source: trunk/src/lol/math/vector.h @ 1314

Last change on this file since 1314 was 1314, checked in by sam, 9 years ago

math: add quat::fromeuler static constructor for quaternions.

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1//
2// Lol Engine
3//
4// Copyright: (c) 2010-2012 Sam Hocevar <sam@hocevar.net>
5//   This program is free software; you can redistribute it and/or
6//   modify it under the terms of the Do What The Fuck You Want To
7//   Public License, Version 2, as published by Sam Hocevar. See
8//   http://sam.zoy.org/projects/COPYING.WTFPL for more details.
9//
10
11//
12// The vector, complex, quaternion and matrix classes
13// --------------------------------------------------
14//
15
16#if !defined __LOL_MATH_VECTOR_H__
17#define __LOL_MATH_VECTOR_H__
18
19#include <stdint.h>
20#include <cmath>
21#if !defined __ANDROID__
22#   include <iostream>
23#endif
24
25#include "lol/math/half.h"
26#include "lol/math/real.h"
27
28namespace lol
29{
30
31/* This is OUR namespace. Don't let Windows headers fuck with it. */
32#undef min
33#undef max
34
35/* Some compilers do not support const members in anonymous unions. So
36 * far, GCC (>= 4.6), CLang (3.0) and Visual Studio (>= 2010) appear to
37 * work properly. */
38#undef LOL_NO_CONST_MEMBERS_IN_ANONYMOUS_UNIONS
39#if defined __GNUC__ && (__GNUC__ < 4 || (__GNUC__ == 4 && __GNUC_MINOR__ < 6))
40#   define LOL_NO_CONST_MEMBERS_IN_ANONYMOUS_UNIONS 1
41#endif
42
43#define DECLARE_VECTOR_TYPEDEFS(tname, suffix) \
44    template <typename T> struct tname; \
45    typedef tname<half> f16##suffix; \
46    typedef tname<float> suffix; \
47    typedef tname<double> f64##suffix; \
48    typedef tname<int8_t> i8##suffix; \
49    typedef tname<uint8_t> u8##suffix; \
50    typedef tname<int16_t> i16##suffix; \
51    typedef tname<uint16_t> u16##suffix; \
52    typedef tname<int32_t> i##suffix; \
53    typedef tname<uint32_t> u##suffix; \
54    typedef tname<int64_t> i64##suffix; \
55    typedef tname<uint64_t> u64##suffix; \
56    typedef tname<real> r##suffix; \
57
58DECLARE_VECTOR_TYPEDEFS(Vec2, vec2)
59DECLARE_VECTOR_TYPEDEFS(Cmplx, cmplx)
60DECLARE_VECTOR_TYPEDEFS(Vec3, vec3)
61DECLARE_VECTOR_TYPEDEFS(Vec4, vec4)
62DECLARE_VECTOR_TYPEDEFS(Quat, quat)
63DECLARE_VECTOR_TYPEDEFS(Mat2, mat2)
64DECLARE_VECTOR_TYPEDEFS(Mat3, mat3)
65DECLARE_VECTOR_TYPEDEFS(Mat4, mat4)
66
67/*
68 * Magic vector swizzling (part 1/2)
69 * These vectors are empty, but thanks to static_cast we can take their
70 * address and access the vector of T's that they are union'ed with. We
71 * use static_cast instead of reinterpret_cast because there is a stronger
72 * guarantee (by the standard) that the address will stay the same across
73 * casts.
74 */
75
76template<typename T, int N> struct XVec2
77{
78    inline Vec2<T> operator =(Vec2<T> const &that);
79
80    inline T& operator[](size_t n)
81    {
82        int i = (N >> (4 * (1 - n))) & 3;
83        return static_cast<T*>(static_cast<void*>(this))[i];
84    }
85    inline T const& operator[](size_t n) const
86    {
87        int i = (N >> (4 * (1 - n))) & 3;
88        return static_cast<T const*>(static_cast<void const *>(this))[i];
89    }
90};
91
92template<typename T, int N> struct XVec3
93{
94    inline Vec3<T> operator =(Vec3<T> const &that);
95
96    inline T& operator[](size_t n)
97    {
98        int i = (N >> (4 * (2 - n))) & 3;
99        return static_cast<T*>(static_cast<void*>(this))[i];
100    }
101    inline T const& operator[](size_t n) const
102    {
103        int i = (N >> (4 * (2 - n))) & 3;
104        return static_cast<T const*>(static_cast<void const *>(this))[i];
105    }
106};
107
108template<typename T, int N> struct XVec4
109{
110    inline Vec4<T> operator =(Vec4<T> const &that);
111
112    inline T& operator[](size_t n)
113    {
114        int i = (N >> (4 * (3 - n))) & 3;
115        return static_cast<T*>(static_cast<void*>(this))[i];
116    }
117    inline T const& operator[](size_t n) const
118    {
119        int i = (N >> (4 * (3 - n))) & 3;
120        return static_cast<T const*>(static_cast<void const *>(this))[i];
