JUMBO vecmath completion update
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@@ -1,11 +1,103 @@
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const std = @import("std");
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const vm = @import("root");
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const vm = @import("root.zig");
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/// The number of radians per one turn (τ).
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pub const rad_per_turn = 1.0 * std.math.tau;
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/// The number of degrees per one turn (360).
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pub const deg_per_turn = 360.0;
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/// The number of turns per one radian (1 / τ).
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pub const turns_per_rad = 1.0 / std.math.tau;
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/// The number of turns per one degree (1 / 360).
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pub const turns_per_deg = 1.0 / 360.0;
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/// Converts an angle in turns to radians. `@TypeOf(ang)` must be a float or
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/// comptime number or a vector of floats.
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pub fn turnsToRadians(ang: anytype) if (@TypeOf(ang) == comptime_int) comptime_float else @TypeOf(ang) {
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const T = @TypeOf(ang);
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switch (@typeInfo(T)) {
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.float, .comptime_float, .comptime_int => return ang * rad_per_turn,
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.vector => |V| if (@typeInfo(V.child) == .float) return ang * @as(T, @splat(rad_per_turn)),
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else => {},
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}
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@compileError("Input must be float or a comptime number, or a vector of floats.");
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}
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test turnsToRadians {
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try std.testing.expectEqual(0, turnsToRadians(@as(f32, 0)));
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try std.testing.expectApproxEqAbs(0.25 * std.math.tau, turnsToRadians(@as(f32, 0.25)), 0x1p-10);
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try std.testing.expectApproxEqAbs(0.5 * std.math.tau, turnsToRadians(@as(f32, 0.5)), 0x1p-10);
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try std.testing.expectApproxEqAbs(0.75 * std.math.tau, turnsToRadians(@as(f32, 0.75)), 0x1p-10);
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try std.testing.expectApproxEqAbs(std.math.tau, turnsToRadians(@as(f32, 1)), 0x1p-10);
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}
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/// Converts an angle in turns to degrees. `@TypeOf(ang)` must be a float or
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/// comptime number or a vector of floats.
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pub fn turnsToDegrees(ang: anytype) if (@TypeOf(ang) == comptime_int) comptime_float else @TypeOf(ang) {
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const T = @TypeOf(ang);
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switch (@typeInfo(T)) {
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.float, .comptime_float, .comptime_int => return ang * deg_per_turn,
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.vector => |V| if (@typeInfo(V.child) == .float) return ang * @as(T, @splat(deg_per_turn)),
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else => {},
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}
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@compileError("Input must be float or a comptime number, or a vector of floats.");
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}
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test turnsToDegrees {
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try std.testing.expectEqual(0, turnsToDegrees(@as(f32, 0)));
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try std.testing.expectEqual(90, turnsToDegrees(@as(f32, 0.25)));
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try std.testing.expectEqual(180, turnsToDegrees(@as(f32, 0.5)));
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try std.testing.expectEqual(270, turnsToDegrees(@as(f32, 0.75)));
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try std.testing.expectEqual(360, turnsToDegrees(@as(f32, 1)));
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}
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/// Converts an angle in radians to turns. `@TypeOf(ang)` must be a float or
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/// comptime number or a vector of floats.
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pub fn radiansToTurns(ang: anytype) if (@TypeOf(ang) == comptime_int) comptime_float else @TypeOf(ang) {
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const T = @TypeOf(ang);
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switch (@typeInfo(T)) {
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.float, .comptime_float, .comptime_int => return ang * turns_per_rad,
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.vector => |V| if (@typeInfo(V.child) == .float) return ang * @as(T, @splat(turns_per_rad)),
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else => {},
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}
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@compileError("Input must be float or a comptime number, or a vector of floats.");
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}
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test radiansToTurns {
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try std.testing.expectEqual(0, radiansToTurns(@as(f32, 0)));
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try std.testing.expectApproxEqAbs(0.25, radiansToTurns(@as(f32, 0.25 * std.math.tau)), 0x1p-10);
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try std.testing.expectApproxEqAbs(0.5, radiansToTurns(@as(f32, 0.5 * std.math.tau)), 0x1p-10);
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try std.testing.expectApproxEqAbs(0.75, radiansToTurns(@as(f32, 0.75 * std.math.tau)), 0x1p-10);
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try std.testing.expectApproxEqAbs(1, radiansToTurns(@as(f32, std.math.tau)), 0x1p-10);
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}
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/// Converts an angle in degrees to turns. `@TypeOf(ang)` must be a float or
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/// comptime number or a vector of floats.
