# # Copyright 2021 Jeroen van Rijn . # Made available under Odin's BSD-3 license. # # A BigInt implementation in Odin. # For the theoretical underpinnings, see Knuth's The Art of Computer Programming, Volume 2, section 4.3. # The code started out as an idiomatic source port of libTomMath, which is in the public domain, with thanks. # from ctypes import * from random import * import math import os import platform import time import gc from enum import Enum import argparse parser = argparse.ArgumentParser( description = "Odin core:math/big test suite", epilog = "By default we run regression and random tests with preset parameters.", formatter_class = argparse.ArgumentDefaultsHelpFormatter, ) # # Normally, we report the number of passes and fails. With this option set, we exit at first fail. # parser.add_argument( "-exit-on-fail", help = "Exit when a test fails", action = "store_true", ) # # We skip randomized tests altogether if this is set. # no_random = parser.add_mutually_exclusive_group() no_random.add_argument( "-no-random", help = "No random tests", action = "store_true", ) # # Normally we run a given number of cycles on each test. # Timed tests budget 1 second per 20_000 bits instead. # # For timed tests we budget a second per `n` bits and iterate until we hit that time. # timed_or_fast = no_random.add_mutually_exclusive_group() timed_or_fast.add_argument( "-timed", type = bool, default = False, help = "Timed tests instead of a preset number of iterations.", ) parser.add_argument( "-timed-bits", type = int, metavar = "BITS", default = 20_000, help = "Timed tests. Every `BITS` worth of input is given a second of running time.", ) # # For normal tests (non-timed), `-fast-tests` cuts down on the number of iterations. # timed_or_fast.add_argument( "-fast-tests", help = "Cut down on the number of iterations of each test", action = "store_true", ) args = parser.parse_args() EXIT_ON_FAIL = args.exit_on_fail # # How many iterations of each random test do we want to run? # BITS_AND_ITERATIONS = [ ( 120, 10_000), ( 1_200, 1_000), ( 4_096, 100), (12_000, 10), ] if args.fast_tests: for k in range(len(BITS_AND_ITERATIONS)): b, i = BITS_AND_ITERATIONS[k] BITS_AND_ITERATIONS[k] = (b, i // 10 if i >= 100 else 5) if args.no_random: BITS_AND_ITERATIONS = [] # # Where is the DLL? If missing, build using: `odin build . -build-mode:shared` # if platform.system() == "Windows": LIB_PATH = os.getcwd() + os.sep + "math_big_test_library.dll" elif platform.system() == "Linux": LIB_PATH = os.getcwd() + os.sep + "math_big_test_library.so" elif platform.system() == "Darwin": LIB_PATH = os.getcwd() + os.sep + "math_big_test_library.dylib" else: print("Platform is unsupported.") exit(1) TOTAL_TIME = 0 UNTIL_TIME = 0 UNTIL_ITERS = 0 def we_iterate(): if args.timed: return TOTAL_TIME < UNTIL_TIME else: global UNTIL_ITERS UNTIL_ITERS -= 1 return UNTIL_ITERS != -1 # # Error enum values # class Error(Enum): Okay = 0 Out_Of_Memory = 1 Invalid_Pointer = 2 Invalid_Argument = 3 Unknown_Error = 4 Assignment_To_Immutable = 10 Max_Iterations_Reached = 11 Buffer_Overflow = 12 Integer_Overflow = 13 Integer_Underflow = 14 Division_by_Zero = 30 Math_Domain_Error = 31 Cannot_Open_File = 50 Cannot_Read_File = 51 Cannot_Write_File = 52 Unimplemented = 127 # # Disable garbage collection # gc.disable() # # Set up exported procedures # try: l = cdll.LoadLibrary(LIB_PATH) except: print("Couldn't find or load " + LIB_PATH + ".") exit(1) def load(export_name, args, res): export_name.argtypes = args export_name.restype = res return export_name # # Result values will be passed in a struct { res: cstring, err: Error } # class Res(Structure): _fields_ = [("res", c_char_p), ("err", c_uint64)] initialize_constants = load(l.test_initialize_constants, [], c_uint64) NAILS = initialize_constants() LEG_BITS = 64 - NAILS print("LEG BITS: ", LEG_BITS) error_string = load(l.test_error_string, [c_byte], c_char_p) add = load(l.test_add, [c_char_p, c_char_p ], Res) sub = load(l.test_sub, [c_char_p, c_char_p ], Res) mul = load(l.test_mul, [c_char_p, c_char_p ], Res) sqr = load(l.test_sqr, [c_char_p ], Res) div = load(l.test_div, [c_char_p, c_char_p ], Res) # Powers and such int_log = load(l.test_log, [c_char_p, c_longlong], Res) int_pow = load(l.test_pow, [c_char_p, c_longlong], Res) int_sqrt = load(l.test_sqrt, [c_char_p ], Res) int_root_n = load(l.test_root_n, [c_char_p, c_longlong], Res) # Logical operations int_shl_leg = load(l.test_shl_leg, [c_char_p, c_longlong], Res) int_shr_leg = load(l.test_shr_leg, [c_char_p, c_longlong], Res) int_shl = load(l.test_shl, [c_char_p, c_longlong], Res) int_shr = load(l.test_shr, [c_char_p, c_longlong], Res) int_shr_signed = load(l.test_shr_signed, [c_char_p, c_longlong], Res) int_factorial = load(l.test_factorial, [c_uint64 ], Res) int_gcd = load(l.test_gcd, [c_char_p, c_char_p ], Res) int_lcm = load(l.test_lcm, [c_char_p, c_char_p ], Res) is_square = load(l.test_is_square, [c_char_p ], Res) def test(test_name: "", res: Res, param=[], expected_error = Error.Okay, expected_result = "", radix=16): passed = True r = None err = Error(res.err) if err != expected_error: error_loc = res.res.decode('utf-8') error = "{}: {} in '{}'".format(test_name, err, error_loc) if len(param): error += " with params {}".format(param) print(error, flush=True) passed = False elif err == Error.Okay: r = None try: r = res.res.decode('utf-8') r = int(res.res, radix) except: pass if r != expected_result: error = "{}: Result was '{}', expected '{}'".format(test_name, r, expected_result) if len(param): error += " with params {}".format(param) print(error, flush=True) passed = False if EXIT_ON_FAIL and not passed: exit(res.err) return passed def arg_to_odin(a): if a >= 0: s = hex(a)[2:] else: s = '-' + hex(a)[3:] return s.encode('utf-8') def big_integer_sqrt(src): # The Python version on Github's CI doesn't offer math.isqrt. # We implement our own count = src.bit_length() a, b = count >> 1, count & 1 x = 1 << (a + b) while True: # y = (x + n // x) // 2 t1 = src // x t2 = t1 + x y = t2 >> 1 if y >= x: return x x, y = y, x def big_integer_lcm(a, b): # Computes least common multiple as `|a*b|/gcd(a,b)` # Divide the smallest by the GCD. if a == 0 or b == 0: return 0 if abs(a) < abs(b): # Store quotient in `t2` such that `t2 * b` is the LCM. lcm = a // math.gcd(a, b) return abs(b * lcm) else: # Store quotient in `t2` such that `t2 * a` is the LCM. lcm = b // math.gcd(a, b) return abs(a * lcm) def test_add(a = 0, b = 0, expected_error = Error.Okay): args = [arg_to_odin(a), arg_to_odin(b)] res = add(*args) expected_result = None if expected_error == Error.Okay: expected_result = a + b return test("test_add", res, [a, b], expected_error, expected_result) def test_sub(a = 0, b = 0, expected_error = Error.Okay): args = [arg_to_odin(a), arg_to_odin(b)] res = sub(*args) expected_result = None if expected_error == Error.Okay: expected_result = a - b return test("test_sub", res, [a, b], expected_error, expected_result) def test_mul(a = 0, b = 0, expected_error = Error.Okay): args = [arg_to_odin(a), arg_to_odin(b)] try: res = mul(*args) except OSError as e: print("{} while trying to multiply {} x {}.".format(e, a, b)) if EXIT_ON_FAIL: exit(3) return False expected_result = None if expected_error == Error.Okay: expected_result = a * b return test("test_mul", res, [a, b], expected_error, expected_result) def test_sqr(a = 0, b = 0, expected_error = Error.Okay): args = [arg_to_odin(a)] try: res = sqr(*args) except OSError as e: print("{} while trying to square {}.".format(e, a)) if EXIT_ON_FAIL: exit(3) return False expected_result = None if expected_error == Error.Okay: expected_result = a * a return test("test_sqr", res, [a], expected_error, expected_result) def test_div(a = 0, b = 0, expected_error = Error.Okay): args = [arg_to_odin(a), arg_to_odin(b)] try: res = div(*args) except OSError as e: print("{} while trying divide to {} / {}.".format(e, a, b)) if EXIT_ON_FAIL: exit(3) return False expected_result = None if expected_error == Error.Okay: # # We don't round the division results, so if one component is negative, we're off by one. # if a < 