121    }
122};
123
124/*
125 * Helper macro for vector type member functions
126 */
127
128#define DECLARE_MEMBER_OPS(tname) \
129    inline T& operator[](size_t n) { return *(&this->x + n); } \
130    inline T const& operator[](size_t n) const { return *(&this->x + n); } \
131    \
132    /* Visual Studio insists on having an assignment operator. */ \
133    inline tname<T> const & operator =(tname<T> const &that) \
134    { \
135        for (size_t n = 0; n < sizeof(*this) / sizeof(T); n++) \
136            (*this)[n] = that[n]; \
137        return *this; \
138    } \
139    \
140    template<typename U> \
141    inline operator tname<U>() const \
142    { \
143        tname<U> ret; \
144        for (size_t n = 0; n < sizeof(*this) / sizeof(T); n++) \
145            ret[n] = static_cast<U>((*this)[n]); \
146        return ret; \
147    } \
148    \
149    void printf() const;
150
151/*
152 * 2-element vectors
153 */
154
155template <typename T> struct BVec2
156{
157    explicit inline BVec2() {}
158    explicit inline BVec2(T X, T Y) : x(X), y(Y) {}
159
160    union
161    {
162        struct { T x, y; };
163        struct { T r, g; };
164        struct { T s, t; };
165
166#if LOL_NO_CONST_MEMBERS_IN_ANONYMOUS_UNIONS
167#   define const /* disabled */
168#endif
169        XVec2<T,0x00> const xx, rr, ss;
170        XVec2<T,0x01> const xy, rg, st; /* lvalue */
171        XVec2<T,0x10> const yx, gr, ts; /* lvalue */
172        XVec2<T,0x11> const yy, gg, tt;
173
174        XVec3<T,0x000> const xxx, rrr, sss;
175        XVec3<T,0x001> const xxy, rrg, sst;
176        XVec3<T,0x010> const xyx, rgr, sts;
177        XVec3<T,0x011> const xyy, rgg, stt;
178        XVec3<T,0x100> const yxx, grr, tss;
179        XVec3<T,0x101> const yxy, grg, tst;
180        XVec3<T,0x110> const yyx, ggr, tts;
181        XVec3<T,0x111> const yyy, ggg, ttt;
182
183        XVec4<T,0x0000> const xxxx, rrrr, ssss;
184        XVec4<T,0x0001> const xxxy, rrrg, ssst;
185        XVec4<T,0x0010> const xxyx, rrgr, ssts;
186        XVec4<T,0x0011> const xxyy, rrgg, sstt;
187        XVec4<T,0x0100> const xyxx, rgrr, stss;
188        XVec4<T,0x0101> const xyxy, rgrg, stst;
189        XVec4<T,0x0110> const xyyx, rggr, stts;
190        XVec4<T,0x0111> const xyyy, rggg, sttt;
191        XVec4<T,0x1000> const yxxx, grrr, tsss;
192        XVec4<T,0x1001> const yxxy, grrg, tsst;
193        XVec4<T,0x1010> const yxyx, grgr, tsts;
194        XVec4<T,0x1011> const yxyy, grgg, tstt;
195        XVec4<T,0x1100> const yyxx, ggrr, ttss;
196        XVec4<T,0x1101> const yyxy, ggrg, ttst;
197        XVec4<T,0x1110> const yyyx, gggr, ttts;
198        XVec4<T,0x1111> const yyyy, gggg, tttt;
199#if LOL_NO_CONST_MEMBERS_IN_ANONYMOUS_UNIONS
200#   undef const
201#endif
202    };
203};
204
205template <> struct BVec2<half>
206{
207    explicit inline BVec2() {}
208    explicit inline BVec2(half X, half Y) : x(X), y(Y) {}
209
210    half x, y;
211};
212
213template <> struct BVec2<real>
214{
215    explicit inline BVec2() {}
216    explicit inline BVec2(real X, real Y) : x(X), y(Y) {}
217
218    real x, y;
219};
220
221template <typename T> struct Vec2 : BVec2<T>
222{
223    inline Vec2() {}
224    inline Vec2(T X, T Y) : BVec2<T>(X, Y) {}
225
226    explicit inline Vec2(T X) : BVec2<T>(X, X) {}
227
228    template<int N>
229    inline Vec2(XVec2<T, N> const &v)
230      : BVec2<T>(v[0], v[1]) {}
231
232    template<typename U, int N>
233    explicit inline Vec2(XVec2<U, N> const &v)
234      : BVec2<T>(v[0], v[1]) {}
235
236    DECLARE_MEMBER_OPS(Vec2)
237
238#if !defined __ANDROID__
239    template<typename U>
240    friend std::ostream &operator<<(std::ostream &stream, Vec2<U> const &v);
241#endif
242};
243
244/*
245 * 2-element complexes
246 */
247
248template <typename T> struct Cmplx
249{
250    inline Cmplx() {}
251    inline Cmplx(T X) : x(X), y(0) {}
252    inline Cmplx(T X, T Y) : x(X), y(Y) {}
253
254    DECLARE_MEMBER_OPS(Cmplx)
255
256    inline Cmplx<T> operator *(Cmplx<T> const &val) const
257    {
258        return Cmplx<T>(x * val.x - y * val.y, x * val.y + y * val.x);
