python数学模块.docx

python数学模块.docx

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python数学模块

9.2. math —Mathematicalfunctions¶

Thismoduleisalwaysavailable.ItprovidesaccesstothemathematicalfunctionsdefinedbytheCstandard.

Thesefunctionscannotbeusedwithcomplexnumbers;usethefunctionsofthesamenamefromthe cmath moduleifyourequiresupportforcomplexnumbers.Thedistinctionbetweenfunctionswhichsupportcomplexnumbersandthosewhichdon’tismadesincemostusersdonotwanttolearnquiteasmuchmathematicsasrequiredtounderstandcomplexnumbers.Receivinganexceptioninsteadofacomplexresultallowsearlierdetectionoftheunexpectedcomplexnumberusedasaparameter,sothattheprogrammercandeterminehowandwhyitwasgeneratedinthefirstplace.

Thefollowingfunctionsareprovidedbythismodule.Exceptwhenexplicitlynotedotherwise,allreturnvaluesarefloats.

9.2.1.Number-theoreticandrepresentationfunctions

math.ceil（x）

Returntheceilingof x,thesmallestintegergreaterthanorequalto x.If x isnotafloat,delegatesto x.__ceil__（）,whichshouldreturnan Integral value.

math.copysign（x, y）

Returnafloatwiththemagnitude（absolutevalue）of x butthesignof y.Onplatformsthatsupportsignedzeros, copysign（1.0, -0.0） returns -1.0.

math.fabs（x）

Returntheabsolutevalueof x.

math.factorial（x）

Return x factorial.Raises ValueError if x isnotintegralorisnegative.

math.floor（x）

Returnthefloorof x,thelargestintegerlessthanorequalto x.If x isnotafloat,

delegatesto x.__floor__（）,whichshouldreturnan Integral value.

math.fmod（x, y）

Return fmod（x, y）,asdefinedbytheplatformClibrary.NotethatthePythonexpression x % y maynotreturnthesameresult.TheintentoftheCstandardisthat fmod（x, y） beexactly（mathematically;toinfiniteprecision）equalto x - n*y forsomeinteger n suchthattheresulthasthesamesignas x andmagnitudelessthan abs（y）.Python’s x % yreturnsaresultwiththesignof y instead,andmaynotbeexactlycomputableforfloatarguments.Forexample, fmod（-1e-100, 1e100） is -1e-100,buttheresultofPython’s -1e-100 % 1e100 is 1e100-1e-100,whichcannotberepresentedexactlyasafloat,androundstothesurprising 1e100.Forthisreason,function fmod（） isgenerallypreferredwhenworkingwithfloats,whilePython’s x % y ispreferredwhenworkingwithintegers.

math.frexp（x）

Returnthemantissaandexponentof x asthepair （m, e）. m isafloatand e isanintegersuchthat x == m * 2**e exactly.If x iszero,returns （0.0, 0）,otherwise 0.5 <= abs（m）< 1.Thisisusedto“pickapart”theinternalrepresentationofafloatinaportableway.

math.fsum（iterable）

Returnanaccuratefloatingpointsumofvaluesintheiterable.Avoidslossofprecisionbytrackingmultipleintermediatepartialsums:

>>>

>>>sum（[.1,.1,.1,.1,.1,.1,.1,.1,.1,.1]）

0.9999999999999999

>>>fsum（[.1,.1,.1,.1,.1,.1,.1,.1,.1,.1]）

1.0

Thealgorithm’saccuracydependsonIEEE-754arithmeticguaranteesandthetypicalcasewheretheroundingmodeishalf-even.Onsomenon-Windowsbuilds,theunderlyingClibraryusesextendedprecisionadditionandmayoccasionallydouble-roundanintermediatesumcausingittobeoffinitsleastsignificantbit.

Forfurtherdiscussionandtwoalternativeapproaches,seethe ASPNcookbookrecipesforaccuratefloatingpointsummation.

math.gcd（a, b）

Returnthegreatestcommondivisoroftheintegers a and b.Ifeither a or b isnonzero,thenthevalueof gcd（a, b） isthelargestpositiveintegerthatdividesboth a and b.gcd（0, 0） returns 0.

Newinversion3.5.

math.isclose（a, b, *, rel_tol=1e-09, abs_tol=0.0）

Return True ifthevalues a and b areclosetoeachotherand False otherwise.

Whetherornottwovaluesareconsideredcloseisdeterminedaccordingtogivenabsoluteandrelativetolerances.

rel_tol istherelativetolerance–itisthemaximumalloweddifferencebetween a and b,relativetothelargerabsolutevalueof a or b.Forexample,tosetatoleranceof5%,pass rel_tol=0.05.Thedefaulttoleranceis 1e-09,whichassuresthatthetwovaluesarethesamewithinabout9decimaldigits. rel_tol mustbegreaterthanzero.

abs_tol istheminimumabsolutetolerance–usefulforcomparisonsnearzero. abs_tolmustbeatleastzero.

Ifnoerrorsoccur,theresultwillbe:

 abs（a-b） <= max（rel_tol * max（abs（a）, abs（b））,abs_tol）.

TheIEEE754specialvaluesof NaN, inf,and -inf willbehandledaccordingtoIEEErules.Specifically, NaN isnotconsideredclosetoanyothervalue,including NaN. inf and -inf areonlyconsideredclosetothemselves.

Newinversion3.5.

Seealso：

PEP485 –Afunctionfortestingapproximateequality

math.isfinite（x）

Return True if x isneitheraninfinitynoraNaN,and False otherwise.（Notethat 0.0 isconsideredfinite.）

Newinversion3.2.

math.isinf（x）

Return True if x isapositiveornegativeinfinity,and False otherwise.

math.isnan（x）

Return True