RealFunctions.swift

//===--- RealFunctions.swift ----------------------------------*- swift -*-===//
//
// This source file is part of the Swift Numerics open source project
//
// Copyright (c) 2019 Apple Inc. and the Swift Numerics project authors
// Licensed under Apache License v2.0 with Runtime Library Exception
//
// See https://swift.org/LICENSE.txt for license information
//
//===----------------------------------------------------------------------===//

publicprotocolRealFunctions:ElementaryFunctions{
 /// `atan(y/x)`, with sign selected according to the quadrant of `(x, y)`.
 ///
 /// See also `atan()`.
staticfunc atan2(y:Self, x:Self)->Self

 /// The error function evaluated at `x`.
 ///
 /// See also `erfc()`.
staticfunc erf(_ x:Self)->Self

 /// The complimentary error function evaluated at `x`.
 ///
 /// See also `erf()`.
staticfunc erfc(_ x:Self)->Self

 /// 2^x
 ///
 /// See also `exp()`, `expMinusOne()`, `exp10()`, `log2()` and `pow()`.
staticfunc exp2(_ x:Self)->Self

 /// 10^x
 ///
 /// See also `exp()`, `expMinusOne()`, `exp2()`, `log10()` and `pow()`.
staticfunc exp10(_ x:Self)->Self

 /// `sqrt(x*x + y*y)`, computed in a manner that avoids spurious overflow or
 /// underflow.
staticfunc hypot(_ x:Self, _ y:Self)->Self

 /// The gamma function Γ(x).
 ///
 /// See also `logGamma()` and `signGamma()`.
staticfunc gamma(_ x:Self)->Self

 /// The base-2 logarithm of `x`.
 ///
 /// See also `exp2()`, `log()`, `log(onePlus:)` and `log10()`.
staticfunc log2(_ x:Self)->Self

 /// The base-10 logarithm of `x`.
 ///
 /// See also: `exp10()`, `log()`, `log(onePlus:)` and `log2()`.
staticfunc log10(_ x:Self)->Self

#if !os(Windows)
 /// The logarithm of the absolute value of the gamma function, log(|Γ(x)|).
 ///
 /// Not available on Windows targets.
 ///
 /// See also `gamma()` and `signGamma()`.
staticfunc logGamma(_ x:Self)->Self

 /// The sign of the gamma function, Γ(x).
 ///
 /// For `x >= 0`, `signGamma(x)` is `.plus`. For negative `x`, `signGamma(x)`
 /// is `.plus` when `x` is an integer, and otherwise it is `.minus` whenever
 /// `trunc(x)` is even, and `.plus` when `trunc(x)` is odd.
 ///
 /// This function is used together with `logGamma`, which computes the
 /// logarithm of the absolute value of Γ(x), to recover the sign information.
 ///
 /// Not available on Windows targets.
 ///
 /// See also `gamma()` and `logGamma()`.
staticfunc signGamma(_ x:Self)->FloatingPointSign
#endif
}