259    }
260
261    inline Cmplx<T> operator *=(Cmplx<T> const &val)
262    {
263        return *this = (*this) * val;
264    }
265
266    inline Cmplx<T> operator ~() const
267    {
268        return Cmplx<T>(x, -y);
269    }
270
271    inline T norm() const { return len(*this); }
272#if !defined __ANDROID__
273    template<typename U>
274    friend std::ostream &operator<<(std::ostream &stream, Cmplx<U> const &v);
275#endif
276
277    T x, y;
278};
279
280template<typename T>
281static inline Cmplx<T> re(Cmplx<T> const &val)
282{
283    return ~val / sqlen(val);
284}
285
286template<typename T>
287static inline Cmplx<T> operator /(T a, Cmplx<T> const &b)
288{
289    return a * re(b);
290}
291
292template<typename T>
293static inline Cmplx<T> operator /(Cmplx<T> a, Cmplx<T> const &b)
294{
295    return a * re(b);
296}
297
298template<typename T>
299static inline bool operator ==(Cmplx<T> const &a, T b)
300{
301    return (a.x == b) && !a.y;
302}
303
304template<typename T>
305static inline bool operator !=(Cmplx<T> const &a, T b)
306{
307    return (a.x != b) || a.y;
308}
309
310template<typename T>
311static inline bool operator ==(T a, Cmplx<T> const &b) { return b == a; }
312
313template<typename T>
314static inline bool operator !=(T a, Cmplx<T> const &b) { return b != a; }
315
316/*
317 * 3-element vectors
318 */
319
320template <typename T> struct BVec3
321{
322    explicit inline BVec3() {}
323    explicit inline BVec3(T X, T Y, T Z) : x(X), y(Y), z(Z) {}
324
325    union
326    {
327        struct { T x, y, z; };
328        struct { T r, g, b; };
329        struct { T s, t, p; };
330
331#if LOL_NO_CONST_MEMBERS_IN_ANONYMOUS_UNIONS
332#   define const /* disabled */
333#endif
334        XVec2<T,0x00> const xx, rr, ss;
335        XVec2<T,0x01> const xy, rg, st; /* lvalue */
336        XVec2<T,0x02> const xz, rb, sp; /* lvalue */
337        XVec2<T,0x10> const yx, gr, ts; /* lvalue */
338        XVec2<T,0x11> const yy, gg, tt;
339        XVec2<T,0x12> const yz, gb, tp; /* lvalue */
340        XVec2<T,0x20> const zx, br, ps; /* lvalue */
341        XVec2<T,0x21> const zy, bg, pt; /* lvalue */
342        XVec2<T,0x22> const zz, bb, pp;
343
344        XVec3<T,0x000> const xxx, rrr, sss;
345        XVec3<T,0x001> const xxy, rrg, sst;
346        XVec3<T,0x002> const xxz, rrb, ssp;
347        XVec3<T,0x010> const xyx, rgr, sts;
348        XVec3<T,0x011> const xyy, rgg, stt;
349        XVec3<T,0x012> const xyz, rgb, stp; /* lvalue */
350        XVec3<T,0x020> const xzx, rbr, sps;
351        XVec3<T,0x021> const xzy, rbg, spt; /* lvalue */
352        XVec3<T,0x022> const xzz, rbb, spp;
353        XVec3<T,0x100> const yxx, grr, tss;
354        XVec3<T,0x101> const yxy, grg, tst;
355        XVec3<T,0x102> const yxz, grb, tsp; /* lvalue */
356        XVec3<T,0x110> const yyx, ggr, tts;
357        XVec3<T,0x111> const yyy, ggg, ttt;
358        XVec3<T,0x112> const yyz, ggb, ttp;
359        XVec3<T,0x120> const yzx, gbr, tps; /* lvalue */
360        XVec3<T,0x121> const yzy, gbg, tpt;
361        XVec3<T,0x122> const yzz, gbb, tpp;
362        XVec3<T,0x200> const zxx, brr, pss;
363        XVec3<T,0x201> const zxy, brg, pst; /* lvalue */
364        XVec3<T,0x202> const zxz, brb, psp;
365        XVec3<T,0x210> const zyx, bgr, pts; /* lvalue */
366        XVec3<T,0x211> const zyy, bgg, ptt;
367        XVec3<T,0x212> const zyz, bgb, ptp;
368        XVec3<T,0x220> const zzx, bbr, pps;
369        XVec3<T,0x221> const zzy, bbg, ppt;
370        XVec3<T,0x222> const zzz, bbb, ppp;
371
372        XVec4<T,0x0000> const xxxx, rrrr, ssss;
373        XVec4<T,0x0001> const xxxy, rrrg, ssst;
374        XVec4<T,0x0002> const xxxz, rrrb, sssp;
375        XVec4<T,0x0010> const xxyx, rrgr, ssts;
376        XVec4<T,0x0011> const xxyy, rrgg, sstt;
377        XVec4<T,0x0012> const xxyz, rrgb, sstp;
378        XVec4<T,0x0020> const xxzx, rrbr, ssps;
379        XVec4<T,0x0021> const xxzy, rrbg, sspt;
380        XVec4<T,0x0022> const xxzz, rrbb, sspp;
381        XVec4<T,0x0100> const xyxx, rgrr, stss;
