# Mathematical functions¶

 `xt::operator+()` identity `xt::operator-()` opposite `xt::operator+()` addition `xt::operator-()` substraction `xt::operator*()` multiplication `xt::operator/()` division `xt::operator||()` logical or `xt::operator&&()` logical and `xt::operator!()` logical not `xt::where()` ternary selection `xt::any()` return true if any value is truthy `xt::all()` return true if all the values are truthy `xt::operator<()` element-wise lesser than `xt::operator<=()` element-wise less or equal `xt::operator>()` element-wise greater than `xt::operator>=()` element-wise greater or equal `xt::operator==()` expression equality `xt::operator!=()` expression inequality `xt::equal()` element-wise equality `xt::not_equal()` element-wise inequality `xt::less()` element-wise lesser than `xt::less_equal()` element-wise less or equal `xt::greater()` element-wise greater than `xt::greater_equal()` element-wise greater or equal `xt::cast()` element-wise `static_cast` `xt::operator&()` bitwise and `xt::operator|()` bitwise or `xt::operator^()` bitwise xor `xt::operator~()` bitwise not `xt::left_shift()` bitwise shift left `xt::right_shift()` bitwise shift right `xt::operator<<()` bitwise shift left `xt::operator>>()` bitwise shift right
 `xt::where()` indices selection `xt::nonzero()` indices selection `xt::argwhere()` indices selection `xt::from_indices()` biulder from indices
 `xt::abs()` absolute value `xt::fabs()` absolute value `xt::fmod()` remainder of the floating point division operation `xt::remainder()` signed remainder of the division operation `xt::fma()` fused multiply-add operation `xt::minimum()` element-wise minimum `xt::maximum()` element-wise maximum `xt::fmin()` element-wise minimum for floating point values `xt::fmax()` element-wise maximum for floating point values `xt::fdim()` element-wise positive difference `xt::clip()` element-wise clipping operation `xt::sign()` element-wise indication of the sign
 `xt::exp()` natural exponential function `xt::exp2()` base 2 exponential function `xt::expm1()` natural exponential function, minus one `xt::log()` natural logarithm function `xt::log2()` base 2 logarithm function `xt::log10()` base 10 logarithm function `xt::log1p()` natural logarithm of one plus function
 `xt::pow()` power function `xt::sqrt()` square root function `xt::cbrt()` cubic root function `xt::hypot()` hypotenuse function
 `xt::sin()` sine function `xt::cos()` cosine function `xt::tan()` tangent function `xt::asin()` arc sine function `xt::acos()` arc cosine function `xt::atan()` arc tangent function `xt::atan2()` arc tangent function, determining quadrants
 `xt::sinh()` hyperbolic sine function `xt::cosh()` hyperbolic cosine function `xt::tanh()` hyperbolic tangent function `xt::asinh()` inverse hyperbolic sine function `xt::acosh()` inverse hyperbolic cosine function `xt::atanh()` inverse hyperbolic tangent function
 `xt::erf()` error function `xt::erfc()` complementary error function `xt::tgamma()` gamma function `xt::lgamma()` natural logarithm of the gamma function
 `xt::ceil()` nearest integers not less `xt::floor()` nearest integers not greater `xt::trunc()` nearest integers not greater in magnitude `xt::round()` nearest integers, rounding away from zero `xt::nearbyint()` nearest integers using current rounding mode `xt::rint()` nearest integers using current rounding mode
 `xt::isfinite()` checks for finite values `xt::isinf()` checks for infinite values `xt::isnan()` checks for NaN values `xt::isclose()` element-wise closeness detection `xt::allclose()` closeness reduction
 `xt::sum()` sum of elements over given axes `xt::prod()` product of elements over given axes `xt::mean()` mean of elements over given axes `xt::average()` weighted average along the specified axis `xt::variance()` variance of elements over given axes `xt::stddev()` standard deviation of elements over given axes `xt::diff()` Calculate the n-th discrete difference along the given axis `xt::amax()` amax of elements over given axes `xt::amin()` amin of elements over given axes `xt::trapz()` Integrate along the given axis using the composite trapezoidal rule `xt::norm_l0()` L0 pseudo-norm over given axes `xt::norm_l1()` L1 norm over given axes `xt::norm_sq()` Squared L2 norm over given axes `xt::norm_l2()` L2 norm over given axes `xt::norm_linf()` Infinity norm over given axes `xt::norm_lp_to_p()` p_th power of Lp norm over given axes `xt::norm_lp()` Lp norm over given axes `xt::norm_induced_l1()` Induced L1 norm of a matrix `xt::norm_induced_linf()` Induced L-infinity norm of a matrix
 `xt::cumsum()` cumulative sum of elements over a given axis `xt::cumprod()` cumulative product of elements over given axes
 `xt::nan_to_num()` convert NaN and +/- inf to finite numbers `xt::nansum()` sum of elements over a given axis, replacing NaN with 0 `xt::nanprod()` product of elements over given axes, replacing NaN with 1 `xt::nancumsum()` cumsum of elements over a given axis, replacing NaN with 0 `xt::nancumprod()` cumprod of elements over given axes, replacing NaN with 1