scirs2-core 0.1.0-alpha.3

//! Numeric traits and utilities for SciRS2
//!
//! This module provides traits and utilities for working with numeric types
//! in scientific computing contexts.

use num_traits::{Float, Num, NumCast, One, Zero};
use std::fmt::Debug;
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

/// A trait for numeric types that can be used in scientific calculations
///
/// This trait combines common numeric traits required for scientific computing
/// operations, providing a unified trait bound for generic code.
pub trait ScientificNumber:
    Num
    + Clone
    + Copy
    + PartialOrd
    + Debug
    + Zero
    + One
    + Add<Output = Self>
    + Sub<Output = Self>
    + Mul<Output = Self>
    + Div<Output = Self>
    + AddAssign
    + SubAssign
    + MulAssign
    + DivAssign
    + NumCast
{
    /// Absolute value
    fn abs(self) -> Self;

    /// Square root
    fn sqrt(self) -> Self;

    /// Square
    fn square(self) -> Self {
        self * self
    }

    /// Maximum of two values
    fn max(self, other: Self) -> Self;

    /// Minimum of two values
    fn min(self, other: Self) -> Self;

    /// Check if the value is finite
    fn is_finite(self) -> bool;

    /// Convert to f64
    fn to_f64(self) -> Option<f64>;

    /// Convert from f64
    fn from_f64(value: f64) -> Option<Self>;
}

/// A trait for real-valued floating point types
pub trait RealNumber: ScientificNumber + Float {
    /// Returns the machine epsilon (the difference between 1.0 and the least value greater than 1.0)
    fn epsilon() -> Self;

    /// Exponential function (e^x)
    fn exp(self) -> Self;

    /// Natural logarithm (ln(x))
    fn ln(self) -> Self;

    /// Base-10 logarithm
    fn log10(self) -> Self;

    /// Base-2 logarithm
    fn log2(self) -> Self;

    /// Sine function
    fn sin(self) -> Self;

    /// Cosine function
    fn cos(self) -> Self;

    /// Tangent function
    fn tan(self) -> Self;

    /// Hyperbolic sine
    fn sinh(self) -> Self;

    /// Hyperbolic cosine
    fn cosh(self) -> Self;

    /// Hyperbolic tangent
    fn tanh(self) -> Self;

    /// Inverse sine
    fn asin(self) -> Self;

    /// Inverse cosine
    fn acos(self) -> Self;

    /// Inverse tangent
    fn atan(self) -> Self;

    /// Inverse tangent of y/x with correct quadrant
    fn atan2(self, other: Self) -> Self;

    /// Power function
    fn powf(self, n: Self) -> Self;

    /// Integer power function
    fn powi(self, n: i32) -> Self;

    /// Factorial function (approximation for non-integers)
    fn factorial(self) -> Self;
}

/// A trait for complex number types
pub trait ComplexNumber: ScientificNumber {
    /// The real part of the complex number
    type RealPart: RealNumber;

    /// Returns the real part of the complex number
    fn re(&self) -> Self::RealPart;

    /// Returns the imaginary part of the complex number
    fn im(&self) -> Self::RealPart;

    /// Create a new complex number from real and imaginary parts
    fn new(re: Self::RealPart, im: Self::RealPart) -> Self;

    /// Returns the complex conjugate
    fn conj(self) -> Self;

    /// Returns the magnitude (absolute value)
    fn abs(self) -> Self::RealPart;

    /// Returns the argument (phase)
    fn arg(self) -> Self::RealPart;

    /// Returns the complex number in exponential form (r, theta)
    fn to_polar(self) -> (Self::RealPart, Self::RealPart);

    /// Creates a complex number from polar coordinates
    fn from_polar(r: Self::RealPart, theta: Self::RealPart) -> Self;

    /// Exponential function
    fn exp(self) -> Self;

    /// Natural logarithm
    fn ln(self) -> Self;

    /// Power function with complex exponent
    fn powc(self, exp: Self) -> Self;

    /// Power function with real exponent
    fn powf(self, exp: Self::RealPart) -> Self;

    /// Square root
    fn sqrt(self) -> Self;
}

/// A trait for integers that can be used in scientific calculations
pub trait ScientificInteger: ScientificNumber + Eq {
    /// Greatest common divisor
    fn gcd(self, other: Self) -> Self;

    /// Least common multiple
    fn lcm(self, other: Self) -> Self;

    /// Check if the number is prime
    fn is_prime(self) -> bool;

    /// Check if the number is even
    fn is_even(self) -> bool;

    /// Check if the number is odd
    fn is_odd(self) -> bool;

    /// Modular exponentiation (self^exp mod modulus)
    fn mod_pow(self, exp: Self, modulus: Self) -> Self;

    /// Factorial
    fn factorial(self) -> Self;

