Adding upstream version 124.0.1.upstream/124.0.1

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 1238 insertions, 0 deletions

diff --git a/third_party/rust/minimal-lexical/src/libm.rs b/third_party/rust/minimal-lexical/src/libm.rs
new file mode 100644
index 0000000000..c9f93d36ac
--- /dev/null
+++ b/third_party/rust/minimal-lexical/src/libm.rs
@@ -0,0 +1,1238 @@
+//! A small number of math routines for floats and doubles.
+//!
+//! 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"), feature = "compact"))]
+#![doc(hidden)]
+
+/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.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.
+ * ====================================================
+ */
+
+/// # Safety
+///
+/// Safe if `index < array.len()`.
+macro_rules! i {
+    ($array:ident, $index:expr) => {
+        // SAFETY: safe if `index < array.len()`.
+        unsafe { *$array.get_unchecked($index) }
+    };
+}
+
+pub fn powf(x: f32, y: f32) -> f32 {
+    const BP: [f32; 2] = [1.0, 1.5];
+    const DP_H: [f32; 2] = [0.0, 5.84960938e-01]; /* 0x3f15c000 */
+    const DP_L: [f32; 2] = [0.0, 1.56322085e-06]; /* 0x35d1cfdc */
+    const TWO24: f32 = 16777216.0; /* 0x4b800000 */
+    const HUGE: f32 = 1.0e30;
+    const TINY: f32 = 1.0e-30;
+    const L1: f32 = 6.0000002384e-01; /* 0x3f19999a */
+    const L2: f32 = 4.2857143283e-01; /* 0x3edb6db7 */
+    const L3: f32 = 3.3333334327e-01; /* 0x3eaaaaab */
+    const L4: f32 = 2.7272811532e-01; /* 0x3e8ba305 */
+    const L5: f32 = 2.3066075146e-01; /* 0x3e6c3255 */
+    const L6: f32 = 2.0697501302e-01; /* 0x3e53f142 */
+    const P1: f32 = 1.6666667163e-01; /* 0x3e2aaaab */
+    const P2: f32 = -2.7777778450e-03; /* 0xbb360b61 */
+    const P3: f32 = 6.6137559770e-05; /* 0x388ab355 */
+    const P4: f32 = -1.6533901999e-06; /* 0xb5ddea0e */
+    const P5: f32 = 4.1381369442e-08; /* 0x3331bb4c */
+    const LG2: f32 = 6.9314718246e-01; /* 0x3f317218 */
+    const LG2_H: f32 = 6.93145752e-01; /* 0x3f317200 */
+    const LG2_L: f32 = 1.42860654e-06; /* 0x35bfbe8c */
+    const OVT: f32 = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */
+    const CP: f32 = 9.6179670095e-01; /* 0x3f76384f =2/(3ln2) */
+    const CP_H: f32 = 9.6191406250e-01; /* 0x3f764000 =12b cp */
+    const CP_L: f32 = -1.1736857402e-04; /* 0xb8f623c6 =tail of cp_h */
+    const IVLN2: f32 = 1.4426950216e+00;
+    const IVLN2_H: f32 = 1.4426879883e+00;
+    const IVLN2_L: f32 = 7.0526075433e-06;
+
+    let mut z: f32;
+    let mut ax: f32;
+    let z_h: f32;
+    let z_l: f32;
+    let mut p_h: f32;
+    let mut p_l: f32;
+    let y1: f32;
+    let mut t1: f32;
+    let t2: f32;
+    let mut r: f32;
+    let s: f32;
+    let mut sn: f32;
+    let mut t: f32;
+    let mut u: f32;
+    let mut v: f32;
+    let mut w: f32;
+    let i: i32;
+    let mut j: i32;
+    let mut k: i32;
+    let mut yisint: i32;
+    let mut n: i32;
+    let hx: i32;
+    let hy: i32;
+    let mut ix: i32;
+    let iy: i32;
+    let mut is: i32;
+
+    hx = x.to_bits() as i32;
+    hy = y.to_bits() as i32;
+
+    ix = hx & 0x7fffffff;
+    iy = hy & 0x7fffffff;
+
+    /* x**0 = 1, even if x is NaN */
+    if iy == 0 {
+        return 1.0;
+    }
+
+    /* 1**y = 1, even if y is NaN */
+    if hx == 0x3f800000 {
+        return 1.0;
+    }
+
+    /* NaN if either arg is NaN */
+    if ix > 0x7f800000 || iy > 0x7f800000 {
+        return x + y;
+    }
+
+    /* determine if y is an odd int when x < 0
+     * yisint = 0       ... y is not an integer
+     * yisint = 1       ... y is an odd int
+     * yisint = 2       ... y is an even int
+     */
+    yisint = 0;
+    if hx < 0 {
+        if iy >= 0x4b800000 {
+            yisint = 2; /* even integer y */
+        } else if iy >= 0x3f800000 {
+            k = (iy >> 23) - 0x7f; /* exponent */
+            j = iy >> (23 - k);
+            if (j << (23 - k)) == iy {
+                yisint = 2 - (j & 1);
+            }
+        }
+    }
+
+    /* special value of y */
+    if iy == 0x7f800000 {
+        /* y is +-inf */
+        if ix == 0x3f800000 {
+            /* (-1)**+-inf is 1 */
+            return 1.0;
+        } else if ix > 0x3f800000 {
+            /* (|x|>1)**+-inf = inf,0 */
+            return if hy >= 0 {
+                y
+            } else {
+                0.0
+            };
