/*

 * // 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

 * // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR

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 * // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

 */

use crate::common::f_fmla;

use crate::double_double::DoubleDouble;

use crate::sin::{get_sin_k_rational, range_reduction_small, sincos_eval};

use crate::sin_table::SIN_K_PI_OVER_128;

use crate::sincos_dyadic::{range_reduction_small_f128, sincos_eval_dyadic};

use crate::sincos_reduce::LargeArgumentReduction;

#[cold]

fn sec_accurate(x: f64, argument_reduction: &mut LargeArgumentReduction, x_e: u64, k: u64) -> f64 {

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

    let u_f128 = if x_e < EXP_BIAS + 16 {

        range_reduction_small_f128(x)

    } else {

        argument_reduction.accurate()

    };

    let sin_cos = sincos_eval_dyadic(&u_f128);

    // -sin(k * pi/128) = sin((k + 128) * pi/128)

    // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).

    let msin_k_f128 = get_sin_k_rational(k.wrapping_add(128));

    let cos_k_f128 = get_sin_k_rational(k.wrapping_add(64));

    // cos(x) = cos((k * pi/128 + u)

    //        = cos(u) * cos(k*pi/128) - sin(u) * sin(k*pi/128)

    let r = (cos_k_f128 * sin_cos.v_cos) + (msin_k_f128 * sin_cos.v_sin);

    r.reciprocal().fast_as_f64()

}

/// Secant for double precision

///

/// ULP 0.5

pub fn f_sec(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| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)

        if x_e < E_BIAS - 7 {

            // |x| < 2^-7

            if x_e < E_BIAS - 27 {

                // |x| < 2^-27

                if x == 0.0 {

                    // Signed zeros.

                    return 1.0;

                }

                // taylor series for sec(x) ~ 1 + x^2/2 + O(x^4)

                return f_fmla(x, x * 0.5, 1.);

            }

            k = 0;

            y = DoubleDouble::new(0.0, x);

        } else {

            // Small range reduction.

            (y, k) = range_reduction_small(x);

        }

    } else {

        // Inf or NaN

        if x_e > 2 * E_BIAS {

            // sec(+-Inf) = NaN

            return x + f64::NAN;

        }

        // Large range reduction.

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

    }

    let r_sincos = sincos_eval(y);

    // Fast look up version, but needs 256-entry table.

    // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).

    let sk = SIN_K_PI_OVER_128[(k.wrapping_add(128) & 255) as usize];

    let ck = SIN_K_PI_OVER_128[((k.wrapping_add(64)) & 255) as usize];

    let msin_k = DoubleDouble::from_bit_pair(sk);

    let cos_k = DoubleDouble::from_bit_pair(ck);

    let cos_k_cos_y = DoubleDouble::quick_mult(r_sincos.v_cos, cos_k);

    let cos_k_msin_y = DoubleDouble::quick_mult(r_sincos.v_sin, msin_k);

    // cos_k_cos_y is always >> cos_k_msin_y

    let mut rr = DoubleDouble::from_exact_add(cos_k_cos_y.hi, cos_k_msin_y.hi);

    rr.lo += cos_k_cos_y.lo + cos_k_msin_y.lo;

    rr = DoubleDouble::from_exact_add(rr.hi, rr.lo);

    rr = rr.recip();

    let rlp = rr.lo + r_sincos.err;

    let rlm = rr.lo - r_sincos.err;

    let r_upper = rr.hi + rlp; // (rr.lo + ERR);

    let r_lower = rr.hi + rlm; // (rr.lo - ERR);

    // Ziv's accuracy test

    if r_upper == r_lower {

        return rr.to_f64();

    }

    sec_accurate(x, &mut argument_reduction, x_e, k)

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_sec() {

        assert_eq!(f_sec(-175432.), 1.461049620895326);

        assert_eq!(f_sec(175432.), 1.461049620895326);

        assert_eq!(f_sec(-10.), -1.1917935066878957);

        assert_eq!(f_sec(10.), -1.1917935066878957);

        assert_eq!(f_sec(5.), 3.5253200858160882);

        assert_eq!(f_sec(-5.), 3.5253200858160882);

        assert_eq!(f_sec(0.), 1.0);

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

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

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

    }

}