    /// Binomial coefficient (n choose k)
    fn binomial(self, k: Self) -> Self;
}

// Implement ScientificNumber for f32
impl ScientificNumber for f32 {
    fn abs(self) -> Self {
        self.abs()
    }

    fn sqrt(self) -> Self {
        self.sqrt()
    }

    fn max(self, other: Self) -> Self {
        self.max(other)
    }

    fn min(self, other: Self) -> Self {
        self.min(other)
    }

    fn is_finite(self) -> bool {
        self.is_finite()
    }

    fn to_f64(self) -> Option<f64> {
        Some(self as f64)
    }

    fn from_f64(value: f64) -> Option<Self> {
        if value.is_finite() && value <= f32::MAX as f64 && value >= f32::MIN as f64 {
            Some(value as f32)
        } else {
            None
        }
    }
}

// Implement RealNumber for f32
impl RealNumber for f32 {
    fn epsilon() -> Self {
        f32::EPSILON
    }

    fn exp(self) -> Self {
        self.exp()
    }

    fn ln(self) -> Self {
        self.ln()
    }

    fn log10(self) -> Self {
        self.log10()
    }

    fn log2(self) -> Self {
        self.log2()
    }

    fn sin(self) -> Self {
        self.sin()
    }

    fn cos(self) -> Self {
        self.cos()
    }

    fn tan(self) -> Self {
        self.tan()
    }

    fn sinh(self) -> Self {
        self.sinh()
    }

    fn cosh(self) -> Self {
        self.cosh()
    }

    fn tanh(self) -> Self {
        self.tanh()
    }

    fn asin(self) -> Self {
        self.asin()
    }

    fn acos(self) -> Self {
        self.acos()
    }

    fn atan(self) -> Self {
        self.atan()
    }

    fn atan2(self, other: Self) -> Self {
        self.atan2(other)
    }

    fn powf(self, n: Self) -> Self {
        self.powf(n)
    }

    fn powi(self, n: i32) -> Self {
        self.powi(n)
    }

    fn factorial(self) -> Self {
        if self < 0.0 {
            return f32::NAN;
        }

        // Use Stirling's approximation for non-integers or large values
        if self != self.trunc() || self > 100.0 {
            const SQRT_TWO_PI: f32 = 2.506_628_3;
            return SQRT_TWO_PI * self.powf(self + 0.5) * (-self).exp();
        }

        let mut result = 1.0;
        let n = self as u32;
        for i in 2..=n {
            result *= i as f32;
        }

        result
    }
}

// Implement ScientificNumber for f64
impl ScientificNumber for f64 {
    fn abs(self) -> Self {
        self.abs()
    }

    fn sqrt(self) -> Self {
        self.sqrt()
    }

    fn max(self, other: Self) -> Self {
        self.max(other)
    }

    fn min(self, other: Self) -> Self {
        self.min(other)
    }

    fn is_finite(self) -> bool {
        self.is_finite()
    }

    fn to_f64(self) -> Option<f64> {
        Some(self)
    }

    fn from_f64(value: f64) -> Option<Self> {
        Some(value)
    }
}

// Implement RealNumber for f64
impl RealNumber for f64 {
    fn epsilon() -> Self {
        f64::EPSILON
    }

    fn exp(self) -> Self {
        self.exp()
    }

    fn ln(self) -> Self {
        self.ln()
    }

    fn log10(self) -> Self {
        self.log10()
    }

    fn log2(self) -> Self {
        self.log2()
    }

    fn sin(self) -> Self {
        self.sin()
    }

    fn cos(self) -> Self {
        self.cos()
    }

    fn tan(self) -> Self {
        self.tan()
    }

    fn sinh(self) -> Self {
        self.sinh()
    }

    fn cosh(self) -> Self {
        self.cosh()
    }

    fn tanh(self) -> Self {
        self.tanh()
    }

    fn asin(self) -> Self {
        self.asin()
    }

    fn acos(self) -> Self {
        self.acos()
    }

    fn atan(self) -> Self {
        self.atan()
    }

    fn atan2(self, other: Self) -> Self {
        self.atan2(other)
    }

    fn powf(self, n: Self) -> Self {
        self.powf(n)
    }

    fn powi(self, n: i32) -> Self {
        self.powi(n)
    }

    fn factorial(self) -> Self {
        if self < 0.0 {
            return f64::NAN;
        }

