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add_and_denorm128

Compute ldexp(a+b, scale) with a single rounding error. It is assumed that the result will be subnormal, and care is taken to ensure that double rounding does not occur.

fma.add_and_denorm128

fn add_and_denorm128(a: f128, b: f128, scale: i32) f128

File

lib/compiler_rt/fma.zig:269

Code

fn add_and_denorm128(a: f128, b: f128, scale: i32) f128 {
    var sum = dd_add128(a, b);
    // If we are losing at least two bits of accuracy to denormalization,
    // then the first lost bit becomes a round bit, and we adjust the
    // lowest bit of sum.hi to make it a sticky bit summarizing all the
    // bits in sum.lo. With the sticky bit adjusted, the hardware will
    // break any ties in the correct direction.
    //
    // If we are losing only one bit to denormalization, however, we must
    // break the ties manually.
    if (sum.lo != 0) {
        var uhii: u128 = @bitCast(sum.hi);
        const bits_lost = -@as(i32, @intCast((uhii >> 112) & 0x7FFF)) - scale + 1;
        if ((bits_lost != 1) == (uhii & 1 != 0)) {
            const uloi: u128 = @bitCast(sum.lo);
            uhii = uhii + 1 - (((uhii ^ uloi) >> 126) & 2);
            sum.hi = @bitCast(uhii);
        }
    }
    return math.scalbn(sum.hi, scale);
}