/*

 * // Copyright (c) Radzivon Bartoshyk 7/2025. All rights reserved.

 * //

 * // Redistribution and use in source and binary forms, with or without modification,

 * // are permitted provided that the following conditions are met:

 * //

 * // 1.  Redistributions of source code must retain the above copyright notice, this

 * // list of conditions and the following disclaimer.

 * //

 * // 2.  Redistributions in binary form must reproduce the above copyright notice,

 * // this list of conditions and the following disclaimer in the documentation

 * // and/or other materials provided with the distribution.

 * //

 * // 3.  Neither the name of the copyright holder nor the names of its

 * // contributors may be used to endorse or promote products derived from

 * // this software without specific prior written permission.

 * //

 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"

 * // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

 * // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE

 * // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE

 * // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL

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 */

use crate::bits::EXP_MASK;

use crate::common::f_fmla;

use crate::double_double::DoubleDouble;

use crate::sin::range_reduction_small;

use crate::sincos_reduce::LargeArgumentReduction;

use crate::tangent::tan::{tan_eval, tan_eval_dd};

use crate::tangent::tanpi_table::TAN_K_PI_OVER_128;

#[cold]

fn cot_accurate(y: DoubleDouble, tan_k: DoubleDouble) -> f64 {

    // Computes tan(x) through identities

    // tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b)) = (tan(y) + tan(k*pi/128)) / (1 - tan(y)*tan(k*pi/128))

    let tan_y = tan_eval_dd(y);

    // num = tan(y) + tan(k*pi/64)

    let num_dd = DoubleDouble::full_dd_add(tan_y, tan_k);

    // den = 1 - tan(y)*tan(k*pi/64)

    let den_dd = DoubleDouble::mul_add_f64(tan_y, -tan_k, 1.);

    let cot_x = DoubleDouble::div(den_dd, num_dd);

    cot_x.to_f64()

}

/// Cotangent in double precision

///

/// ULP 0.5

pub fn f_cot(x: f64) -> f64 {

    let x_e = (x.to_bits() >> 52) & 0x7ff;

    const E_BIAS: u64 = (1u64 << (11 - 1u64)) - 1u64;

    let y: DoubleDouble;

    let k;

    let mut argument_reduction = LargeArgumentReduction::default();

    if x_e < E_BIAS + 16 {

        // |x| < 2^16

        if x_e < E_BIAS - 7 {

            // |x| < 2^-7

            if x_e < E_BIAS - 27 {

                // |x| < 2^-27, |cot(x) - x| < ulp(x)/2.

                if x == 0.0 {

                    // Signed zeros.

                    return if x.is_sign_negative() {

                        f64::NEG_INFINITY

                    } else {

                        f64::INFINITY

                    };

                }

                if x_e < E_BIAS - 53 {

                    return 1. / x;

                }

                let dx = DoubleDouble::from_quick_recip(x);

                // taylor order 3

                return DoubleDouble::f64_mul_f64_add(x, f64::from_bits(0xbfd5555555555555), dx)

                    .to_f64();

            }

            // No range reduction needed.

            k = 0;

            y = DoubleDouble::new(0., x);

        } else {

            // Small range reduction.

            (y, k) = range_reduction_small(x);

        }

    } else {

        // Inf or NaN

        if x_e > 2 * E_BIAS {

            if x.is_nan() {

                return f64::NAN;

            }

            // tan(+-Inf) = NaN

            return x + f64::NAN;

        }

        // Large range reduction.

        (k, y) = argument_reduction.reduce(x);

    }

    let (tan_y, err) = tan_eval(y);

    // Computes tan(x) through identities.

    // tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b)) = (tan(y) + tan(k*pi/128)) / (1 - tan(y)*tan(k*pi/128))

    let tan_k = DoubleDouble::from_bit_pair(TAN_K_PI_OVER_128[(k & 255) as usize]);

    // num = tan(y) + tan(k*pi/64)

    let num_dd = DoubleDouble::add(tan_y, tan_k);

    // den = 1 - tan(y)*tan(k*pi/64)

    let den_dd = DoubleDouble::mul_add_f64(tan_y, -tan_k, 1.);

    // num and den shifted for cot

    let cot_x = DoubleDouble::div(den_dd, num_dd);

    // Simple error bound: |1 / den_dd| < 2^(1 + floor(-log2(den_dd)))).

    let den_inv = ((E_BIAS + 1) << (52 + 1)) - (den_dd.hi.to_bits() & EXP_MASK);

    // For tan_x = (num_dd + err) / (den_dd + err), the error is bounded by:

    //   | tan_x - num_dd / den_dd |  <= err * ( 1 + | tan_x * den_dd | ).

    let tan_err = err * f_fmla(f64::from_bits(den_inv), cot_x.hi.abs(), 1.0);

    let err_higher = cot_x.lo + tan_err;

    let err_lower = cot_x.lo - tan_err;

    let tan_upper = cot_x.hi + err_higher;

    let tan_lower = cot_x.hi + err_lower;

    // Ziv_s rounding test.

    if tan_upper == tan_lower {

        return tan_upper;

    }

    cot_accurate(y, tan_k)

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn cot_test() {

        assert_eq!(f_cot(2.3006805685393681E-308), 4.346539948546049e307);

        assert_eq!(f_cot(5070552515158872000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.), 25.068466719883585);

        assert_eq!(f_cot(4.9406564584124654E-324), f64::INFINITY);

        assert_eq!(f_cot(0.0), f64::INFINITY);

        assert_eq!(f_cot(1.0), 0.6420926159343308);

        assert_eq!(f_cot(-0.5), -1.830487721712452);

        assert_eq!(f_cot(12.0), -1.5726734063976893);

        assert_eq!(f_cot(-12.0), 1.5726734063976893);

        assert!(f_cot(f64::INFINITY).is_nan());

        assert!(f_cot(f64::NEG_INFINITY).is_nan());

        assert!(f_cot(f64::NAN).is_nan());

    }

}