module math

import math.internal

const (
    f64_max_exp = f64(1024)
    f64_min_exp = f64(-1021)
    threshold   = 7.09782712893383973096e+02 // 0x40862E42FEFA39EF
    ln2_x56     = 3.88162421113569373274e+01 // 0x4043687a9f1af2b1
    ln2_halfx3  = 1.03972077083991796413e+00 // 0x3ff0a2b23f3bab73
    ln2_half    = 3.46573590279972654709e-01 // 0x3fd62e42fefa39ef
    ln2hi       = 6.93147180369123816490e-01 // 0x3fe62e42fee00000
    ln2lo       = 1.90821492927058770002e-10 // 0x3dea39ef35793c76
    inv_ln2     = 1.44269504088896338700e+00 // 0x3ff71547652b82fe
    // scaled coefficients related to expm1
    expm1_q1    = -3.33333333333331316428e-02 // 0xBFA11111111110F4
    expm1_q2    = 1.58730158725481460165e-03 // 0x3F5A01A019FE5585
    expm1_q3    = -7.93650757867487942473e-05 // 0xBF14CE199EAADBB7
    expm1_q4    = 4.00821782732936239552e-06 // 0x3ED0CFCA86E65239
    expm1_q5    = -2.01099218183624371326e-07 // 0xBE8AFDB76E09C32D
)

// exp returns e**x, the base-e exponential of x.
//
// special cases are:
// exp(+inf) = +inf
// exp(nan) = nan
// Very large values overflow to 0 or +inf.
// Very small values underflow to 1.
pub fn exp(x f64) f64 {
    log2e := 1.44269504088896338700e+00
    overflow := 7.09782712893383973096e+02
    underflow := -7.45133219101941108420e+02
    near_zero := 1.0 / (1 << 28) // 2**-28
    // special cases
    if is_nan(x) || is_inf(x, 1) {
        return x
    }
    if is_inf(x, -1) {
        return 0.0
    }
    if x > overflow {
        return inf(1)
    }
    if x < underflow {
        return 0.0
    }
    if -near_zero < x && x < near_zero {
        return 1.0 + x
    }
    // reduce; computed as r = hi - lo for extra precision.
    mut k := 0
    if x < 0 {
        k = int(log2e * x - 0.5)
    }
    if x > 0 {
        k = int(log2e * x + 0.5)
    }
    hi := x - f64(k) * math.ln2hi
    lo := f64(k) * math.ln2lo
    // compute
    return expmulti(hi, lo, k)
}

// exp2 returns 2**x, the base-2 exponential of x.
//
// special cases are the same as exp.
pub fn exp2(x f64) f64 {
    overflow := 1.0239999999999999e+03
    underflow := -1.0740e+03
    if is_nan(x) || is_inf(x, 1) {
        return x
    }
    if is_inf(x, -1) {
        return 0
    }
    if x > overflow {
        return inf(1)
    }
    if x < underflow {
        return 0
    }
    // argument reduction; x = r×lg(e) + k with |r| ≤ ln(2)/2.
    // computed as r = hi - lo for extra precision.
    mut k := 0
    if x > 0 {
        k = int(x + 0.5)
    }
    if x < 0 {
        k = int(x - 0.5)
    }
    mut t := x - f64(k)
    hi := t * math.ln2hi
    lo := -t * math.ln2lo
    // compute
    return expmulti(hi, lo, k)
}

// ldexp calculates frac*(2**exp)
pub fn ldexp(frac f64, exp int) f64 {
    return scalbn(frac, exp)
}

// frexp breaks f into a normalized fraction
// and an integral power of two.
// It returns frac and exp satisfying f == frac × 2**exp,
// with the absolute value of frac in the interval [½, 1).
//
// special cases are:
// frexp(±0) = ±0, 0
// frexp(±inf) = ±inf, 0
// frexp(nan) = nan, 0
// pub fn frexp(f f64) (f64, int) {
// mut y := f64_bits(x)
// ee := int((y >> 52) & 0x7ff)
// // special cases
// if ee == 0 {
//    if x != 0.0 {
//     x1p64 := f64_from_bits(0x43f0000000000000)
//     z,e_ := frexp(x * x1p64)
//     return z,e_ - 64
// }
// return x,0
// } else if ee == 0x7ff {
// return x,0
// }
// e_ := ee - 0x3fe
// y &= 0x800fffffffffffff
// y |= 0x3fe0000000000000
// return f64_from_bits(y),e_
pub fn frexp(x f64) (f64, int) {
    mut y := f64_bits(x)
    ee := int((y >> 52) & 0x7ff)
    if ee == 0 {
        if x != 0.0 {
            x1p64 := f64_from_bits(u64(0x43f0000000000000))
            z, e_ := frexp(x * x1p64)
            return z, e_ - 64
        }
        return x, 0
    } else if ee == 0x7ff {
        return x, 0
    }
    e_ := ee - 0x3fe
    y &= u64(0x800fffffffffffff)
    y |= u64(0x3fe0000000000000)
    return f64_from_bits(y), e_
}

// expm1 calculates e**x - 1
// special cases are:
// expm1(+inf) = +inf
// expm1(-inf) = -1
// expm1(nan) = nan
pub fn expm1(x f64) f64 {
    if is_inf(x, 1) || is_nan(x) {
        return x
    }
    if is_inf(x, -1) {
        return f64(-1)
    }
    // FIXME: this should be improved
    if abs(x) < ln2 { // Compute the taylor series S = x + (1/2!) x^2 + (1/3!) x^3 + ...
        mut i := 1.0
        mut sum := x
        mut term := x / 1.0
        i++
        term *= x / f64(i)
        sum += term
        for abs(term) > abs(sum) * internal.f64_epsilon {
            i++
            term *= x / f64(i)
            sum += term
        }
        return sum
    } else {
        return exp(x) - 1
    }
}

fn expmulti(hi f64, lo f64, k int) f64 {
    exp_p1 := 1.66666666666666657415e-01 // 0x3FC55555; 0x55555555
    exp_p2 := -2.77777777770155933842e-03 // 0xBF66C16C; 0x16BEBD93
    exp_p3 := 6.61375632143793436117e-05 // 0x3F11566A; 0xAF25DE2C
    exp_p4 := -1.65339022054652515390e-06 // 0xBEBBBD41; 0xC5D26BF1
    exp_p5 := 4.13813679705723846039e-08 // 0x3E663769; 0x72BEA4D0
    r := hi - lo
    t := r * r
    c := r - t * (exp_p1 + t * (exp_p2 + t * (exp_p3 + t * (exp_p4 + t * exp_p5))))
    y := 1 - ((lo - (r * c) / (2 - c)) - hi)
    // TODO(rsc): make sure ldexp can handle boundary k
    return ldexp(y, k)
}