        // Use Stirling's approximation for non-integers or large values
        if self != self.trunc() || self > 170.0 {
            const SQRT_TWO_PI: f64 = 2.5066282746310002;
            return SQRT_TWO_PI * self.powf(self + 0.5) * (-self).exp();
        }

        let mut result = 1.0;
        let n = self as u32;
        for i in 2..=n {
            result *= i as f64;
        }

        result
    }
}

// Implement ScientificNumber for i32
impl ScientificNumber for i32 {
    fn abs(self) -> Self {
        self.abs()
    }

    fn sqrt(self) -> Self {
        (self as f64).sqrt() as i32
    }

    fn max(self, other: Self) -> Self {
        std::cmp::max(self, other)
    }

    fn min(self, other: Self) -> Self {
        std::cmp::min(self, other)
    }

    fn is_finite(self) -> bool {
        true // integers are always finite
    }

    fn to_f64(self) -> Option<f64> {
        Some(self as f64)
    }

    fn from_f64(value: f64) -> Option<Self> {
        if value.is_finite() && value <= i32::MAX as f64 && value >= i32::MIN as f64 {
            Some(value as i32)
        } else {
            None
        }
    }
}

// Implement ScientificInteger for i32
impl ScientificInteger for i32 {
    fn gcd(self, other: Self) -> Self {
        let mut a = self.abs();
        let mut b = other.abs();

        if a == 0 {
            return b;
        }
        if b == 0 {
            return a;
        }

        while b != 0 {
            let temp = b;
            b = a % b;
            a = temp;
        }

        a
    }

    fn lcm(self, other: Self) -> Self {
        if self == 0 || other == 0 {
            return 0;
        }

        let gcd = self.gcd(other);

        (self / gcd) * other
    }

    fn is_prime(self) -> bool {
        if self <= 1 {
            return false;
        }
        if self <= 3 {
            return true;
        }
        if self % 2 == 0 || self % 3 == 0 {
            return false;
        }

        let mut i = 5;
        while i * i <= self {
            if self % i == 0 || self % (i + 2) == 0 {
                return false;
            }
            i += 6;
        }

        true
    }

    fn is_even(self) -> bool {
        self % 2 == 0
    }

    fn is_odd(self) -> bool {
        self % 2 != 0
    }

    fn mod_pow(self, exp: Self, modulus: Self) -> Self {
        if modulus == 1 {
            return 0;
        }

        let mut base = self % modulus;
        let mut result = 1;
        let mut exponent = exp;

        while exponent > 0 {
            if exponent % 2 == 1 {
                result = (result * base) % modulus;
            }
            exponent >>= 1;
            base = (base * base) % modulus;
        }

        result
    }

    fn factorial(self) -> Self {
        if self < 0 {
            panic!("Factorial not defined for negative numbers");
        }

        let mut result = 1;
        for i in 2..=self {
            result *= i;
        }

        result
    }

    fn binomial(self, k: Self) -> Self {
        if k < 0 || k > self {
            return 0;
        }

        let k = std::cmp::min(k, self - k);
        let mut result = 1;

        for i in 0..k {
            result = result * (self - i) / (i + 1);
        }

        result
    }
}

/// Conversion between different numeric types
pub trait NumericConversion<T> {
    /// Try to convert to the target type
    fn try_convert(self) -> Option<T>;

    /// Convert to the target type, or a default value if conversion fails
    fn convert_or(self, default: T) -> T;

    /// Convert to the target type, or panic if conversion fails
    fn convert(self) -> T;
}

/// Implement NumericConversion for all types that implement NumCast
impl<F, T> NumericConversion<T> for F
where
    F: NumCast,
    T: NumCast,
{
    fn try_convert(self) -> Option<T> {
        num_traits::cast(self)
    }

    fn convert_or(self, default: T) -> T {
        self.try_convert().unwrap_or(default)
    }

    fn convert(self) -> T {
        self.try_convert().expect("Numeric conversion failed")
    }
}

/// Trait for converting between degrees and radians
pub trait AngleConversion {
    /// Convert from degrees to radians
    fn to_radians(self) -> Self;

    /// Convert from radians to degrees
    fn to_degrees(self) -> Self;
}

/// Implement AngleConversion for all RealNumber types
impl<T: RealNumber> AngleConversion for T {
    fn to_radians(self) -> Self {
        let pi = T::from_f64(std::f64::consts::PI).unwrap();
        self * pi / T::from_f64(180.0).unwrap()
    }

    fn to_degrees(self) -> Self {
        let pi = T::from_f64(std::f64::consts::PI).unwrap();
        self * T::from_f64(180.0).unwrap() / pi
    }
}

/// Type-safe representation of a unitless quantity
#[derive(Clone, Copy, PartialEq, Debug)]
pub struct Scalar<T: ScientificNumber>(pub T);

impl<T: ScientificNumber> Scalar<T> {
    /// Create a new scalar
    pub fn new(value: T) -> Self {
        Scalar(value)
    }

