Zig 0.17.0-dev (Split by item)

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exp32

exp.exp32

fn exp32(z: Complex(f32)) Complex(f32)

File

lib/std/math/complex/exp.zig:26

Code

fn exp32(z: Complex(f32)) Complex(f32) {
    const exp_overflow = 0x42b17218; // max_exp * ln2 ~= 88.72283955
    const cexp_overflow = 0x43400074; // (max_exp - min_denom_exp) * ln2

    const x = z.re;
    const y = z.im;

    const hy = @as(u32, @bitCast(y)) & 0x7fffffff;
    // cexp(x + i0) = exp(x) + i0
    if (hy == 0) {
        return Complex(f32).init(@exp(x), y);
    }

    const hx = @as(u32, @bitCast(x));
    // cexp(0 + iy) = cos(y) + isin(y)
    if ((hx & 0x7fffffff) == 0) {
        return Complex(f32).init(@cos(y), @sin(y));
    }

    if (hy >= 0x7f800000) {
        // cexp(finite|nan +- i inf|nan) = nan + i nan
        if ((hx & 0x7fffffff) != 0x7f800000) {
            return Complex(f32).init(y - y, y - y);
        } // cexp(-inf +- i inf|nan) = 0 + i0
        else if (hx & 0x80000000 != 0) {
            return Complex(f32).init(0, 0);
        } // cexp(+inf +- i inf|nan) = inf + i nan
        else {
            return Complex(f32).init(x, y - y);
        }
    }

    // 88.7 <= x <= 192 so must scale
    if (hx >= exp_overflow and hx <= cexp_overflow) {
        return ldexp_cexp(z, 0);
    } // - x < exp_overflow => exp(x) won't overflow (common)
    // - x > cexp_overflow, so exp(x) * s overflows for s > 0
    // - x = +-inf
    // - x = nan
    else {
        const exp_x = @exp(x);
        return Complex(f32).init(exp_x * @cos(y), exp_x * @sin(y));
    }
}