0 and b > 0: expected_result = int(-(abs(a) // b)) elif b < 0 and a > 0: expected_result = int(-(a // abs((b)))) else: expected_result = a // b if b != 0 else None return test("test_div", res, [a, b], expected_error, expected_result) def test_log(a = 0, base = 0, expected_error = Error.Okay): args = [arg_to_odin(a), base] res = int_log(*args) expected_result = None if expected_error == Error.Okay: expected_result = int(math.log(a, base)) return test("test_log", res, [a, base], expected_error, expected_result) def test_pow(base = 0, power = 0, expected_error = Error.Okay): args = [arg_to_odin(base), power] res = int_pow(*args) expected_result = None if expected_error == Error.Okay: if power < 0: expected_result = 0 else: # NOTE(Jeroen): Don't use `math.pow`, it's a floating point approximation. # Use built-in `pow` or `a**b` instead. expected_result = pow(base, power) return test("test_pow", res, [base, power], expected_error, expected_result) def test_sqrt(number = 0, expected_error = Error.Okay): args = [arg_to_odin(number)] try: res = int_sqrt(*args) except OSError as e: print("{} while trying to sqrt {}.".format(e, number)) if EXIT_ON_FAIL: exit(3) return False expected_result = None if expected_error == Error.Okay: if number < 0: expected_result = 0 else: expected_result = big_integer_sqrt(number) return test("test_sqrt", res, [number], expected_error, expected_result) def root_n(number, root): u, s = number, number + 1 while u < s: s = u t = (root-1) * s + number // pow(s, root - 1) u = t // root return s def test_root_n(number = 0, root = 0, expected_error = Error.Okay): args = [arg_to_odin(number), root] res = int_root_n(*args) expected_result = None if expected_error == Error.Okay: if number < 0: expected_result = 0 else: expected_result = root_n(number, root) return test("test_root_n", res, [number, root], expected_error, expected_result) def test_shl_leg(a = 0, digits = 0, expected_error = Error.Okay): args = [arg_to_odin(a), digits] res = int_shl_leg(*args) expected_result = None if expected_error == Error.Okay: expected_result = a << (digits * LEG_BITS) return test("test_shl_leg", res, [a, digits], expected_error, expected_result) def test_shr_leg(a = 0, digits = 0, expected_error = Error.Okay): args = [arg_to_odin(a), digits] res = int_shr_leg(*args) expected_result = None if expected_error == Error.Okay: if a < 0: # Don't pass negative numbers. We have a shr_signed. return False else: expected_result = a >> (digits * LEG_BITS) return test("test_shr_leg", res, [a, digits], expected_error, expected_result) def test_shl(a = 0, bits = 0, expected_error = Error.Okay): args = [arg_to_odin(a), bits] res = int_shl(*args) expected_result = None if expected_error == Error.Okay: expected_result = a << bits return test("test_shl", res, [a, bits], expected_error, expected_result) def test_shr(a = 0, bits = 0, expected_error = Error.Okay): args = [arg_to_odin(a), bits] res = int_shr(*args) expected_result = None if expected_error == Error.Okay: if a < 0: # Don't pass negative numbers. We have a shr_signed. return False else: expected_result = a >> bits return test("test_shr", res, [a, bits], expected_error, expected_result) def test_shr_signed(a = 0, bits = 0, expected_error = Error.Okay): args = [arg_to_odin(a), bits] res = int_shr_signed(*args) expected_result = None if expected_error == Error.Okay: expected_result = a >> bits return test("test_shr_signed", res, [a, bits], expected_error, expected_result) def test_factorial(number = 0, expected_error = Error.Okay): args = [number] try: res = int_factorial(*args) except OSError as e: print("{} while trying to factorial {}.".format(e, number)) if EXIT_ON_FAIL: exit(3) return False expected_result = None if expected_error == Error.Okay: expected_result = math.factorial(number) return test("test_factorial", res, [number], expected_error, expected_result) def test_gcd(a = 0, b = 0, expected_error = Error.Okay): args = [arg_to_odin(a), arg_to_odin(b)] res = int_gcd(*args) expected_result = None if expected_error == Error.Okay: expected_result = math.gcd(a, b) return test("test_gcd", res, [a, b], expected_error, expected_result) def test_lcm(a = 0, b = 0, expected_error = Error.Okay): args = [arg_to_odin(a), arg_to_odin(b)] res = int_lcm(*args) expected_result = None if expected_error == Error.Okay: expected_result = big_integer_lcm(a, b) return test("test_lcm", res, [a, b], expected_error, expected_result) def test_is_square(a = 0, b = 0, expected_error = Error.Okay): args = [arg_to_odin(a)] res = is_square(*args) expected_result = None if expected_error == Error.Okay: expected_result = str(big_integer_sqrt(a) ** 2 == a) if a > 0 else "False" return test("test_is_square", res, [a], expected_error, expected_result) # TODO(Jeroen): Make sure tests cover edge cases, fast paths, and so on. # # The last two arguments in tests are the expected error and expected result. # # The expected error defaults to None. # By default the Odin implementation will be tested against the Python one. # You can override that by supplying an expected result as the last argument instead. TESTS = { test_add: [ [ 1234, 5432], ], test_sub: [ [ 1234, 5432], ], test_mul: [ [ 1234, 5432], [ 0xd3b4e926aaba3040e1c12b5ea553b5, 0x1a821e41257ed9281bee5bc7789ea7 ], [ 1 << 21_105, 1 << 21_501 ], [ 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] ], test_sqr: [ [ 5432], [ 0xd3b4e926aaba3040e1c12b5ea553b5 ], ], test_div: [ [ 54321, 12345], [ 55431, 0, Error.Division_by_Zero], [ 12980742146337069150589594264770969721, 4611686018427387904 ], [ 831956404029821402159719858789932422, 243087903122332132 ], ], test_log: [ [ 3192, 1, Error.Invalid_Argument], [ -1234, 2, Error.Math_Domain_Error], [ 0, 2, Error.Math_Domain_Error], [ 1024, 2], ], test_pow: [ [ 0, -1, Error.Math_Domain_Error ], # Math [ 0, 0 ], # 1 [ 0, 2 ], # 0 [ 42, -1,], # 0 [ 42, 1 ], # 1 [ 42, 0 ], # 42 [ 42, 2 ], # 42*42 [ 1023423462055631945665902260039819522, 6], [ 2351415513563017480724958108064794964140712340951636081608226461329298597792428177392182921045756382154475969841516481766099091057155043079113409578271460350765774152509347176654430118446048617733844782454267084644777022821998489944144604889308377152515711394170267839394315842510152114743680838721625924309675796181595284284935359605488617487126635442626578631, 4], ], test_sqrt: [ [ -1, Error.Invalid_Argument, ], [ 42, Error.Okay, ], [ 12345678901234567890, Error.Okay, ], [ 1298074214633706907132624082305024, Error.Okay, ], [ 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Error.Okay, ], ], test_root_n: [ [ 1298074214633706907132624082305024, 2, Error.Okay, ], ], test_shl_leg: [ [ 3192, 1 ], [ 1298074214633706907132624082305024, 2 ], [ 1024, 3 ], ], test_shr_leg: [ [ 3680125442705055547392, 1 ], [ 1725436586697640946858688965569256363112777243042596638790631055949824, 2 ], [ 219504133884436710204395031992179571, 2 ], ], test_shl: [ [ 3192, 1 ], [ 1298074214633706907132624082305024, 2 ], [ 1024, 3 ], ], test_shr: [ [ 3680125442705055547392, 1 ], [ 1725436586697640946858688965569256363112777243042596638790631055949824, 2 ], [ 219504133884436710204395031992179571, 2 ], ], test_shr_signed: [ [ -611105530635358368578155082258244262, 12 ], [ -149195686190273039203651143129455, 12 ], [ 611105530635358368578155082258244262, 12 ], [ 149195686190273039203651143129455, 12 ], ], test_factorial: [ [ 6_000 ], # Regular factorial, see cutoff in common.odin. [ 12_345 ], # Binary split factorial ], test_gcd: [ [ 23, 25, ], [ 125, 25, ], [ 125, 0, ], [ 0, 0, ], [ 0, 125,], ], test_lcm: [ [ 23, 25,], [ 125, 25, ], [ 125, 0, ], [ 0, 0, ], [ 0, 125,], ], test_is_square: [ [ 12, ], [ 92232459121502451677697058974826760244863271517919321608054113675118660929276431348516553336313179167211015633639725554914519355444316239500734169769447134357534241879421978647995614218985202290368055757891124109355450669008628757662409138767505519391883751112010824030579849970582074544353971308266211776494228299586414907715854328360867232691292422194412634523666770452490676515117702116926803826546868467146319938818238521874072436856528051486567230096290549225463582766830777324099589751817442141036031904145041055454639783559905920619197290800070679733841430619962318433709503256637256772215111521321630777950145713049902839937043785039344243357384899099910837463164007565230287809026956254332260375327814271845678201, ] ], } if