1 files changed, 142 insertions, 0 deletions
diff --git a/lib/std/math/complex/atan.zig b/lib/std/math/complex/atan.zig
new file mode 100644
index 0000000000..3cd19961c8
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+++ b/lib/std/math/complex/atan.zig
@@ -0,0 +1,142 @@
+// 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/catanf.c
+// https://git.musl-libc.org/cgit/musl/tree/src/complex/catan.c
+
+const std = @import("../../std.zig");
+const builtin = @import("builtin");
+const testing = std.testing;
+const math = std.math;
+const cmath = math.complex;
+const Complex = cmath.Complex;
+
+/// Returns the arc-tangent of z.
+pub fn atan(z: var) @typeOf(z) {
+    const T = @typeOf(z.re);
+    return switch (T) {
+        f32 => atan32(z),
+        f64 => atan64(z),
+        else => @compileError("atan not implemented for " ++ @typeName(z)),
+    };
+}
+
+fn redupif32(x: f32) f32 {
+    const DP1 = 3.140625;
+    const DP2 = 9.67502593994140625e-4;
+    const DP3 = 1.509957990978376432e-7;
+
+    var t = x / math.pi;
+    if (t >= 0.0) {
+        t += 0.5;
+    } else {
+        t -= 0.5;
+    }
+
+    const u = @intToFloat(f32, @floatToInt(i32, t));
+    return ((x - u * DP1) - u * DP2) - t * DP3;
+}
+
+fn atan32(z: Complex(f32)) Complex(f32) {
+    const maxnum = 1.0e38;
+
+    const x = z.re;
+    const y = z.im;
+
+    if ((x == 0.0) and (y > 1.0)) {
+        // overflow
+        return Complex(f32).new(maxnum, maxnum);
+    }
+
+    const x2 = x * x;
+    var a = 1.0 - x2 - (y * y);
+    if (a == 0.0) {
+        // overflow
+        return Complex(f32).new(maxnum, maxnum);
+    }
+
+    var t = 0.5 * math.atan2(f32, 2.0 * x, a);
+    var w = redupif32(t);
+
+    t = y - 1.0;
+    a = x2 + t * t;
+    if (a == 0.0) {
+        // overflow
+        return Complex(f32).new(maxnum, maxnum);
+    }
+
+    t = y + 1.0;
+    a = (x2 + (t * t)) / a;
+    return Complex(f32).new(w, 0.25 * math.ln(a));
+}
+
+fn redupif64(x: f64) f64 {
+    const DP1 = 3.14159265160560607910;
+    const DP2 = 1.98418714791870343106e-9;
+    const DP3 = 1.14423774522196636802e-17;
+
+    var t = x / math.pi;
+    if (t >= 0.0) {
+        t += 0.5;
+    } else {
+        t -= 0.5;
+    }
+
+    const u = @intToFloat(f64, @floatToInt(i64, t));
+    return ((x - u * DP1) - u * DP2) - t * DP3;
+}
+
+fn atan64(z: Complex(f64)) Complex(f64) {
+    const maxnum = 1.0e308;
+
+    const x = z.re;
+    const y = z.im;
+
+    if ((x == 0.0) and (y > 1.0)) {
+        // overflow
+        return Complex(f64).new(maxnum, maxnum);
+    }
+
+    const x2 = x * x;
+    var a = 1.0 - x2 - (y * y);
+    if (a == 0.0) {
+        // overflow
+        return Complex(f64).new(maxnum, maxnum);
+    }
+
+    var t = 0.5 * math.atan2(f64, 2.0 * x, a);
+    var w = redupif64(t);
+
+    t = y - 1.0;
+    a = x2 + t * t;
+    if (a == 0.0) {
+        // overflow
+        return Complex(f64).new(maxnum, maxnum);
+    }
+
+    t = y + 1.0;
+    a = (x2 + (t * t)) / a;
+    return Complex(f64).new(w, 0.25 * math.ln(a));
+}
+
+const epsilon = 0.0001;
+
+test "complex.catan32" {
+    const a = Complex(f32).new(5, 3);
+    const c = atan(a);
+
+    testing.expect(math.approxEq(f32, c.re, 1.423679, epsilon));
+    testing.expect(math.approxEq(f32, c.im, 0.086569, epsilon));
+}
+
+test "complex.catan64" {
+    if (builtin.os == .linux and builtin.arch == .arm and builtin.abi == .musleabihf) {
+        // TODO https://github.com/ziglang/zig/issues/3289
+        return error.SkipZigTest;
+    }
+    const a = Complex(f64).new(5, 3);
+    const c = atan(a);
+
+    testing.expect(math.approxEq(f64, c.re, 1.423679, epsilon));
+    testing.expect(math.approxEq(f64, c.im, 0.086569, epsilon));
+}