rmathlib 1.1.0

A Rust Port of R's C Library of Special Functions
Documentation 
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use crate::gammafn;
use crate::lgammacor;
use crate::nmath::*;
use crate::sinpi;

/// Machine dependent constants for IEEE double precision
const XMAX: f64 = 2.532_737_276_080_075_8e305;
const DXREL: f64 = 1.490_116_119_384_765_6e-8;

/// The function lgammafn computes log|gamma(x)|.  The function
/// lgammafn_sign in addition assigns the sign of the gamma function
/// to the address in the second argument if this is not NULL.
///
/// ## NOTES
///
/// This routine is a translation into C of a Fortran subroutine
/// by W. Fullerton of Los Alamos Scientific Laboratory.
///
/// The accuracy of this routine compares (very) favourably
/// with those of the Sun Microsystems portable mathematical
/// library.
///
/// ./toms708.c  has  gamln()
pub fn lgammafn(x: f64) -> f64 {
    lgammafn_sign(x, None)
}

/// Compute the log gamma function and its sign.
///
/// This function computes the logarithm of the absolute value of the gamma function of x
/// and also sets the sign of the gamma function in `sgn`.
pub fn lgammafn_sign(x: f64, sgn: Option<&mut i32>) -> f64 {
    if let Some(sgn) = sgn {
        *sgn = 1;
        if x < 0.0 && ((-x).floor() % 2.0) == 0.0 {
            *sgn = -1;
        }
    }

    if x.is_nan() {
        return ML_NAN;
    }

    if x <= 0.0 && x == x.trunc() {
        // Negative integer argument
        return f64::INFINITY; // +Inf, since lgamma(x) = log|gamma(x)|
    }

    let y = x.abs();

    if y < 1e-306 {
        return -y.ln();
    }
    if y <= 10.0 {
        return gammafn(x).abs().ln();
    }

    // y = |x| > 10
    if y > XMAX {
        return f64::INFINITY;
    }

    if x > 0.0 {
        // Positive x
        if x > 1e17 {
            x * (x.ln() - 1.0)
        } else if x > 4934720.0 {
            return M_LN_SQRT_2PI + (x - 0.5) * x.ln() - x;
        } else {
            return M_LN_SQRT_2PI + (x - 0.5) * x.ln() - x + lgammacor(x);
        }
    } else {
        // x < -10; y = -x
        let sinpiy = sinpi(y).abs();

        if sinpiy == 0.0 {
            // Handle error: Negative integer argument
            return ML_NAN;
        }

        let ans = M_LN_SQRT_2PI + (x - 0.5) * y.ln() - x - sinpiy.ln() - lgammacor(y);

        // Check for accuracy
        if ((x - x.trunc() - 0.5) * ans / x).abs() < DXREL {
            // Warning: answer less than half precision
            // because the argument is too near a negative integer
            println!("** should NEVER happen! *** [lgamma.rs: Neg.int, y={}]", y);
            return ML_NAN; // Placeholder for warning
        }
        ans
    }
}