fma.rs - source
Description: Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.6/src/math/fma.rs`.
Keywords: rust, rustlang, rust-lang

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    use core::{f32, f64};

    use super::scalbn;

    const ZEROINFNAN: i32 = 0x7ff - 0x3ff - 52 - 1;

    struct Num {
        m: u64,
        e: i32,
        sign: i32,
    }

    fn normalize(x: f64) -> Num {
        let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63

        let mut ix: u64 = x.to_bits();
        let mut e: i32 = (ix >> 52) as i32;
        let sign: i32 = e & 0x800;
        e &= 0x7ff;
        if e == 0 {
            ix = (x * x1p63).to_bits();
            e = (ix >> 52) as i32 & 0x7ff;
            e = if e != 0 { e - 63 } else { 0x800 };
        }
        ix &= (1 << 52) - 1;
        ix |= 1 << 52;
        ix <<= 1;
        e -= 0x3ff + 52 + 1;
        Num { m: ix, e, sign }
    }

    fn mul(x: u64, y: u64) -> (u64, u64) {
        let t1: u64;
        let t2: u64;
        let t3: u64;
        let xlo: u64 = x as u32 as u64;
        let xhi: u64 = x >> 32;
        let ylo: u64 = y as u32 as u64;
        let yhi: u64 = y >> 32;

        t1 = xlo * ylo;
        t2 = xlo * yhi + xhi * ylo;
        t3 = xhi * yhi;
        let lo = t1.wrapping_add(t2 << 32);
        let hi = t3 + (t2 >> 32) + (t1 > lo) as u64;
        (hi, lo)
    }

    /// Floating multiply add (f64)
    ///
    /// Computes `(x*y)+z`, rounded as one ternary operation:
    /// Computes the value (as if) to infinite precision and rounds once to the result format,
    /// according to the rounding mode characterized by the value of FLT_ROUNDS.
    #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
    pub fn fma(x: f64, y: f64, z: f64) -> f64 {
        let x1p63: f64 = f64::from_bits(0x43e0000000000000); // 0x1p63 === 2 ^ 63
        let x0_ffffff8p_63 = f64::from_bits(0x3bfffffff0000000); // 0x0.ffffff8p-63

        /* normalize so top 10bits and last bit are 0 */
        let nx = normalize(x);
        let ny = normalize(y);
        let nz = normalize(z);

        if nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN {
            return x * y + z;
        }
        if nz.e >= ZEROINFNAN {
            if nz.e > ZEROINFNAN {
                /* z==0 */
                return x * y + z;
            }
            return z;
        }

        /* mul: r = x*y */
        let zhi: u64;
        let zlo: u64;
        let (mut rhi, mut rlo) = mul(nx.m, ny.m);
        /* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */

        /* align exponents */
        let mut e: i32 = nx.e + ny.e;
        let mut d: i32 = nz.e - e;
        /* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
        if d > 0 {
            if d < 64 {
                zlo = nz.m << d;
                zhi = nz.m >> (64 - d);
            } else {
                zlo = 0;
                zhi = nz.m;
                e = nz.e - 64;
                d -= 64;
                if d == 0 {
                } else if d < 64 {
                    rlo = rhi << (64 - d) | rlo >> d | ((rlo << (64 - d)) != 0) as u64;
                    rhi = rhi >> d;
                } else {
                    rlo = 1;
                    rhi = 0;
                }
            }
        } else {
            zhi = 0;
            d = -d;
            if d == 0 {
                zlo = nz.m;
            } else if d < 64 {
                zlo = nz.m >> d | ((nz.m << (64 - d)) != 0) as u64;
            } else {
                zlo = 1;
            }
        }

