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exp64

exp.exp64

fn exp64(z: Complex(f64)) Complex(f64)

File

lib/std/math/complex/exp.zig:71

Code

fn exp64(z: Complex(f64)) Complex(f64) {
    const exp_overflow = 0x40862e42; // high bits of max_exp * ln2 ~= 710
    const cexp_overflow = 0x4096b8e4; // (max_exp - min_denorm_exp) * ln2

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

    const fy: u64 = @bitCast(y);
    const hy: u32 = @intCast((fy >> 32) & 0x7fffffff);
    const ly: u32 = @truncate(fy);

    // cexp(x + i0) = exp(x) + i0
    if (hy | ly == 0) {
        return Complex(f64).init(@exp(x), y);
    }

    const fx: u64 = @bitCast(x);
    const hx: u32 = @intCast(fx >> 32);
    const lx: u32 = @truncate(fx);

    // cexp(0 + iy) = cos(y) + isin(y)
    if ((hx & 0x7fffffff) | lx == 0) {
        return Complex(f64).init(@cos(y), @sin(y));
    }

    if (hy >= 0x7ff00000) {
        // cexp(finite|nan +- i inf|nan) = nan + i nan
        if (lx != 0 or (hx & 0x7fffffff) != 0x7ff00000) {
            return Complex(f64).init(y - y, y - y);
        } // cexp(-inf +- i inf|nan) = 0 + i0
        else if (hx & 0x80000000 != 0) {
            return Complex(f64).init(0, 0);
        } // cexp(+inf +- i inf|nan) = inf + i nan
        else {
            return Complex(f64).init(x, y - y);
        }
    }

    // 709.7 <= x <= 1454.3 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(f64).init(exp_x * @cos(y), exp_x * @sin(y));
    }
}