+        } else {
+            /* (|x|<1)**+-inf = 0,inf */
+            return if hy >= 0 {
+                0.0
+            } else {
+                -y
+            };
+        }
+    }
+    if iy == 0x3f800000 {
+        /* y is +-1 */
+        return if hy >= 0 {
+            x
+        } else {
+            1.0 / x
+        };
+    }
+
+    if hy == 0x40000000 {
+        /* y is 2 */
+        return x * x;
+    }
+
+    if hy == 0x3f000000
+       /* y is  0.5 */
+       && hx >= 0
+    {
+        /* x >= +0 */
+        return sqrtf(x);
+    }
+
+    ax = fabsf(x);
+    /* special value of x */
+    if ix == 0x7f800000 || ix == 0 || ix == 0x3f800000 {
+        /* x is +-0,+-inf,+-1 */
+        z = ax;
+        if hy < 0 {
+            /* z = (1/|x|) */
+            z = 1.0 / z;
+        }
+
+        if hx < 0 {
+            if ((ix - 0x3f800000) | yisint) == 0 {
+                z = (z - z) / (z - z); /* (-1)**non-int is NaN */
+            } else if yisint == 1 {
+                z = -z; /* (x<0)**odd = -(|x|**odd) */
+            }
+        }
+        return z;
+    }
+
+    sn = 1.0; /* sign of result */
+    if hx < 0 {
+        if yisint == 0 {
+            /* (x<0)**(non-int) is NaN */
+            return (x - x) / (x - x);
+        }
+
+        if yisint == 1 {
+            /* (x<0)**(odd int) */
+            sn = -1.0;
+        }
+    }
+
+    /* |y| is HUGE */
+    if iy > 0x4d000000 {
+        /* if |y| > 2**27 */
+        /* over/underflow if x is not close to one */
+        if ix < 0x3f7ffff8 {
+            return if hy < 0 {
+                sn * HUGE * HUGE
+            } else {
+                sn * TINY * TINY
+            };
+        }
+
+        if ix > 0x3f800007 {
+            return if hy > 0 {
+                sn * HUGE * HUGE
+            } else {
+                sn * TINY * TINY
+            };
+        }
+
+        /* now |1-x| is TINY <= 2**-20, suffice to compute
+        log(x) by x-x^2/2+x^3/3-x^4/4 */
+        t = ax - 1.; /* t has 20 trailing zeros */
+        w = (t * t) * (0.5 - t * (0.333333333333 - t * 0.25));
+        u = IVLN2_H * t; /* IVLN2_H has 16 sig. bits */
+        v = t * IVLN2_L - w * IVLN2;
+        t1 = u + v;
+        is = t1.to_bits() as i32;
+        t1 = f32::from_bits(is as u32 & 0xfffff000);
+        t2 = v - (t1 - u);
+    } else {
+        let mut s2: f32;
+        let mut s_h: f32;
+        let s_l: f32;
+        let mut t_h: f32;
+        let mut t_l: f32;
+
+        n = 0;
+        /* take care subnormal number */
+        if ix < 0x00800000 {
+            ax *= TWO24;
+            n -= 24;
+            ix = ax.to_bits() as i32;
+        }
+        n += ((ix) >> 23) - 0x7f;
+        j = ix & 0x007fffff;
+        /* determine interval */
+        ix = j | 0x3f800000; /* normalize ix */
+        if j <= 0x1cc471 {
+            /* |x|<sqrt(3/2) */
+            k = 0;
+        } else if j < 0x5db3d7 {
+            /* |x|<sqrt(3)   */
+            k = 1;
+        } else {
+            k = 0;
+            n += 1;
+            ix -= 0x00800000;
+        }
+        ax = f32::from_bits(ix as u32);
+
+        /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+        u = ax - i!(BP, k as usize); /* bp[0]=1.0, bp[1]=1.5 */
+        v = 1.0 / (ax + i!(BP, k as usize));
+        s = u * v;
+        s_h = s;
+        is = s_h.to_bits() as i32;
+        s_h = f32::from_bits(is as u32 & 0xfffff000);
+        /* t_h=ax+bp[k] High */
+        is = (((ix as u32 >> 1) & 0xfffff000) | 0x20000000) as i32;
+        t_h = f32::from_bits(is as u32 + 0x00400000 + ((k as u32) << 21));
+        t_l = ax - (t_h - i!(BP, k as usize));
+        s_l = v * ((u - s_h * t_h) - s_h * t_l);
+        /* compute log(ax) */
+        s2 = s * s;
+        r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
+        r += s_l * (s_h + s);
+        s2 = s_h * s_h;
+        t_h = 3.0 + s2 + r;
+        is = t_h.to_bits() as i32;
+        t_h = f32::from_bits(is as u32 & 0xfffff000);
+        t_l = r - ((t_h - 3.0) - s2);
+        /* u+v = s*(1+...) */
+        u = s_h * t_h;
+        v = s_l * t_h + t_l * s;
+        /* 2/(3log2)*(s+...) */
+        p_h = u + v;
+        is = p_h.to_bits() as i32;
+        p_h = f32::from_bits(is as u32 & 0xfffff000);
+        p_l = v - (p_h - u);
