation internally. + +Installation +------------ + +Use the [Nimble][2] package manager to add `poseidon2-goldilocks` to an existing +project. Add the following to its `.nimble` file: + +```nim +requires "poseidon2-goldilocks >= 0.0.1 & < 0.0.1" +``` + +Usage +----- + +Hashing bytes into a field element with the sponge construction: +```nim +import poseidon2_goldilocks + +let input = [1'u8, 2'u8, 3'u8] # some bytes that you want to hash +let digest: F = Sponge.digest(input) # a field element +``` + +Converting a hash digest (4 field elements) into bytes: +```nim +let output: array[32, byte] = digest.toBytes +``` + +Combining field elements, useful for constructing a binary Merkle tree: +```nim +let left = Sponge.digest([1'u8, 2'u8, 3'u8]) +let right = Sponge.digest([4'u8, 5'u8, 6'u8]) +let combination = compress(left, right) +``` + +[1]: https://eprint.iacr.org/2023/323.pdf +[2]: https://github.com/nim-lang/nimble diff --git a/cbits/goldilocks.c b/cbits/goldilocks.c new file mode 100644 index 0000000..8fcdeb5 --- /dev/null +++ b/cbits/goldilocks.c @@ -0,0 +1,417 @@ + +#include +#include // for testing only + +#include "goldilocks.h" + +//============================================================================== +// *** Goldilocks field *** + +uint64_t goldilocks_neg(uint64_t x) { + return (x==0) ? 0 : (GOLDILOCKS_PRIME - x); +} + +uint64_t goldilocks_add(uint64_t x, uint64_t y) { + uint64_t z = x + y; + return ( (z >= GOLDILOCKS_PRIME) || (z x) ? (z + GOLDILOCKS_PRIME) : z; +} + +uint64_t goldilocks_sub_safe(uint64_t x, uint64_t y) { + return goldilocks_add( x , goldilocks_neg(y) ); +} + +/* + +// add together 3 field elements +uint64_t goldilocks_add3( uint64_t x0, uint64_t x1, uint64_t x2 ) { + uint64_t x01 = goldilocks_add( x0 , x1 ); + return goldilocks_add( x01, x2 ); +} + +//-------------------------------------- + +uint64_t goldilocks_div_by_2(uint64_t x) { + return (x & 1) ? (x/2 + 0x7fffffff80000001) : (x/2); +} + +uint64_t goldilocks_div_by_3(uint64_t x) { + uint64_t m = x % 3; + uint64_t r; + switch(m) { + case 0: + r = (x/3); + break; + case 1: + r = (x/3 + 0xaaaaaaaa00000001); // (x+2*p) / 3 = x/3 + (2*p+1)/3 + break; + case 2: + r = (x/3 + 0x5555555500000001); // (x+p) / 3 = x/3 + (p+1)/3 + break; + } + return r; +} + +uint64_t goldilocks_div_by_4(uint64_t x) { + return goldilocks_div_by_2(goldilocks_div_by_2(x)); +} + +*/ + +//-------------------------------------- + +uint64_t goldilocks_rdc(__uint128_t x) { + // x = n0 + 2^64 * n1 + 2^96 * n2 + uint64_t n0 = (uint64_t)x; + uint64_t n1 = (x >> 64) & 0xffffffff; + uint64_t n2 = (x >> 96); + + uint64_t mid = (n1 << 32) - n1; // (2^32 - 1) * n1 + uint64_t tmp = n0 + mid; + if (tmp < n0) { tmp -= GOLDILOCKS_PRIME; } + + uint64_t res = tmp - n2; + if (res > tmp) { res += GOLDILOCKS_PRIME; } + return (res >= GOLDILOCKS_PRIME) ? (res - GOLDILOCKS_PRIME) : res; +} + +// reduce to 64-bit, but it can be still bigger than `p` +uint64_t goldilocks_rdc_to_uint64(__uint128_t x) { + // x = n0 + 2^64 * n1 + 2^96 * n2 + uint64_t n0 = (uint64_t)x; + uint64_t n1 = (x >> 64) & 0xffffffff; + uint64_t n2 = (x >> 96); + + uint64_t mid = (n1 << 32) - n1; // (2^32 - 1) * n1 + uint64_t tmp = n0 + mid; + if (tmp < n0) { tmp -= GOLDILOCKS_PRIME; } + + uint64_t res = tmp - n2; + if (res > tmp) { res += GOLDILOCKS_PRIME; } + return res; +} + +// we assume x < 2^96 +uint64_t goldilocks_rdc_small(__uint128_t x) { + // x = n0 + 2^64 * n1 + uint64_t n0 = (uint64_t)x; + uint64_t n1 = (x >> 64); + + uint64_t mid = (n1 << 32) - n1; // (2^32 - 1) * n1 + uint64_t tmp = n0 + mid; + if (tmp < n0) { tmp -= GOLDILOCKS_PRIME; } + + uint64_t res = tmp; + return (res >= GOLDILOCKS_PRIME) ? (res - GOLDILOCKS_PRIME) : res; +} + +//-------------------------------------- + +uint64_t goldilocks_mul(uint64_t x, uint64_t y) { + __uint128_t z = (__uint128_t)x * (__uint128_t)y; + return goldilocks_rdc(z); +} + +uint64_t goldilocks_mul_add128(uint64_t x, uint64_t y, __uint128_t z) { + __uint128_t w = (__uint128_t)x * (__uint128_t)y + z; + return goldilocks_rdc(w); +} + +uint64_t goldilocks_sqr(uint64_t x) { + __uint128_t z = (__uint128_t)x * (__uint128_t)x; + return goldilocks_rdc(z); +} + +uint64_t goldilocks_sqr_add(uint64_t x, uint64_t y) { + __uint128_t z = (__uint128_t)x * x + y; + return goldilocks_rdc(z); +} + +// only reduce to uint64, not to [0..p-1] +uint64_t goldilocks_sqr_add_to_uint64(uint64_t x, uint64_t y) { + __uint128_t z = (__uint128_t)x * x + y; + return goldilocks_rdc_to_uint64(z); +} + +uint64_t goldilocks_mul_small(uint64_t x, uint32_t y) { + __uint128_t z = (__uint128_t)x * (__uint128_t)y; + return goldilocks_rdc_small(z); +} + +//============================================================================== +// *** debugging *** + +void debug_print_state(const char *msg, int n, uint64_t *state) { + printf("-----------------\n"); + printf("%s\n",msg); + for(int i=0;i +// NOT compatible with +// (presumably they use different constants or whatever) +// + +#include "poseidon2_constants.inc" + +/* +poseidon2 test vector (permutation of [0..11]) +---------------------------------------------- +from + +0x01eaef96bdf1c0c1 +0x1f0d2cc525b2540c +0x6282c1dfe1e0358d +0xe780d721f698e1e6 +0x280c0b6f753d833b +0x1b942dd5023156ab +0x43f0df3fcccb8398 +0xe8e8190585489025 +0x56bdbf72f77ada22 +0x7911c32bf9dcd705 +0xec467926508fbe67 +0x6a50450ddf85a6ed +*/ + +uint64_t goldilocks_poseidon2_sbox(uint64_t x0, uint64_t rc) { + uint64_t x = goldilocks_add( x0 , rc ); + uint64_t x2 = goldilocks_sqr( x ); + uint64_t x4 = goldilocks_sqr( x2 ); + uint64_t x6 = goldilocks_mul( x4 , x2 ); + uint64_t x7 = goldilocks_mul( x6 , x ); + return x7; +} + +// remark: (p-1)^2 + 12*(p-1) does not overflow in 2^128 +void goldilocks_poseidon2_internal_diffusion(uint64_t *inp, uint64_t *out) { + __uint128_t s0 = inp[0]; + __uint128_t s1 = inp[6]; + s0 += inp[1]; s1 += inp[7]; + s0 += inp[2]; s1 += inp[8]; + s0 += inp[3]; s1 += inp[9]; + s0 += inp[4]; s1 += inp[10]; + s0 += inp[5]; s1 += inp[11]; +// uint64_t s = goldilocks_rdc_small( s0 + s1 ); + __uint128_t s = s0 + s1; + + for(int i=0; i<12; i++) { + out[i] = goldilocks_mul_add128( inp[i] , internal_diag[i] , s ); + } +} + +//-------------------------------------- + +/* + +// multiplies a vector of size 4 by the 4x4 MDS matrix on the left: +// +// [ 5 7 1 3 ] +// M4 = [ 4 6 1 1 ] +// [ 1 3 5 7 ] +// [ 1 1 4 6 ] +// +void goldilocks_mul_by_M4(uint64_t *inp, uint64_t *out) { + uint64_t a = inp[0]; + uint64_t b = inp[1]; + uint64_t c = inp[2]; + uint64_t d = inp[3]; + + uint64_t a2 = goldilocks_add( a , a ); + uint64_t a4 = goldilocks_add( a2 , a2 ); + uint64_t a5 = goldilocks_add( a4 , a ); + + uint64_t b2 = goldilocks_add( b , b ); + uint64_t b3 = goldilocks_add( b2 , b ); + uint64_t b6 = goldilocks_add( b3 , b3 ); + uint64_t b7 = goldilocks_add( b6 , b ); + + uint64_t c2 = goldilocks_add( c , c ); + uint64_t c4 = goldilocks_add( c2 , c2 ); + uint64_t c5 = goldilocks_add( c4 , c ); + + uint64_t d2 = goldilocks_add( d , d ); + uint64_t d3 = goldilocks_add( d2 , d ); + uint64_t d6 = goldilocks_add( d3 , d3 ); + uint64_t d7 = goldilocks_add( d6 , d ); + + out[0] = goldilocks_add( goldilocks_add( a5 , b7 ) , goldilocks_add( c , d3 ) ); + out[1] = goldilocks_add( goldilocks_add( a4 , b6 ) , goldilocks_add( c , d ) ); + out[2] = goldilocks_add( goldilocks_add( a , b3 ) , goldilocks_add( c5 , d7 ) ); + out[3] = goldilocks_add( goldilocks_add( a , b ) , goldilocks_add( c4 , d6 ) ); +} + +// returns 2*a + b + c +uint64_t goldilocks_weighted_add_211(uint64_t a, uint64_t b, uint64_t c) { + uint64_t a2 = goldilocks_add( a , a ); + uint64_t bc = goldilocks_add( b , c ); + return goldilocks_add( a2 , bc ); +} + +// multiplies by 12x12 block-circulant matrix [2*M4, M4, M4] +void goldilocks_poseidon2_external_diffusion(uint64_t *inp, uint64_t *out) { + uint64_t us[4]; + uint64_t vs[4]; + uint64_t ws[4]; + + goldilocks_mul_by_M4( inp + 0 , us ); + goldilocks_mul_by_M4( inp + 4 , vs ); + goldilocks_mul_by_M4( inp + 8 , ws ); + + out[0] = goldilocks_weighted_add_211( us[0] , vs[0] , ws[0] ); + out[1] = goldilocks_weighted_add_211( us[1] , vs[1] , ws[1] ); + out[2] = goldilocks_weighted_add_211( us[2] , vs[2] , ws[2] ); + out[3] = goldilocks_weighted_add_211( us[3] , vs[3] , ws[3] ); + + out[4] = goldilocks_weighted_add_211( vs[0] , ws[0] , us[0] ); + out[5] = goldilocks_weighted_add_211( vs[1] , ws[1] , us[1] ); + out[6] = goldilocks_weighted_add_211( vs[2] , ws[2] , us[2] ); + out[7] = goldilocks_weighted_add_211( vs[3] , ws[3] , us[3] ); + + out[ 8] = goldilocks_weighted_add_211( ws[0] , us[0] , vs[0] ); + out[ 9] = goldilocks_weighted_add_211( ws[1] , us[1] , vs[1] ); + out[10] = goldilocks_weighted_add_211( ws[2] , us[2] , vs[2] ); + out[11] = goldilocks_weighted_add_211( ws[3] , us[3] , vs[3] ); +} + +*/ + +//-------------------------------------- + +// multiplies a vector of size 4 by the 4x4 MDS matrix on the left +void uint64_mul_by_M4(uint64_t *inp, uint64_t *out) { + uint64_t a = inp[0]; + uint64_t b = inp[1]; + uint64_t c = inp[2]; + uint64_t d = inp[3]; + + uint64_t a4 = a << 2; + uint64_t a5 = a4 + a; + + uint64_t b2 = b + b ; + uint64_t b3 = b2 + b ; + uint64_t b6 = b3 + b3 ; + uint64_t b7 = b6 + b ; + + uint64_t c4 = c << 2 ; + uint64_t c5 = c4 + c ; + + uint64_t d2 = d + d ; + uint64_t d3 = d2 + d ; + uint64_t d6 = d3 + d3 ; + uint64_t d7 = d6 + d ; + + out[0] = a5 + b7 + c + d3 ; + out[1] = a4 + b6 + c + d ; + out[2] = a + b3 + c5 + d7 ; + out[3] = a + b + c4 + d6 ; +} + +// multiplies by 12x12 block-circulant matrix [2*M4, M4, M4] +void uint64_mul_by_poseidon2_circulant12(uint64_t *inp, uint64_t *out) { + uint64_t us[4]; + uint64_t vs[4]; + uint64_t ws[4]; + + uint64_mul_by_M4( inp + 0 , us ); + uint64_mul_by_M4( inp + 4 , vs ); + uint64_mul_by_M4( inp + 8 , ws ); + + out[0] = 2*us[0] + vs[0] + ws[0]; + out[1] = 2*us[1] + vs[1] + ws[1]; + out[2] = 2*us[2] + vs[2] + ws[2]; + out[3] = 2*us[3] + vs[3] + ws[3]; + + out[4] = us[0] + 2*vs[0] + ws[0]; + out[5] = us[1] + 2*vs[1] + ws[1]; + out[6] = us[2] + 2*vs[2] + ws[2]; + out[7] = us[3] + 2*vs[3] + ws[3]; + + out[ 8] = us[0] + vs[0] + 2*ws[0]; + out[ 9] = us[1] + vs[1] + 2*ws[1]; + out[10] = us[2] + vs[2] + 2*ws[2]; + out[11] = us[3] + vs[3] + 2*ws[3]; +} + +void goldilocks_poseidon2_external_diffusion_split(uint64_t *inp, uint64_t *out) { + uint64_t inp_lo[12]; + uint64_t inp_hi[12]; + uint64_t out_lo[12]; + uint64_t out_hi[12]; + + for(int i=0; i<12; i++) { + uint64_t x = inp[i]; + inp_lo[i] = x & 0xffffffff; + inp_hi[i] = x >> 32; + } + + uint64_mul_by_poseidon2_circulant12(inp_lo, out_lo); + uint64_mul_by_poseidon2_circulant12(inp_hi, out_hi); + + for(int i=0; i<12; i++) { + __uint128_t x = (((__uint128_t)out_hi[i]) << 32) + out_lo[i]; + out[i] = goldilocks_rdc_small(x); + } +} + +//-------------------------------------- + +// 0 <= round_idx < 22 +void goldilocks_poseidon2_internal_round(int round_idx, uint64_t *state) { + state[0] = goldilocks_poseidon2_sbox( state[0] , internal_round_consts[round_idx] ); + goldilocks_poseidon2_internal_diffusion( state, state ); +} + +void goldilocks_poseidon2_external_round(const uint64_t *rcs, uint64_t *state) { + for (int i=0; i<12; i++) { + state[i] = goldilocks_poseidon2_sbox( state[i] , rcs[i] ); + } + goldilocks_poseidon2_external_diffusion_split( state, state ); +} + +void goldilocks_poseidon2_permutation(uint64_t *state) { + goldilocks_poseidon2_external_diffusion_split( state, state ); + goldilocks_poseidon2_external_round( intial_round_consts + 0 , state ); + goldilocks_poseidon2_external_round( intial_round_consts + 12 , state ); + goldilocks_poseidon2_external_round( intial_round_consts + 24 , state ); + goldilocks_poseidon2_external_round( intial_round_consts + 36 , state ); + for(int idx=0; idx<22; idx++) { + goldilocks_poseidon2_internal_round( idx, state ); + } + goldilocks_poseidon2_external_round( final_round_consts + 0 , state ); + goldilocks_poseidon2_external_round( final_round_consts + 12 , state ); + goldilocks_poseidon2_external_round( final_round_consts + 24 , state ); + goldilocks_poseidon2_external_round( final_round_consts + 36 , state ); +} + +//------------------------------------------------------------------------------ + +// compression function: input is two 4-element vector of field elements, +// and the output is a vector of 4 field elements +void goldilocks_poseidon2_keyed_compress(uint64_t key, const uint64_t *x, const uint64_t *y, uint64_t *out) { + uint64_t state[12]; + for(int i=0; i<4; i++) { + state[i ] = x[i]; + state[i+4] = y[i]; + state[i+8] = 0; + } + state[8] = key; + goldilocks_poseidon2_permutation(state); + for(int i=0; i<4; i++) { + out[i] = state[i]; + } +} + +void goldilocks_poseidon2_compress(const uint64_t *x, const uint64_t *y, uint64_t *out) { + goldilocks_poseidon2_keyed_compress(0, x, y, out); +} + +//------------------------------------------------------------------------------ diff --git a/cbits/goldilocks.h b/cbits/goldilocks.h new file mode 100644 index 0000000..3bfc4ca --- /dev/null +++ b/cbits/goldilocks.h @@ -0,0 +1,32 @@ + +#include + +//------------------------------------------------------------------------------ + +#define GOLDILOCKS_PRIME 0xffffffff00000001 + +//------------------------------------------------------------------------------ + +uint64_t goldilocks_neg(uint64_t x); +uint64_t goldilocks_add(uint64_t x, uint64_t y); +uint64_t goldilocks_sub(uint64_t x, uint64_t y); +uint64_t goldilocks_mul(uint64_t x, uint64_t y); +uint64_t goldilocks_mul_small(uint64_t x, uint32_t y); + +uint64_t goldilocks_div_by_2(uint64_t x); +uint64_t goldilocks_div_by_3(uint64_t x); +uint64_t goldilocks_div_by_4(uint64_t x); + +uint64_t goldilocks_add3(uint64_t x, uint64_t y, uint64_t z); + +//uint64_t goldilocks_rdc(__uint128_t x); + +//------------------------------------------------------------------------------ + +void goldilocks_poseidon2_permutation(uint64_t *state); +void goldilocks_monolith_permutation (uint64_t *state); + +void monolith_print_sbox_table(); +void monolith_print_sbox_table_c_format(); + +//------------------------------------------------------------------------------ diff --git a/cbits/poseidon2_constants.inc b/cbits/poseidon2_constants.inc new file mode 100644 index 0000000..fb1be2f --- /dev/null +++ b/cbits/poseidon2_constants.inc @@ -0,0 +1,165 @@ + +// based on the reference implementation: +// + +#include + +//------------------------------------------------------------------------------ + +// internal matrices are the constant 1 matrix + diagonal of these +// (in particular the diagonals of the resulting matrix will be these plus one!) +const uint64_t internal_diag[12] = + { 0xc3b6c08e23ba9300 + , 0xd84b5de94a324fb6 + , 0x0d0c371c5b35b84f + , 0x7964f570e7188037 + , 0x5daf18bbd996604b + , 0x6743bc47b9595257 + , 0x5528b9362c59bb70 + , 0xac45e25b7127b68b + , 0xa2077d7dfbb606b5 + , 0xf3faac6faee378ae + , 0x0c6388b51545e883 + , 0xd27dbb6944917b60 + }; + +//------------------------------------------------------------------------------ + +const uint64_t intial_round_consts[4*12] = + { 0x13dcf33aba214f46 + , 0x30b3b654a1da6d83 + , 0x1fc634ada6159b56 + , 0x937459964dc03466 + , 0xedd2ef2ca7949924 + , 0xede9affde0e22f68 + , 0x8515b9d6bac9282d + , 0x6b5c07b4e9e900d8 + , 0x1ec66368838c8a08 + , 0x9042367d80d1fbab + , 0x400283564a3c3799 + , 0x4a00be0466bca75e + // ----------------- + , 0x7913beee58e3817f + , 0xf545e88532237d90 + , 0x22f8cb8736042005 + , 0x6f04990e247a2623 + , 0xfe22e87ba37c38cd + , 0xd20e32c85ffe2815 + , 0x117227674048fe73 + , 0x4e9fb7ea98a6b145 + , 0xe0866c232b8af08b + , 0x00bbc77916884964 + , 0x7031c0fb990d7116 + , 0x240a9e87cf35108f + // ----------------- + , 0x2e6363a5a12244b3 + , 0x5e1c3787d1b5011c + , 0x4132660e2a196e8b + , 0x3a013b648d3d4327 + , 0xf79839f49888ea43 + , 0xfe85658ebafe1439 + , 0xb6889825a14240bd + , 0x578453605541382b + , 0x4508cda8f6b63ce9 + , 0x9c3ef35848684c91 + , 0x0812bde23c87178c + , 0xfe49638f7f722c14 + // ----------------- + , 0x8e3f688ce885cbf5 + , 0xb8e110acf746a87d + , 0xb4b2e8973a6dabef + , 0x9e714c5da3d462ec + , 0x6438f9033d3d0c15 + , 0x24312f7cf1a27199 + , 0x23f843bb47acbf71 + , 0x9183f11a34be9f01 + , 0x839062fbb9d45dbf + , 0x24b56e7e6c2e43fa + , 0xe1683da61c962a72 + , 0xa95c63971a19bfa7 + }; + +//------------------------------------------------------------------------------ + +const uint64_t final_round_consts[4*12] = + { 0xc68be7c94882a24d + , 0xaf996d5d5cdaedd9 + , 0x9717f025e7daf6a5 + , 0x6436679e6e7216f4 + , 0x8a223d99047af267 + , 0xbb512e35a133ba9a + , 0xfbbf44097671aa03 + , 0xf04058ebf6811e61 + , 0x5cca84703fac7ffb + , 0x9b55c7945de6469f + , 0x8e05bf09808e934f + , 0x2ea900de876307d7 + //------------------ + , 0x7748fff2b38dfb89 + , 0x6b99a676dd3b5d81 + , 0xac4bb7c627cf7c13 + , 0xadb6ebe5e9e2f5ba + , 0x2d33378cafa24ae3 + , 0x1e5b73807543f8c2 + , 0x09208814bfebb10f + , 0x782e64b6bb5b93dd + , 0xadd5a48eac90b50f + , 0xadd4c54c736ea4b1 + , 0xd58dbb86ed817fd8 + , 0x6d5ed1a533f34ddd + //------------------ + , 0x28686aa3e36b7cb9 + , 0x591abd3476689f36 + , 0x047d766678f13875 + , 0xa2a11112625f5b49 + , 0x21fd10a3f8304958 + , 0xf9b40711443b0280 + , 0xd2697eb8b2bde88e + , 0x3493790b51731b3f + , 0x11caf9dd73764023 + , 0x7acfb8f72878164e + , 0x744ec4db23cefc26 + , 0x1e00e58f422c6340 + //------------------ + , 0x21dd28d906a62dda + , 0xf32a46ab5f465b5f + , 0xbfce13201f3f7e6b + , 0xf30d2e7adb5304e2 + , 0xecdf4ee4abad48e9 + , 0xf94e82182d395019 + , 0x4ee52e3744d887c5 + , 0xa1341c7cac0083b2 + , 0x2302fb26c30c834a + , 0xaea3c587273bf7d3 + , 0xf798e24961823ec7 + , 0x962deba3e9a2cd94 + }; + +//------------------------------------------------------------------------------ + +const uint64_t internal_round_consts[22] = + { 0x4adf842aa75d4316 + , 0xf8fbb871aa4ab4eb + , 0x68e85b6eb2dd6aeb + , 0x07a0b06b2d270380 + , 0xd94e0228bd282de4 + , 0x8bdd91d3250c5278 + , 0x209c68b88bba778f + , 0xb5e18cdab77f3877 + , 0xb296a3e808da93fa + , 0x8370ecbda11a327e + , 0x3f9075283775dad8 + , 0xb78095bb23c6aa84 + , 0x3f36b9fe72ad4e5f + , 0x69bc96780b10b553 + , 0x3f1d341f2eb7b881 + , 0x4e939e9815838818 + , 0xda366b3ae2a31604 + , 0xbc89db1e7287d509 + , 0x6102f411f9ef5659 + , 0x58725c5e7ac1f0ab + , 0x0df5856c798883e7 + , 0xf7bb62a8da4c961b + }; + +//------------------------------------------------------------------------------ diff --git a/poseidon2/goldilocks.nim b/poseidon2/goldilocks.nim new file mode 100644 index 0000000..683d8b4 --- /dev/null +++ b/poseidon2/goldilocks.nim @@ -0,0 +1,8 @@ +{. compile: "../cbits/goldilocks.c" .