/* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunSoft, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice

 * is preserved.

 * ====================================================

 */

/*

 * Return the base 10 logarithm of x.  See log.c for most comments.

 *

 * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2

 * as in log.c, then combine and scale in extra precision:

 *    log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)

 */

const IVLN10HI: f64 = 4.34294481878168880939e-01; /* 0x3fdbcb7b, 0x15200000 */

const IVLN10LO: f64 = 2.50829467116452752298e-11; /* 0x3dbb9438, 0xca9aadd5 */

const LOG10_2HI: f64 = 3.01029995663611771306e-01; /* 0x3FD34413, 0x509F6000 */

const LOG10_2LO: f64 = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */

const LG1: f64 = 6.666666666666735130e-01; /* 3FE55555 55555593 */

const LG2: f64 = 3.999999999940941908e-01; /* 3FD99999 9997FA04 */

const LG3: f64 = 2.857142874366239149e-01; /* 3FD24924 94229359 */

const LG4: f64 = 2.222219843214978396e-01; /* 3FCC71C5 1D8E78AF */

const LG5: f64 = 1.818357216161805012e-01; /* 3FC74664 96CB03DE */

const LG6: f64 = 1.531383769920937332e-01; /* 3FC39A09 D078C69F */

const LG7: f64 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */

/// The base 10 logarithm of `x` (f64).

#[cfg_attr(assert_no_panic, no_panic::no_panic)]

pub fn log10(mut x: f64) -> f64 {

    let x1p54 = f64::from_bits(0x4350000000000000); // 0x1p54 === 2 ^ 54

    let mut ui: u64 = x.to_bits();

    let hfsq: f64;

    let f: f64;

    let s: f64;

    let z: f64;

    let r: f64;

    let mut w: f64;

    let t1: f64;

    let t2: f64;

    let dk: f64;

    let y: f64;

    let mut hi: f64;

    let lo: f64;

    let mut val_hi: f64;

    let mut val_lo: f64;

    let mut hx: u32;

    let mut k: i32;

    hx = (ui >> 32) as u32;

    k = 0;

    if hx < 0x00100000 || (hx >> 31) > 0 {

        if ui << 1 == 0 {

            return -1. / (x * x); /* log(+-0)=-inf */

        }

        if (hx >> 31) > 0 {

            return (x - x) / 0.0; /* log(-#) = NaN */

        }

        /* subnormal number, scale x up */

        k -= 54;

        x *= x1p54;

        ui = x.to_bits();

        hx = (ui >> 32) as u32;

    } else if hx >= 0x7ff00000 {

        return x;

    } else if hx == 0x3ff00000 && ui << 32 == 0 {

        return 0.;

    }

    /* reduce x into [sqrt(2)/2, sqrt(2)] */

    hx += 0x3ff00000 - 0x3fe6a09e;

    k += (hx >> 20) as i32 - 0x3ff;

    hx = (hx & 0x000fffff) + 0x3fe6a09e;

    ui = ((hx as u64) << 32) | (ui & 0xffffffff);

    x = f64::from_bits(ui);

    f = x - 1.0;

    hfsq = 0.5 * f * f;

    s = f / (2.0 + f);

    z = s * s;

    w = z * z;

    t1 = w * (LG2 + w * (LG4 + w * LG6));

    t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));

    r = t2 + t1;

    /* See log2.c for details. */

    /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */

    hi = f - hfsq;

    ui = hi.to_bits();

    ui &= (-1i64 as u64) << 32;

    hi = f64::from_bits(ui);

    lo = f - hi - hfsq + s * (hfsq + r);

    /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */

    val_hi = hi * IVLN10HI;

    dk = k as f64;

    y = dk * LOG10_2HI;

    val_lo = dk * LOG10_2LO + (lo + hi) * IVLN10LO + lo * IVLN10HI;

    /*

     * Extra precision in for adding y is not strictly needed

     * since there is no very large cancellation near x = sqrt(2) or

     * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs

     * with some parallelism and it reduces the error for many args.

     */

    w = y + val_hi;

    val_lo += (y - w) + val_hi;

    val_hi = w;

    val_lo + val_hi

}