+        z_h = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
+        z_l = CP_L * p_h + p_l * CP + i!(DP_L, k as usize);
+        /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+        t = n as f32;
+        t1 = ((z_h + z_l) + i!(DP_H, k as usize)) + t;
+        is = t1.to_bits() as i32;
+        t1 = f32::from_bits(is as u32 & 0xfffff000);
+        t2 = z_l - (((t1 - t) - i!(DP_H, k as usize)) - z_h);
+    };
+
+    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+    is = y.to_bits() as i32;
+    y1 = f32::from_bits(is as u32 & 0xfffff000);
+    p_l = (y - y1) * t1 + y * t2;
+    p_h = y1 * t1;
+    z = p_l + p_h;
+    j = z.to_bits() as i32;
+    if j > 0x43000000 {
+        /* if z > 128 */
+        return sn * HUGE * HUGE; /* overflow */
+    } else if j == 0x43000000 {
+        /* if z == 128 */
+        if p_l + OVT > z - p_h {
+            return sn * HUGE * HUGE; /* overflow */
+        }
+    } else if (j & 0x7fffffff) > 0x43160000 {
+        /* z < -150 */
+        // FIXME: check should be  (uint32_t)j > 0xc3160000
+        return sn * TINY * TINY; /* underflow */
+    } else if j as u32 == 0xc3160000
+              /* z == -150 */
+              && p_l <= z - p_h
+    {
+        return sn * TINY * TINY; /* underflow */
+    }
+
+    /*
+     * compute 2**(p_h+p_l)
+     */
+    i = j & 0x7fffffff;
+    k = (i >> 23) - 0x7f;
+    n = 0;
+    if i > 0x3f000000 {
+        /* if |z| > 0.5, set n = [z+0.5] */
+        n = j + (0x00800000 >> (k + 1));
+        k = ((n & 0x7fffffff) >> 23) - 0x7f; /* new k for n */
+        t = f32::from_bits(n as u32 & !(0x007fffff >> k));
+        n = ((n & 0x007fffff) | 0x00800000) >> (23 - k);
+        if j < 0 {
+            n = -n;
+        }
+        p_h -= t;
+    }
+    t = p_l + p_h;
+    is = t.to_bits() as i32;
+    t = f32::from_bits(is as u32 & 0xffff8000);
+    u = t * LG2_H;
+    v = (p_l - (t - p_h)) * LG2 + t * LG2_L;
+    z = u + v;
+    w = v - (z - u);
+    t = z * z;
+    t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
+    r = (z * t1) / (t1 - 2.0) - (w + z * w);
+    z = 1.0 - (r - z);
+    j = z.to_bits() as i32;
+    j += n << 23;
+    if (j >> 23) <= 0 {
+        /* subnormal output */
+        z = scalbnf(z, n);
+    } else {
+        z = f32::from_bits(j as u32);
+    }
+    sn * z
+}
+
+/* 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.
+ * ====================================================
+ */
+
+pub fn sqrtf(x: f32) -> f32 {
+    #[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::*;
+        // SAFETY: safe, since `_mm_set_ss` takes a 32-bit float, and returns
+        // a 128-bit type with the lowest 32-bits as `x`, `_mm_sqrt_ss` calculates
+        // the sqrt of this 128-bit vector, and `_mm_cvtss_f32` extracts the lower
+        // 32-bits as a 32-bit float.
+        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)
+    }
+}
+
+/// Absolute value (magnitude) (f32)
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+pub fn fabsf(x: f32) -> f32 {
+    f32::from_bits(x.to_bits() & 0x7fffffff)
+}
+
+pub fn scalbnf(mut x: f32, mut n: i32) -> f32 {
+    let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
+    let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126
+    let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
+
+    if n > 127 {
+        x *= x1p127;
+        n -= 127;
+        if n > 127 {
+            x *= x1p127;
+            n -= 127;
+            if n > 127 {
+                n = 127;
+            }
+        }
+    } else if n < -126 {
+        x *= x1p_126 * x1p24;
+        n += 126 - 24;
+        if n < -126 {
+            x *= x1p_126 * x1p24;
+            n += 126 - 24;
+            if n < -126 {
+                n = -126;
+            }
+        }
+    }
+    x * f32::from_bits(((0x7f + n) as u32) << 23)
+}
+
+/* origin: FreeBSD /usr/src/lib/msun/src/e_pow.c */
+/*
+ * ====================================================
+ * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+// pow(x,y) return x**y
+//
+//                    n
+// Method:  Let x =  2   * (1+f)
+//      1. Compute and return log2(x) in two pieces:
+//              log2(x) = w1 + w2,
+//         where w1 has 53-24 = 29 bit trailing zeros.
+//      2. Perform y*log2(x) = n+y' by simulating muti-precision
+//         arithmetic, where |y'|<=0.5.