} + +import ./types + +func neg* (x: F ): F {. header: "../cbits/goldilocks.h", importc: "goldilocks_neg", cdecl .} +func `+`* (x, y: F): F {. header: "../cbits/goldilocks.h", importc: "goldilocks_add", cdecl .} +func `-`* (x, y: F): F {. header: "../cbits/goldilocks.h", importc: "goldilocks_sub", cdecl .} +func `*`* (x, y: F): F {. header: "../cbits/goldilocks.h", importc: "goldilocks_mul", cdecl .} diff --git a/poseidon2/types.nim b/poseidon2/types.nim new file mode 100644 index 0000000..9d3e5e5 --- /dev/null +++ b/poseidon2/types.nim @@ -0,0 +1,29 @@ + +#------------------------------------------------------------------------------- + +type F* = distinct uint64 + +func `==`* (x, y: F): bool = + return (uint64(x) == uint64(y)) + +func fromF* (x: F): uint64 = + return uint64(x) + +func toF* (x: uint64): F = + return F(x) + +#------------------------------------------------------------------------------- + +const zero* : F = toF(0) +const one* : F = toF(1) +const two* : F = toF(2) + +#------------------------------------------------------------------------------- + +type F4* = array[4 , F] +type F12* = array[12, F] + +type Digest* = distinct F4 +type State* = distinct F12 + +#------------------------------------------------------------------------------- diff --git a/poseidon2_goldilocks.nim b/poseidon2_goldilocks.nim new file mode 100644 index 0000000..a10e85d --- /dev/null +++ b/poseidon2_goldilocks.nim @@ -0,0 +1,17 @@ +# import poseidon2/types +# import poseidon2/io +# import poseidon2/sponge +# import poseidon2/compress +# import poseidon2/merkle +# import poseidon2/spongemerkle + +# export sponge +# export compress +# export merkle +# export spongemerkle +# export fromBytes +# export toBytes +# export toF +# export elements +# export types + diff --git a/poseidon2_goldilocks.nimble b/poseidon2_goldilocks.nimble new file mode 100644 index 0000000..9ee7a18 --- /dev/null +++ b/poseidon2_goldilocks.nimble @@ -0,0 +1,5 @@ +version = "0.0.1" +author = "Balazs Komuves" +description = "Poseidon2 hash function over the goldilocks field" +license = "MIT" + diff --git a/reference/Goldilocks.hs b/reference/Goldilocks.hs new file mode 100644 index 0000000..92c44e9 --- /dev/null +++ b/reference/Goldilocks.hs @@ -0,0 +1,93 @@ + +-- | Reference (slow) implementation of the Goldilocks prime field + +{-# LANGUAGE BangPatterns, NumericUnderscores #-} +module Goldilocks where + +-------------------------------------------------------------------------------- + +import Prelude hiding ( div ) +import qualified Prelude + +import Data.Bits +import Data.Ratio + +import Text.Printf + +-------------------------------------------------------------------------------- + +type F = Goldilocks + +newtype Goldilocks + = Goldilocks Integer + deriving Eq + +instance Show Goldilocks where + show (Goldilocks k) = printf "0x%016x" k + +-------------------------------------------------------------------------------- + +instance Num Goldilocks where + fromInteger = mkGoldilocks + negate = neg + (+) = add + (-) = sub + (*) = mul + abs = id + signum _ = Goldilocks 1 + +instance Fractional Goldilocks where + fromRational y = fromInteger (numerator y) `div` fromInteger (denominator y) + recip = inv + (/) = div + +-------------------------------------------------------------------------------- + +-- | @p = 2^64 - 2^32 + 1@ +goldilocksPrime :: Integer +goldilocksPrime = 0x_ffff_ffff_0000_0001 + +modp :: Integer -> Integer +modp a = mod a goldilocksPrime + +mkGoldilocks :: Integer -> Goldilocks +mkGoldilocks = Goldilocks . modp + +-------------------------------------------------------------------------------- + +neg :: Goldilocks -> Goldilocks +neg (Goldilocks k) = mkGoldilocks (negate k) + +add :: Goldilocks -> Goldilocks -> Goldilocks +add (Goldilocks a) (Goldilocks b) = mkGoldilocks (a+b) + +sub :: Goldilocks -> Goldilocks -> Goldilocks +sub (Goldilocks a) (Goldilocks b) = mkGoldilocks (a-b) + +sqr :: Goldilocks -> Goldilocks +sqr x = mul x x + +mul :: Goldilocks -> Goldilocks -> Goldilocks +mul (Goldilocks a) (Goldilocks b) = mkGoldilocks (a*b) + +inv :: Goldilocks -> Goldilocks +inv x = pow x (goldilocksPrime - 2) + +div :: Goldilocks -> Goldilocks -> Goldilocks +div a b = mul a (inv b) + +-------------------------------------------------------------------------------- + +pow :: Goldilocks -> Integer -> Goldilocks +pow x e + | e == 0 = 1 + | e < 0 = pow (inv x) (negate e) + | otherwise = go 1 x e + where + go !acc _ 0 = acc + go !acc !s !expo = case expo .&. 1 of + 0 -> go acc (sqr s) (shiftR expo 1) + _ -> go (acc*s) (sqr s) (shiftR expo 1) + +-------------------------------------------------------------------------------- + diff --git a/reference/README.md b/reference/README.md new file mode 100644 index 0000000..82ae2bd --- /dev/null +++ b/reference/README.md @@ -0,0 +1,6 @@ + +Haskell reference implementation +-------------------------------- + +Used for generating test cases (as Nim doesn't support integers larger than 64 bit) + diff --git a/reference/TestGen.hs b/reference/TestGen.hs new file mode 100644 index 0000000..4dfc793 --- /dev/null +++ b/reference/TestGen.hs @@ -0,0 +1,87 @@ + +-- | Generate test cases for Nim + +module TestGen where + +-------------------------------------------------------------------------------- + +import System.IO + +import Goldilocks + +-------------------------------------------------------------------------------- + +centered :: Integer -> Integer -> [Integer] +centered center width = [center-width .. center+width] + +mkTestFieldElems :: Integer -> [F] +mkTestFieldElems width = map fromInteger $ concat + [ centered (0 ) width + , centered (2^16) width + , centered (2^31) width + , centered (2^32) width + , centered (2^33) width + , centered (2^48) width + , centered (2^63) width + ] + +testFieldElems :: [F] +testFieldElems = mkTestFieldElems 7 + +testFieldPairs :: [(F,F)] +testFieldPairs = [ (x,y) | x<-list, y<-list ] where + list = mkTestFieldElems 3 + +-------------------------------------------------------------------------------- + +nimShow :: F -> String +nimShow x = show x ++ "'u64" + +nimShowPair :: (F,F) -> String +nimShowPair (x,y) = "( " ++ nimShow x ++ " , " ++ nimShow y ++ " )" + +nimShowTriple :: (F,F,F) -> String +nimShowTriple (x,y,z) = "( " ++ nimShow x ++ " , " ++ nimShow y ++ " , " ++ nimShow z ++ " )" + +showPairs :: [(F,F)] -> [String] +showPairs xys = zipWith (++) prefix (map nimShowPair xys) where + prefix = " [ " : repeat " , " + +showTriples :: [(F,F,F)] -> [String] +showTriples xyzs = zipWith (++) prefix (map nimShowTriple xyzs) where + prefix = " [ " : repeat " , " + +---------------------------------------- + +unary :: String -> (F -> F) -> [F] -> String +unary varname f xs = unlines (header : stuff ++ footer) where + header = "const " ++ varname ++ "* : array[" ++ show (length xs) ++ ", tuple[x:uint64, y:uint64]] = " + footer = [" ]",""] + stuff = showPairs [ (x, f x) | x<-xs ] + +binary :: String -> (F -> F -> F) -> [(F,F)] -> String +binary varname f xys = unlines (header : stuff ++ footer) where + header = "const " ++ varname ++ "* : array[" ++ show (length xys) ++ ", tuple[x:uint64, y:uint64, z:uint64]] = " + footer = [" ]",""] + stuff = showTriples [ (x, y, f x y) | (x,y)<-xys ] + +-------------------------------------------------------------------------------- + +printTests :: IO () +printTests = hPrintTests stdout + +hPrintTests :: Handle -> IO () +hPrintTests h = hPutStrLn h $ unlines + [ unary "testcases_neg" negate testFieldElems + , binary "testcases_add" (+) testFieldPairs + , binary "testcases_sub" (-) testFieldPairs + , binary "testcases_mul" (*) testFieldPairs + ] + +writeTests :: IO () +writeTests = withFile "fieldTestCases.nim" WriteMode $ \h -> do + hPutStrLn h "# generated by TestGen.hs\n" + -- hPutStrLn h "import poseidon2/types\n" + hPrintTests h + +-------------------------------------------------------------------------------- diff --git a/tests/nim.cfg b/tests/nim.cfg new file mode 100644 index 0000000..0f840a1 --- /dev/null +++ b/tests/nim.cfg @@ -0,0 +1 @@ +--path:".." diff --git a/tests/poseidon2/fieldTestCases.nim b/tests/poseidon2/fieldTestCases.nim new file mode 100644 index 0000000..0c6b234 --- /dev/null +++ b/tests/poseidon2/fieldTestCases.nim @@ -0,0 +1,7327 @@ +# generated by TestGen.hs + +const testcases_neg* : array[105, tuple[x:uint64, y:uint64]] = + [ ( 0xfffffffefffffffa'u64 , 0x0000000000000007'u64 ) + , ( 0xfffffffefffffffb'u64 , 0x0000000000000006'u64 ) + , ( 0xfffffffefffffffc'u64 , 0x0000000000000005'u64 ) + , ( 0xfffffffefffffffd'u64 , 0x0000000000000004'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000003'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000002'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000000001'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000000000'u64 ) + , ( 0x0000000000000001'u64 , 0xffffffff00000000'u64 ) + , ( 