diff --git a/jsntlib/NTLArchive/NTLBezoutEquation.py b/jsntlib/NTLArchive/NTLBezoutEquation.py index c1f75f5..fc9298b 100644 --- a/jsntlib/NTLArchive/NTLBezoutEquation.py +++ b/jsntlib/NTLArchive/NTLBezoutEquation.py @@ -14,7 +14,7 @@ '''Usage sample: -print('%d*-179 + %d*-367 = (-179,-367)' % bezout(-179,-367)) +print('%d*-179 + %d*-367 = (-179,-367)' % bezout(-179, -367)) ''' @@ -22,42 +22,45 @@ def bezoutEquation(a, b): int_check(a, b) - exflag = pn_a = pn_b = 0 - if a < 0: a *= -1; pn_a = 1 - if b < 0: b *= -1; pn_b = 1 - if a < b: a, b = b, a; pn_a, pn_b = pn_b, pn_a; exflag = 1 # 交換a與b的次序，使得a≥b + exflag = pn_a = pn_b = False + if a < 0: a *= -1; pn_a = True + if b < 0: b *= -1; pn_b = True + if a < b: a, b = b, a; pn_a, pn_b = pn_b, pn_a; exflag = True # 交換a與b的次序，使得a≥b q = [0] + euclideanAlgorithm(a, b) # 廣義歐幾里德除法（輾轉相除法），求不完全商數組q - s = coefficient_s(q, 1, 0, 0) # 求係數s - t = coefficient_t(q, 0, 1, 0) # 求係數t + s, t = coefficients(q) # 求係數s和t + + if pn_a ^ pn_b: + if exflag: + tmp = s + s = -t if pn_b else t + t = -tmp if pn_a else tmp + + else: + if pn_b: s = -s + if pn_a: t = -t + + elif pn_a and pn_b: + if exflag: s, t = -t, -s + else: s, t = -s, -t - if exflag: - s *= -1 if pn_b else 1; t *= -1 if pn_a else 1 else: - s *= -1 if pn_a else 1; t *= -1 if pn_b else 1 + if exflag: s, t = t, s return s, t -def coefficient_s(q_j, s_j1, s_j2, ctr): - try: - s = -1 * q_j[ctr] * s_j1 + s_j2 # s_j = (-q_j) * s_j-1 + s_j-2 - except IndexError: - return s_j1 +def coefficients(q): + s_j1 = 1; s_j2 = 0 + t_j1 = 0; t_j2 = 1 - s_j2 = s_j1 - s_j1 = s - ctr += 1 - return coefficient_t(q_j, s_j1, s_j2, ctr) + for q_j in q: + s_j = -q_j * s_j1 + s_j2 # s_j = (-q_j) * s_j-1 + s_j-2 + t_j = -q_j * t_j1 + t_j2 # t_j = (-q_j) * t_j-1 + t_j-2 + s_j2 = s_j1; s_j1 = s_j + t_j2 = t_j1; t_j1 = t_j + else: + return s_j, t_j -def coefficient_t(q_j, t_j1, t_j2, ctr): - try: - t = -1 * q_j[ctr] * t_j1 + t_j2 # t_j = (-q_j) * t_j-1 + t_j-2 - except IndexError: - return t_j1 - - t_j2 = t_j1 - t_j1 = t - ctr += 1 - return coefficient_t(q_j, t_j1, t_j2, ctr) + return (0, 1) diff --git a/jsntlib/NTLArchive/NTLChineseRemainderTheorem.py b/jsntlib/NTLArchive/NTLChineseRemainderTheorem.py index 62dd830..8e3aaef 100644 --- a/jsntlib/NTLArchive/NTLChineseRemainderTheorem.py +++ b/jsntlib/NTLArchive/NTLChineseRemainderTheorem.py @@ -5,6 +5,7 @@ # 求基本同餘式組的通解 +from .NTLBezoutEquation import bezoutEquation from .NTLExceptions import DefinitionError from .NTLUtilities import jsrange from .NTLValidations import int_check, list_check, tuple_check @@ -50,25 +51,15 @@ def CHNRemainderTheorem(*args): modulo *= tmpMod1 # M(original modulo) = ∏m_i bList = [] - for tmpMod2 in mod: - M = modulo // tmpMod2 # M_i = M / m_i - t = solve(M, tmpMod2) # t_i * M_i ≡ 1 (mod m_i) + for tmpMod in mod: + M = modulo // tmpMod # M_i = M / m_i + t = bezoutEquation(M, tmpMod)[0] # t_i * M_i ≡ 1 (mod m_i) bList.append(t * M) # b_i = t_i * M_i remainder = iterCalc(rmd, bList, modulo) # x_j = Σ(b_i * r_i) (mod M) return sorted(remainder) -# 求解M_i^-1 (mod m_i) -def solve(variable, modulo): - polyCgc = '%d*x - 1' % variable # 將係數與指數數組生成多項式 - - r = lambda x: eval(polyCgc) # 用於計算多項式的取值 - for x in jsrange(modulo): # 逐一驗算，如模為0則加入結果數組 - if r(x) % modulo == 0: - return x - - # 對rmd多維數組（層，號）中的數進行全排列並計算結果 def iterCalc(ognList, coeList, modulo): ptrList = [] # 寄存指向每一數組層的號 diff --git a/jsntlib/NTLArchive/NTLCongruence.py b/jsntlib/NTLArchive/NTLCongruence.py index d2e27ee..afca4e4 100644 --- a/jsntlib/NTLArchive/NTLCongruence.py +++ b/jsntlib/NTLArchive/NTLCongruence.py @@ -8,6 +8,7 @@ # 由多項式衍生的同餘式 +from .NTLBezoutEquation import bezoutEquation from .NTLExceptions import DefinitionError, PCError, PolyError, SolutionError from .NTLGreatestCommonDivisor import greatestCommonDivisor from .NTLPolynomial import Polynomial @@ -235,22 +236,12 @@ def _primePro(self, rem, exp): # 中國剩餘定理 def _CTR(self, rem, mod): - - # 