+//      3. Return x**y = 2**n*exp(y'*log2)
+//
+// Special cases:
+//      1.  (anything) ** 0  is 1
+//      2.  1 ** (anything)  is 1
+//      3.  (anything except 1) ** NAN is NAN
+//      4.  NAN ** (anything except 0) is NAN
+//      5.  +-(|x| > 1) **  +INF is +INF
+//      6.  +-(|x| > 1) **  -INF is +0
+//      7.  +-(|x| < 1) **  +INF is +0
+//      8.  +-(|x| < 1) **  -INF is +INF
+//      9.  -1          ** +-INF is 1
+//      10. +0 ** (+anything except 0, NAN)               is +0
+//      11. -0 ** (+anything except 0, NAN, odd integer)  is +0
+//      12. +0 ** (-anything except 0, NAN)               is +INF, raise divbyzero
+//      13. -0 ** (-anything except 0, NAN, odd integer)  is +INF, raise divbyzero
+//      14. -0 ** (+odd integer) is -0
+//      15. -0 ** (-odd integer) is -INF, raise divbyzero
+//      16. +INF ** (+anything except 0,NAN) is +INF
+//      17. +INF ** (-anything except 0,NAN) is +0
+//      18. -INF ** (+odd integer) is -INF
+//      19. -INF ** (anything) = -0 ** (-anything), (anything except odd integer)
+//      20. (anything) ** 1 is (anything)
+//      21. (anything) ** -1 is 1/(anything)
+//      22. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+//      23. (-anything except 0 and inf) ** (non-integer) is NAN
+//
+// Accuracy:
+//      pow(x,y) returns x**y nearly rounded. In particular
+//                      pow(integer,integer)
+//      always returns the correct integer provided it is
+//      representable.
+//
+// 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.
+
+pub fn powd(x: f64, y: f64) -> f64 {
+    const BP: [f64; 2] = [1.0, 1.5];
+    const DP_H: [f64; 2] = [0.0, 5.84962487220764160156e-01]; /* 0x3fe2b803_40000000 */
+    const DP_L: [f64; 2] = [0.0, 1.35003920212974897128e-08]; /* 0x3E4CFDEB, 0x43CFD006 */
+    const TWO53: f64 = 9007199254740992.0; /* 0x43400000_00000000 */
+    const HUGE: f64 = 1.0e300;
+    const TINY: f64 = 1.0e-300;
+
+    // poly coefs for (3/2)*(log(x)-2s-2/3*s**3:
+    const L1: f64 = 5.99999999999994648725e-01; /* 0x3fe33333_33333303 */
+    const L2: f64 = 4.28571428578550184252e-01; /* 0x3fdb6db6_db6fabff */
+    const L3: f64 = 3.33333329818377432918e-01; /* 0x3fd55555_518f264d */
+    const L4: f64 = 2.72728123808534006489e-01; /* 0x3fd17460_a91d4101 */
+    const L5: f64 = 2.30660745775561754067e-01; /* 0x3fcd864a_93c9db65 */
+    const L6: f64 = 2.06975017800338417784e-01; /* 0x3fca7e28_4a454eef */
+    const P1: f64 = 1.66666666666666019037e-01; /* 0x3fc55555_5555553e */
+    const P2: f64 = -2.77777777770155933842e-03; /* 0xbf66c16c_16bebd93 */
+    const P3: f64 = 6.61375632143793436117e-05; /* 0x3f11566a_af25de2c */
+    const P4: f64 = -1.65339022054652515390e-06; /* 0xbebbbd41_c5d26bf1 */
+    const P5: f64 = 4.13813679705723846039e-08; /* 0x3e663769_72bea4d0 */
+    const LG2: f64 = 6.93147180559945286227e-01; /* 0x3fe62e42_fefa39ef */
+    const LG2_H: f64 = 6.93147182464599609375e-01; /* 0x3fe62e43_00000000 */
+    const LG2_L: f64 = -1.90465429995776804525e-09; /* 0xbe205c61_0ca86c39 */
+    const OVT: f64 = 8.0085662595372944372e-017; /* -(1024-log2(ovfl+.5ulp)) */
+    const CP: f64 = 9.61796693925975554329e-01; /* 0x3feec709_dc3a03fd =2/(3ln2) */
+    const CP_H: f64 = 9.61796700954437255859e-01; /* 0x3feec709_e0000000 =(float)cp */
+    const CP_L: f64 = -7.02846165095275826516e-09; /* 0xbe3e2fe0_145b01f5 =tail of cp_h*/
+    const IVLN2: f64 = 1.44269504088896338700e+00; /* 0x3ff71547_652b82fe =1/ln2 */
+    const IVLN2_H: f64 = 1.44269502162933349609e+00; /* 0x3ff71547_60000000 =24b 1/ln2*/
+    const IVLN2_L: f64 = 1.92596299112661746887e-08; /* 0x3e54ae0b_f85ddf44 =1/ln2 tail*/
+
+    let t1: f64;
+    let t2: f64;
+
+    let (hx, lx): (i32, u32) = ((x.to_bits() >> 32) as i32, x.to_bits() as u32);
+    let (hy, ly): (i32, u32) = ((y.to_bits() >> 32) as i32, y.to_bits() as u32);
+
+    let mut ix: i32 = (hx & 0x7fffffff) as i32;
+    let iy: i32 = (hy & 0x7fffffff) as i32;
+
+    /* x**0 = 1, even if x is NaN */
+    if ((iy as u32) | ly) == 0 {
+        return 1.0;
+    }
+
+    /* 1**y = 1, even if y is NaN */
+    if hx == 0x3ff00000 && lx == 0 {
+        return 1.0;
+    }
+
+    /* NaN if either arg is NaN */
+    if ix > 0x7ff00000
+        || (ix == 0x7ff00000 && lx != 0)
+        || iy > 0x7ff00000
+        || (iy == 0x7ff00000 && ly != 0)
+    {
+        return x + y;
+    }
+
+    /* determine if y is an odd int when x < 0