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pub fn degreesToTurns(ang: anytype) if (@TypeOf(ang) == comptime_int) comptime_float else @TypeOf(ang) {
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const T = @TypeOf(ang);
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switch (@typeInfo(T)) {
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.float, .comptime_float, .comptime_int => return ang / deg_per_turn,
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.vector => |V| if (@typeInfo(V.child) == .float) return ang / @as(T, @splat(deg_per_turn)),
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else => {},
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}
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@compileError("Input must be float or a comptime number, or a vector of floats.");
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}
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test degreesToTurns {
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try std.testing.expectEqual(0, degreesToTurns(@as(f32, 0)));
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try std.testing.expectEqual(0.25, degreesToTurns(@as(f32, 90)));
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try std.testing.expectEqual(0.5, degreesToTurns(@as(f32, 180)));
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try std.testing.expectEqual(0.75, degreesToTurns(@as(f32, 270)));
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try std.testing.expectEqual(1, degreesToTurns(@as(f32, 360)));
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}
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pub fn cos(angle_turns: f32) f32 {
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return cossin(angle_turns).re;
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}
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test "cos" {
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test cos {
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try std.testing.expectEqual(1, cos(-1));
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try std.testing.expectEqual(0, cos(-0.75));
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try std.testing.expectEqual(-1, cos(-0.5));
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@@ -20,7 +112,7 @@ pub fn cos_x8(angle_turns: vm.f32x8) vm.f32x8 {
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return cossin_x8(angle_turns).re;
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}
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test "cos_x8" {
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test cos_x8 {
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try std.testing.expectEqual(
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.{ 1, 0, -1, 0, 1, 0, -1, 0 },
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cos_x8(.{ -1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75 }),
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@@ -31,7 +123,7 @@ pub fn sin(angle_turns: f32) f32 {
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return cossin(angle_turns).im;
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}
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test "sin" {
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test sin {
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try std.testing.expectEqual(0, sin(-1));
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try std.testing.expectEqual(1, sin(-0.75));
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try std.testing.expectEqual(0, sin(-0.5));
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@@ -46,7 +138,7 @@ pub fn sin_x8(angle_turns: vm.f32x8) vm.f32x8 {
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return cossin_x8(angle_turns).im;
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}
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test "sin_x8" {
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test sin_x8 {
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try std.testing.expectEqual(
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.{ 0, 1, 0, -1, 0, 1, 0, -1 },
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sin_x8(.{ -1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75 }),
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@@ -69,31 +161,31 @@ pub fn cossin(angle_turns: f32) vm.Complex {
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const angle_04 = 4.0 * angle_01;
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const quadrant: u32 = @intFromFloat(angle_04);
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const quadrant_odd = (quadrant & 1) * 0xFFFFFFFF;
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const sign_mask_cos = ((quadrant + 1) & 0b10) << 30;
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const sign_mask_sin = (quadrant & 0b10) << 30;
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const x = angle_04 - @floor(angle_04);
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const x2 = x * x;
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const c = ((term_cos_6 * x2 + term_cos_4) * x2 + term_cos_2) * x2 + term_cos_0;
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const s = ((term_sin_5 * x2 + term_sin_3) * x2 + term_sin_1) * x;
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const c: u32 = @bitCast(((term_cos_6 * x2 + term_cos_4) * x2 + term_cos_2) * x2 + term_cos_0);
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const s: u32 = @bitCast(((term_sin_5 * x2 + term_sin_3) * x2 + term_sin_1) * x);
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return switch (quadrant) {
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0 => .init(c, s),
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1 => .init(-s, c),
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2 => .init(-c, -s),
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3 => .init(s, -c),
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else => unreachable,
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};
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const result_cos: f32 = @bitCast(((s & quadrant_odd) | (c & ~quadrant_odd)) ^ sign_mask_cos);
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const result_sin: f32 = @bitCast(((c & quadrant_odd) | (s & ~quadrant_odd)) ^ sign_mask_sin);
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return .init(result_cos, result_sin);
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}
