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1、9.2.math Mathematical functionsThis module is always available. It provides access to the mathematical functions defined by the C standard.These functions cannot be used with complex numbers; use the functions of the same name from thecmathmodule if you require support for complex numbers. The disti
2、nction between functions which support complex numbers and those which dont is made since most users do not want to learn quite as much mathematics as required to understand complex numbers. Receiving an exception instead of a complex result allows earlier detection of the unexpected complex number
3、used as a parameter, so that the programmer can determine how and why it was generated in the first place.The following functions are provided by this module. Except when explicitly noted otherwise, all return values are floats.9.2.1. Number-theoretic and representation functionsmath.ceil(x)Return t
4、he ceiling ofx, the smallest integer greater than or equal tox. Ifxis not a float, delegates tox._ceil_(), which should return anIntegralvalue.math.copysign(x,y)Return a float with the magnitude (absolute value) ofxbut the sign ofy. On platforms that support signed zeros,copysign(1.0,-0.0)returns-1.
5、0.math.fabs(x)Return the absolute value ofx.math.factorial(x)Returnxfactorial. RaisesValueErrorifxis not integral or is negative.math.floor(x)Return the floor ofx, the largest integer less than or equal tox. Ifxis not a float, delegates tox._floor_(), which should return anIntegralvalue.math.fmod(x,
6、y)Returnfmod(x,y), as defined by the platform C library. Note that the Python expressionx%ymay not return the same result. The intent of the C standard is thatfmod(x,y)be exactly (mathematically; to infinite precision) equal tox-n*yfor some integernsuch that the result has the same sign asxand magni
7、tude less thanabs(y). Pythonsx%yreturns a result with the sign ofyinstead, and may not be exactly computable for float arguments. For example,fmod(-1e-100,1e100)is-1e-100, but the result of Pythons-1e-100%1e100is1e100-1e-100, which cannot be represented exactly as a float, and rounds to the surprisi
8、ng1e100. For this reason, functionfmod()is generally preferred when working with floats, while Pythonsx%yis preferred when working with integers.math.frexp(x)Return the mantissa and exponent ofxas the pair(m,e).mis a float andeis an integer such thatx=m*2*eexactly. Ifxis zero, returns(0.0,0), otherw
9、ise0.5=abs(m) sum(.1, .1, .1, .1, .1, .1, .1, .1, .1, .1)0.9999999999999999 fsum(.1, .1, .1, .1, .1, .1, .1, .1, .1, .1)1.0The algorithms accuracy depends on IEEE-754 arithmetic guarantees and the typical case where the rounding mode is half-even. On some non-Windows builds, the underlying C library
10、 uses extended precision addition and may occasionally double-round an intermediate sum causing it to be off in its least significant bit.For further discussion and two alternative approaches, see theASPN cookbook recipes for accurate floating point summation.math.gcd(a,b)Return the greatest common
11、divisor of the integersaandb. If eitheraorbis nonzero, then the value ofgcd(a,b)is the largest positive integer that divides bothaandb.gcd(0,0)returns0.New in version 3.5.math.isclose(a,b,*,rel_tol=1e-09,abs_tol=0.0)ReturnTrueif the valuesaandbare close to each other andFalseotherwise.Whether or not
12、 two values are considered close is determined according to given absolute and relative tolerances.rel_tolis the relative tolerance it is the maximum allowed difference betweenaandb, relative to the larger absolute value ofaorb. For example, to set a tolerance of 5%, passrel_tol=0.05. The default to
13、lerance is1e-09, which assures that the two values are the same within about 9 decimal digits.rel_tolmust be greater than zero.abs_tolis the minimum absolute tolerance useful for comparisons near zero.abs_tolmust be at least zero.If no errors occur, the result will be:abs(a-b)=max(rel_tol*max(abs(a)
14、,abs(b),abs_tol).The IEEE 754 special values ofNaN,inf, and-infwill be handled according to IEEE rules. Specifically,NaNis not considered close to any other value, includingNaN.infand-infare only considered close to themselves.New in version 3.5.See also：PEP 485 A function for testing approximate equalitymath.isfinite(x)ReturnTrueifxis neither an infinity nor a NaN, andFalseotherwise. (Note that0.0isconsidered finite.)New in version 3.2.math.isinf(x)ReturnTrueifxis a positive or negative infinity, andFalseotherwise.math.isnan(x)ReturnTrueifx