+     * yisint = 0       ... y is not an integer
+     * yisint = 1       ... y is an odd int
+     * yisint = 2       ... y is an even int
+     */
+    let mut yisint: i32 = 0;
+    let mut k: i32;
+    let mut j: i32;
+    if hx < 0 {
+        if iy >= 0x43400000 {
+            yisint = 2; /* even integer y */
+        } else if iy >= 0x3ff00000 {
+            k = (iy >> 20) - 0x3ff; /* exponent */
+
+            if k > 20 {
+                j = (ly >> (52 - k)) as i32;
+
+                if (j << (52 - k)) == (ly as i32) {
+                    yisint = 2 - (j & 1);
+                }
+            } else if ly == 0 {
+                j = iy >> (20 - k);
+
+                if (j << (20 - k)) == iy {
+                    yisint = 2 - (j & 1);
+                }
+            }
+        }
+    }
+
+    if ly == 0 {
+        /* special value of y */
+        if iy == 0x7ff00000 {
+            /* y is +-inf */
+
+            return if ((ix - 0x3ff00000) | (lx as i32)) == 0 {
+                /* (-1)**+-inf is 1 */
+                1.0
+            } else if ix >= 0x3ff00000 {
+                /* (|x|>1)**+-inf = inf,0 */
+                if hy >= 0 {
+                    y
+                } else {
+                    0.0
+                }
+            } else {
+                /* (|x|<1)**+-inf = 0,inf */
+                if hy >= 0 {
+                    0.0
+                } else {
+                    -y
+                }
+            };
+        }
+
+        if iy == 0x3ff00000 {
+            /* y is +-1 */
+            return if hy >= 0 {
+                x
+            } else {
+                1.0 / x
+            };
+        }
+
+        if hy == 0x40000000 {
+            /* y is 2 */
+            return x * x;
+        }
+
+        if hy == 0x3fe00000 {
+            /* y is 0.5 */
+            if hx >= 0 {
+                /* x >= +0 */
+                return sqrtd(x);
+            }
+        }
+    }
+
+    let mut ax: f64 = fabsd(x);
+    if lx == 0 {
+        /* special value of x */
+        if ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000 {
+            /* x is +-0,+-inf,+-1 */
+            let mut z: f64 = ax;
+
+            if hy < 0 {
+                /* z = (1/|x|) */
+                z = 1.0 / z;
+            }
+
+            if hx < 0 {
+                if ((ix - 0x3ff00000) | yisint) == 0 {
+                    z = (z - z) / (z - z); /* (-1)**non-int is NaN */
+                } else if yisint == 1 {
+                    z = -z; /* (x<0)**odd = -(|x|**odd) */
+                }
+            }
+
+            return z;
+        }
+    }
+
+    let mut s: f64 = 1.0; /* sign of result */
+    if hx < 0 {
+        if yisint == 0 {
+            /* (x<0)**(non-int) is NaN */
+            return (x - x) / (x - x);
+        }
+
+        if yisint == 1 {
+            /* (x<0)**(odd int) */
+            s = -1.0;
+        }
+    }
+
+    /* |y| is HUGE */
+    if iy > 0x41e00000 {
+        /* if |y| > 2**31 */
+        if iy > 0x43f00000 {
+            /* if |y| > 2**64, must o/uflow */
+            if ix <= 0x3fefffff {
+                return if hy < 0 {
+                    HUGE * HUGE
+                } else {
+                    TINY * TINY
+                };
+            }
+
+            if ix >= 0x3ff00000 {
+                return if hy > 0 {
+                    HUGE * HUGE
+                } else {
+                    TINY * TINY
+                };
+            }
+        }
+
+        /* over/underflow if x is not close to one */
+        if ix < 0x3fefffff {
+            return if hy < 0 {
+                s * HUGE * HUGE
+            } else {
+                s * TINY * TINY
+            };
+        }
+        if ix > 0x3ff00000 {
+            return if hy > 0 {
+                s * HUGE * HUGE
+            } else {
+                s * TINY * TINY
+            };
+        }
+
+        /* now |1-x| is TINY <= 2**-20, suffice to compute
+        log(x) by x-x^2/2+x^3/3-x^4/4 */
+        let t: f64 = ax - 1.0; /* t has 20 trailing zeros */
+        let w: f64 = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
+        let u: f64 = IVLN2_H * t; /* ivln2_h has 21 sig. bits */
+        let v: f64 = t * IVLN2_L - w * IVLN2;
+        t1 = with_set_low_word(u + v, 0);
+        t2 = v - (t1 - u);
+    } else {
+        // double ss,s2,s_h,s_l,t_h,t_l;
+        let mut n: i32 = 0;
+
+        if ix < 0x00100000 {
+            /* take care subnormal number */