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test "cossin" {
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try std.testing.expectEqual(vm.Vector2.unit_x, cossin(-1));
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try std.testing.expectEqual(vm.Vector2.unit_y, cossin(-0.75));
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try std.testing.expectEqual(vm.Vector2.unit_nx, cossin(-0.5));
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try std.testing.expectEqual(vm.Vector2.unit_ny, cossin(-0.25));
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try std.testing.expectEqual(vm.Vector2.unit_x, cossin(0));
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try std.testing.expectEqual(vm.Vector2.unit_y, cossin(0.25));
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try std.testing.expectEqual(vm.Vector2.unit_nx, cossin(0.5));
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try std.testing.expectEqual(vm.Vector2.unit_ny, cossin(0.75));
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test cossin {
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try std.testing.expectEqual(vm.Complex.initVector2(.unit_x), cossin(-1));
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try std.testing.expectEqual(vm.Complex.initVector2(.unit_y), cossin(-0.75));
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try std.testing.expectEqual(vm.Complex.initVector2(.unit_nx), cossin(-0.5));
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try std.testing.expectEqual(vm.Complex.initVector2(.unit_ny), cossin(-0.25));
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try std.testing.expectEqual(vm.Complex.initVector2(.unit_x), cossin(0));
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try std.testing.expectEqual(vm.Complex.initVector2(.unit_y), cossin(0.25));
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try std.testing.expectEqual(vm.Complex.initVector2(.unit_nx), cossin(0.5));
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try std.testing.expectEqual(vm.Complex.initVector2(.unit_ny), cossin(0.75));
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}
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pub fn cossin_x8(angle_turns: vm.f32x8) vm.Complex_x8 {
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@@ -119,39 +211,27 @@ pub fn cossin_x8(angle_turns: vm.f32x8) vm.Complex_x8 {
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const x = angle_04 - @floor(angle_04);
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const x2 = x * x;
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const c = ((term_cos_6 * x2 + term_cos_4) * x2 + term_cos_2) * x2 + term_cos_0;
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const s = ((term_sin_5 * x2 + term_sin_3) * x2 + term_sin_1) * x;
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const c: vm.u32x8 = @bitCast(((term_cos_6 * x2 + term_cos_4) * x2 + term_cos_2) * x2 + term_cos_0);
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const s: vm.u32x8 = @bitCast(((term_sin_5 * x2 + term_sin_3) * x2 + term_sin_1) * x);
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var result_cos = @select(f32, quadrant_odd, s, c);
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var result_sin = @select(f32, quadrant_odd, c, s);
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result_cos = @bitCast(@as(vm.u32x8, @bitCast(result_cos)) ^ sign_mask_cos);
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result_sin = @bitCast(@as(vm.u32x8, @bitCast(result_sin)) ^ sign_mask_sin);
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const result_cos: vm.f32x8 = @bitCast(@select(u32, quadrant_odd, s, c) ^ sign_mask_cos);
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const result_sin: vm.f32x8 = @bitCast(@select(u32, quadrant_odd, c, s) ^ sign_mask_sin);
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return .init(result_cos, result_sin);
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}
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test "cossin_x8" {
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test cossin_x8 {
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try std.testing.expectEqual(
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vm.Vector2x8.initArrayOfVectors(.{
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vm.Vector2.unit_x,
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vm.Vector2.unit_y,
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vm.Vector2.unit_nx,
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vm.Vector2.unit_ny,
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vm.Vector2.unit_x,
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vm.Vector2.unit_y,
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vm.Vector2.unit_nx,
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vm.Vector2.unit_ny,
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}),
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cossin_x8(.{
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-1,
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-0.75,
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-0.5,
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-0.25,
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0,
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0.25,
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0.5,
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0.75,
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vm.Complex_x8.initArrayOfComplex(.{
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.initVector2(.unit_x),
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.initVector2(.unit_y),
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.initVector2(.unit_nx),
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.initVector2(.unit_ny),
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.initVector2(.unit_x),
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.initVector2(.unit_y),
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.initVector2(.unit_nx),
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.initVector2(.unit_ny),
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}),
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cossin_x8(.{ -1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75 }),
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);
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}
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