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GeezerVison is showing github.com — Python-1/maths/gamma_recursive.py at master · https-github-com-nzysoft/Python-1 Expand file tree/ Copy pathgamma_recursive.pyMore file actions 77 lines (70 loc) · 2.08 KB / Copy pathgamma_recursive.pyFile metadata and controls77 lines (70 loc) · 2.08 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 """ Gamma function is a very useful tool in math and physics. It helps calculating complex integral in a convenient way. for more info: https://en.wikipedia.org/wiki/Gamma_function Python's Standard Library math.gamma() function overflows around gamma(171.624). """ from math import pi, sqrt def gamma(num: float) -> float: """ Calculates the value of Gamma function of num where num is either an integer (1, 2, 3..) or a half-integer (0.5, 1.5, 2.5 ...). Implemented using recursion Examples: >>> from math import isclose, gamma as math_gamma >>> gamma(0.5) 1.7724538509055159 >>> gamma(2) 1.0 >>> gamma(3.5) 3.3233509704478426 >>> gamma(171.5) 9.483367566824795e+307 >>> all(isclose(gamma(num), math_gamma(num)) for num in (0.5, 2, 3.5, 171.5)) True >>> gamma(0) Traceback (most recent call last): ... ValueError: math domain error >>> gamma(-1.1) Traceback (most recent call last): ... ValueError: math domain error >>> gamma(-4) Traceback (most recent call last): ... ValueError: math domain error >>> gamma(172) Traceback (most recent call last): ... OverflowError: math range error >>> gamma(1.1) Traceback (most recent call last): ... NotImplementedError: num must be an integer or a half-integer """ if num <= 0: raise ValueError("math domain error") if num > 171.5: raise OverflowError("math range error") elif num - int(num) not in (0, 0.5): raise NotImplementedError("num must be an integer or a half-integer") elif num == 0.5: return sqrt(pi) else: return 1.0 if num == 1 else (num - 1) * gamma(num - 1) def test_gamma() -> None: """ >>> test_gamma() """ assert gamma(0.5) == sqrt(pi) assert gamma(1) == 1.0 assert gamma(2) == 1.0 if __name__ == "__main__": from doctest import testmod testmod() num = 1.0 while num: num = float(input("Gamma of: ")) print(f"gamma({num}) = {gamma(num)}") print("\nEnter 0 to exit...") |
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