zig/lib/std/math/complex/ldexp.zig

// Ported from musl, which is licensed under the MIT license:
// https://git.musl-libc.org/cgit/musl/tree/COPYRIGHT
//
// https://git.musl-libc.org/cgit/musl/tree/src/complex/__cexpf.c
// https://git.musl-libc.org/cgit/musl/tree/src/complex/__cexp.c

const std = @import("../../std.zig");
const debug = std.debug;
const math = std.math;
const testing = std.testing;
const cmath = math.complex;
const Complex = cmath.Complex;

/// Returns exp(z) scaled to avoid overflow.
pub fn ldexp_cexp(z: anytype, expt: i32) Complex(@TypeOf(z.re, z.im)) {
    const T = @TypeOf(z.re, z.im);

    return switch (T) {
        f32 => ldexp_cexp32(z, expt),
        f64 => ldexp_cexp64(z, expt),
        else => unreachable,
    };
}

fn frexp_exp32(x: f32, expt: *i32) f32 {
    const k = 235; // reduction constant
    const kln2 = 162.88958740; // k * ln2

    const exp_x = @exp(x - kln2);
    const hx = @as(u32, @bitCast(exp_x));
    // TODO zig should allow this cast implicitly because it should know the value is in range
    expt.* = @as(i32, @intCast(hx >> 23)) - (0x7f + 127) + k;
    return @as(f32, @bitCast((hx & 0x7fffff) | ((0x7f + 127) << 23)));
}

fn ldexp_cexp32(z: Complex(f32), expt: i32) Complex(f32) {
    var ex_expt: i32 = undefined;
    const exp_x = frexp_exp32(z.re, &ex_expt);
    const exptf = expt + ex_expt;

    const half_expt1 = @divTrunc(exptf, 2);
    const scale1 = @as(f32, @bitCast((0x7f + half_expt1) << 23));

    const half_expt2 = exptf - half_expt1;
    const scale2 = @as(f32, @bitCast((0x7f + half_expt2) << 23));

    return Complex(f32).init(
        @cos(z.im) * exp_x * scale1 * scale2,
        @sin(z.im) * exp_x * scale1 * scale2,
    );
}

fn frexp_exp64(x: f64, expt: *i32) f64 {
    const k = 1799; // reduction constant
    const kln2 = 1246.97177782734161156; // k * ln2

    const exp_x = @exp(x - kln2);

    const fx = @as(u64, @bitCast(exp_x));
    const hx = @as(u32, @intCast(fx >> 32));
    const lx = @as(u32, @truncate(fx));

    expt.* = @as(i32, @intCast(hx >> 20)) - (0x3ff + 1023) + k;

    const high_word = (hx & 0xfffff) | ((0x3ff + 1023) << 20);
    return @as(f64, @bitCast((@as(u64, high_word) << 32) | lx));
}

fn ldexp_cexp64(z: Complex(f64), expt: i32) Complex(f64) {
    var ex_expt: i32 = undefined;
    const exp_x = frexp_exp64(z.re, &ex_expt);
    const exptf = @as(i64, expt + ex_expt);

    const half_expt1 = @divTrunc(exptf, 2);
    const scale1 = @as(f64, @bitCast((0x3ff + half_expt1) << (20 + 32)));

    const half_expt2 = exptf - half_expt1;
    const scale2 = @as(f64, @bitCast((0x3ff + half_expt2) << (20 + 32)));

    return Complex(f64).init(
        @cos(z.im) * exp_x * scale1 * scale2,
        @sin(z.im) * exp_x * scale1 * scale2,
    );
}