sigils/src/trig/trig.rs

use binding::{CDouble, CFloat};

use crate::real::Real;
use crate::trig::radian::Radian;



/// The available trigonometric functions.
pub trait Trig: Real
{
   /// Computes the cosine of this angle.
   ///
   /// ```
   /// use sigils::{Constants, Radian, Trig};
   ///
   /// let abs_difference: f64;
   /// let radians: Radian<f64>;
   ///
   /// radians = Radian::new(2.0f64 * f64::PI);
   /// abs_difference = (Trig::cos(radians) - 1.0f64).abs();
   ///
   /// assert!(abs_difference < 1e-10);
   /// ```
   fn cos<T>(arg: T) -> Self
      where T: Into<Radian<Self>>;

   /// Computes the sine of this angle.
   ///
   /// ```
   /// use sigils::{Constants, Radian, Trig};
   ///
   /// let abs_difference: f64;
   /// let radians: Radian<f64>;
   ///
   /// let radians: Radian<f64> = Radian::new(f64::PI / 2.0f64);
   /// let abs_difference = (Trig::sin(radians) - 1.0f64).abs();
   ///
   /// assert!(abs_difference < 1e-10);
   /// ```
   fn sin<T>(arg: T) -> Self
      where T: Into<Radian<Self>>;

   /// Computes the tangent of this angle.
   ///
   /// ```
   /// use sigils::{Constants, Radian, Trig};
   ///
   /// let abs_difference: f64;
   /// let radians: Radian<f64>;
   ///
   /// radians = Radian::new(f64::PI / 4.0f64);
   /// abs_difference = (Trig::tan(radians) - 1.0f64).abs();
   ///
   /// assert!(abs_difference < 1e-14);
   /// ```
   fn tan<T>(arg: T) -> Self
      where T: Into<Radian<Self>>;

   /// Computes the arccosine of a number. Return value is in Degrees in
   /// the range [0, pi] or NaN if the number is outside the range
   /// [-1, 1].
   ///
   ///```
   /// use sigils::{Constants, Radian, Trig};
   ///
   /// let angle: f64;
   /// let radians: Radian<f64>;
   /// let test: Radian<f64>;
   ///
   /// angle = f64::PI / 4.0f64;
   /// radians = Radian::new(angle);
   /// test = Trig::acos(Trig::cos(radians));
   ///
   /// assert!((angle - *test) < 1e-10);
   ///```
   fn acos<T>(arg: Self) -> T
      where T: From<Radian<Self>>;

   /// Computes the arcsine of a number. Return value is in Degrees in
   /// the range [-pi/2, pi/2] or NaN if the number is
   /// outside the range [-1, 1].
   ///
   ///```
   /// use sigils::{Constants, Radian, Trig};
   ///
   /// let angle: f64;
   /// let radians: Radian<f64>;
   /// let test: Radian<f64>;
   ///
   /// angle = f64::PI / 4.0f64;
   /// radians = Radian::new(angle);
   /// test = Trig::asin(Trig::sin(radians));
   ///
   /// assert!((angle - *test) < 1e-10);
   ///```
   fn asin<T>(arg: Self) -> T
      where T: From<Radian<Self>>;

   /// Computes the arctangent of a number. Return value is in degrees in the
   /// range [-pi/2, pi/2];
   ///
   ///```
   /// use sigils::{Constants, Radian, Trig};
   ///
   /// let angle: f64;
   /// let radians: Radian<f64>;
   /// let test: Radian<f64>;
   ///
   /// angle = f64::PI / 4.0f64;
   /// radians = Radian::new(angle);
   /// test = Trig::atan(Trig::tan(radians));
   ///
   /// assert!((angle - *test) < 1e-10);
   ///```
   fn atan<T>(arg: Self) -> T
      where T: From<Radian<Self>>;

   /// Computes the four quadrant arctangent of y and x.
   fn atan2<T>(y: Self, x: Self) -> T
      where T: From<Radian<Self>>;


   /// Hyperbolic cosine function.
   ///
   /// ```
   /// use sigils::{Constants, Trig};
   ///
   /// let f_val: f32;
   /// let g_val: f32;
   /// let abs_difference: f32;
   ///
   /// f_val = Trig::cosh(1.0f32);
   /// g_val = (f32::E * f32::E + 1.0f32) / (2.0f32 * f32::E);
   /// abs_difference = (f_val - g_val).abs();
   ///
   /// // Solving cosh() at 1 gives this result
   /// assert!(abs_difference < 1.0e-10);
   /// ```
   fn cosh(arg: Self) -> Self;

   /// Hyperbolic sine function.
   ///
   /// ```
   /// use sigils::{Constants, Trig};
   ///
   /// let f_val: f32;
   /// let g_val: f32;
   /// let abs_difference: f32;
   ///
   /// f_val = Trig::sinh(1.0f32);
   /// g_val = (f32::E * f32::E - 1.0f32) / (2.0f32 * f32::E);
   /// abs_difference = (f_val - g_val).abs();
   ///
   /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
   /// assert!(abs_difference < 1e-10);
   /// ```
   fn sinh(arg: Self) -> Self;

