src/math/sqrtf.rs

/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.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.
 * ====================================================
 */

#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn sqrtf(x: f32) -> f32 {
    // On wasm32 we know that LLVM's intrinsic will compile to an optimized
    // `f32.sqrt` native instruction, so we can leverage this for both code size
    // and speed.
    llvm_intrinsically_optimized! {
        #[cfg(target_arch = "wasm32")] {
            return if x < 0.0 {
                ::core::f32::NAN
            } else {
                unsafe { ::core::intrinsics::sqrtf32(x) }
            }
        }
    }
    #[cfg(target_feature = "sse")]
    {
        // Note: This path is unlikely since LLVM will usually have already
        // optimized sqrt calls into hardware instructions if sse is available,
        // but if someone does end up here they'll apprected the speed increase.
        #[cfg(target_arch = "x86")]
        use core::arch::x86::*;
        #[cfg(target_arch = "x86_64")]
        use core::arch::x86_64::*;
        unsafe {
            let m = _mm_set_ss(x);
            let m_sqrt = _mm_sqrt_ss(m);
            _mm_cvtss_f32(m_sqrt)
        }
    }
    #[cfg(not(target_feature = "sse"))]
    {
        const TINY: f32 = 1.0e-30;

        let mut z: f32;
        let sign: i32 = 0x80000000u32 as i32;
        let mut ix: i32;
        let mut s: i32;
        let mut q: i32;
        let mut m: i32;
        let mut t: i32;
        let mut i: i32;
        let mut r: u32;

        ix = x.to_bits() as i32;

        /* take care of Inf and NaN */
        if (ix as u32 & 0x7f800000) == 0x7f800000 {
            return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
        }

        /* take care of zero */
        if ix <= 0 {
            if (ix & !sign) == 0 {
                return x; /* sqrt(+-0) = +-0 */
            }
            if ix < 0 {
                return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
            }
        }

        /* normalize x */
        m = ix >> 23;
        if m == 0 {
            /* subnormal x */
            i = 0;
            while ix & 0x00800000 == 0 {
                ix <<= 1;
                i = i + 1;
            }
            m -= i - 1;
        }
        m -= 127; /* unbias exponent */
        ix = (ix & 0x007fffff) | 0x00800000;
        if m & 1 == 1 {
            /* odd m, double x to make it even */
            ix += ix;
        }
        m >>= 1; /* m = [m/2] */

        /* generate sqrt(x) bit by bit */
        ix += ix;
        q = 0;
        s = 0;
        r = 0x01000000; /* r = moving bit from right to left */

        while r != 0 {
            t = s + r as i32;
            if t <= ix {
                s = t + r as i32;
                ix -= t;
                q += r as i32;
            }
            ix += ix;
            r >>= 1;
        }

        /* use floating add to find out rounding direction */
        if ix != 0 {
            z = 1.0 - TINY; /* raise inexact flag */
            if z >= 1.0 {
                z = 1.0 + TINY;
                if z > 1.0 {
                    q += 2;
                } else {
                    q += q & 1;
                }
            }
        }

        ix = (q >> 1) + 0x3f000000;
        ix += m << 23;
        f32::from_bits(ix as u32)
    }
}

// PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
#[cfg(not(target_arch = "powerpc64"))]
#[cfg(test)]
mod tests {
    use super::*;
    use core::f32::*;

    #[test]
    fn sanity_check() {
        assert_eq!(sqrtf(100.0), 10.0);
        assert_eq!(sqrtf(4.0), 2.0);
    }

    /// The spec: https://en.cppreference.com/w/cpp/numeric/math/sqrt
    #[test]
    fn spec_tests() {
        // Not Asserted: FE_INVALID exception is raised if argument is negative.
        assert!(sqrtf(-1.0).is_nan());
        assert!(sqrtf(NAN).is_nan());
        for f in [0.0, -0.0, INFINITY].iter().copied() {
            assert_eq!(sqrtf(f), f);
        }
    }

    #[test]
    fn conformance_tests() {
        let values = [
            3.14159265359f32,
            10000.0f32,
            f32::from_bits(0x0000000f),
            INFINITY,
        ];
        let results = [1071833029u32, 1120403456u32, 456082799u32, 2139095040u32];

        for i in 0..values.len() {
            let bits = f32::to_bits(sqrtf(values[i]));
            assert_eq!(results[i], bits);
        }
    }
}