/*

 * // 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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 */

use crate::common::f_fmla;

use crate::double_double::DoubleDouble;

use crate::sincospi::reduce_pi_64;

use crate::tangent::tanpi_table::TANPI_K_PI_OVER_64;

#[inline]

pub(crate) fn tanpi_eval(x: f64) -> DoubleDouble {

    let x2 = DoubleDouble::from_exact_mult(x, x);

    // tan(pi*x) generated by Sollya:

    // d = [0, 0.0078128];

    // f_tan = tan(y*pi)/y;

    // Q = fpminimax(f_tan, [|0, 2, 4, 6, 8|], [|107, D...|], d, relative, floating);

    const C: [u64; 4] = [

        0x4024abbce625be51,

        0x404466bc677698e5,

        0x40645fff70379ae3,

        0x4084626b091b7fd0,

    ];

    const C0: DoubleDouble = DoubleDouble::from_bit_pair((0x3ca1a6444aa5b996, 0x400921fb54442d18));

    // polyeval 4, estrin scheme

    let u0 = f_fmla(x2.hi, f64::from_bits(C[1]), f64::from_bits(C[0]));

    let u1 = f_fmla(x2.hi, f64::from_bits(C[3]), f64::from_bits(C[2]));

    let tan_poly_lo = f_fmla(x2.hi * x2.hi, u1, u0);

    // We're splitting polynomial in two parts, since first term dominates

    // we compute: (a0_lo + a0_hi) * x + x * (a1 * x^2 + a2 + x^4) ...

    let r_lo = DoubleDouble::quick_mult_f64(x2, tan_poly_lo);

    let tan_lo = f_fmla(r_lo.lo, x, r_lo.hi * x);

    let tan_hi = DoubleDouble::quick_mult_f64(C0, x);

    DoubleDouble::full_add_f64(tan_hi, tan_lo)

}

#[cold]

fn tanpi_hard(x: f64, tan_k: DoubleDouble) -> DoubleDouble {

    const C: [(u64, u64); 6] = [

        (0x3ca1a62632712fc8, 0x400921fb54442d18),

        (0xbcc052338fbb4528, 0x4024abbce625be53),

        (0x3ced42454c5f85b3, 0x404466bc6775aad9),

        (0xbd00c7d6a971a560, 0x40645fff9b4b244d),

        (0x3d205970eff53274, 0x40845f46e96c3a0b),

        (0xbd3589489ad24fc4, 0x40a4630551cd123d),

    ];

    let x2 = DoubleDouble::from_exact_mult(x, x);

    let mut tan_y = DoubleDouble::quick_mul_add(

        x2,

        DoubleDouble::from_bit_pair(C[5]),

        DoubleDouble::from_bit_pair(C[4]),

    );

    tan_y = DoubleDouble::quick_mul_add(x2, tan_y, DoubleDouble::from_bit_pair(C[3]));

    tan_y = DoubleDouble::quick_mul_add(x2, tan_y, DoubleDouble::from_bit_pair(C[2]));

    tan_y = DoubleDouble::quick_mul_add(x2, tan_y, DoubleDouble::from_bit_pair(C[1]));

    tan_y = DoubleDouble::quick_mul_add(x2, tan_y, DoubleDouble::from_bit_pair(C[0]));

    tan_y = DoubleDouble::quick_mult_f64(tan_y, x);

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

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

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

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

    // tan = num / den

    DoubleDouble::div(num, den)

}

/// Computes tan(PI*x)

///

/// Max found ULP 0.5

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

    if x == 0. {

        return x;

    }

    let ax = x.to_bits() & 0x7fff_ffff_ffff_ffff;

    if ax >= (0x7ffu64 << 52) {

        // NaN, Inf

        if ax > (0x7ffu64 << 52) {

            return x + x;

        } // NaN

        return f64::NAN; // x=Inf

    }

    let e: i32 = (ax >> 52) as i32 - 1023;

    if e > 0 {

        if e >= 52 {

            // when |x| > 2^53 it's always an integer

            return f64::copysign(0., x);

