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//===--- 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
//
//===----------------------------------------------------------------------===//
public protocol RealFunctions: ElementaryFunctions {
/// `atan(y/x)`, with sign selected according to the quadrant of `(x, y)`.
///
/// See also:
/// -
/// - `atan()`
static func atan2(y: Self, x: Self) -> Self
/// The error function evaluated at `x`.
///
/// See also:
/// -
/// - `erfc()`
static func erf(_ x: Self) -> Self
/// The complimentary error function evaluated at `x`.
///
/// See also:
/// -
/// - `erf()`
static func erfc(_ x: Self) -> Self
/// 2^x
///
/// See also:
/// -
/// - `exp()`
/// - `expMinusOne()`
/// - `exp10()`
/// - `log2()`
/// - `pow()`
static func exp2(_ x: Self) -> Self
/// 10^x
///
/// See also:
/// -
/// - `exp()`
/// - `expMinusOne()`
/// - `exp2()`
/// - `log10()`
/// - `pow()`
static func exp10(_ x: Self) -> Self
/// `sqrt(x*x + y*y)`, computed in a manner that avoids spurious overflow or
/// underflow.
static func hypot(_ x: Self, _ y: Self) -> Self
/// The gamma function Γ(x).
///
/// See also:
/// -
/// - `logGamma()`
/// - `signGamma()`
static func gamma(_ x: Self) -> Self
/// The base-2 logarithm of `x`.
///
/// See also:
/// -
/// - `exp2()`
/// - `log()`
/// - `log(onePlus:)`
/// - `log10()`
static func log2(_ x: Self) -> Self
/// The base-10 logarithm of `x`.
///
/// See also:
/// -
/// - `exp10()`
/// - `log()`
/// - `log(onePlus:)`
/// - `log2()`
static func 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()`
/// - `signGamma()`
static func 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()`
/// - `logGamma()`
static func signGamma(_ x: Self) -> FloatingPointSign
#endif
/// a*b + c, computed _either_ with an FMA or with separate multiply and add.
///
/// Whichever is faster should be chosen by the compiler statically.
static func _mulAdd(_ a: Self, _ b: Self, _ c: Self) -> Self
}
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