# Mathematical functions

Operations and functions of xtensor are not evaluated until they are assigned. In the following, `e1`, `e2` and `e3` can be arbitrary tensor expressions. The results of operations and functions are assigned to `xt::xarray` in the examples, but that could be any other container (or even views). To keep an unevaluated operator / function, assign to an `auto` variable:

```auto res = e1 + e2;
```

See Expressions and lazy evaluation for more details on unevaluated expressions.

## Basic functions

```xt::xarray<double> res0 = xt::abs(e1);
xt::xarray<double> res1 = xt::fabs(e1);
xt::xarray<double> res2 = xt::fmod(e1, e2);
xt::xarray<double> res3 = xt::remainder(e1, e2);
xt::xarray<double> res4 = xt::fma(e1, e2, e3);
xt::xarray<double> res5 = xt::maximum(e1, e2);
xt::xarray<double> res6 = xt::minimum(e2, e2);
xt::xarray<double> res7 = xt::fmax(e1, e2);
xt::xarray<double> res8 = xt::fmin(e1, e2);
xt::xarray<double> res9 = xt::fdim(e1, e2);
xt::xarray<double> res10 = xt::clip(e1, e2, e3);
xt::xarray<double> res11 = xt::sign(e1);
```

## Exponential functions

```xt::xarray<double> res0 = xt::exp(e1);
xt::xarray<double> res2 = xt::exp2(e1);
xt::xarray<double> res3 = xt::expm1(e1);
xt::xarray<double> res4 = xt::log(e1);
xt::xarray<double> res5 = xt::log2(e1);
xt::xarray<double> res6 = xt::log10(e1);
xt::xarray<double> res7 = xt::log1p(e1);
```

## Power functions

```xt::xarray<double> res0 = xt::pow(e1, e2);
xt::xarray<double> res1 = xt::sqrt(e1);
xt::xarray<double> res2 = xt::cbrt(e1);
xt::xarray<double> res3 = xt::hypot(e1, e2);
```

## Trigonometric functions

```xt::xarray<double> res0 = xt::cos(e1);
xt::xarray<double> res1 = xt::sin(e1);
xt::xarray<double> res2 = xt::tan(e1);
xt::xarray<double> res3 = xt::acos(e2);
xt::xarray<double> res4 = xt::asin(e2);
xt::xarray<double> res5 = xt::atan(e2);
xt::xarray<double> res6 = xt::atan2(e2, e3);
```

## Hyperbolic functions

```xt::xarray<double> res0 = xt::cosh(e1);
xt::xarray<double> res1 = xt::sinh(e1);
xt::xarray<double> res2 = xt::tanh(e1);
xt::xarray<double> res3 = xt::acosh(e2);
xt::xarray<double> res4 = xt::asinh(e2);
xt::xarray<double> res5 = xt::atanh(e2);
```

## Error and gamma functions

```xt::xarray<double> res0 = xt::erf(e1);
xt::xarray<double> res1 = xt::erfc(e1);
xt::xarray<double> res2 = xt::tgamma(e1);
xt::xarray<double> res3 = xt::lgamma(e1);
```

## Nearest integer operations

```xt::xarray<double> res0 = xt::ceil(e1);
xt::xarray<double> res1 = xt::floor(e1);
xt::xarray<double> res2 = xt::trunc(e1);
xt::xarray<double> res3 = xt::round(e1);
xt::xarray<double> res4 = xt::nearbyint(e1);
xt::xarray<double> res5 = xt::rint(e1);
```

## Classification functions

```xt::xarray<double> res0 = xt::isfinite(e1);
xt::xarray<double> res1 = xt::isinf(e1);
xt::xarray<double> res2 = xt::isnan(e1);
xt::xarray<double> res3 = xt::isclose(e1, e2);
bool res4 = xt::allclose(e1, e2);
```