// 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/math/atan2f.c // https://git.musl-libc.org/cgit/musl/tree/src/math/atan2.c const std = @import("../std.zig"); const math = std.math; const expect = std.testing.expect; /// Returns the arc-tangent of y/x. /// /// Special Cases: /// | y | x | radians | /// |-------|-------|---------| /// | fin | nan | nan | /// | nan | fin | nan | /// | +0 | >=+0 | +0 | /// | -0 | >=+0 | -0 | /// | +0 | <=-0 | pi | /// | -0 | <=-0 | -pi | /// | pos | 0 | +pi/2 | /// | neg | 0 | -pi/2 | /// | +inf | +inf | +pi/4 | /// | -inf | +inf | -pi/4 | /// | +inf | -inf | 3pi/4 | /// | -inf | -inf | -3pi/4 | /// | fin | +inf | 0 | /// | pos | -inf | +pi | /// | neg | -inf | -pi | /// | +inf | fin | +pi/2 | /// | -inf | fin | -pi/2 | pub fn atan2(y: anytype, x: anytype) @TypeOf(x, y) { const T = @TypeOf(x, y); return switch (T) { f32 => atan2_32(y, x), f64 => atan2_64(y, x), else => @compileError("atan2 not implemented for " ++ @typeName(T)), }; } fn atan2_32(y: f32, x: f32) f32 { const pi: f32 = 3.1415927410e+00; const pi_lo: f32 = -8.7422776573e-08; if (math.isNan(x) or math.isNan(y)) { return x + y; } var ix = @as(u32, @bitCast(x)); var iy = @as(u32, @bitCast(y)); // x = 1.0 if (ix == 0x3F800000) { return math.atan(y); } // 2 * sign(x) + sign(y) const m = ((iy >> 31) & 1) | ((ix >> 30) & 2); ix &= 0x7FFFFFFF; iy &= 0x7FFFFFFF; if (iy == 0) { switch (m) { 0, 1 => return y, // atan(+-0, +...) 2 => return pi, // atan(+0, -...) 3 => return -pi, // atan(-0, -...) else => unreachable, } } if (ix == 0) { if (m & 1 != 0) { return -pi / 2; } else { return pi / 2; } } if (ix == 0x7F800000) { if (iy == 0x7F800000) { switch (m) { 0 => return pi / 4, // atan(+inf, +inf) 1 => return -pi / 4, // atan(-inf, +inf) 2 => return 3 * pi / 4, // atan(+inf, -inf) 3 => return -3 * pi / 4, // atan(-inf, -inf) else => unreachable, } } else { switch (m) { 0 => return 0.0, // atan(+..., +inf) 1 => return -0.0, // atan(-..., +inf) 2 => return pi, // atan(+..., -inf) 3 => return -pi, // atan(-...f, -inf) else => unreachable, } } } // |y / x| > 0x1p26 if (ix + (26 << 23) < iy or iy == 0x7F800000) { if (m & 1 != 0) { return -pi / 2; } else { return pi / 2; } } // z = atan(|y / x|) with correct underflow const z = z: { if ((m & 2) != 0 and iy + (26 << 23) < ix) { break :z 0.0; } else { break :z math.atan(@abs(y / x)); } }; switch (m) { 0 => return z, // atan(+, +) 1 => return -z, // atan(-, +) 2 => return pi - (z - pi_lo), // atan(+, -) 3 => return (z - pi_lo) - pi, // atan(-, -) else => unreachable, } } fn atan2_64(y: f64, x: f64) f64 { const pi: f64 = 3.1415926535897931160E+00; const pi_lo: f64 = 1.2246467991473531772E-16; if (math.isNan(x) or math.isNan(y)) { return x + y; } const ux: u64 = @bitCast(x); var ix: u32 = @intCast(ux >> 32); const lx: u32 = @intCast(ux & 0xFFFFFFFF); const uy: u64 = @bitCast(y); var iy: u32 = @intCast(uy >> 32); const ly: u32 = @intCast(uy & 0xFFFFFFFF); // x = 1.0 if ((ix -% 0x3FF00000) | lx == 0) { return math.atan(y); } // 2 * sign(x) + sign(y) const m = ((iy >> 31) & 1) | ((ix >> 30) & 2); ix &= 0x7FFFFFFF; iy &= 0x7FFFFFFF; if (iy | ly == 0) { switch (m) { 0, 1 => return y, // atan(+-0, +...) 2 => return pi, // atan(+0, -...) 3 => return -pi, // atan(-0, -...) else => unreachable, } } if (ix | lx == 0) { if (m & 1 != 0) { return -pi / 2; } else { return pi / 2; } } if (ix == 0x7FF00000) { if (iy == 0x7FF00000) { switch (m) { 0 => return pi / 4, // atan(+inf, +inf) 1 => return -pi / 4, // atan(-inf, +inf) 2 => return 3 * pi / 4, // atan(+inf, -inf) 3 => return -3 * pi / 4, // atan(-inf, -inf) else => unreachable, } } else { switch (m) { 0 => return 0.0, // atan(+..., +inf) 1 => return -0.0, // atan(-..., +inf) 2 => return pi, // atan(+..., -inf) 3 => return -pi, // atan(-...f, -inf) else => unreachable, } } } // |y / x| > 0x1p64 if (ix +% (64 << 20) < iy or iy == 0x7FF00000) { if (m & 1 != 0) { return -pi / 2; } else { return pi / 2; } } // z = atan(|y / x|) with correct underflow const z = z: { if ((m & 2) != 0 and iy +% (64 << 20) < ix) { break :z 0.0; } else { break :z math.atan(@abs(y / x)); } }; switch (m) { 0 => return z, // atan(+, +) 1 => return -z, // atan(-, +) 2 => return pi - (z - pi_lo), // atan(+, -) 3 => return (z - pi_lo) - pi, // atan(-, -) else => unreachable, } } test atan2 { const y32: f32 = 0.2; const x32: f32 = 0.21; const y64: f64 = 0.2; const x64: f64 = 0.21; try expect(atan2(y32, x32) == atan2_32(0.2, 0.21)); try expect(atan2(y64, x64) == atan2_64(0.2, 0.21)); } test atan2_32 { const epsilon = 0.000001; try expect(math.approxEqAbs(f32, atan2_32(0.0, 0.0), 0.