Just another update
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Ingy döt Net
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6591 changed files with 94363 additions and 23227 deletions
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@ -2,92 +2,96 @@ import std.math, std.numeric, std.traits, std.conv, std.complex;
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struct Quat(T) if (isFloatingPoint!T) {
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alias Complex!T CT;
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alias CT = Complex!T;
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union {
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struct { T re, i, j, k; } // Default init to NaN
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struct { T re, i, j, k; } // Default init to NaN.
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struct { CT x, y; }
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struct { T[4] vector; }
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}
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string toString() const /*pure nothrow*/ {
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return text(vector);
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string toString() const pure /*nothrow*/ @safe {
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return vector.text;
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}
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@property T norm2() const pure nothrow { /// Norm squared
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@property T norm2() const pure nothrow @safe @nogc { /// Norm squared.
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return re ^^ 2 + i ^^ 2 + j ^^ 2 + k ^^ 2;
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}
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@property T abs() const pure nothrow { /// Norm
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@property T abs() const pure nothrow @safe @nogc { /// Norm.
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return sqrt(norm2);
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}
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@property T arg() const pure nothrow { /// Theta
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@property T arg() const pure nothrow @safe @nogc { /// Theta.
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return acos(re / abs); // this may be incorrect...
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}
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@property Quat!T conj() const pure nothrow { /// Conjugate
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@property Quat!T conj() const pure nothrow @safe @nogc { /// Conjugate.
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return Quat!T(re, -i, -j, -k);
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}
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@property Quat!T recip() const pure nothrow { /// Reciprocal
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@property Quat!T recip() const pure nothrow @safe @nogc { /// Reciprocal.
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return Quat!T(re / norm2, -i / norm2, -j / norm2, -k / norm2);
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}
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@property Quat!T pureim() const pure nothrow { /// Pure imagery
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@property Quat!T pureim() const pure nothrow @safe @nogc { /// Pure imagery.
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return Quat!T(0, i, j, k);
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}
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@property Quat!T versor() const pure nothrow { /// Unit versor
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@property Quat!T versor() const pure nothrow @safe @nogc { /// Unit versor.
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return this / abs;
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}
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/// Unit versor of imagery part
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@property Quat!T iversor() const pure nothrow {
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/// Unit versor of imagery part.
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@property Quat!T iversor() const pure nothrow @safe @nogc {
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return pureim / pureim.abs;
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}
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/// Assignment
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Quat!T opAssign(U : T)(Quat!U z) pure nothrow {
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/// Assignment.
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Quat!T opAssign(U : T)(Quat!U z) pure nothrow @safe @nogc {
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x = z.x; y = z.y;
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return this;
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}
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Quat!T opAssign(U : T)(Complex!U c) pure nothrow {
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Quat!T opAssign(U : T)(Complex!U c) pure nothrow @safe @nogc {
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x = c; y = 0;
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return this;
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}
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Quat!T opAssign(U : T)(U r) pure nothrow if (isNumeric!U) {
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Quat!T opAssign(U : T)(U r) pure nothrow @safe @nogc
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if (isNumeric!U) {
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re = r; i = 0; y = 0;
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return this;
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}
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/// Test for equal, not ordered so no opCmp
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bool opEquals(U : T)(Quat!U z) const pure nothrow {
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/// Test for equal, not ordered so no opCmp.
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bool opEquals(U : T)(Quat!U z) const pure nothrow @safe @nogc {
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return re == z.re && i == z.i && j == z.j && k == z.k;
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}
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bool opEquals(U : T)(Complex!U c) const pure nothrow {
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bool opEquals(U : T)(Complex!U c) const pure nothrow @safe @nogc {
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return re == c.re && i == c.im && j == 0 && k == 0;
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}
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bool opEquals(U : T)(U r) const pure nothrow if (isNumeric!U) {
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bool opEquals(U : T)(U r) const pure nothrow @safe @nogc
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if (isNumeric!U) {
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return re == r && i == 0 && j == 0 && k == 0;
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}
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/// Unary op
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Quat!T opUnary(string op)() const pure nothrow if (op == "+") {
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/// Unary op.