    /// Get the underlying value
    pub fn value(&self) -> T {
        self.0
    }
}

impl<T: ScientificNumber> From<T> for Scalar<T> {
    fn from(value: T) -> Self {
        Scalar(value)
    }
}

impl<T: ScientificNumber> Add for Scalar<T> {
    type Output = Self;

    fn add(self, other: Self) -> Self::Output {
        Scalar(self.0 + other.0)
    }
}

impl<T: ScientificNumber> Sub for Scalar<T> {
    type Output = Self;

    fn sub(self, other: Self) -> Self::Output {
        Scalar(self.0 - other.0)
    }
}

impl<T: ScientificNumber> Mul for Scalar<T> {
    type Output = Self;

    fn mul(self, other: Self) -> Self::Output {
        Scalar(self.0 * other.0)
    }
}

impl<T: ScientificNumber> Div for Scalar<T> {
    type Output = Self;

    fn div(self, other: Self) -> Self::Output {
        Scalar(self.0 / other.0)
    }
}

impl<T: ScientificNumber + Neg<Output = T>> Neg for Scalar<T> {
    type Output = Self;

    fn neg(self) -> Self::Output {
        Scalar(self.0.neg())
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_scientific_number_f32() {
        let a: f32 = 3.0;
        let b: f32 = 4.0;

        assert_eq!(a.abs(), 3.0);
        assert_eq!(a.sqrt(), (3.0_f32).sqrt());
        assert_eq!(a.square(), 9.0);
        assert_eq!(a.max(b), 4.0);
        assert_eq!(a.min(b), 3.0);
        assert!(a.is_finite());
        assert_eq!(a.to_f64(), Some(3.0));
        assert_eq!(f32::from_f64(3.5), Some(3.5));
    }

    #[test]
    fn test_scientific_number_f64() {
        let a: f64 = 3.0;
        let b: f64 = 4.0;

        assert_eq!(a.abs(), 3.0);
        assert_eq!(a.sqrt(), (3.0_f64).sqrt());
        assert_eq!(a.square(), 9.0);
        assert_eq!(a.max(b), 4.0);
        assert_eq!(a.min(b), 3.0);
        assert!(a.is_finite());
        assert_eq!(a.to_f64(), Some(3.0));
        assert_eq!(f64::from_f64(3.5), Some(3.5));
    }

    #[test]
    fn test_real_number_f32() {
        let a: f32 = 3.0;

        assert_eq!(<f32 as RealNumber>::epsilon(), f32::EPSILON);
        assert_eq!(a.exp(), (3.0_f32).exp());
        assert_eq!(a.ln(), (3.0_f32).ln());
        assert_eq!(a.sin(), (3.0_f32).sin());
        assert_eq!(a.cos(), (3.0_f32).cos());
        assert_eq!(a.powf(2.0), 9.0);
    }

    #[test]
    fn test_real_number_f64() {
        let a: f64 = 3.0;

        assert_eq!(<f64 as RealNumber>::epsilon(), f64::EPSILON);
        assert_eq!(a.exp(), (3.0_f64).exp());
        assert_eq!(a.ln(), (3.0_f64).ln());
        assert_eq!(a.sin(), (3.0_f64).sin());
        assert_eq!(a.cos(), (3.0_f64).cos());
        assert_eq!(a.powf(2.0), 9.0);
    }

    #[test]
    fn test_scientific_integer_i32() {
        let a: i32 = 12;
        let b: i32 = 8;

        assert_eq!(a.gcd(b), 4);
        assert_eq!(a.lcm(b), 24);
        assert!(!a.is_prime());
        assert!(11_i32.is_prime());
        assert!(a.is_even());
        assert!(!a.is_odd());
        assert_eq!(a.mod_pow(2, 10), 4); // 12^2 mod 10 = 4
        assert_eq!(5_i32.factorial(), 120);
        assert_eq!(5_i32.binomial(2), 10); // 5 choose 2 = 10
    }

    #[test]
    fn test_numeric_conversion() {
        let a: f64 = 3.5;
        let b: i32 = a.try_convert().unwrap();
        assert_eq!(b, 3);

        let c: f32 = 100.5;
        let d: f64 = c.convert();
        assert_eq!(d, 100.5);

        let e: i32 = 100;
        let f: f32 = e.convert();
        assert_eq!(f, 100.0);
    }

    #[test]
    fn test_angle_conversion() {
        let degrees: f64 = 180.0;
        let radians = degrees.to_radians();
        assert_eq!(radians, std::f64::consts::PI);

        let radians: f64 = std::f64::consts::PI / 2.0;
        let degrees = radians.to_degrees();
        assert_eq!(degrees, 90.0);
    }

    #[test]
    fn test_scalar() {
        let a = Scalar::new(3.0_f64);
        let b = Scalar::new(4.0_f64);

        assert_eq!((a + b).value(), 7.0);
        assert_eq!((a - b).value(), -1.0);
        assert_eq!((a * b).value(), 12.0);
        assert_eq!((a / b).value(), 0.75);
        assert_eq!((-a).value(), -3.0);

        let c: Scalar<f64> = 5.0.into();
        assert_eq!(c.value(), 5.0);
    }
}