   /// Hyperbolic tangent function.
   ///
   /// ```
   /// use sigils::{Constants, Trig};
   ///
   /// let f_val: f32;
   /// let g_val: f32;
   /// let abs_difference: f32;

   /// f_val = Trig::tanh(1.0f32);
   /// g_val = (1.0f32 - f32::E.powi(-2i32)) / (1.0f32 + f32::E.powi(-2i32));
   /// abs_difference = (f_val - g_val).abs();
   ///
   /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
   /// assert!(abs_difference < 1.0e-6);
   /// ```
   fn tanh(arg: Self) -> Self;

   /// Inverse hyperbolic cosine function.
   fn acosh(arg: Self) -> Self;

   /// Inverse hyperbolic sine function.
   fn asinh(arg: Self) -> Self;

   /// Inverse hyperbolic tangent function.
   fn atanh(arg: Self) -> Self;
}



impl Trig for f32
{
   fn cos<T>(arg: T) -> Self
      where T: Into<Radian<Self>>
   {
      unsafe
      {
         ::pact::math::cosf(*arg.into() as CFloat) as Self
      }
   }

   fn sin<T>(arg: T) -> Self
      where T: Into<Radian<Self>>
   {
      unsafe
      {
         ::pact::math::sinf(*arg.into() as CFloat) as Self
      }
   }

   fn tan<T>(arg: T) -> Self
      where T: Into<Radian<Self>>
   {
      unsafe
      {
         ::pact::math::tanf(*arg.into() as CFloat) as Self
      }
   }

   fn acos<T>(arg: Self) -> T
      where T: From<Radian<Self>>
   {
      unsafe
      {
         Radian::new(::pact::math::acosf(arg as CFloat) as Self).into()
      }
   }

   fn asin<T>(arg: Self) -> T
      where T: From<Radian<Self>>
   {
      unsafe
      {
         Radian::new(::pact::math::asinf(arg as CFloat) as Self).into()
      }
   }

   fn atan<T>(arg: Self) -> T
      where T: From<Radian<Self>>
   {
      unsafe
      {
         Radian::new(::pact::math::atanf(arg as CFloat) as Self).into()
      }
   }

   fn atan2<T>(y: Self, x: Self) -> T
      where T: From<Radian<Self>>
   {
      unsafe
      {
         Radian::new(
            ::pact::math::atan2f(y as CFloat, x as CFloat) as Self).into()
      }
   }


   fn cosh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::coshf(arg as CFloat) as Self
      }
   }

   fn sinh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::sinhf(arg as CFloat) as Self
      }
   }

   fn tanh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::tanhf(arg as CFloat) as Self
      }
   }

   fn acosh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::acoshf(arg as CFloat) as Self
      }
   }

   fn asinh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::asinhf(arg as CFloat) as Self
      }
   }

   fn atanh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::atanhf(arg as CFloat) as Self
      }
   }
}

impl Trig for f64
{
   fn cos<T>(arg: T) -> Self
      where T: Into<Radian<Self>>
   {
      unsafe
      {
         ::pact::math::cos(*arg.into() as CDouble) as Self
      }
   }

   fn sin<T>(arg: T) -> Self
      where T: Into<Radian<Self>>
   {
      unsafe
      {
         ::pact::math::sin(*arg.into() as CDouble) as Self
      }
   }

   fn tan<T>(arg: T) -> Self
      where T: Into<Radian<Self>>
   {
      unsafe
      {
         ::pact::math::tan(*arg.into() as CDouble) as Self
      }
   }

   fn acos<T>(arg: Self) -> T
      where T: From<Radian<Self>>
   {
      unsafe
      {
         Radian::new(::pact::math::acos(arg as CDouble) as Self).into()
      }
   }

   fn asin<T>(arg: Self) -> T
      where T: From<Radian<Self>>
   {
      unsafe
      {
         Radian::new(::pact::math::asin(arg as CDouble) as Self).into()
      }
   }

   fn atan<T>(arg: Self) -> T
      where T: From<Radian<Self>>
   {
      unsafe
      {
         Radian::new(::pact::math::atan(arg as CDouble) as Self).into()
      }
   }

   fn atan2<T>(y: Self, x: Self) -> T
      where T: From<Radian<Self>>
   {
      unsafe
      {
         Radian::new(
            ::pact::math::atan2(y as CDouble, x as CDouble) as Self).into()
      }
   }


   fn cosh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::cosh(arg as CDouble) as Self
      }
   }

   fn sinh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::sinh(arg as CDouble) as Self
      }
   }

   fn tanh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::tanh(arg as CDouble) as Self
      }
   }

   fn acosh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::acosh(arg as CDouble) as Self
      }
   }

   fn asinh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::asinh(arg as CDouble) as Self
      }
   }

   fn atanh(arg: Self) -> Self
   {
      unsafe
      {
         ::pact::math::atanh(arg as CDouble) as Self
      }
   }
}