382        XVec4<T,0x0101> const xyxy, rgrg, stst;
383        XVec4<T,0x0102> const xyxz, rgrb, stsp;
384        XVec4<T,0x0110> const xyyx, rggr, stts;
385        XVec4<T,0x0111> const xyyy, rggg, sttt;
386        XVec4<T,0x0112> const xyyz, rggb, sttp;
387        XVec4<T,0x0120> const xyzx, rgbr, stps;
388        XVec4<T,0x0121> const xyzy, rgbg, stpt;
389        XVec4<T,0x0122> const xyzz, rgbb, stpp;
390        XVec4<T,0x0200> const xzxx, rbrr, spss;
391        XVec4<T,0x0201> const xzxy, rbrg, spst;
392        XVec4<T,0x0202> const xzxz, rbrb, spsp;
393        XVec4<T,0x0210> const xzyx, rbgr, spts;
394        XVec4<T,0x0211> const xzyy, rbgg, sptt;
395        XVec4<T,0x0212> const xzyz, rbgb, sptp;
396        XVec4<T,0x0220> const xzzx, rbbr, spps;
397        XVec4<T,0x0221> const xzzy, rbbg, sppt;
398        XVec4<T,0x0222> const xzzz, rbbb, sppp;
399        XVec4<T,0x1000> const yxxx, grrr, tsss;
400        XVec4<T,0x1001> const yxxy, grrg, tsst;
401        XVec4<T,0x1002> const yxxz, grrb, tssp;
402        XVec4<T,0x1010> const yxyx, grgr, tsts;
403        XVec4<T,0x1011> const yxyy, grgg, tstt;
404        XVec4<T,0x1012> const yxyz, grgb, tstp;
405        XVec4<T,0x1020> const yxzx, grbr, tsps;
406        XVec4<T,0x1021> const yxzy, grbg, tspt;
407        XVec4<T,0x1022> const yxzz, grbb, tspp;
408        XVec4<T,0x1100> const yyxx, ggrr, ttss;
409        XVec4<T,0x1101> const yyxy, ggrg, ttst;
410        XVec4<T,0x1102> const yyxz, ggrb, ttsp;
411        XVec4<T,0x1110> const yyyx, gggr, ttts;
412        XVec4<T,0x1111> const yyyy, gggg, tttt;
413        XVec4<T,0x1112> const yyyz, gggb, tttp;
414        XVec4<T,0x1120> const yyzx, ggbr, ttps;
415        XVec4<T,0x1121> const yyzy, ggbg, ttpt;
416        XVec4<T,0x1122> const yyzz, ggbb, ttpp;
417        XVec4<T,0x1200> const yzxx, gbrr, tpss;
418        XVec4<T,0x1201> const yzxy, gbrg, tpst;
419        XVec4<T,0x1202> const yzxz, gbrb, tpsp;
420        XVec4<T,0x1210> const yzyx, gbgr, tpts;
421        XVec4<T,0x1211> const yzyy, gbgg, tptt;
422        XVec4<T,0x1212> const yzyz, gbgb, tptp;
423        XVec4<T,0x1220> const yzzx, gbbr, tpps;
424        XVec4<T,0x1221> const yzzy, gbbg, tppt;
425        XVec4<T,0x1222> const yzzz, gbbb, tppp;
426        XVec4<T,0x2000> const zxxx, brrr, psss;
427        XVec4<T,0x2001> const zxxy, brrg, psst;
428        XVec4<T,0x2002> const zxxz, brrb, pssp;
429        XVec4<T,0x2010> const zxyx, brgr, psts;
430        XVec4<T,0x2011> const zxyy, brgg, pstt;
431        XVec4<T,0x2012> const zxyz, brgb, pstp;
432        XVec4<T,0x2020> const zxzx, brbr, psps;
433        XVec4<T,0x2021> const zxzy, brbg, pspt;
434        XVec4<T,0x2022> const zxzz, brbb, pspp;
435        XVec4<T,0x2100> const zyxx, bgrr, ptss;
436        XVec4<T,0x2101> const zyxy, bgrg, ptst;
437        XVec4<T,0x2102> const zyxz, bgrb, ptsp;
438        XVec4<T,0x2110> const zyyx, bggr, ptts;
439        XVec4<T,0x2111> const zyyy, bggg, pttt;
440        XVec4<T,0x2112> const zyyz, bggb, pttp;
441        XVec4<T,0x2120> const zyzx, bgbr, ptps;
442        XVec4<T,0x2121> const zyzy, bgbg, ptpt;
443        XVec4<T,0x2122> const zyzz, bgbb, ptpp;
444        XVec4<T,0x2200> const zzxx, bbrr, ppss;
445        XVec4<T,0x2201> const zzxy, bbrg, ppst;
446        XVec4<T,0x2202> const zzxz, bbrb, ppsp;
447        XVec4<T,0x2210> const zzyx, bbgr, ppts;
448        XVec4<T,0x2211> const zzyy, bbgg, pptt;
449        XVec4<T,0x2212> const zzyz, bbgb, pptp;
450        XVec4<T,0x2220> const zzzx, bbbr, ppps;
451        XVec4<T,0x2221> const zzzy, bbbg, pppt;
452        XVec4<T,0x2222> const zzzz, bbbb, pppp;
453#if LOL_NO_CONST_MEMBERS_IN_ANONYMOUS_UNIONS
454#   undef const
455#endif
456    };
457};
458
459template <> struct BVec3<half>
460{
461    explicit inline BVec3() {}
462    explicit inline BVec3(half X, half Y, half Z) : x(X), y(Y), z(Z) {}
463
464    half x, y, z;
465};
466
467template <> struct BVec3<real>
468{
469    explicit inline BVec3() {}
470    explicit inline BVec3(real X, real Y, real Z) : x(X), y(Y), z(Z) {}
471
472    real x, y, z;
473};
474