        }

        // |x| > 1 and |x| < 2^53

        let m = (ax & ((1u64 << 52) - 1)) | (1u64 << 52); // mantissa with hidden 1

        let shift = 52 - e;

        let frac = m & ((1u64 << shift) - 1);

        if frac == (1u64 << (shift - 1)) {

            // |x| is always integer.5 means it's inf

            return f64::INFINITY;

        }

    }

    if ax <= 0x3cb0000000000000 {

        // for tiny x ( |x| < f64::EPSILON ) just small taylor expansion

        // tan(PI*x) ~ PI*x + PI^3*x^3/3 + O(x^5)

        const PI: DoubleDouble =

            DoubleDouble::from_bit_pair((0x3ca1a62633145c07, 0x400921fb54442d18));

        if ax <= 0x3ca0000000000000 {

            // |x| <= 2^-53, renormalize value

            let e: i32 = (ax >> 52) as i32;

            let sc = f64::from_bits((2045i64 - e as i64).wrapping_shl(52) as u64);

            let isc = f64::from_bits(1i64.wrapping_add(e as i64).wrapping_shl(52) as u64);

            let dx = x * sc;

            let q0 = DoubleDouble::quick_mult_f64(PI, dx);

            let r = q0.to_f64() * isc;

            return r;

        }

        let q0 = DoubleDouble::quick_mult_f64(PI, x);

        let r = q0.to_f64();

        return r;

    }

    // argument reduction

    let (y, k) = reduce_pi_64(x);

    if y == 0.0 {

        let km = (k.abs() & 63) as i32; // k mod 64

        match km {

            0 => return f64::copysign(0f64, x),           // tanpi(n) = 0

            32 => return f64::copysign(f64::INFINITY, x), // tanpi(n+0.5) = ±∞

            16 => return f64::copysign(1.0, x),           // tanpi(n+0.25) = ±1

            48 => return -f64::copysign(1.0, x),          // tanpi(n+0.75) = ∓1

            _ => {}

        }

    }

    let tan_k = DoubleDouble::from_bit_pair(TANPI_K_PI_OVER_64[((k as u64) & 127) as usize]);

    // Computes tan(pi*x) through identities.

    // tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b)) = (tan(y*pi/64) + tan(k*pi/64)) / (1 - tan(y*pi/64)*tan(k*pi/64))

    let tan_y = tanpi_eval(y);

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

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

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

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

    // tan = num / den

    let tan_value = DoubleDouble::div(num, den);

    let err = f_fmla(

        tan_value.hi,

        f64::from_bits(0x3bf0000000000000), // 2^-64

        f64::from_bits(0x3b60000000000000), // 2^-73

    );

    let ub = tan_value.hi + (tan_value.lo + err);

    let lb = tan_value.hi + (tan_value.lo - err);

    if ub == lb {

        return tan_value.to_f64();

    }

    tanpi_hard(y, tan_k).to_f64()

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn test_tanpi() {

        assert_eq!(f_tanpi(0.4999999999119535), 3615246871.564404);

        assert_eq!(f_tanpi(7119681148991743.0), 0.);

        assert_eq!(f_tanpi(63.5), f64::INFINITY);

        assert_eq!(f_tanpi(63.99935913085936), -0.0020133525045719896);

        assert_eq!(f_tanpi(3.3821122649309461E-306), 1.0625219045122997E-305);

        assert_eq!(f_tanpi(1.8010707049867402E-255), 5.6582304953821333E-255);

        assert_eq!(f_tanpi(1.001000000061801), 0.0031416031832113213);

        assert_eq!(f_tanpi(-0.5000000000000226), 14054316517702.594);

        assert_eq!(f_tanpi(0.5000000000000001), -2867080569611329.5);

        assert_eq!(f_tanpi(0.02131), 0.06704753721009375);

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

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

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

    }

}