log10

pub fn log10(x_: f64) callconv(.c) f64

File

Code

pub fn log10(x_: f64) callconv(.c) f64 {
    const ivln10hi: f64 = 4.34294481878168880939e-01;
    const ivln10lo: f64 = 2.50829467116452752298e-11;
    const log10_2hi: f64 = 3.01029995663611771306e-01;
    const log10_2lo: f64 = 3.69423907715893078616e-13;
    const Lg1: f64 = 6.666666666666735130e-01;
    const Lg2: f64 = 3.999999999940941908e-01;
    const Lg3: f64 = 2.857142874366239149e-01;
    const Lg4: f64 = 2.222219843214978396e-01;
    const Lg5: f64 = 1.818357216161805012e-01;
    const Lg6: f64 = 1.531383769920937332e-01;
    const Lg7: f64 = 1.479819860511658591e-01;

    var x = x_;
    var ix: u64 = @bitCast(x);
    var hx: u32 = @intCast(ix >> 32);
    var k: i32 = 0;

    if (hx < 0x00100000 or hx >> 31 != 0) {
        // log(+-0) = -inf
        if (ix << 1 == 0) {
            return if (compiler_rt.want_float_exceptions) -1 / (x * x) else -std.math.inf(f64);
        }
        // log(-#) = nan
        if (hx >> 31 != 0) {
            return if (compiler_rt.want_float_exceptions) (x - x) / 0.0 else math.nan(f64);
        }

        // subnormal, scale x
        k -= 54;
        x *= 0x1.0p54;
        hx = @intCast(@as(u64, @bitCast(x)) >> 32);
    } else if (hx >= 0x7FF00000) {
        return x;
    } else if (hx == 0x3FF00000 and ix << 32 == 0) {
        return 0;
    }

    // x into [sqrt(2) / 2, sqrt(2)]
    hx += 0x3FF00000 - 0x3FE6A09E;
    k += @as(i32, @intCast(hx >> 20)) - 0x3FF;
    hx = (hx & 0x000FFFFF) + 0x3FE6A09E;
    ix = (@as(u64, hx) << 32) | (ix & 0xFFFFFFFF);
    x = @bitCast(ix);

    const f = x - 1.0;
    const hfsq = 0.5 * f * f;
    const s = f / (2.0 + f);
    const z = s * s;
    const w = z * z;
    const t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
    const t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
    const R = t2 + t1;

    // hi + lo = f - hfsq + s * (hfsq + R) ~ log(1 + f)
    var hi = f - hfsq;
    var hii: u64 = @bitCast(hi);
    hii &= @as(u64, maxInt(u64)) << 32;
    hi = @bitCast(hii);
    const lo = f - hi - hfsq + s * (hfsq + R);

    // val_hi + val_lo ~ log10(1 + f) + k * log10(2)
    var val_hi = hi * ivln10hi;
    const dk: f64 = @floatFromInt(k);
    const y = dk * log10_2hi;
    var val_lo = dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi;

    // Extra precision multiplication
    const ww = y + val_hi;
    val_lo += (y - ww) + val_hi;
    val_hi = ww;

    return val_lo + val_hi;
}