475template <typename T> struct Vec3 : BVec3<T>
476{
477    inline Vec3() {}
478    inline Vec3(T X, T Y, T Z) : BVec3<T>(X, Y, Z) {}
479    inline Vec3(Vec2<T> XY, T Z) : BVec3<T>(XY.x, XY.y, Z) {}
480    inline Vec3(T X, Vec2<T> YZ) : BVec3<T>(X, YZ.x, YZ.y) {}
481
482    explicit inline Vec3(T X) : BVec3<T>(X, X, X) {}
483
484    template<int N>
485    inline Vec3(XVec3<T, N> const &v)
486      : BVec3<T>(v[0], v[1], v[2]) {}
487
488    template<typename U, int N>
489    explicit inline Vec3(XVec3<U, N> const &v)
490      : BVec3<T>(v[0], v[1], v[2]) {}
491
492    DECLARE_MEMBER_OPS(Vec3)
493
494#if !defined __ANDROID__
495    template<typename U>
496    friend std::ostream &operator<<(std::ostream &stream, Vec3<U> const &v);
497#endif
498};
499
500/*
501 * 4-element vectors
502 */
503
504template <typename T> struct BVec4
505{
506    explicit inline BVec4() {}
507    explicit inline BVec4(T X, T Y, T Z, T W) : x(X), y(Y), z(Z), w(W) {}
508
509    union
510    {
511        struct { T x, y, z, w; };
512        struct { T r, g, b, a; };
513        struct { T s, t, p, q; };
514
515#if LOL_NO_CONST_MEMBERS_IN_ANONYMOUS_UNIONS
516#   define const /* disabled */
517#endif
518        XVec2<T,0x00> const xx, rr, ss;
519        XVec2<T,0x01> const xy, rg, st; /* lvalue */
520        XVec2<T,0x02> const xz, rb, sp; /* lvalue */
521        XVec2<T,0x03> const xw, ra, sq; /* lvalue */
522        XVec2<T,0x10> const yx, gr, ts; /* lvalue */
523        XVec2<T,0x11> const yy, gg, tt;
524        XVec2<T,0x12> const yz, gb, tp; /* lvalue */
525        XVec2<T,0x13> const yw, ga, tq; /* lvalue */
526        XVec2<T,0x20> const zx, br, ps; /* lvalue */
527        XVec2<T,0x21> const zy, bg, pt; /* lvalue */
528        XVec2<T,0x22> const zz, bb, pp;
529        XVec2<T,0x23> const zw, ba, pq; /* lvalue */
530        XVec2<T,0x30> const wx, ar, qs; /* lvalue */
531        XVec2<T,0x31> const wy, ag, qt; /* lvalue */
532        XVec2<T,0x32> const wz, ab, qp; /* lvalue */
533        XVec2<T,0x33> const ww, aa, qq;
534
535        XVec3<T,0x000> const xxx, rrr, sss;
536        XVec3<T,0x001> const xxy, rrg, sst;
537        XVec3<T,0x002> const xxz, rrb, ssp;
538        XVec3<T,0x003> const xxw, rra, ssq;
539        XVec3<T,0x010> const xyx, rgr, sts;
540        XVec3<T,0x011> const xyy, rgg, stt;
541        XVec3<T,0x012> const xyz, rgb, stp; /* lvalue */
542        XVec3<T,0x013> const xyw, rga, stq; /* lvalue */
543        XVec3<T,0x020> const xzx, rbr, sps;
544        XVec3<T,0x021> const xzy, rbg, spt; /* lvalue */
545        XVec3<T,0x022> const xzz, rbb, spp;
546        XVec3<T,0x023> const xzw, rba, spq; /* lvalue */
547        XVec3<T,0x030> const xwx, rar, sqs;
548        XVec3<T,0x031> const xwy, rag, sqt; /* lvalue */
549        XVec3<T,0x032> const xwz, rab, sqp; /* lvalue */
550        XVec3<T,0x033> const xww, raa, sqq;
551        XVec3<T,0x100> const yxx, grr, tss;
552        XVec3<T,0x101> const yxy, grg, tst;
553        XVec3<T,0x102> const yxz, grb, tsp; /* lvalue */
554        XVec3<T,0x103> const yxw, gra, tsq; /* lvalue */
555        XVec3<T,0x110> const yyx, ggr, tts;
556        XVec3<T,0x111> const yyy, ggg, ttt;
557        XVec3<T,0x112> const yyz, ggb, ttp;
558        XVec3<T,0x113> const yyw, gga, ttq;
559        XVec3<T,0x120> const yzx, gbr, tps; /* lvalue */
560        XVec3<T,0x121> const yzy, gbg, tpt;
561        XVec3<T,0x122> const yzz, gbb, tpp;
562        XVec3<T,0x123> const yzw, gba, tpq; /* lvalue */
563        XVec3<T,0x130> const ywx, gar, tqs; /* lvalue */
564        XVec3<T,0x131> const ywy, gag, tqt;
565        XVec3<T,0x132> const ywz, gab, tqp; /* lvalue */
566        XVec3<T,0x133> const yww, gaa, tqq;
567        XVec3<T,0x200> const zxx, brr, pss;
568        XVec3<T,0x201> const zxy, brg, pst; /* lvalue */
569        XVec3<T,0x202> const zxz, brb, psp;
570        XVec3<T,0x203> const zxw, bra, psq; /* lvalue */
571        XVec3<T,0x210> const zyx, bgr, pts; /* lvalue */
572        XVec3<T,0x211> const zyy, bgg, ptt;
573        XVec3<T,0x212> const zyz, bgb, ptp;
574        XVec3<T,0x213> const zyw, bga, ptq; /* lvalue */