not args.fast_tests: TESTS[test_factorial].append( # This one on its own takes around 800ms, so we exclude it for FAST_TESTS [ 10_000 ], ) total_passes = 0 total_failures = 0 # # test_shr_signed also tests shr, so we're not going to test shr randomly. # RANDOM_TESTS = [ test_add, test_sub, test_mul, test_sqr, test_log, test_pow, test_sqrt, test_root_n, test_shl_leg, test_shr_leg, test_shl, test_shr_signed, test_gcd, test_lcm, test_is_square, test_div, ] SKIP_LARGE = [ test_pow, test_root_n, # test_gcd, ] SKIP_LARGEST = [] # Untimed warmup. for test_proc in TESTS: for t in TESTS[test_proc]: res = test_proc(*t) if __name__ == '__main__': print("\n---- math/big tests ----") print() max_name = 0 for test_proc in TESTS: max_name = max(max_name, len(test_proc.__name__)) fmt_string = "{name:>{max_name}}: {count_pass:7,} passes and {count_fail:7,} failures in {timing:9.3f} ms." fmt_string = fmt_string.replace("{max_name}", str(max_name)) for test_proc in TESTS: count_pass = 0 count_fail = 0 TIMINGS = {} for t in TESTS[test_proc]: start = time.perf_counter() res = test_proc(*t) diff = time.perf_counter() - start TOTAL_TIME += diff if test_proc not in TIMINGS: TIMINGS[test_proc] = diff else: TIMINGS[test_proc] += diff if res: count_pass += 1 total_passes += 1 else: count_fail += 1 total_failures += 1 print(fmt_string.format(name=test_proc.__name__, count_pass=count_pass, count_fail=count_fail, timing=TIMINGS[test_proc] * 1_000)) for BITS, ITERATIONS in BITS_AND_ITERATIONS: print() print("---- math/big with two random {bits:,} bit numbers ----".format(bits=BITS)) print() # # We've already tested up to the 10th root. # TEST_ROOT_N_PARAMS = [2, 3, 4, 5, 6] for test_proc in RANDOM_TESTS: if BITS > 1_200 and test_proc in SKIP_LARGE: continue if BITS > 4_096 and test_proc in SKIP_LARGEST: continue count_pass = 0 count_fail = 0 TIMINGS = {} UNTIL_ITERS = ITERATIONS if test_proc == test_root_n and BITS == 1_200: UNTIL_ITERS /= 10 UNTIL_TIME = TOTAL_TIME + BITS / args.timed_bits # We run each test for a second per 20k bits index = 0 while we_iterate(): a = randint(-(1 << BITS), 1 << BITS) b = randint(-(1 << BITS), 1 << BITS) if test_proc == test_div: # We've already tested division by zero above. bits = int(BITS * 0.6) b = randint(-(1 << bits), 1 << bits) if b == 0: b == 42 elif test_proc == test_log: # We've already tested log's domain errors. a = randint(1, 1 << BITS) b = randint(2, 1 << 60) elif test_proc == test_pow: b = randint(1, 10) elif test_proc == test_sqrt: a = randint(1, 1 << BITS) b = Error.Okay elif test_proc == test_root_n: a = randint(1, 1 << BITS) b = TEST_ROOT_N_PARAMS[index] index = (index + 1) % len(TEST_ROOT_N_PARAMS) elif test_proc == test_shl_leg: b = randint(0, 10); elif test_proc == test_shr_leg: a = abs(a) b = randint(0, 10); elif test_proc == test_shl: b = randint(0, min(BITS, 120)) elif test_proc == test_shr_signed: b = randint(0, min(BITS, 120)) elif test_proc == test_is_square: a = randint(0, 1 << BITS) elif test_proc == test_lcm: smallest = min(a, b) biggest = max(a, b) # Randomly swap biggest and smallest if randint(1, 11) % 2 == 0: smallest, biggest = biggest, smallest a, b = smallest, biggest else: b = randint(0, 1 << BITS) res = None start = time.perf_counter() res = test_proc(a, b) diff = time.perf_counter() - start TOTAL_TIME += diff if test_proc not in TIMINGS: TIMINGS[test_proc] = diff else: TIMINGS[test_proc] += diff if res: count_pass += 1; total_passes += 1 else: count_fail += 1; total_failures += 1 print(fmt_string.format(name=test_proc.__name__, count_pass=count_pass, count_fail=count_fail, timing=TIMINGS[test_proc] * 1_000)) print() print("---- THE END ----") print() print(fmt_string.format(name="total", count_pass=total_passes, count_fail=total_failures, timing=TOTAL_TIME * 1_000)) if total_failures: exit(1)