+            ax *= TWO53;
+            n -= 53;
+            ix = get_high_word(ax) as i32;
+        }
+
+        n += (ix >> 20) - 0x3ff;
+        j = ix & 0x000fffff;
+
+        /* determine interval */
+        let k: i32;
+        ix = j | 0x3ff00000; /* normalize ix */
+        if j <= 0x3988E {
+            /* |x|<sqrt(3/2) */
+            k = 0;
+        } else if j < 0xBB67A {
+            /* |x|<sqrt(3)   */
+            k = 1;
+        } else {
+            k = 0;
+            n += 1;
+            ix -= 0x00100000;
+        }
+        ax = with_set_high_word(ax, ix as u32);
+
+        /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+        let u: f64 = ax - i!(BP, k as usize); /* bp[0]=1.0, bp[1]=1.5 */
+        let v: f64 = 1.0 / (ax + i!(BP, k as usize));
+        let ss: f64 = u * v;
+        let s_h = with_set_low_word(ss, 0);
+
+        /* t_h=ax+bp[k] High */
+        let t_h: f64 = with_set_high_word(
+            0.0,
+            ((ix as u32 >> 1) | 0x20000000) + 0x00080000 + ((k as u32) << 18),
+        );
+        let t_l: f64 = ax - (t_h - i!(BP, k as usize));
+        let s_l: f64 = v * ((u - s_h * t_h) - s_h * t_l);
+
+        /* compute log(ax) */
+        let s2: f64 = ss * ss;
+        let mut r: f64 = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
+        r += s_l * (s_h + ss);
+        let s2: f64 = s_h * s_h;
+        let t_h: f64 = with_set_low_word(3.0 + s2 + r, 0);
+        let t_l: f64 = r - ((t_h - 3.0) - s2);
+
+        /* u+v = ss*(1+...) */
+        let u: f64 = s_h * t_h;
+        let v: f64 = s_l * t_h + t_l * ss;
+
+        /* 2/(3log2)*(ss+...) */
+        let p_h: f64 = with_set_low_word(u + v, 0);
+        let p_l = v - (p_h - u);
+        let z_h: f64 = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
+        let z_l: f64 = CP_L * p_h + p_l * CP + i!(DP_L, k as usize);
+
+        /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+        let t: f64 = n as f64;
+        t1 = with_set_low_word(((z_h + z_l) + i!(DP_H, k as usize)) + t, 0);
+        t2 = z_l - (((t1 - t) - i!(DP_H, k as usize)) - z_h);
+    }
+
+    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+    let y1: f64 = with_set_low_word(y, 0);
+    let p_l: f64 = (y - y1) * t1 + y * t2;
+    let mut p_h: f64 = y1 * t1;
+    let z: f64 = p_l + p_h;
+    let mut j: i32 = (z.to_bits() >> 32) as i32;
+    let i: i32 = z.to_bits() as i32;
+    // let (j, i): (i32, i32) = ((z.to_bits() >> 32) as i32, z.to_bits() as i32);
+
+    if j >= 0x40900000 {
+        /* z >= 1024 */
+        if (j - 0x40900000) | i != 0 {
+            /* if z > 1024 */
+            return s * HUGE * HUGE; /* overflow */
+        }
+
+        if p_l + OVT > z - p_h {
+            return s * HUGE * HUGE; /* overflow */
+        }
+    } else if (j & 0x7fffffff) >= 0x4090cc00 {
+        /* z <= -1075 */
+        // FIXME: instead of abs(j) use unsigned j
+
+        if (((j as u32) - 0xc090cc00) | (i as u32)) != 0 {
+            /* z < -1075 */
+            return s * TINY * TINY; /* underflow */
+        }
+
+        if p_l <= z - p_h {
+            return s * TINY * TINY; /* underflow */
+        }
+    }
+
+    /* compute 2**(p_h+p_l) */
+    let i: i32 = j & (0x7fffffff as i32);
+    k = (i >> 20) - 0x3ff;
+    let mut n: i32 = 0;
+
+    if i > 0x3fe00000 {
+        /* if |z| > 0.5, set n = [z+0.5] */
+        n = j + (0x00100000 >> (k + 1));
+        k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
+        let t: f64 = with_set_high_word(0.0, (n & !(0x000fffff >> k)) as u32);
+        n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
+        if j < 0 {
+            n = -n;
+        }
+        p_h -= t;
+    }
+
+    let t: f64 = with_set_low_word(p_l + p_h, 0);
+    let u: f64 = t * LG2_H;
+    let v: f64 = (p_l - (t - p_h)) * LG2 + t * LG2_L;
+    let mut z: f64 = u + v;
+    let w: f64 = v - (z - u);
+    let t: f64 = z * z;
+    let t1: f64 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
+    let r: f64 = (z * t1) / (t1 - 2.0) - (w + z * w);
+    z = 1.0 - (r - z);
+    j = get_high_word(z) as i32;
+    j += n << 20;
+
+    if (j >> 20) <= 0 {
+        /* subnormal output */
+        z = scalbnd(z, n);
+    } else {
+        z = with_set_high_word(z, j as u32);
+    }
+
+    s * z
+}
+
+/// Absolute value (magnitude) (f64)
+/// Calculates the absolute value (magnitude) of the argument `x`,
+/// by direct manipulation of the bit representation of `x`.