575        XVec3<T,0x220> const zzx, bbr, pps;
576        XVec3<T,0x221> const zzy, bbg, ppt;
577        XVec3<T,0x222> const zzz, bbb, ppp;
578        XVec3<T,0x223> const zzw, bba, ppq;
579        XVec3<T,0x230> const zwx, bar, pqs; /* lvalue */
580        XVec3<T,0x231> const zwy, bag, pqt; /* lvalue */
581        XVec3<T,0x232> const zwz, bab, pqp;
582        XVec3<T,0x233> const zww, baa, pqq;
583        XVec3<T,0x300> const wxx, arr, qss;
584        XVec3<T,0x301> const wxy, arg, qst; /* lvalue */
585        XVec3<T,0x302> const wxz, arb, qsp; /* lvalue */
586        XVec3<T,0x303> const wxw, ara, qsq;
587        XVec3<T,0x310> const wyx, agr, qts; /* lvalue */
588        XVec3<T,0x311> const wyy, agg, qtt;
589        XVec3<T,0x312> const wyz, agb, qtp; /* lvalue */
590        XVec3<T,0x313> const wyw, aga, qtq;
591        XVec3<T,0x320> const wzx, abr, qps; /* lvalue */
592        XVec3<T,0x321> const wzy, abg, qpt; /* lvalue */
593        XVec3<T,0x322> const wzz, abb, qpp;
594        XVec3<T,0x323> const wzw, aba, qpq;
595        XVec3<T,0x330> const wwx, aar, qqs;
596        XVec3<T,0x331> const wwy, aag, qqt;
597        XVec3<T,0x332> const wwz, aab, qqp;
598        XVec3<T,0x333> const www, aaa, qqq;
599
600        XVec4<T,0x0000> const xxxx, rrrr, ssss;
601        XVec4<T,0x0001> const xxxy, rrrg, ssst;
602        XVec4<T,0x0002> const xxxz, rrrb, sssp;
603        XVec4<T,0x0003> const xxxw, rrra, sssq;
604        XVec4<T,0x0010> const xxyx, rrgr, ssts;
605        XVec4<T,0x0011> const xxyy, rrgg, sstt;
606        XVec4<T,0x0012> const xxyz, rrgb, sstp;
607        XVec4<T,0x0013> const xxyw, rrga, sstq;
608        XVec4<T,0x0020> const xxzx, rrbr, ssps;
609        XVec4<T,0x0021> const xxzy, rrbg, sspt;
610        XVec4<T,0x0022> const xxzz, rrbb, sspp;
611        XVec4<T,0x0023> const xxzw, rrba, sspq;
612        XVec4<T,0x0030> const xxwx, rrar, ssqs;
613        XVec4<T,0x0031> const xxwy, rrag, ssqt;
614        XVec4<T,0x0032> const xxwz, rrab, ssqp;
615        XVec4<T,0x0033> const xxww, rraa, ssqq;
616        XVec4<T,0x0100> const xyxx, rgrr, stss;
617        XVec4<T,0x0101> const xyxy, rgrg, stst;
618        XVec4<T,0x0102> const xyxz, rgrb, stsp;
619        XVec4<T,0x0103> const xyxw, rgra, stsq;
620        XVec4<T,0x0110> const xyyx, rggr, stts;
621        XVec4<T,0x0111> const xyyy, rggg, sttt;
622        XVec4<T,0x0112> const xyyz, rggb, sttp;
623        XVec4<T,0x0113> const xyyw, rgga, sttq;
624        XVec4<T,0x0120> const xyzx, rgbr, stps;
625        XVec4<T,0x0121> const xyzy, rgbg, stpt;
626        XVec4<T,0x0122> const xyzz, rgbb, stpp;
627        XVec4<T,0x0123> const xyzw, rgba, stpq; /* lvalue */
628        XVec4<T,0x0130> const xywx, rgar, stqs;
629        XVec4<T,0x0131> const xywy, rgag, stqt;
630        XVec4<T,0x0132> const xywz, rgab, stqp; /* lvalue */
631        XVec4<T,0x0133> const xyww, rgaa, stqq;
632        XVec4<T,0x0200> const xzxx, rbrr, spss;
633        XVec4<T,0x0201> const xzxy, rbrg, spst;
634        XVec4<T,0x0202> const xzxz, rbrb, spsp;
635        XVec4<T,0x0203> const xzxw, rbra, spsq;
636        XVec4<T,0x0210> const xzyx, rbgr, spts;
637        XVec4<T,0x0211> const xzyy, rbgg, sptt;
638        XVec4<T,0x0212> const xzyz, rbgb, sptp;
639        XVec4<T,0x0213> const xzyw, rbga, sptq; /* lvalue */
640        XVec4<T,0x0220> const xzzx, rbbr, spps;
641        XVec4<T,0x0221> const xzzy, rbbg, sppt;
642        XVec4<T,0x0222> const xzzz, rbbb, sppp;
643        XVec4<T,0x0223> const xzzw, rbba, sppq;
644        XVec4<T,0x0230> const xzwx, rbar, spqs;
645        XVec4<T,0x0231> const xzwy, rbag, spqt; /* lvalue */
646        XVec4<T,0x0232> const xzwz, rbab, spqp;
647        XVec4<T,0x0233> const xzww, rbaa, spqq;
648        XVec4<T,0x0300> const xwxx, rarr, sqss;
649        XVec4<T,0x0301> const xwxy, rarg, sqst;
650        XVec4<T,0x0302> const xwxz, rarb, sqsp;
651        XVec4<T,0x0303> const xwxw, rara, sqsq;
652        XVec4<T,0x0310> const xwyx, ragr, sqts;
653        XVec4<T,0x0311> const xwyy, ragg, sqtt;
654        XVec4<T,0x0312> const xwyz, ragb, sqtp; /* lvalue */
