9.2.1.Number-theoretic and representation functions¶

math.ceil(x)¶

Return the ceiling ofx as a float, the smallest integer value greater than orequal tox.

math.copysign(x,y)¶

Returnx with the sign ofy. On a platform that supportssigned zeros,copysign(1.0,-0.0) returns-1.0.

New in version 2.6.

math.fabs(x)¶

Return the absolute value ofx.

math.factorial(x)¶

Returnx factorial. RaisesValueError ifx is not integral oris negative.

New in version 2.6.

math.floor(x)¶

Return the floor ofx as a float, the largest integer value less than or equaltox.

math.fmod(x,y)¶

Returnfmod(x,y), as defined by the platform C library. Note that thePython expressionx%y may not return the same result. The intent of the Cstandard is thatfmod(x,y) be exactly (mathematically; to infiniteprecision) equal tox-n*y for some integern such that the result hasthe same sign asx and magnitude less thanabs(y). Python’sx%yreturns a result with the sign ofy instead, and may not be exactly computablefor float arguments. For example,fmod(-1e-100,1e100) is-1e-100, butthe result of Python’s-1e-100%1e100 is1e100-1e-100, which cannot berepresented exactly as a float, and rounds to the surprising1e100. Forthis reason, functionfmod() is generally preferred when working withfloats, while Python’sx%y is preferred when working with integers.

math.frexp(x)¶

Return the mantissa and exponent ofx as the pair(m,e).m is a floatande is an integer such thatx==m*2**e exactly. Ifx is zero,returns(0.0,0), otherwise0.5<=abs(m)<1. This is used to “pickapart” the internal representation of a float in a portable way.

math.fsum(iterable)¶

Return an accurate floating point sum of values in the iterable. Avoidsloss of precision by tracking multiple intermediate partial sums:

>>>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

The algorithm’s accuracy depends on IEEE-754 arithmetic guarantees and thetypical case where the rounding mode is half-even. On some non-Windowsbuilds, the underlying C library uses extended precision addition and mayoccasionally double-round an intermediate sum causing it to be off in itsleast significant bit.

For further discussion and two alternative approaches, see theASPN cookbookrecipes for accurate floating point summation.

New in version 2.6.

math.isinf(x)¶

Check if the floatx is positive or negative infinity.

New in version 2.6.

math.isnan(x)¶

Check if the floatx is a NaN (not a number). For more informationon NaNs, see the IEEE 754 standards.

New in version 2.6.

math.ldexp(x,i)¶

Returnx*(2**i). This is essentially the inverse of functionfrexp().

math.modf(x)¶

Return the fractional and integer parts ofx. Both results carry the signofx and are floats.

math.trunc(x)¶

Return theReal valuex truncated to anIntegral (usually a long integer). Uses the__trunc__ method.

New in version 2.6.

Note thatfrexp() andmodf() have a different call/return patternthan their C equivalents: they take a single argument and return a pair ofvalues, rather than returning their second return value through an ‘outputparameter’ (there is no such thing in Python).

For theceil(),floor(), andmodf() functions, note thatallfloating-point numbers of sufficiently large magnitude are exact integers.Python floats typically carry no more than 53 bits of precision (the same as theplatform C double type), in which case any floatx withabs(x)>=2**52necessarily has no fractional bits.

9.2.2.Power and logarithmic functions¶

math.exp(x)¶

Returne**x.

math.expm1(x)¶

Returne**x-1. For small floatsx, the subtraction inexp(x)-1 can result in a significant loss of precision; theexpm1() function provides a way to compute this quantity tofull precision:

>>>frommathimportexp,expm1>>>exp(1e-5)-1# gives result accurate to 11 places1.0000050000069649e-05>>>expm1(1e-5)# result accurate to full precision1.0000050000166668e-05

New in version 2.7.

math.log(x[,base])¶

With one argument, return the natural logarithm ofx (to basee).

With two arguments, return the logarithm ofx to the givenbase,calculated aslog(x)/log(base).

Changed in version 2.3:base argument added.

math.log1p(x)¶

Return the natural logarithm of1+x (basee). Theresult is calculated in a way which is accurate forx near zero.

New in version 2.6.

math.log10(x)¶

Return the base-10 logarithm ofx. This is usually more accuratethanlog(x,10).

math.pow(x,y)¶

Returnx raised to the powery. Exceptional cases followAnnex ‘F’ of the C99 standard as far as possible. In particular,pow(1.0,x) andpow(x,0.0) always return1.0, evenwhenx is a zero or a NaN. If bothx andy are finite,x is negative, andy is not an integer thenpow(x,y)is undefined, and raisesValueError.

Unlike the built-in** operator,math.pow() converts bothits arguments to typefloat. Use** or the built-inpow() function for computing exact integer powers.

Changed in version 2.6:The outcome of1**nan andnan**0 was undefined.

math.sqrt(x)¶

Return the square root ofx.

9.2.3.Trigonometric functions¶

math.acos(x)¶

Return the arc cosine ofx, in radians.

math.asin(x)¶

Return the arc sine ofx, in radians.

math.atan(x)¶

Return the arc tangent ofx, in radians.

math.atan2(y,x)¶

Returnatan(y/x), in radians. The result is between-pi andpi.The vector in the plane from the origin to point(x,y) makes this anglewith the positive X axis. The point ofatan2() is that the signs of bothinputs are known to it, so it can compute the correct quadrant for the angle.For example,atan(1) andatan2(1,1) are bothpi/4, butatan2(-1,-1) is-3*pi/4.

math.cos(x)¶

Return the cosine ofx radians.

math.hypot(x,y)¶

Return the Euclidean norm,sqrt(x*x+y*y). This is the length of the vectorfrom the origin to point(x,y).

math.sin(x)¶

Return the sine ofx radians.

math.tan(x)¶

Return the tangent ofx radians.

9.2.4.Angular conversion¶

math.degrees(x)¶

Convert anglex from radians to degrees.

math.radians(x)¶

Convert anglex from degrees to radians.

9.2.5.Hyperbolic functions¶

math.acosh(x)¶

Return the inverse hyperbolic cosine ofx.

New in version 2.6.

math.asinh(x)¶

Return the inverse hyperbolic sine ofx.

New in version 2.6.

math.atanh(x)¶

Return the inverse hyperbolic tangent ofx.

New in version 2.6.

math.cosh(x)¶

Return the hyperbolic cosine ofx.

math.sinh(x)¶

Return the hyperbolic sine ofx.

math.tanh(x)¶

Return the hyperbolic tangent ofx.

9.2.6.Special functions¶

math.erf(x)¶

Return the error function atx.

New in version 2.7.

math.erfc(x)¶

Return the complementary error function atx.

New in version 2.7.

math.gamma(x)¶

Return the Gamma function atx.

New in version 2.7.

math.lgamma(x)¶

Return the natural logarithm of the absolute value of the Gammafunction atx.

New in version 2.7.

9.2.7.Constants¶

math.pi¶

The mathematical constant π = 3.141592…, to available precision.

math.e¶

The mathematical constant e = 2.718281…, to available precision.