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log1p_32

log1p.log1p_32

fn log1p_32(x: f32) f32

File

lib/std/math/log1p.zig:30

Code

fn log1p_32(x: f32) f32 {
    const ln2_hi = 6.9313812256e-01;
    const ln2_lo = 9.0580006145e-06;
    const Lg1: f32 = 0xaaaaaa.0p-24;
    const Lg2: f32 = 0xccce13.0p-25;
    const Lg3: f32 = 0x91e9ee.0p-25;
    const Lg4: f32 = 0xf89e26.0p-26;

    const u: u32 = @bitCast(x);
    const ix = u;
    var k: i32 = 1;
    var f: f32 = undefined;
    var c: f32 = undefined;

    // 1 + x < sqrt(2)+
    if (ix < 0x3ED413D0 or ix >> 31 != 0) {
        // x = -1.0
        if (ix == 0xBF800000)
            // log1p(-1) = -inf
            return x / 0.0;
        // x < -1.0
        if (ix > 0xBF800000)
            // log1p(x < -1) = nan
            return (x - x) / 0.0;
        // |x| < 2^(-24)
        if ((ix << 1) < (0x33800000 << 1)) {
            // underflow if subnormal
            if (ix & 0x7F800000 == 0) {
                mem.doNotOptimizeAway(x * x);
            }
            return x;
        }
        // sqrt(2) / 2- <= 1 + x < sqrt(2)+
        if (ix <= 0xBE95F619) {
            k = 0;
            c = 0;
            f = x;
        }
    } else if (ix >= 0x7F800000) {
        return x;
    }

    if (k != 0) {
        const uf = 1 + x;
        var iu = @as(u32, @bitCast(uf));
        iu += 0x3F800000 - 0x3F3504F3;
        k = @as(i32, @intCast(iu >> 23)) - 0x7F;

        // correction to avoid underflow in c / u
        if (k < 25) {
            c = if (k >= 2) 1 - (uf - x) else x - (uf - 1);
            c /= uf;
        } else {
            c = 0;
        }

        // u into [sqrt(2)/2, sqrt(2)]
        iu = (iu & 0x007FFFFF) + 0x3F3504F3;
        f = @as(f32, @bitCast(iu)) - 1;
    }

    const s = f / (2.0 + f);
    const z = s * s;
    const w = z * z;
    const t1 = w * (Lg2 + w * Lg4);
    const t2 = z * (Lg1 + w * Lg3);
    const R = t2 + t1;
    const hfsq = 0.5 * f * f;
    const dk = @as(f32, @floatFromInt(k));

    return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi;
}