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acosBinary128

acos.acosBinary128

fn acosBinary128(x: f128) f128

File

lib/std/math/acos.zig:299

Code

fn acosBinary128(x: f128) f128 {
    const pio2_hi: f128 = 1.57079632679489661923132169163975140;
    const pio2_lo: f128 = 4.33590506506189051239852201302167613e-35;

    const hx: u128 = @bitCast(x);
    const se: u16 = @truncate(hx >> 112);
    const e = se & 0x7fff;

    // |x| >= 1 or nan
    if (e >= 0x3fff) {
        if (x == 1.0) {
            return 0.0;
        }
        if (x == -1.0) {
            return 2 * pio2_hi + 0x1p-120;
        }
        return 0.0 / (x - x);
    }
    // |x| < 0.5
    if (e < 0x3fff - 1) {
        if (e < 0x3fff - math.floatFractionalBits(f128)) {
            return pio2_hi + 0x1p-120;
        }
        return pio2_hi - (rationalApproxBinary128(x * x) * x - pio2_lo + x);
    }
    // x < -0.5
    if (se >> 15 != 0) {
        const z = (1 + x) * 0.5;
        const s = @sqrt(z);
        return 2 * (pio2_hi - (rationalApproxBinary128(z) * s - pio2_lo + s));
    }
    // x > 0.5
    const z = (1.0 - x) * 0.5;
    const s = @sqrt(z);
    const hs: u128 = @bitCast(s);
    const f: f128 = @bitCast(hs & 0xffff_ffff_ffff_ffff_0000_0000_0000_0000);
    const c = (z - f * f) / (s + f);
    return 2.0 * (rationalApproxBinary128(z) * s + c + f);
}