655        XVec4<T,0x0313> const xwyw, raga, sqtq;
656        XVec4<T,0x0320> const xwzx, rabr, sqps;
657        XVec4<T,0x0321> const xwzy, rabg, sqpt; /* lvalue */
658        XVec4<T,0x0322> const xwzz, rabb, sqpp;
659        XVec4<T,0x0323> const xwzw, raba, sqpq;
660        XVec4<T,0x0330> const xwwx, raar, sqqs;
661        XVec4<T,0x0331> const xwwy, raag, sqqt;
662        XVec4<T,0x0332> const xwwz, raab, sqqp;
663        XVec4<T,0x0333> const xwww, raaa, sqqq;
664        XVec4<T,0x1000> const yxxx, grrr, tsss;
665        XVec4<T,0x1001> const yxxy, grrg, tsst;
666        XVec4<T,0x1002> const yxxz, grrb, tssp;
667        XVec4<T,0x1003> const yxxw, grra, tssq;
668        XVec4<T,0x1010> const yxyx, grgr, tsts;
669        XVec4<T,0x1011> const yxyy, grgg, tstt;
670        XVec4<T,0x1012> const yxyz, grgb, tstp;
671        XVec4<T,0x1013> const yxyw, grga, tstq;
672        XVec4<T,0x1020> const yxzx, grbr, tsps;
673        XVec4<T,0x1021> const yxzy, grbg, tspt;
674        XVec4<T,0x1022> const yxzz, grbb, tspp;
675        XVec4<T,0x1023> const yxzw, grba, tspq; /* lvalue */
676        XVec4<T,0x1030> const yxwx, grar, tsqs;
677        XVec4<T,0x1031> const yxwy, grag, tsqt;
678        XVec4<T,0x1032> const yxwz, grab, tsqp; /* lvalue */
679        XVec4<T,0x1033> const yxww, graa, tsqq;
680        XVec4<T,0x1100> const yyxx, ggrr, ttss;
681        XVec4<T,0x1101> const yyxy, ggrg, ttst;
682        XVec4<T,0x1102> const yyxz, ggrb, ttsp;
683        XVec4<T,0x1103> const yyxw, ggra, ttsq;
684        XVec4<T,0x1110> const yyyx, gggr, ttts;
685        XVec4<T,0x1111> const yyyy, gggg, tttt;
686        XVec4<T,0x1112> const yyyz, gggb, tttp;
687        XVec4<T,0x1113> const yyyw, ggga, tttq;
688        XVec4<T,0x1120> const yyzx, ggbr, ttps;
689        XVec4<T,0x1121> const yyzy, ggbg, ttpt;
690        XVec4<T,0x1122> const yyzz, ggbb, ttpp;
691        XVec4<T,0x1123> const yyzw, ggba, ttpq;
692        XVec4<T,0x1130> const yywx, ggar, ttqs;
693        XVec4<T,0x1131> const yywy, ggag, ttqt;
694        XVec4<T,0x1132> const yywz, ggab, ttqp;
695        XVec4<T,0x1133> const yyww, ggaa, ttqq;
696        XVec4<T,0x1200> const yzxx, gbrr, tpss;
697        XVec4<T,0x1201> const yzxy, gbrg, tpst;
698        XVec4<T,0x1202> const yzxz, gbrb, tpsp;
699        XVec4<T,0x1203> const yzxw, gbra, tpsq; /* lvalue */
700        XVec4<T,0x1210> const yzyx, gbgr, tpts;
701        XVec4<T,0x1211> const yzyy, gbgg, tptt;
702        XVec4<T,0x1212> const yzyz, gbgb, tptp;
703        XVec4<T,0x1213> const yzyw, gbga, tptq;
704        XVec4<T,0x1220> const yzzx, gbbr, tpps;
705        XVec4<T,0x1221> const yzzy, gbbg, tppt;
706        XVec4<T,0x1222> const yzzz, gbbb, tppp;
707        XVec4<T,0x1223> const yzzw, gbba, tppq;
708        XVec4<T,0x1230> const yzwx, gbar, tpqs; /* lvalue */
709        XVec4<T,0x1231> const yzwy, gbag, tpqt;
710        XVec4<T,0x1232> const yzwz, gbab, tpqp;
711        XVec4<T,0x1233> const yzww, gbaa, tpqq;
712        XVec4<T,0x1300> const ywxx, garr, tqss;
713        XVec4<T,0x1301> const ywxy, garg, tqst;
714        XVec4<T,0x1302> const ywxz, garb, tqsp; /* lvalue */
715        XVec4<T,0x1303> const ywxw, gara, tqsq;
716        XVec4<T,0x1310> const ywyx, gagr, tqts;
717        XVec4<T,0x1311> const ywyy, gagg, tqtt;
718        XVec4<T,0x1312> const ywyz, gagb, tqtp;
719        XVec4<T,0x1313> const ywyw, gaga, tqtq;
720        XVec4<T,0x1320> const ywzx, gabr, tqps; /* lvalue */
721        XVec4<T,0x1321> const ywzy, gabg, tqpt;
722        XVec4<T,0x1322> const ywzz, gabb, tqpp;
723        XVec4<T,0x1323> const ywzw, gaba, tqpq;
724        XVec4<T,0x1330> const ywwx, gaar, tqqs;
725        XVec4<T,0x1331> const ywwy, gaag, tqqt;
726        XVec4<T,0x1332> const ywwz, gaab, tqqp;
727        XVec4<T,0x1333> const ywww, gaaa, tqqq;
728        XVec4<T,0x2000> const zxxx, brrr, psss;
729        XVec4<T,0x2001> const zxxy, brrg, psst;
730        XVec4<T,0x2002> const zxxz, brrb, pssp;
731        XVec4<T,0x2003> const zxxw, brra, pssq;
732        XVec4<T,0x2010> const zxyx, brgr, psts;