求解M_i^-1 (mod m_i) - def solve(variable, modulo): - polyCgc = '%d*x - 1' % variable # 將係數與指數數組生成多項式 - - r = lambda x: eval(polyCgc) # 用於計算多項式的取值 - for x in jsrange(modulo): # 逐一驗算，如模為0則加入結果數組 - if r(x) % modulo == 0: - return x - modulo = self._modulo # M(original modulo) = ∏m_i bList = [] for tmpMod in mod: M = modulo // tmpMod # M_i = M / m_i - t = solve(M, tmpMod) # t_i * M_i ≡ 1 (mod m_i) + t = bezoutEquation(M, tmpMod)[0] # t_i * M_i ≡ 1 (mod m_i) bList.append(t * M) # b_i = t_i * M_i _rem = self._iterCalc(rem, bList) # x_j = Σ(b_i * r_i) (mod M) diff --git a/jsntlib/NTLArchive/NTLEratosthenesSieve.py b/jsntlib/NTLArchive/NTLEratosthenesSieve.py index d56f58a..03f5efc 100644 --- a/jsntlib/NTLArchive/NTLEratosthenesSieve.py +++ b/jsntlib/NTLArchive/NTLEratosthenesSieve.py @@ -11,6 +11,8 @@ from .NTLUtilities import jsrange from .NTLValidations import int_check, pos_check +# from NTLTrivialDivision import trivialDivision + __all__ = ['eratosthenesSieve'] nickname = 'primelist' @@ -24,7 +26,7 @@ # 前1280個素數表，簡化小素數的求取 -PRIME_LIST = [ +_PRIME_LIST = [ [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97], [101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199], [211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293], @@ -142,42 +144,63 @@ def eratosthenesSieve(upper, lower=None): if upper <= 10100: _llevel = lower // 100; _ulevel = upper // 100 - for ptr_1 in jsrange(len(PRIME_LIST[_llevel])): - if PRIME_LIST[_llevel][ptr_1] >= lower: + for ptr_1 in jsrange(len(_PRIME_LIST[_llevel])): + if _PRIME_LIST[_llevel][ptr_1] >= lower: llevel = ptr_1; break else: _llevel += 1; llevel = 0 - for ptr_2 in jsrange(len(PRIME_LIST[_ulevel])): - if PRIME_LIST[_ulevel][ptr_2] >= upper: + for ptr_2 in jsrange(len(_PRIME_LIST[_ulevel])): + if _PRIME_LIST[_ulevel][ptr_2] >= upper: ulevel = ptr_2; break else: ulevel = None if _llevel != _ulevel: - rst = PRIME_LIST[_llevel][llevel:] + rst = _PRIME_LIST[_llevel][llevel:] for _level in jsrange(_llevel+1, _ulevel): - rst += PRIME_LIST[_level] - rst += PRIME_LIST[_ulevel][:ulevel] + rst += _PRIME_LIST[_level] + rst += _PRIME_LIST[_ulevel][:ulevel] else: - rst = PRIME_LIST[_llevel][llevel:ulevel] + rst = _PRIME_LIST[_llevel][llevel:ulevel] else: - # 用於存儲upper個正整數的表格／狀態；其中，0表示篩去，1表示保留 - table = [1]*(upper+1) - - # 篩法（平凡除法） - for index in jsrange(2, int(math.sqrt(upper))+1): - tmp = index * 2 - if table[index] == 1: - while tmp <= upper: - # 將index的倍數篩去 - table[tmp] = 0; tmp += index - - # 獲取結果 - rst = [] - for ptr in jsrange(lower, upper+1): - if table[ptr] == 1: - rst.append(ptr) + from NTLTrivialDivision import trivialDivision + + def _eratosthenesSieve(upper, lower): + # 用於存儲upper個正整數的表格／狀態；其中，0表示篩去，1表示保留 + table = [1]*(upper+1) + + # 篩法（平凡除法） + for index in jsrange(2, int(math.sqrt(upper))+1): + tmp = index * 2 + if table[index] == 1: + while tmp <= upper: + # 將index的倍數篩去 + table[tmp] = 0; tmp += index + + # 獲取結果 + rst = [] + for ptr in jsrange(lower, upper+1): + if table[ptr] == 1: + rst.append(ptr) + + return rst + + if math.log(upper, 10) > 4.0: + if math.log(lower, 10) > 4.0: + rst = [] + start = lower if lower % 2 == 1 else lower + 1 + + else: + rst = _eratosthenesSieve(10000, lower) + start = 10001 + + for _int in jsrange(start, upper, 2): + if trivialDivision(_int): + rst.append(_int) + + else: + rst = _eratosthenesSieve(upper, lower) return rst diff --git a/setup.py b/setup.py index acaeb58..14692f9 100644 --- a/setup.py +++ b/setup.py @@ -11,7 +11,7 @@ name = 'jsntlib', - version = '1.1.1', + version = '1.1.2', description = 'A number theory library adapted from mathematic fundamentals of information security homework codes.', @@ -32,7 +32,7 @@ url = 'https://github.com/JarryShaw/jsntlib/tree/release', - download_url = 'https://github.com/JarryShaw/jsntlib/archive/1.1.1.tar.gz', + download_url = 'https://github.com/JarryShaw/jsntlib/archive/1.1.2.tar.gz', packages = [ 'jsntlib',