        /* add */
        let mut sign: i32 = nx.sign ^ ny.sign;
        let samesign: bool = (sign ^ nz.sign) == 0;
        let mut nonzero: i32 = 1;
        if samesign {
            /* r += z */
            rlo = rlo.wrapping_add(zlo);
            rhi += zhi + (rlo < zlo) as u64;
        } else {
            /* r -= z */
            let (res, borrow) = rlo.overflowing_sub(zlo);
            rlo = res;
            rhi = rhi.wrapping_sub(zhi.wrapping_add(borrow as u64));
            if (rhi >> 63) != 0 {
                rlo = (rlo as i64).wrapping_neg() as u64;
                rhi = (rhi as i64).wrapping_neg() as u64 - (rlo != 0) as u64;
                sign = (sign == 0) as i32;
            }
            nonzero = (rhi != 0) as i32;
        }

        /* set rhi to top 63bit of the result (last bit is sticky) */
        if nonzero != 0 {
            e += 64;
            d = rhi.leading_zeros() as i32 - 1;
            /* note: d > 0 */
            rhi = rhi << d | rlo >> (64 - d) | ((rlo << d) != 0) as u64;
        } else if rlo != 0 {
            d = rlo.leading_zeros() as i32 - 1;
            if d < 0 {
                rhi = rlo >> 1 | (rlo & 1);
            } else {
                rhi = rlo << d;
            }
        } else {
            /* exact +-0 */
            return x * y + z;
        }
        e -= d;

        /* convert to double */
        let mut i: i64 = rhi as i64; /* i is in [1<<62,(1<<63)-1] */
        if sign != 0 {
            i = -i;
        }
        let mut r: f64 = i as f64; /* |r| is in [0x1p62,0x1p63] */

        if e < -1022 - 62 {
            /* result is subnormal before rounding */
            if e == -1022 - 63 {
                let mut c: f64 = x1p63;
                if sign != 0 {
                    c = -c;
                }
                if r == c {
                    /* min normal after rounding, underflow depends
                    on arch behaviour which can be imitated by
                    a double to float conversion */
                    let fltmin: f32 = (x0_ffffff8p_63 * f32::MIN_POSITIVE as f64 * r) as f32;
                    return f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * fltmin as f64;
                }
                /* one bit is lost when scaled, add another top bit to
                only round once at conversion if it is inexact */
                if (rhi << 53) != 0 {
                    i = (rhi >> 1 | (rhi & 1) | 1 << 62) as i64;
                    if sign != 0 {
                        i = -i;
                    }
                    r = i as f64;
                    r = 2. * r - c; /* remove top bit */

                    /* raise underflow portably, such that it
                    cannot be optimized away */
                    {
                        let tiny: f64 = f64::MIN_POSITIVE / f32::MIN_POSITIVE as f64 * r;
                        r += (tiny * tiny) * (r - r);
                    }
                }
            } else {
                /* only round once when scaled */
                d = 10;
                i = ((rhi >> d | ((rhi << (64 - d)) != 0) as u64) << d) as i64;
                if sign != 0 {
                    i = -i;
                }
                r = i as f64;
            }
        }
        scalbn(r, e)
    }

    #[cfg(test)]
    mod tests {
        use super::*;
        #[test]
        fn fma_segfault() {
            // These two inputs cause fma to segfault on release due to overflow:
            assert_eq!(
                fma(
                    -0.0000000000000002220446049250313,
                    -0.0000000000000002220446049250313,
                    -0.0000000000000002220446049250313
                ),
                -0.00000000000000022204460492503126,
            );

            let result = fma(-0.992, -0.992, -0.992);
            //force rounding to storage format on x87 to prevent superious errors.
            #[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
            let result = force_eval!(result);
            assert_eq!(result, -0.007936000000000007,);
        }

        #[test]
        fn fma_sbb() {
            assert_eq!(
                fma(-(1.0 - f64::EPSILON), f64::MIN, f64::MIN),
                -3991680619069439e277
            );
        }

        #[test]
        fn fma_underflow() {
            assert_eq!(
                fma(1.1102230246251565e-16, -9.812526705433188e-305, 1.0894e-320),
                0.0,
            );
        }
    }