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(0.2, 0.2), 0.785398, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(-0.2, 0.2), -0.785398, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(0.2, -0.2), 2.356194, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(-0.2, -0.2), -2.356194, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(0.34, -0.4), 2.437099, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(0.34, 1.243), 0.267001, epsilon)); } test atan2_64 { const epsilon = 0.000001; try expect(math.approxEqAbs(f64, atan2_64(0.0, 0.0), 0.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(0.2, 0.2), 0.785398, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(-0.2, 0.2), -0.785398, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(0.2, -0.2), 2.356194, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(-0.2, -0.2), -2.356194, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(0.34, -0.4), 2.437099, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(0.34, 1.243), 0.267001, epsilon)); } test "atan2_32.special" { const epsilon = 0.000001; try expect(math.isNan(atan2_32(1.0, math.nan(f32)))); try expect(math.isNan(atan2_32(math.nan(f32), 1.0))); try expect(atan2_32(0.0, 5.0) == 0.0); try expect(atan2_32(-0.0, 5.0) == -0.0); try expect(math.approxEqAbs(f32, atan2_32(0.0, -5.0), math.pi, epsilon)); //expect(math.approxEqAbs(f32, atan2_32(-0.0, -5.0), -math.pi, .{.rel=0,.abs=epsilon})); TODO support negative zero? try expect(math.approxEqAbs(f32, atan2_32(1.0, 0.0), math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(1.0, -0.0), math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(-1.0, 0.0), -math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(-1.0, -0.0), -math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(math.inf(f32), math.inf(f32)), math.pi / 4.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(-math.inf(f32), math.inf(f32)), -math.pi / 4.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(math.inf(f32), -math.inf(f32)), 3.0 * math.pi / 4.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(-math.inf(f32), -math.inf(f32)), -3.0 * math.pi / 4.0, epsilon)); try expect(atan2_32(1.0, math.inf(f32)) == 0.0); try expect(math.approxEqAbs(f32, atan2_32(1.0, -math.inf(f32)), math.pi, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(-1.0, -math.inf(f32)), -math.pi, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(math.inf(f32), 1.0), math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f32, atan2_32(-math.inf(f32), 1.0), -math.pi / 2.0, epsilon)); } test "atan2_64.special" { const epsilon = 0.000001; try expect(math.isNan(atan2_64(1.0, math.nan(f64)))); try expect(math.isNan(atan2_64(math.nan(f64), 1.0))); try expect(atan2_64(0.0, 5.0) == 0.0); try expect(atan2_64(-0.0, 5.0) == -0.0); try expect(math.approxEqAbs(f64, atan2_64(0.0, -5.0), math.pi, epsilon)); //expect(math.approxEqAbs(f64, atan2_64(-0.0, -5.0), -math.pi, .{.rel=0,.abs=epsilon})); TODO support negative zero? try expect(math.approxEqAbs(f64, atan2_64(1.0, 0.0), math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(1.0, -0.0), math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(-1.0, 0.0), -math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(-1.0, -0.0), -math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(math.inf(f64), math.inf(f64)), math.pi / 4.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(-math.inf(f64), math.inf(f64)), -math.pi / 4.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(math.inf(f64), -math.inf(f64)), 3.0 * math.pi / 4.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(-math.inf(f64), -math.inf(f64)), -3.0 * math.pi / 4.0, epsilon)); try expect(atan2_64(1.0, math.inf(f64)) == 0.0); try expect(math.approxEqAbs(f64, atan2_64(1.0, -math.inf(f64)), math.pi, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(-1.0, -math.inf(f64)), -math.pi, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(math.inf(f64), 1.0), math.pi / 2.0, epsilon)); try expect(math.approxEqAbs(f64, atan2_64(-math.inf(f64), 1.0), -math.pi / 2.0, epsilon)); }