0x0000000000000002'u64 , 0xfffffffeffffffff'u64 ) + , ( 0x0000000000000003'u64 , 0xfffffffefffffffe'u64 ) + , ( 0x0000000000000004'u64 , 0xfffffffefffffffd'u64 ) + , ( 0x0000000000000005'u64 , 0xfffffffefffffffc'u64 ) + , ( 0x0000000000000006'u64 , 0xfffffffefffffffb'u64 ) + , ( 0x0000000000000007'u64 , 0xfffffffefffffffa'u64 ) + , ( 0x000000000000fff9'u64 , 0xfffffffeffff0008'u64 ) + , ( 0x000000000000fffa'u64 , 0xfffffffeffff0007'u64 ) + , ( 0x000000000000fffb'u64 , 0xfffffffeffff0006'u64 ) + , ( 0x000000000000fffc'u64 , 0xfffffffeffff0005'u64 ) + , ( 0x000000000000fffd'u64 , 0xfffffffeffff0004'u64 ) + , ( 0x000000000000fffe'u64 , 0xfffffffeffff0003'u64 ) + , ( 0x000000000000ffff'u64 , 0xfffffffeffff0002'u64 ) + , ( 0x0000000000010000'u64 , 0xfffffffeffff0001'u64 ) + , ( 0x0000000000010001'u64 , 0xfffffffeffff0000'u64 ) + , ( 0x0000000000010002'u64 , 0xfffffffefffeffff'u64 ) + , ( 0x0000000000010003'u64 , 0xfffffffefffefffe'u64 ) + , ( 0x0000000000010004'u64 , 0xfffffffefffefffd'u64 ) + , ( 0x0000000000010005'u64 , 0xfffffffefffefffc'u64 ) + , ( 0x0000000000010006'u64 , 0xfffffffefffefffb'u64 ) + , ( 0x0000000000010007'u64 , 0xfffffffefffefffa'u64 ) + , ( 0x000000007ffffff9'u64 , 0xfffffffe80000008'u64 ) + , ( 0x000000007ffffffa'u64 , 0xfffffffe80000007'u64 ) + , ( 0x000000007ffffffb'u64 , 0xfffffffe80000006'u64 ) + , ( 0x000000007ffffffc'u64 , 0xfffffffe80000005'u64 ) + , ( 0x000000007ffffffd'u64 , 0xfffffffe80000004'u64 ) + , ( 0x000000007ffffffe'u64 , 0xfffffffe80000003'u64 ) + , ( 0x000000007fffffff'u64 , 0xfffffffe80000002'u64 ) + , ( 0x0000000080000000'u64 , 0xfffffffe80000001'u64 ) + , ( 0x0000000080000001'u64 , 0xfffffffe80000000'u64 ) + , ( 0x0000000080000002'u64 , 0xfffffffe7fffffff'u64 ) + , ( 0x0000000080000003'u64 , 0xfffffffe7ffffffe'u64 ) + , ( 0x0000000080000004'u64 , 0xfffffffe7ffffffd'u64 ) + , ( 0x0000000080000005'u64 , 0xfffffffe7ffffffc'u64 ) + , ( 0x0000000080000006'u64 , 0xfffffffe7ffffffb'u64 ) + , ( 0x0000000080000007'u64 , 0xfffffffe7ffffffa'u64 ) + , ( 0x00000000fffffff9'u64 , 0xfffffffe00000008'u64 ) + , ( 0x00000000fffffffa'u64 , 0xfffffffe00000007'u64 ) + , ( 0x00000000fffffffb'u64 , 0xfffffffe00000006'u64 ) + , ( 0x00000000fffffffc'u64 , 0xfffffffe00000005'u64 ) + , ( 0x00000000fffffffd'u64 , 0xfffffffe00000004'u64 ) + , ( 0x00000000fffffffe'u64 , 0xfffffffe00000003'u64 ) + , ( 0x00000000ffffffff'u64 , 0xfffffffe00000002'u64 ) + , ( 0x0000000100000000'u64 , 0xfffffffe00000001'u64 ) + , ( 0x0000000100000001'u64 , 0xfffffffe00000000'u64 ) + , ( 0x0000000100000002'u64 , 0xfffffffdffffffff'u64 ) + , ( 0x0000000100000003'u64 , 0xfffffffdfffffffe'u64 ) + , ( 0x0000000100000004'u64 , 0xfffffffdfffffffd'u64 ) + , ( 0x0000000100000005'u64 , 0xfffffffdfffffffc'u64 ) + , ( 0x0000000100000006'u64 , 0xfffffffdfffffffb'u64 ) + , ( 0x0000000100000007'u64 , 0xfffffffdfffffffa'u64 ) + , ( 0x00000001fffffff9'u64 , 0xfffffffd00000008'u64 ) + , ( 0x00000001fffffffa'u64 , 0xfffffffd00000007'u64 ) + , ( 0x00000001fffffffb'u64 , 0xfffffffd00000006'u64 ) + , ( 0x00000001fffffffc'u64 , 0xfffffffd00000005'u64 ) + , ( 0x00000001fffffffd'u64 , 0xfffffffd00000004'u64 ) + , ( 0x00000001fffffffe'u64 , 0xfffffffd00000003'u64 ) + , ( 0x00000001ffffffff'u64 , 0xfffffffd00000002'u64 ) + , ( 0x0000000200000000'u64 , 0xfffffffd00000001'u64 ) + , ( 0x0000000200000001'u64 , 0xfffffffd00000000'u64 ) + , ( 0x0000000200000002'u64 , 0xfffffffcffffffff'u64 ) + , ( 0x0000000200000003'u64 , 0xfffffffcfffffffe'u64 ) + , ( 0x0000000200000004'u64 , 0xfffffffcfffffffd'u64 ) + , ( 0x0000000200000005'u64 , 0xfffffffcfffffffc'u64 ) + , ( 0x0000000200000006'u64 , 0xfffffffcfffffffb'u64 ) + , ( 0x0000000200000007'u64 , 0xfffffffcfffffffa'u64 ) + , ( 0x0000fffffffffff9'u64 , 0xfffeffff00000008'u64 ) + , ( 0x0000fffffffffffa'u64 , 0xfffeffff00000007'u64 ) + , ( 0x0000fffffffffffb'u64 , 0xfffeffff00000006'u64 ) + , ( 0x0000fffffffffffc'u64 , 0xfffeffff00000005'u64 ) + , ( 0x0000fffffffffffd'u64 , 0xfffeffff00000004'u64 ) + , ( 0x0000fffffffffffe'u64 , 0xfffeffff00000003'u64 ) + , ( 0x0000ffffffffffff'u64 , 0xfffeffff00000002'u64 ) + , ( 0x0001000000000000'u64 , 0xfffeffff00000001'u64 ) + , ( 0x0001000000000001'u64 , 0xfffeffff00000000'u64 ) + , ( 0x0001000000000002'u64 , 0xfffefffeffffffff'u64 ) + , ( 0x0001000000000003'u64 , 0xfffefffefffffffe'u64 ) + , ( 0x0001000000000004'u64 , 0xfffefffefffffffd'u64 ) + , ( 0x0001000000000005'u64 , 0xfffefffefffffffc'u64 ) + , ( 0x0001000000000006'u64 , 0xfffefffefffffffb'u64 ) + , ( 0x0001000000000007'u64 , 0xfffefffefffffffa'u64 ) + , ( 0x7ffffffffffffff9'u64 , 0x7fffffff00000008'u64 ) + , ( 0x7ffffffffffffffa'u64 , 0x7fffffff00000007'u64 ) + , ( 0x7ffffffffffffffb'u64 , 0x7fffffff00000006'u64 ) + , ( 0x7ffffffffffffffc'u64 , 0x7fffffff00000005'u64 ) + , ( 0x7ffffffffffffffd'u64 , 0x7fffffff00000004'u64 ) + , ( 0x7ffffffffffffffe'u64 , 0x7fffffff00000003'u64 ) + , ( 0x7fffffffffffffff'u64 , 0x7fffffff00000002'u64 ) + , ( 0x8000000000000000'u64 , 0x7fffffff00000001'u64 ) + , ( 0x8000000000000001'u64 , 0x7fffffff00000000'u64 ) + , ( 0x8000000000000002'u64 , 0x7ffffffeffffffff'u64 ) + , ( 0x8000000000000003'u64 , 0x7ffffffefffffffe'u64 ) + , ( 0x8000000000000004'u64 , 0x7ffffffefffffffd'u64 ) + , ( 0x8000000000000005'u64 , 0x7ffffffefffffffc'u64 ) + , ( 0x8000000000000006'u64 , 0x7ffffffefffffffb'u64 ) + , ( 0x8000000000000007'u64 , 0x7ffffffefffffffa'u64 ) + ] + + +const testcases_add* : array[2401, tuple[x:uint64, y:uint64, z:uint64]] = + [ ( 0xfffffffefffffffe'u64 , 0xfffffffefffffffe'u64 , 0xfffffffefffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0xfffffffeffffffff'u64 , 0xfffffffefffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0xffffffff00000000'u64 , 0xfffffffefffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000000'u64 , 0xfffffffefffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000001'u64 , 0xfffffffeffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000002'u64 , 0xffffffff00000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000003'u64 , 0x0000000000000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000fffd'u64 , 0x000000000000fffa'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000fffe'u64 , 0x000000000000fffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000ffff'u64 , 0x000000000000fffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010000'u64 , 0x000000000000fffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010001'u64 , 0x000000000000fffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010002'u64 , 0x000000000000ffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010003'u64 , 0x0000000000010000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007ffffffd'u64 , 0x000000007ffffffa'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007ffffffe'u64 , 0x000000007ffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007fffffff'u64 , 0x000000007ffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000000'u64 , 0x000000007ffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000001'u64 , 0x000000007ffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000002'u64 , 0x000000007fffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000003'u64 , 0x0000000080000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000fffffffd'u64 , 0x00000000fffffffa'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000fffffffe'u64 , 0x00000000fffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000ffffffff'u64 , 0x00000000fffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000000'u64 , 0x00000000fffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000001'u64 , 0x00000000fffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000002'u64 , 0x00000000ffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000003'u64 , 0x0000000100000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001fffffffd'u64 , 0x00000001fffffffa'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001fffffffe'u64 , 0x00000001fffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001ffffffff'u64 , 0x00000001fffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000000'u64 , 0x00000001fffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000001'u64 , 0x00000001fffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000002'u64 , 0x00000001ffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000003'u64 , 0x0000000200000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000fffffffffffd'u64 , 0x0000fffffffffffa'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000fffffffffffe'u64 , 0x0000fffffffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000ffffffffffff'u64 , 0x0000fffffffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000000'u64 , 0x0000fffffffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000001'u64 , 0x0000fffffffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000002'u64 , 0x0000ffffffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000003'u64 , 0x0001000000000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x7ffffffffffffffd'u64 , 0x7ffffffffffffffa'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x7ffffffffffffffe'u64 , 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0x0000000000010000'u64 , 0x8000000000010003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000010001'u64 , 0x8000000000010004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000010002'u64 , 0x8000000000010005'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000010003'u64 , 0x8000000000010006'u64 ) + , ( 0x8000000000000003'u64 , 0x000000007ffffffd'u64 , 0x8000000080000000'u64 ) + , ( 0x8000000000000003'u64 , 0x000000007ffffffe'u64 , 0x8000000080000001'u64 ) + , ( 0x8000000000000003'u64 , 0x000000007fffffff'u64 , 0x8000000080000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000080000000'u64 , 0x8000000080000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000080000001'u64 , 0x8000000080000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000080000002'u64 , 0x8000000080000005'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000080000003'u64 , 0x8000000080000006'u64 ) + , ( 0x8000000000000003'u64 , 0x00000000fffffffd'u64 , 0x8000000100000000'u64 ) + , ( 0x8000000000000003'u64 , 0x00000000fffffffe'u64 , 0x8000000100000001'u64 ) + , ( 0x8000000000000003'u64 , 0x00000000ffffffff'u64 , 0x8000000100000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000100000000'u64 , 0x8000000100000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000100000001'u64 , 0x8000000100000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000100000002'u64 , 0x8000000100000005'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000100000003'u64 , 0x8000000100000006'u64 ) + , ( 0x8000000000000003'u64 , 0x00000001fffffffd'u64 , 0x8000000200000000'u64 ) + , ( 0x8000000000000003'u64 , 0x00000001fffffffe'u64 , 0x8000000200000001'u64 ) + , ( 0x8000000000000003'u64 , 0x00000001ffffffff'u64 , 0x8000000200000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000200000000'u64 , 0x8000000200000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000200000001'u64 , 0x8000000200000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000200000002'u64 , 0x8000000200000005'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000200000003'u64 , 0x8000000200000006'u64 ) + , ( 0x8000000000000003'u64 , 0x0000fffffffffffd'u64 , 0x8001000000000000'u64 ) + , ( 0x8000000000000003'u64 , 0x0000fffffffffffe'u64 , 0x8001000000000001'u64 ) + , ( 0x8000000000000003'u64 , 0x0000ffffffffffff'u64 , 0x8001000000000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0001000000000000'u64 , 0x8001000000000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0001000000000001'u64 , 0x8001000000000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0001000000000002'u64 , 0x8001000000000005'u64 ) + , ( 0x8000000000000003'u64 , 0x0001000000000003'u64 , 0x8001000000000006'u64 ) + , ( 0x8000000000000003'u64 , 0x7ffffffffffffffd'u64 , 0x00000000ffffffff'u64 ) + , ( 0x8000000000000003'u64 , 0x7ffffffffffffffe'u64 , 0x0000000100000000'u64 ) + , ( 0x8000000000000003'u64 , 0x7fffffffffffffff'u64 , 0x0000000100000001'u64 ) + , ( 0x8000000000000003'u64 , 0x8000000000000000'u64 , 0x0000000100000002'u64 ) + , ( 0x8000000000000003'u64 , 0x8000000000000001'u64 , 0x0000000100000003'u64 ) + , ( 0x8000000000000003'u64 , 0x8000000000000002'u64 , 0x0000000100000004'u64 ) + , ( 0x8000000000000003'u64 , 0x8000000000000003'u64 , 0x0000000100000005'u64 ) + ] + + +const testcases_sub* : array[2401, tuple[x:uint64, y:uint64, z:uint64]] = + [ ( 0xfffffffefffffffe'u64 , 0xfffffffefffffffe'u64 , 0x0000000000000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0xfffffffeffffffff'u64 , 0xffffffff00000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0xffffffff00000000'u64 , 0xfffffffeffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000000'u64 , 0xfffffffefffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000001'u64 , 0xfffffffefffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000002'u64 , 0xfffffffefffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000003'u64 , 0xfffffffefffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000fffd'u64 , 0xfffffffeffff0001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000fffe'u64 , 0xfffffffeffff0000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000ffff'u64 , 0xfffffffefffeffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010000'u64 , 0xfffffffefffefffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010001'u64 , 0xfffffffefffefffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010002'u64 , 0xfffffffefffefffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010003'u64 , 0xfffffffefffefffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007ffffffd'u64 , 0xfffffffe80000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007ffffffe'u64 , 0xfffffffe80000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007fffffff'u64 , 0xfffffffe7fffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000000'u64 , 0xfffffffe7ffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000001'u64 , 0xfffffffe7ffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000002'u64 , 0xfffffffe7ffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000003'u64 , 0xfffffffe7ffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000fffffffd'u64 , 0xfffffffe00000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000fffffffe'u64 , 0xfffffffe00000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000ffffffff'u64 , 0xfffffffdffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000000'u64 , 0xfffffffdfffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000001'u64 , 0xfffffffdfffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000002'u64 , 0xfffffffdfffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000003'u64 , 0xfffffffdfffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001fffffffd'u64 , 0xfffffffd00000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001fffffffe'u64 , 0xfffffffd00000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001ffffffff'u64 , 0xfffffffcffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000000'u64 , 0xfffffffcfffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000001'u64 , 0xfffffffcfffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000002'u64 , 0xfffffffcfffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000003'u64 , 0xfffffffcfffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000fffffffffffd'u64 , 0xfffeffff00000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000fffffffffffe'u64 , 0xfffeffff00000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000ffffffffffff'u64 , 0xfffefffeffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000000'u64 , 0xfffefffefffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000001'u64 , 0xfffefffefffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000002'u64 , 0xfffefffefffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000003'u64 , 0xfffefffefffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x7ffffffffffffffd'u64 , 0x7fffffff00000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x7ffffffffffffffe'u64 , 0x7fffffff00000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x7fffffffffffffff'u64 , 0x7ffffffeffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x8000000000000000'u64 , 0x7ffffffefffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x8000000000000001'u64 , 0x7ffffffefffffffd'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x8000000000000002'u64 , 0x7ffffffefffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x8000000000000003'u64 , 0x7ffffffefffffffb'u64 ) + , ( 0xfffffffeffffffff'u64 , 0xfffffffefffffffe'u64 , 0x0000000000000001'u64 ) + , ( 0xfffffffeffffffff'u64 , 0xfffffffeffffffff'u64 , 0x0000000000000000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0xffffffff00000000'u64 , 0xffffffff00000000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000000'u64 , 0xfffffffeffffffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000001'u64 , 0xfffffffefffffffe'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000002'u64 , 0xfffffffefffffffd'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000003'u64 , 0xfffffffefffffffc'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000000000fffd'u64 , 0xfffffffeffff0002'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000000000fffe'u64 , 0xfffffffeffff0001'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000000000ffff'u64 , 0xfffffffeffff0000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000010000'u64 , 0xfffffffefffeffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000010001'u64 , 0xfffffffefffefffe'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000010002'u64 , 0xfffffffefffefffd'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000010003'u64 , 0xfffffffefffefffc'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000007ffffffd'u64 , 0xfffffffe80000002'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000007ffffffe'u64 , 0xfffffffe80000001'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000007fffffff'u64 , 0xfffffffe80000000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000080000000'u64 , 0xfffffffe7fffffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000080000001'u64 , 0xfffffffe7ffffffe'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000080000002'u64 , 0xfffffffe7ffffffd'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000080000003'u64 , 0xfffffffe7ffffffc'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x00000000fffffffd'u64 , 0xfffffffe00000002'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x00000000fffffffe'u64 , 0xfffffffe00000001'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x00000000ffffffff'u64 , 0xfffffffe00000000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000100000000'u64 , 0xfffffffdffffffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000100000001'u64 , 0xfffffffdfffffffe'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000100000002'u64 , 0xfffffffdfffffffd'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000100000003'u64 , 0xfffffffdfffffffc'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x00000001fffffffd'u64 , 0xfffffffd00000002'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x00000001fffffffe'u64 , 0xfffffffd00000001'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x00000001ffffffff'u64 , 0xfffffffd00000000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000200000000'u64 , 0xfffffffcffffffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000200000001'u64 , 0xfffffffcfffffffe'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000200000002'u64 , 0xfffffffcfffffffd'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000200000003'u64 , 0xfffffffcfffffffc'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000fffffffffffd'u64 , 0xfffeffff00000002'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000fffffffffffe'u64 , 0xfffeffff00000001'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000ffffffffffff'u64 , 0xfffeffff00000000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0001000000000000'u64 , 0xfffefffeffffffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0001000000000001'u64 , 0xfffefffefffffffe'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0001000000000002'u64 , 0xfffefffefffffffd'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0001000000000003'u64 , 0xfffefffefffffffc'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x7ffffffffffffffd'u64 , 0x7fffffff00000002'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x7ffffffffffffffe'u64 , 0x7fffffff00000001'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x7fffffffffffffff'u64 , 0x7fffffff00000000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x8000000000000000'u64 , 0x7ffffffeffffffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x8000000000000001'u64 , 0x7ffffffefffffffe'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x8000000000000002'u64 , 0x7ffffffefffffffd'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x8000000000000003'u64 , 0x7ffffffefffffffc'u64 ) + , ( 0xffffffff00000000'u64 , 0xfffffffefffffffe'u64 , 0x0000000000000002'u64 ) + , ( 0xffffffff00000000'u64 , 0xfffffffeffffffff'u64 , 0x0000000000000001'u64 ) + , ( 0xffffffff00000000'u64 , 0xffffffff00000000'u64 , 0x0000000000000000'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000000000'u64 , 0xffffffff00000000'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000000001'u64 , 0xfffffffeffffffff'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000000002'u64 , 0xfffffffefffffffe'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000000003'u64 , 0xfffffffefffffffd'u64 ) + , ( 0xffffffff00000000'u64 , 0x000000000000fffd'u64 , 0xfffffffeffff0003'u64 ) + , ( 0xffffffff00000000'u64 , 0x000000000000fffe'u64 , 0xfffffffeffff0002'u64 ) + , ( 0xffffffff00000000'u64 , 0x000000000000ffff'u64 , 0xfffffffeffff0001'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000010000'u64 , 0xfffffffeffff0000'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000010001'u64 , 0xfffffffefffeffff'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000010002'u64 , 0xfffffffefffefffe'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000000010003'u64 , 0xfffffffefffefffd'u64 ) + , ( 0xffffffff00000000'u64 , 0x000000007ffffffd'u64 , 0xfffffffe80000003'u64 ) + , ( 0xffffffff00000000'u64 , 0x000000007ffffffe'u64 , 0xfffffffe80000002'u64 ) + , ( 0xffffffff00000000'u64 , 0x000000007fffffff'u64 , 0xfffffffe80000001'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000080000000'u64 , 0xfffffffe80000000'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000080000001'u64 , 0xfffffffe7fffffff'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000080000002'u64 , 0xfffffffe7ffffffe'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000080000003'u64 , 0xfffffffe7ffffffd'u64 ) + , ( 0xffffffff00000000'u64 , 0x00000000fffffffd'u64 , 0xfffffffe00000003'u64 ) + , ( 0xffffffff00000000'u64 , 0x00000000fffffffe'u64 , 0xfffffffe00000002'u64 ) + , ( 0xffffffff00000000'u64 , 0x00000000ffffffff'u64 , 0xfffffffe00000001'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000100000000'u64 , 0xfffffffe00000000'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000100000001'u64 , 0xfffffffdffffffff'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000100000002'u64 , 0xfffffffdfffffffe'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000100000003'u64 , 0xfffffffdfffffffd'u64 ) + , ( 0xffffffff00000000'u64 , 0x00000001fffffffd'u64 , 0xfffffffd00000003'u64 ) + , ( 0xffffffff00000000'u64 , 0x00000001fffffffe'u64 , 0xfffffffd00000002'u64 ) + , ( 0xffffffff00000000'u64 , 0x00000001ffffffff'u64 , 0xfffffffd00000001'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000200000000'u64 , 0xfffffffd00000000'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000200000001'u64 , 0xfffffffcffffffff'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000200000002'u64 , 0xfffffffcfffffffe'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000000200000003'u64 , 0xfffffffcfffffffd'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000fffffffffffd'u64 , 0xfffeffff00000003'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000fffffffffffe'u64 , 0xfffeffff00000002'u64 ) + , ( 0xffffffff00000000'u64 , 0x0000ffffffffffff'u64 , 0xfffeffff00000001'u64 ) + , ( 0xffffffff00000000'u64 , 0x0001000000000000'u64 , 0xfffeffff00000000'u64 ) + , ( 0xffffffff00000000'u64 , 0x0001000000000001'u64 , 0xfffefffeffffffff'u64 ) + , ( 0xffffffff00000000'u64 , 0x0001000000000002'u64 , 0xfffefffefffffffe'u64 ) + , ( 0xffffffff00000000'u64 , 0x0001000000000003'u64 , 0xfffefffefffffffd'u64 ) + , ( 0xffffffff00000000'u64 , 0x7ffffffffffffffd'u64 , 0x7fffffff00000003'u64 ) + , ( 0xffffffff00000000'u64 , 0x7ffffffffffffffe'u64 , 0x7fffffff00000002'u64 ) + , ( 0xffffffff00000000'u64 , 0x7fffffffffffffff'u64 , 0x7fffffff00000001'u64 ) + , ( 0xffffffff00000000'u64 , 0x8000000000000000'u64 , 0x7fffffff00000000'u64 ) + , ( 0xffffffff00000000'u64 , 0x8000000000000001'u64 , 0x7ffffffeffffffff'u64 ) + , ( 0xffffffff00000000'u64 , 0x8000000000000002'u64 , 0x7ffffffefffffffe'u64 ) + , ( 0xffffffff00000000'u64 , 0x8000000000000003'u64 , 0x7ffffffefffffffd'u64 ) + , ( 0x0000000000000000'u64 , 0xfffffffefffffffe'u64 , 0x0000000000000003'u64 ) + , ( 0x0000000000000000'u64 , 0xfffffffeffffffff'u64 , 0x0000000000000002'u64 ) + , ( 0x0000000000000000'u64 , 0xffffffff00000000'u64 , 0x0000000000000001'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000000000'u64 , 0x0000000000000000'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000000001'u64 , 0xffffffff00000000'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000000002'u64 , 0xfffffffeffffffff'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000000003'u64 , 0xfffffffefffffffe'u64 ) + , ( 0x0000000000000000'u64 , 0x000000000000fffd'u64 , 0xfffffffeffff0004'u64 ) + , ( 0x0000000000000000'u64 , 0x000000000000fffe'u64 , 0xfffffffeffff0003'u64 ) + , ( 0x0000000000000000'u64 , 0x000000000000ffff'u64 , 0xfffffffeffff0002'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000010000'u64 , 0xfffffffeffff0001'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000010001'u64 , 0xfffffffeffff0000'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000010002'u64 , 0xfffffffefffeffff'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000000010003'u64 , 0xfffffffefffefffe'u64 ) + , ( 0x0000000000000000'u64 , 0x000000007ffffffd'u64 , 0xfffffffe80000004'u64 ) + , ( 0x0000000000000000'u64 , 0x000000007ffffffe'u64 , 0xfffffffe80000003'u64 ) + , ( 0x0000000000000000'u64 , 0x000000007fffffff'u64 , 0xfffffffe80000002'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000080000000'u64 , 0xfffffffe80000001'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000080000001'u64 , 0xfffffffe80000000'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000080000002'u64 , 0xfffffffe7fffffff'u64 ) + , ( 0x0000000000000000'u64 , 0x0000000080000003'u64 , 0xfffffffe7ffffffe'u64 ) + , ( 0x0000000000000000'u64 , 0x00000000fffffffd'u64 , 0xfffffffe00000004'u64 ) + , ( 0x0000000000000000'u64 , 0x00000000fffffffe'u64 , 0xfffffffe00000003'u64 ) + , 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0x7ffffffffffeffff'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000000010003'u64 , 0x7ffffffffffefffe'u64 ) + , ( 0x8000000000000001'u64 , 0x000000007ffffffd'u64 , 0x7fffffff80000004'u64 ) + , ( 0x8000000000000001'u64 , 0x000000007ffffffe'u64 , 0x7fffffff80000003'u64 ) + , ( 0x8000000000000001'u64 , 0x000000007fffffff'u64 , 0x7fffffff80000002'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000080000000'u64 , 0x7fffffff80000001'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000080000001'u64 , 0x7fffffff80000000'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000080000002'u64 , 0x7fffffff7fffffff'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000080000003'u64 , 0x7fffffff7ffffffe'u64 ) + , ( 0x8000000000000001'u64 , 0x00000000fffffffd'u64 , 0x7fffffff00000004'u64 ) + , ( 0x8000000000000001'u64 , 0x00000000fffffffe'u64 , 0x7fffffff00000003'u64 ) + , ( 0x8000000000000001'u64 , 0x00000000ffffffff'u64 , 0x7fffffff00000002'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000100000000'u64 , 0x7fffffff00000001'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000100000001'u64 , 0x7fffffff00000000'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000100000002'u64 , 0x7ffffffeffffffff'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000100000003'u64 , 0x7ffffffefffffffe'u64 ) + , ( 0x8000000000000001'u64 , 0x00000001fffffffd'u64 , 0x7ffffffe00000004'u64 ) + , ( 0x8000000000000001'u64 , 0x00000001fffffffe'u64 , 0x7ffffffe00000003'u64 ) + , ( 0x8000000000000001'u64 , 0x00000001ffffffff'u64 , 0x7ffffffe00000002'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000200000000'u64 , 0x7ffffffe00000001'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000200000001'u64 , 0x7ffffffe00000000'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000200000002'u64 , 0x7ffffffdffffffff'u64 ) + , ( 0x8000000000000001'u64 , 0x0000000200000003'u64 , 0x7ffffffdfffffffe'u64 ) + , ( 0x8000000000000001'u64 , 0x0000fffffffffffd'u64 , 0x7fff000000000004'u64 ) + , ( 0x8000000000000001'u64 , 0x0000fffffffffffe'u64 , 0x7fff000000000003'u64 ) + , ( 0x8000000000000001'u64 , 0x0000ffffffffffff'u64 , 0x7fff000000000002'u64 ) + , ( 0x8000000000000001'u64 , 0x0001000000000000'u64 , 0x7fff000000000001'u64 ) + , ( 0x8000000000000001'u64 , 0x0001000000000001'u64 , 0x7fff000000000000'u64 ) + , ( 0x8000000000000001'u64 , 0x0001000000000002'u64 , 0x7ffeffffffffffff'u64 ) + , ( 0x8000000000000001'u64 , 0x0001000000000003'u64 , 0x7ffefffffffffffe'u64 ) + , ( 0x8000000000000001'u64 , 0x7ffffffffffffffd'u64 , 0x0000000000000004'u64 ) + , ( 0x8000000000000001'u64 , 0x7ffffffffffffffe'u64 , 0x0000000000000003'u64 ) + , ( 0x8000000000000001'u64 , 0x7fffffffffffffff'u64 , 0x0000000000000002'u64 ) + , ( 0x8000000000000001'u64 , 0x8000000000000000'u64 , 0x0000000000000001'u64 ) + , ( 0x8000000000000001'u64 , 0x8000000000000001'u64 , 0x0000000000000000'u64 ) + , ( 0x8000000000000001'u64 , 0x8000000000000002'u64 , 0xffffffff00000000'u64 ) + , ( 0x8000000000000001'u64 , 0x8000000000000003'u64 , 0xfffffffeffffffff'u64 ) + , ( 0x8000000000000002'u64 , 0xfffffffefffffffe'u64 , 0x8000000000000005'u64 ) + , ( 0x8000000000000002'u64 , 0xfffffffeffffffff'u64 , 0x8000000000000004'u64 ) + , ( 0x8000000000000002'u64 , 0xffffffff00000000'u64 , 0x8000000000000003'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000000000000'u64 , 0x8000000000000002'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000000000001'u64 , 0x8000000000000001'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000000000002'u64 , 0x8000000000000000'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000000000003'u64 , 0x7fffffffffffffff'u64 ) + , ( 0x8000000000000002'u64 , 0x000000000000fffd'u64 , 0x7fffffffffff0005'u64 ) + , ( 0x8000000000000002'u64 , 0x000000000000fffe'u64 , 0x7fffffffffff0004'u64 ) + , ( 0x8000000000000002'u64 , 0x000000000000ffff'u64 , 0x7fffffffffff0003'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000000010000'u64 , 0x7fffffffffff0002'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000000010001'u64 , 0x7fffffffffff0001'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000000010002'u64 , 0x7fffffffffff0000'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000000010003'u64 , 0x7ffffffffffeffff'u64 ) + , ( 0x8000000000000002'u64 , 0x000000007ffffffd'u64 , 0x7fffffff80000005'u64 ) + , ( 0x8000000000000002'u64 , 0x000000007ffffffe'u64 , 0x7fffffff80000004'u64 ) + , ( 0x8000000000000002'u64 , 0x000000007fffffff'u64 , 0x7fffffff80000003'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000080000000'u64 , 0x7fffffff80000002'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000080000001'u64 , 0x7fffffff80000001'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000080000002'u64 , 0x7fffffff80000000'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000080000003'u64 , 0x7fffffff7fffffff'u64 ) + , ( 0x8000000000000002'u64 , 0x00000000fffffffd'u64 , 0x7fffffff00000005'u64 ) + , ( 0x8000000000000002'u64 , 0x00000000fffffffe'u64 , 0x7fffffff00000004'u64 ) + , ( 0x8000000000000002'u64 , 0x00000000ffffffff'u64 , 0x7fffffff00000003'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000100000000'u64 , 0x7fffffff00000002'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000100000001'u64 , 0x7fffffff00000001'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000100000002'u64 , 0x7fffffff00000000'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000100000003'u64 , 0x7ffffffeffffffff'u64 ) + , ( 0x8000000000000002'u64 , 0x00000001fffffffd'u64 , 0x7ffffffe00000005'u64 ) + , ( 0x8000000000000002'u64 , 0x00000001fffffffe'u64 , 0x7ffffffe00000004'u64 ) + , ( 0x8000000000000002'u64 , 0x00000001ffffffff'u64 , 0x7ffffffe00000003'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000200000000'u64 , 0x7ffffffe00000002'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000200000001'u64 , 0x7ffffffe00000001'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000200000002'u64 , 0x7ffffffe00000000'u64 ) + , ( 0x8000000000000002'u64 , 0x0000000200000003'u64 , 0x7ffffffdffffffff'u64 ) + , ( 0x8000000000000002'u64 , 0x0000fffffffffffd'u64 , 0x7fff000000000005'u64 ) + , ( 0x8000000000000002'u64 , 0x0000fffffffffffe'u64 , 0x7fff000000000004'u64 ) + , ( 0x8000000000000002'u64 , 0x0000ffffffffffff'u64 , 0x7fff000000000003'u64 ) + , ( 0x8000000000000002'u64 , 0x0001000000000000'u64 , 0x7fff000000000002'u64 ) + , ( 0x8000000000000002'u64 , 0x0001000000000001'u64 , 0x7fff000000000001'u64 ) + , ( 0x8000000000000002'u64 , 0x0001000000000002'u64 , 0x7fff000000000000'u64 ) + , ( 0x8000000000000002'u64 , 0x0001000000000003'u64 , 0x7ffeffffffffffff'u64 ) + , ( 0x8000000000000002'u64 , 0x7ffffffffffffffd'u64 , 0x0000000000000005'u64 ) + , ( 0x8000000000000002'u64 , 0x7ffffffffffffffe'u64 , 0x0000000000000004'u64 ) + , ( 0x8000000000000002'u64 , 0x7fffffffffffffff'u64 , 0x0000000000000003'u64 ) + , ( 0x8000000000000002'u64 , 0x8000000000000000'u64 , 0x0000000000000002'u64 ) + , ( 0x8000000000000002'u64 , 0x8000000000000001'u64 , 0x0000000000000001'u64 ) + , ( 0x8000000000000002'u64 , 0x8000000000000002'u64 , 0x0000000000000000'u64 ) + , ( 0x8000000000000002'u64 , 0x8000000000000003'u64 , 0xffffffff00000000'u64 ) + , ( 0x8000000000000003'u64 , 0xfffffffefffffffe'u64 , 0x8000000000000006'u64 ) + , ( 0x8000000000000003'u64 , 0xfffffffeffffffff'u64 , 0x8000000000000005'u64 ) + , ( 0x8000000000000003'u64 , 0xffffffff00000000'u64 , 0x8000000000000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000000000'u64 , 0x8000000000000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000000001'u64 , 0x8000000000000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000000002'u64 , 0x8000000000000001'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000000003'u64 , 0x8000000000000000'u64 ) + , ( 0x8000000000000003'u64 , 0x000000000000fffd'u64 , 0x7fffffffffff0006'u64 ) + , ( 0x8000000000000003'u64 , 0x000000000000fffe'u64 , 0x7fffffffffff0005'u64 ) + , ( 0x8000000000000003'u64 , 0x000000000000ffff'u64 , 0x7fffffffffff0004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000010000'u64 , 0x7fffffffffff0003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000010001'u64 , 0x7fffffffffff0002'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000010002'u64 , 0x7fffffffffff0001'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000000010003'u64 , 0x7fffffffffff0000'u64 ) + , ( 0x8000000000000003'u64 , 0x000000007ffffffd'u64 , 0x7fffffff80000006'u64 ) + , ( 0x8000000000000003'u64 , 0x000000007ffffffe'u64 , 0x7fffffff80000005'u64 ) + , ( 0x8000000000000003'u64 , 0x000000007fffffff'u64 , 0x7fffffff80000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000080000000'u64 , 0x7fffffff80000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000080000001'u64 , 0x7fffffff80000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000080000002'u64 , 0x7fffffff80000001'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000080000003'u64 , 0x7fffffff80000000'u64 ) + , ( 0x8000000000000003'u64 , 0x00000000fffffffd'u64 , 0x7fffffff00000006'u64 ) + , ( 0x8000000000000003'u64 , 0x00000000fffffffe'u64 , 0x7fffffff00000005'u64 ) + , ( 0x8000000000000003'u64 , 0x00000000ffffffff'u64 , 0x7fffffff00000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000100000000'u64 , 