+pub fn fabsd(x: f64) -> f64 {
+    f64::from_bits(x.to_bits() & (u64::MAX / 2))
+}
+
+pub fn scalbnd(x: f64, mut n: i32) -> f64 {
+    let x1p1023 = f64::from_bits(0x7fe0000000000000); // 0x1p1023 === 2 ^ 1023
+    let x1p53 = f64::from_bits(0x4340000000000000); // 0x1p53 === 2 ^ 53
+    let x1p_1022 = f64::from_bits(0x0010000000000000); // 0x1p-1022 === 2 ^ (-1022)
+
+    let mut y = x;
+
+    if n > 1023 {
+        y *= x1p1023;
+        n -= 1023;
+        if n > 1023 {
+            y *= x1p1023;
+            n -= 1023;
+            if n > 1023 {
+                n = 1023;
+            }
+        }
+    } else if n < -1022 {
+        /* make sure final n < -53 to avoid double
+        rounding in the subnormal range */
+        y *= x1p_1022 * x1p53;
+        n += 1022 - 53;
+        if n < -1022 {
+            y *= x1p_1022 * x1p53;
+            n += 1022 - 53;
+            if n < -1022 {
+                n = -1022;
+            }
+        }
+    }
+    y * f64::from_bits(((0x3ff + n) as u64) << 52)
+}
+
+/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrt.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.
+ * ====================================================
+ */
+/* sqrt(x)
+ * Return correctly rounded sqrt.
+ *           ------------------------------------------
+ *           |  Use the hardware sqrt if you have one |
+ *           ------------------------------------------
+ * Method:
+ *   Bit by bit method using integer arithmetic. (Slow, but portable)
+ *   1. Normalization
+ *      Scale x to y in [1,4) with even powers of 2:
+ *      find an integer k such that  1 <= (y=x*2^(2k)) < 4, then
+ *              sqrt(x) = 2^k * sqrt(y)
+ *   2. Bit by bit computation
+ *      Let q  = sqrt(y) truncated to i bit after binary point (q = 1),
+ *           i                                                   0
+ *                                     i+1         2
+ *          s  = 2*q , and      y  =  2   * ( y - q  ).         (1)
+ *           i      i            i                 i
+ *
+ *      To compute q    from q , one checks whether
+ *                  i+1       i
+ *
+ *                            -(i+1) 2
+ *                      (q + 2      ) <= y.                     (2)
+ *                        i
+ *                                                            -(i+1)
+ *      If (2) is false, then q   = q ; otherwise q   = q  + 2      .
+ *                             i+1   i             i+1   i
+ *
+ *      With some algebraic manipulation, it is not difficult to see
+ *      that (2) is equivalent to
+ *                             -(i+1)
+ *                      s  +  2       <= y                      (3)
+ *                       i                i
+ *
+ *      The advantage of (3) is that s  and y  can be computed by
+ *                                    i      i
+ *      the following recurrence formula:
+ *          if (3) is false
+ *
+ *          s     =  s  ,       y    = y   ;                    (4)
+ *           i+1      i          i+1    i
+ *
+ *          otherwise,
+ *                         -i                     -(i+1)
+ *          s     =  s  + 2  ,  y    = y  -  s  - 2             (5)
+ *           i+1      i          i+1    i     i
+ *
+ *      One may easily use induction to prove (4) and (5).
+ *      Note. Since the left hand side of (3) contain only i+2 bits,
+ *            it does not necessary to do a full (53-bit) comparison
+ *            in (3).
+ *   3. Final rounding
+ *      After generating the 53 bits result, we compute one more bit.
+ *      Together with the remainder, we can decide whether the
+ *      result is exact, bigger than 1/2ulp, or less than 1/2ulp
+ *      (it will never equal to 1/2ulp).
+ *      The rounding mode can be detected by checking whether
+ *      huge + tiny is equal to huge, and whether huge - tiny is
+ *      equal to huge for some floating point number "huge" and "tiny".
+ *
+ * Special cases:
+ *      sqrt(+-0) = +-0         ... exact
+ *      sqrt(inf) = inf
+ *      sqrt(-ve) = NaN         ... with invalid signal
+ *      sqrt(NaN) = NaN         ... with invalid signal for signaling NaN
+ */
+
+pub fn sqrtd(x: f64) -> f64 {
+    #[cfg(target_feature = "sse2")]
+    {
+        // Note: This path is unlikely since LLVM will usually have already
+        // optimized sqrt calls into hardware instructions if sse2 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::*;
+        // SAFETY: safe, since `_mm_set_sd` takes a 64-bit float, and returns
+        // a 128-bit type with the lowest 64-bits as `x`, `_mm_sqrt_ss` calculates
+        // the sqrt of this 128-bit vector, and `_mm_cvtss_f64` extracts the lower
+        // 64-bits as a 64-bit float.
