python数学模块Word文档格式.docx

python数学模块Word文档格式.docx

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isnotafloat,delegatesto 

x.__ceil__（）,whichshouldreturnan 

Integral 

value.

math.copysign（x, 

y）

Returnafloatwiththemagnitude（absolutevalue）of 

butthesignof 

y.Onplatformsthatsupportsignedzeros, 

copysign（1.0, 

-0.0） 

returns 

-1.0.

math.fabs（x）

Returntheabsolutevalueof 

x.

math.factorial（x）

Return 

factorial.Raises 

ValueError 

if 

isnotintegralorisnegative.

math.floor（x）

Returnthefloorof 

x,thelargestintegerlessthanorequalto 

isnotafloat,

delegatesto 

x.__floor__（）,whichshouldreturnan 

math.fmod（x, 

fmod（x, 

y）,asdefinedbytheplatformClibrary.NotethatthePythonexpression 

% 

y 

maynotreturnthesameresult.TheintentoftheCstandardisthat 

y） 

beexactly（mathematically;

toinfiniteprecision）equalto 

- 

n*y 

forsomeinteger 

n 

suchthattheresulthasthesamesignas 

andmagnitudelessthan 

abs（y）.Python’s 

yreturnsaresultwiththesignof 

instead,andmaynotbeexactlycomputableforfloatarguments.Forexample, 

fmod（-1e-100, 

1e100） 

is 

-1e-100,buttheresultofPython’s 

-1e-100 

1e100 

1e100-1e-100,whichcannotberepresentedexactlyasafloat,androundstothesurprising 

1e100.Forthisreason,function 

fmod（） 

isgenerallypreferredwhenworkingwithfloats,whilePython’s 

ispreferredwhenworkingwithintegers.

math.frexp（x）

Returnthemantissaandexponentof 

asthepair 

（m, 

e）. 

m 

isafloatand 

e 

isanintegersuchthat 

== 

* 

2**e 

exactly.If 

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 

or 

b 

isnonzero,thenthevalueof 

gcd（a, 

b） 

isthelargestpositiveintegerthatdividesboth 

b.gcd（0, 

0） 

0.

Newinversion3.5.

math.isclose（a, 

b, 

*, 

rel_tol=1e-09, 

abs_tol=0.0）

True 

ifthevalues 

areclosetoeachotherand 

False 

otherwise.

Whetherornottwovaluesareconsideredcloseisdeterminedaccordingtogivenabsoluteandrelativetolerances.

rel_tol 

istherelativetolerance–itisthemaximumalloweddifferencebetween 

b,relativetothelargerabsolutevalueof 

b.Forexample,tosetatoleranceof5%,pass 

rel_tol=0.05.Thedefaulttoleranceis 

1e-09,whichassuresthatthetwovaluesarethesamewithinabout9decimaldigits. 

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 

areonlyconsideredclosetothemselves.

Seealso：

PEP485 

–Afunctionfortestingapproximateequality

math.isfinite（x）

isneitheraninfinitynoraNaN,and 

otherwise.（Notethat 

0.0 

isconsideredfinite.）

Newinversion3.2.

math.isinf（x）

isapositiveornegativeinfinity,and 

math.isnan（x）