0x7fffffff00000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000100000001'u64 , 0x7fffffff00000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000100000002'u64 , 0x7fffffff00000001'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000100000003'u64 , 0x7fffffff00000000'u64 ) + , ( 0x8000000000000003'u64 , 0x00000001fffffffd'u64 , 0x7ffffffe00000006'u64 ) + , ( 0x8000000000000003'u64 , 0x00000001fffffffe'u64 , 0x7ffffffe00000005'u64 ) + , ( 0x8000000000000003'u64 , 0x00000001ffffffff'u64 , 0x7ffffffe00000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000200000000'u64 , 0x7ffffffe00000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000200000001'u64 , 0x7ffffffe00000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000200000002'u64 , 0x7ffffffe00000001'u64 ) + , ( 0x8000000000000003'u64 , 0x0000000200000003'u64 , 0x7ffffffe00000000'u64 ) + , ( 0x8000000000000003'u64 , 0x0000fffffffffffd'u64 , 0x7fff000000000006'u64 ) + , ( 0x8000000000000003'u64 , 0x0000fffffffffffe'u64 , 0x7fff000000000005'u64 ) + , ( 0x8000000000000003'u64 , 0x0000ffffffffffff'u64 , 0x7fff000000000004'u64 ) + , ( 0x8000000000000003'u64 , 0x0001000000000000'u64 , 0x7fff000000000003'u64 ) + , ( 0x8000000000000003'u64 , 0x0001000000000001'u64 , 0x7fff000000000002'u64 ) + , ( 0x8000000000000003'u64 , 0x0001000000000002'u64 , 0x7fff000000000001'u64 ) + , ( 0x8000000000000003'u64 , 0x0001000000000003'u64 , 0x7fff000000000000'u64 ) + , ( 0x8000000000000003'u64 , 0x7ffffffffffffffd'u64 , 0x0000000000000006'u64 ) + , ( 0x8000000000000003'u64 , 0x7ffffffffffffffe'u64 , 0x0000000000000005'u64 ) + , ( 0x8000000000000003'u64 , 0x7fffffffffffffff'u64 , 0x0000000000000004'u64 ) + , ( 0x8000000000000003'u64 , 0x8000000000000000'u64 , 0x0000000000000003'u64 ) + , ( 0x8000000000000003'u64 , 0x8000000000000001'u64 , 0x0000000000000002'u64 ) + , ( 0x8000000000000003'u64 , 0x8000000000000002'u64 , 0x0000000000000001'u64 ) + , ( 0x8000000000000003'u64 , 0x8000000000000003'u64 , 0x0000000000000000'u64 ) + ] + + +const testcases_mul* : array[2401, tuple[x:uint64, y:uint64, z:uint64]] = + [ ( 0xfffffffefffffffe'u64 , 0xfffffffefffffffe'u64 , 0x0000000000000009'u64 ) + , ( 0xfffffffefffffffe'u64 , 0xfffffffeffffffff'u64 , 0x0000000000000006'u64 ) + , ( 0xfffffffefffffffe'u64 , 0xffffffff00000000'u64 , 0x0000000000000003'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000000'u64 , 0x0000000000000000'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000001'u64 , 0xfffffffefffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000002'u64 , 0xfffffffefffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000000003'u64 , 0xfffffffefffffff8'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000fffd'u64 , 0xfffffffefffd000a'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000fffe'u64 , 0xfffffffefffd0007'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000000000ffff'u64 , 0xfffffffefffd0004'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010000'u64 , 0xfffffffefffd0001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010001'u64 , 0xfffffffefffcfffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010002'u64 , 0xfffffffefffcfffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000000010003'u64 , 0xfffffffefffcfff8'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007ffffffd'u64 , 0xfffffffd8000000a'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007ffffffe'u64 , 0xfffffffd80000007'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x000000007fffffff'u64 , 0xfffffffd80000004'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000000'u64 , 0xfffffffd80000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000001'u64 , 0xfffffffd7ffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000002'u64 , 0xfffffffd7ffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000080000003'u64 , 0xfffffffd7ffffff8'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000fffffffd'u64 , 0xfffffffc0000000a'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000fffffffe'u64 , 0xfffffffc00000007'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000000ffffffff'u64 , 0xfffffffc00000004'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000000'u64 , 0xfffffffc00000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000001'u64 , 0xfffffffbfffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000002'u64 , 0xfffffffbfffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000100000003'u64 , 0xfffffffbfffffff8'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001fffffffd'u64 , 0xfffffff90000000a'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001fffffffe'u64 , 0xfffffff900000007'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x00000001ffffffff'u64 , 0xfffffff900000004'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000000'u64 , 0xfffffff900000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000001'u64 , 0xfffffff8fffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000002'u64 , 0xfffffff8fffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000000200000003'u64 , 0xfffffff8fffffff8'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000fffffffffffd'u64 , 0xfffcffff0000000a'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000fffffffffffe'u64 , 0xfffcffff00000007'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0000ffffffffffff'u64 , 0xfffcffff00000004'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000000'u64 , 0xfffcffff00000001'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000001'u64 , 0xfffcfffefffffffe'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000002'u64 , 0xfffcfffefffffffb'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x0001000000000003'u64 , 0xfffcfffefffffff8'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x7ffffffffffffffd'u64 , 0x7ffffffe0000000b'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x7ffffffffffffffe'u64 , 0x7ffffffe00000008'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x7fffffffffffffff'u64 , 0x7ffffffe00000005'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x8000000000000000'u64 , 0x7ffffffe00000002'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x8000000000000001'u64 , 0x7ffffffdffffffff'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x8000000000000002'u64 , 0x7ffffffdfffffffc'u64 ) + , ( 0xfffffffefffffffe'u64 , 0x8000000000000003'u64 , 0x7ffffffdfffffff9'u64 ) + , ( 0xfffffffeffffffff'u64 , 0xfffffffefffffffe'u64 , 0x0000000000000006'u64 ) + , ( 0xfffffffeffffffff'u64 , 0xfffffffeffffffff'u64 , 0x0000000000000004'u64 ) + , ( 0xfffffffeffffffff'u64 , 0xffffffff00000000'u64 , 0x0000000000000002'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000000'u64 , 0x0000000000000000'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000001'u64 , 0xfffffffeffffffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000002'u64 , 0xfffffffefffffffd'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000000003'u64 , 0xfffffffefffffffb'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000000000fffd'u64 , 0xfffffffefffe0007'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000000000fffe'u64 , 0xfffffffefffe0005'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x000000000000ffff'u64 , 0xfffffffefffe0003'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000010000'u64 , 0xfffffffefffe0001'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000010001'u64 , 0xfffffffefffdffff'u64 ) + , ( 0xfffffffeffffffff'u64 , 0x0000000000010002'u64 , 0xfffffffefffdfffd'u64 ) + , 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b/tests/poseidon2/testField.nim new file mode 100644 index 0000000..0850c08 --- /dev/null +++ b/tests/poseidon2/testField.nim @@ -0,0 +1,58 @@ + +import std/unittest +# import std/sequtils + +import poseidon2/types +import poseidon2/goldilocks + +import ./fieldTestCases + +#------------------------------------------------------------------------------- + +suite "field": + + test "negation": + var ok = true + for (x0,y0) in testcases_neg: + let x = toF(x0) + let y = toF(y0) + if neg(x) != y: + ok = false + break + check ok + + test "addition": + var ok = true + for (x0,y0,z0) in testcases_add: + let x = toF(x0) + let y = toF(y0) + let z = toF(z0) + if x + y != z: + ok = false + break + check ok + + test "subtraction": + var ok = true + for (x0,y0,z0) in testcases_sub: + let x = toF(x0) + let y = toF(y0) + let z = toF(z0) + if x - y != z: + ok = false + break + check ok + + test "multiplication": + var ok = true + for (x0,y0,z0) in testcases_mul: + let x = toF(x0) + let y = toF(y0) + let z = toF(z0) + if x * y != z: + ok = false + break + check ok + +#------------------------------------------------------------------------------- + diff --git a/tests/test.nim b/tests/test.nim new file mode 100644 index 0000000..dd76375 --- /dev/null +++ b/tests/test.nim @@ -0,0 +1,11 @@ +#import ./poseidon2/testPermutation +#import ./poseidon2/testSponge +#import ./poseidon2/testCompress +#import ./poseidon2/testMerkle +#import ./poseidon2/testSpongeMerkle +#import ./poseidon2/testIo +#import ./poseidon2/testReadme + +import ./poseidon2/testField + +{.warning[UnusedImport]: off.}