lexical-util 1.0.7

//! Float helpers for a `no_std` environment.
//!
//! These are adapted from libm, a port of musl libc's libm to Rust.
//! libm can be found online [here](https://github.com/rust-lang/libm),
//! and is similarly licensed under an Apache2.0/MIT license

#![cfg(all(not(feature = "std"), any(feature = "parse-floats", feature = "write-floats")))]
#![cfg_attr(any(), rustfmt::skip)]

/// # Safety
///
/// Safe as long as `e` is properly initialized.
macro_rules! volatile {
($e:expr) => {
    // SAFETY: safe as long as `$e` has been properly initialized.
    unsafe {
        core::ptr::read_volatile(&$e);
    }
};
}

/// Floor (f64)
///
/// Finds the nearest integer less than or equal to `x`.
pub(crate) fn floord(x: f64) -> f64 {
    const TOINT: f64 = 1. / f64::EPSILON;

    let ui = x.to_bits();
    let e = ((ui >> 52) & 0x7ff) as i32;

    if (e >= 0x3ff + 52) || (x == 0.) {
        return x;
    }
    /* y = int(x) - x, where int(x) is an integer neighbor of x */
    let y = if (ui >> 63) != 0 {
        x - TOINT + TOINT - x
    } else {
        x + TOINT - TOINT - x
    };
    /* special case because of non-nearest rounding modes */
    if e < 0x3ff {
        volatile!(y);
        return if (ui >> 63) != 0 {
            -1.
        } else {
            0.
        };
    }
    if y > 0. {
        x + y - 1.
    } else {
        x + y
    }
}

/// Floor (f32)
///
/// Finds the nearest integer less than or equal to `x`.
pub(crate) fn floorf(x: f32) -> f32 {
    let mut ui = x.to_bits();
    let e = (((ui >> 23) as i32) & 0xff) - 0x7f;

    if e >= 23 {
        return x;
    }
    if e >= 0 {
        let m: u32 = 0x007fffff >> e;
        if (ui & m) == 0 {
            return x;
        }
        volatile!(x + f32::from_bits(0x7b800000));
        if ui >> 31 != 0 {
            ui += m;
        }
        ui &= !m;
    } else {
        volatile!(x + f32::from_bits(0x7b800000));
        if ui >> 31 == 0 {
            ui = 0;
        } else if ui << 1 != 0 {
            return -1.0;
        }
    }
    f32::from_bits(ui)
}

/* origin: FreeBSD /usr/src/lib/msun/src/e_log.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.
 * ====================================================
 */
/* log(x)
 * Return the logarithm of x
 *
 * Method :
 *   1. Argument Reduction: find k and f such that
 *                      x = 2^k * (1+f),
 *         where  sqrt(2)/2 < 1+f < sqrt(2) .
 *
 *   2. Approximation of log(1+f).
 *      Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
 *               = 2s + 2/3 s**3 + 2/5 s**5 + .....,
 *               = 2s + s*R
 *      We use a special Remez algorithm on [0,0.1716] to generate
 *      a polynomial of degree 14 to approximate R The maximum error
 *      of this polynomial approximation is bounded by 2**-58.45. In
 *      other words,
 *                      2      4      6      8      10      12      14
 *          R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
 *      (the values of Lg1 to Lg7 are listed in the program)
 *      and
 *          |      2          14          |     -58.45
 *          | Lg1*s +...+Lg7*s    -  R(z) | <= 2
 *          |                             |
 *      Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
 *      In order to guarantee error in log below 1ulp, we compute log
 *      by
 *              log(1+f) = f - s*(f - R)        (if f is not too large)
 *              log(1+f) = f - (hfsq - s*(hfsq+R)).     (better accuracy)
 *
 *      3. Finally,  log(x) = k*ln2 + log(1+f).
 *                          = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
 *         Here ln2 is split into two floating point number:
 *                      ln2_hi + ln2_lo,
 *         where n*ln2_hi is always exact for |n| < 2000.
 *
 * Special cases:
 *      log(x) is NaN with signal if x < 0 (including -INF) ;
 *      log(+INF) is +INF; log(0) is -INF with signal;
 *      log(NaN) is that NaN with no signal.
 *
 * Accuracy:
 *      according to an error analysis, the error is always less than
 *      1 ulp (unit in the last place).
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

#[allow(clippy::eq_op, clippy::excessive_precision)] // reason="values need to be exact under all conditions"
pub(crate) fn logd(mut x: f64) -> f64 {
    const LN2_HI: f64 = 6.93147180369123816490e-01; /* 3fe62e42 fee00000 */
    const LN2_LO: f64 = 1.90821492927058770002e-10; /* 3dea39ef 35793c76 */
    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 */

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

    let mut ui = x.to_bits();
    let mut hx: u32 = (ui >> 32) as u32;
    let mut k: i32 = 0;

    if (hx < 0x00100000) || ((hx >> 31) != 0) {
        /* x < 2**-126 */
        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);

    let f: f64 = x - 1.0;
    let hfsq: f64 = 0.5 * f * f;
    let s: f64 = f / (2.0 + f);
    let z: f64 = s * s;
    let w: f64 = z * z;
    let t1: f64 = w * (LG2 + w * (LG4 + w * LG6));
    let t2: f64 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7)));
    let r: f64 = t2 + t1;
    let dk: f64 = k as f64;
    s * (hfsq + r) + dk * LN2_LO - hfsq + f + dk * LN2_HI
}

/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.c */
/*
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#[allow(clippy::eq_op, clippy::excessive_precision)] // reason="values need to be exact under all conditions"
pub(crate) fn logf(mut x: f32) -> f32 {
    const LN2_HI: f32 = 6.9313812256e-01; /* 0x3f317180 */
    const LN2_LO: f32 = 9.0580006145e-06; /* 0x3717f7d1 */
    /* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
    const LG1: f32 = 0.66666662693; /* 0xaaaaaa.0p-24 */
    const LG2: f32 = 0.40000972152; /* 0xccce13.0p-25 */
    const LG3: f32 = 0.28498786688; /* 0x91e9ee.0p-25 */
    const LG4: f32 = 0.24279078841; /* 0xf89e26.0p-26 */

    let x1p25 = f32::from_bits(0x4c000000); // 0x1p25f === 2 ^ 25

    let mut ix = x.to_bits();
    let mut k = 0i32;

    if (ix < 0x00800000) || ((ix >> 31) != 0) {
        /* x < 2**-126 */
        if ix << 1 == 0 {
            return -1. / (x * x); /* log(+-0)=-inf */
        }
        if (ix >> 31) != 0 {
            return (x - x) / 0.; /* log(-#) = NaN */
        }
        /* subnormal number, scale up x */
        k -= 25;
        x *= x1p25;
        ix = x.to_bits();
    } else if ix >= 0x7f800000 {
        return x;
    } else if ix == 0x3f800000 {
        return 0.;
    }

    /* reduce x into [sqrt(2)/2, sqrt(2)] */
    ix += 0x3f800000 - 0x3f3504f3;
    k += ((ix >> 23) as i32) - 0x7f;
    ix = (ix & 0x007fffff) + 0x3f3504f3;
    x = f32::from_bits(ix);

    let f = x - 1.;
    let s = f / (2. + f);
    let z = s * s;
    let w = z * z;
    let t1 = w * (LG2 + w * LG4);
    let t2 = z * (LG1 + w * LG3);
    let r = t2 + t1;
    let hfsq = 0.5 * f * f;
    let dk = k as f32;
    s * (hfsq + r) + dk * LN2_LO - hfsq + f + dk * LN2_HI
}