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Quat!T opUnary(string op)() const pure nothrow @safe @nogc
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if (op == "+") {
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return this;
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}
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Quat!T opUnary(string op)() const pure nothrow if (op == "-") {
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Quat!T opUnary(string op)() const pure nothrow @safe @nogc
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if (op == "-") {
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return Quat!T(-re, -i, -j, -k);
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}
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/// Binary op, Quaternion on left of op
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/// Binary op, Quaternion on left of op.
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Quat!(CommonType!(T,U)) opBinary(string op, U)(Quat!U z)
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const pure nothrow {
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const pure nothrow @safe @nogc {
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alias typeof(return) C;
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static if (op == "+" ) {
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@ -104,15 +108,16 @@ struct Quat(T) if (isFloatingPoint!T) {
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}
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}
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/// Extend complex to quaternion
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/// Extend complex to quaternion.
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Quat!(CommonType!(T,U)) opBinary(string op, U)(Complex!U c)
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const pure nothrow {
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const pure nothrow @safe @nogc {
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return opBinary!op(typeof(return)(c.re, c.im, 0, 0));
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}
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/// For scalar
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/// For scalar.
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Quat!(CommonType!(T,U)) opBinary(string op, U)(U r)
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const pure nothrow if (isNumeric!U) {
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const pure nothrow @safe @nogc
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if (isNumeric!U) {
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alias typeof(return) C;
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static if (op == "+" ) {
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@ -128,23 +133,25 @@ struct Quat(T) if (isFloatingPoint!T) {
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}
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}
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/// Power function
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/// Power function.
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Quat!(CommonType!(T,U)) pow(U)(U r)
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const pure nothrow if (isNumeric!U) {
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const pure nothrow @safe @nogc
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if (isNumeric!U) {
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return (abs^^r) * exp(r * iversor * arg);
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}
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/// Handle binary op if Quaternion on right of op and left is
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/// not quaternion.
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Quat!(CommonType!(T,U)) opBinaryRight(string op, U)(Complex!U c)
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const pure nothrow {
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const pure nothrow @safe @nogc {
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alias typeof(return) C;
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auto w = C(c.re, c.im, 0, 0);
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return w.opBinary!(op)(this);
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}
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Quat!(CommonType!(T,U)) opBinaryRight(string op, U)(U r)
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const pure nothrow if (isNumeric!U) {
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const pure nothrow @safe @nogc
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if (isNumeric!U) {
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alias typeof(return) C;
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static if (op == "+" || op == "*") {
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@ -159,20 +166,23 @@ struct Quat(T) if (isFloatingPoint!T) {
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}
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HT exp(HT)(HT z) pure nothrow if (is(HT T == Quat!T)) {
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HT exp(HT)(HT z) pure nothrow @safe @nogc
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if (is(HT T == Quat!T)) {
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immutable inorm = z.pureim.abs;
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return std.math.exp(z.re) * (cos(inorm) + z.iversor * sin(inorm));
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}
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HT log(HT)(HT z) pure nothrow if (is(HT T == Quat!T)) {
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HT log(HT)(HT z) pure nothrow @safe @nogc
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if (is(HT T == Quat!T)) {
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return std.math.log(z.abs) + z.iversor * acos(z.re / z.abs);
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}
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void main() { // Demo code
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void main() @safe { // Demo code.
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import std.stdio;
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alias Quat!real QR;
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immutable real r = 7;
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alias QR = Quat!real;
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enum real r = 7.0;
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immutable QR q = QR(2, 3, 4, 5),
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q1 = QR(2, 3, 4, 5),
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@ -207,7 +217,7 @@ void main() { // Demo code
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writeln(" log(q): ", log(q));
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writeln(" exp(log(q)): ", exp(log(q)));
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writeln(" log(exp(q)): ", log(exp(q)));
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immutable s = log(exp(q));
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immutable s = q.exp.log;
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writeln("9.5 let s = log(exp(q)): ", s);
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writeln(" exp(s): ", exp(s));
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writeln(" log(s): ", log(s));
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