+        unsafe {
+            let m = _mm_set_sd(x);
+            let m_sqrt = _mm_sqrt_pd(m);
+            _mm_cvtsd_f64(m_sqrt)
+        }
+    }
+    #[cfg(not(target_feature = "sse2"))]
+    {
+        use core::num::Wrapping;
+
+        const TINY: f64 = 1.0e-300;
+
+        let mut z: f64;
+        let sign: Wrapping<u32> = Wrapping(0x80000000);
+        let mut ix0: i32;
+        let mut s0: i32;
+        let mut q: i32;
+        let mut m: i32;
+        let mut t: i32;
+        let mut i: i32;
+        let mut r: Wrapping<u32>;
+        let mut t1: Wrapping<u32>;
+        let mut s1: Wrapping<u32>;
+        let mut ix1: Wrapping<u32>;
+        let mut q1: Wrapping<u32>;
+
+        ix0 = (x.to_bits() >> 32) as i32;
+        ix1 = Wrapping(x.to_bits() as u32);
+
+        /* take care of Inf and NaN */
+        if (ix0 & 0x7ff00000) == 0x7ff00000 {
+            return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
+        }
+        /* take care of zero */
+        if ix0 <= 0 {
+            if ((ix0 & !(sign.0 as i32)) | ix1.0 as i32) == 0 {
+                return x; /* sqrt(+-0) = +-0 */
+            }
+            if ix0 < 0 {
+                return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
+            }
+        }
+        /* normalize x */
+        m = ix0 >> 20;
+        if m == 0 {
+            /* subnormal x */
+            while ix0 == 0 {
+                m -= 21;
+                ix0 |= (ix1 >> 11).0 as i32;
+                ix1 <<= 21;
+            }
+            i = 0;
+            while (ix0 & 0x00100000) == 0 {
+                i += 1;
+                ix0 <<= 1;
+            }
+            m -= i - 1;
+            ix0 |= (ix1 >> (32 - i) as usize).0 as i32;
+            ix1 = ix1 << i as usize;
+        }
+        m -= 1023; /* unbias exponent */
+        ix0 = (ix0 & 0x000fffff) | 0x00100000;
+        if (m & 1) == 1 {
+            /* odd m, double x to make it even */
+            ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+            ix1 += ix1;
+        }
+        m >>= 1; /* m = [m/2] */
+
+        /* generate sqrt(x) bit by bit */
+        ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+        ix1 += ix1;
+        q = 0; /* [q,q1] = sqrt(x) */
+        q1 = Wrapping(0);
+        s0 = 0;
+        s1 = Wrapping(0);
+        r = Wrapping(0x00200000); /* r = moving bit from right to left */
+
+        while r != Wrapping(0) {
+            t = s0 + r.0 as i32;
+            if t <= ix0 {
+                s0 = t + r.0 as i32;
+                ix0 -= t;
+                q += r.0 as i32;
+            }
+            ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+            ix1 += ix1;
+            r >>= 1;
+        }
+
+        r = sign;
+        while r != Wrapping(0) {
+            t1 = s1 + r;
+            t = s0;
+            if t < ix0 || (t == ix0 && t1 <= ix1) {
+                s1 = t1 + r;
+                if (t1 & sign) == sign && (s1 & sign) == Wrapping(0) {
+                    s0 += 1;
+                }
+                ix0 -= t;
+                if ix1 < t1 {
+                    ix0 -= 1;
+                }
+                ix1 -= t1;
+                q1 += r;
+            }
+            ix0 += ix0 + ((ix1 & sign) >> 31).0 as i32;
+            ix1 += ix1;
+            r >>= 1;
+        }
+
+        /* use floating add to find out rounding direction */
+        if (ix0 as u32 | ix1.0) != 0 {
+            z = 1.0 - TINY; /* raise inexact flag */
+            if z >= 1.0 {
+                z = 1.0 + TINY;
+                if q1.0 == 0xffffffff {
+                    q1 = Wrapping(0);
+                    q += 1;
+                } else if z > 1.0 {
+                    if q1.0 == 0xfffffffe {
+                        q += 1;
+                    }
+                    q1 += Wrapping(2);
+                } else {
+                    q1 += q1 & Wrapping(1);
+                }
+            }
+        }
+        ix0 = (q >> 1) + 0x3fe00000;
+        ix1 = q1 >> 1;
+        if (q & 1) == 1 {
+            ix1 |= sign;
+        }
+        ix0 += m << 20;
+        f64::from_bits((ix0 as u64) << 32 | ix1.0 as u64)
+    }
+}
+
+#[inline]
+fn get_high_word(x: f64) -> u32 {
+    (x.to_bits() >> 32) as u32
+}
+
+#[inline]
+fn with_set_high_word(f: f64, hi: u32) -> f64 {
+    let mut tmp = f.to_bits();
+    tmp &= 0x00000000_ffffffff;
+    tmp |= (hi as u64) << 32;
+    f64::from_bits(tmp)
+}
+
+#[inline]
+fn with_set_low_word(f: f64, lo: u32) -> f64 {
+    let mut tmp = f.to_bits();
+    tmp &= 0xffffffff_00000000;
+    tmp |= lo as u64;
+    f64::from_bits(tmp)
+}