733        XVec4<T,0x2011> const zxyy, brgg, pstt;
734        XVec4<T,0x2012> const zxyz, brgb, pstp;
735        XVec4<T,0x2013> const zxyw, brga, pstq; /* lvalue */
736        XVec4<T,0x2020> const zxzx, brbr, psps;
737        XVec4<T,0x2021> const zxzy, brbg, pspt;
738        XVec4<T,0x2022> const zxzz, brbb, pspp;
739        XVec4<T,0x2023> const zxzw, brba, pspq;
740        XVec4<T,0x2030> const zxwx, brar, psqs;
741        XVec4<T,0x2031> const zxwy, brag, psqt; /* lvalue */
742        XVec4<T,0x2032> const zxwz, brab, psqp;
743        XVec4<T,0x2033> const zxww, braa, psqq;
744        XVec4<T,0x2100> const zyxx, bgrr, ptss;
745        XVec4<T,0x2101> const zyxy, bgrg, ptst;
746        XVec4<T,0x2102> const zyxz, bgrb, ptsp;
747        XVec4<T,0x2103> const zyxw, bgra, ptsq; /* lvalue */
748        XVec4<T,0x2110> const zyyx, bggr, ptts;
749        XVec4<T,0x2111> const zyyy, bggg, pttt;
750        XVec4<T,0x2112> const zyyz, bggb, pttp;
751        XVec4<T,0x2113> const zyyw, bgga, pttq;
752        XVec4<T,0x2120> const zyzx, bgbr, ptps;
753        XVec4<T,0x2121> const zyzy, bgbg, ptpt;
754        XVec4<T,0x2122> const zyzz, bgbb, ptpp;
755        XVec4<T,0x2123> const zyzw, bgba, ptpq;
756        XVec4<T,0x2130> const zywx, bgar, ptqs; /* lvalue */
757        XVec4<T,0x2131> const zywy, bgag, ptqt;
758        XVec4<T,0x2132> const zywz, bgab, ptqp;
759        XVec4<T,0x2133> const zyww, bgaa, ptqq;
760        XVec4<T,0x2200> const zzxx, bbrr, ppss;
761        XVec4<T,0x2201> const zzxy, bbrg, ppst;
762        XVec4<T,0x2202> const zzxz, bbrb, ppsp;
763        XVec4<T,0x2203> const zzxw, bbra, ppsq;
764        XVec4<T,0x2210> const zzyx, bbgr, ppts;
765        XVec4<T,0x2211> const zzyy, bbgg, pptt;
766        XVec4<T,0x2212> const zzyz, bbgb, pptp;
767        XVec4<T,0x2213> const zzyw, bbga, pptq;
768        XVec4<T,0x2220> const zzzx, bbbr, ppps;
769        XVec4<T,0x2221> const zzzy, bbbg, pppt;
770        XVec4<T,0x2222> const zzzz, bbbb, pppp;
771        XVec4<T,0x2223> const zzzw, bbba, pppq;
772        XVec4<T,0x2230> const zzwx, bbar, ppqs;
773        XVec4<T,0x2231> const zzwy, bbag, ppqt;
774        XVec4<T,0x2232> const zzwz, bbab, ppqp;
775        XVec4<T,0x2233> const zzww, bbaa, ppqq;
776        XVec4<T,0x2300> const zwxx, barr, pqss;
777        XVec4<T,0x2301> const zwxy, barg, pqst; /* lvalue */
778        XVec4<T,0x2302> const zwxz, barb, pqsp;
779        XVec4<T,0x2303> const zwxw, bara, pqsq;
780        XVec4<T,0x2310> const zwyx, bagr, pqts; /* lvalue */
781        XVec4<T,0x2311> const zwyy, bagg, pqtt;
782        XVec4<T,0x2312> const zwyz, bagb, pqtp;
783        XVec4<T,0x2313> const zwyw, baga, pqtq;
784        XVec4<T,0x2320> const zwzx, babr, pqps;
785        XVec4<T,0x2321> const zwzy, babg, pqpt;
786        XVec4<T,0x2322> const zwzz, babb, pqpp;
787        XVec4<T,0x2323> const zwzw, baba, pqpq;
788        XVec4<T,0x2330> const zwwx, baar, pqqs;
789        XVec4<T,0x2331> const zwwy, baag, pqqt;
790        XVec4<T,0x2332> const zwwz, baab, pqqp;
791        XVec4<T,0x2333> const zwww, baaa, pqqq;
792        XVec4<T,0x3000> const wxxx, arrr, qsss;
793        XVec4<T,0x3001> const wxxy, arrg, qsst;
794        XVec4<T,0x3002> const wxxz, arrb, qssp;
795        XVec4<T,0x3003> const wxxw, arra, qssq;
796        XVec4<T,0x3010> const wxyx, argr, qsts;
797        XVec4<T,0x3011> const wxyy, argg, qstt;
798        XVec4<T,0x3012> const wxyz, argb, qstp; /* lvalue */
799        XVec4<T,0x3013> const wxyw, arga, qstq;
800        XVec4<T,0x3020> const wxzx, arbr, qsps;
801        XVec4<T,0x3021> const wxzy, arbg, qspt; /* lvalue */
802        XVec4<T,0x3022> const wxzz, arbb, qspp;
803        XVec4<T,0x3023> const wxzw, arba, qspq;
804        XVec4<T,0x3030> const wxwx, arar, qsqs;
805        XVec4<T,0x3031> const wxwy, arag, qsqt;
806        XVec4<T,0x3032> const wxwz, arab, qsqp;
807        XVec4<T,0x3033> const wxww, araa, qsqq;
808        XVec4<T,0x3100> const wyxx, agrr, qtss;
809        XVec4<T,0x3101> const wyxy, agrg, qtst;
810        XVec4<T,0x3102> const wyxz, agrb, qtsp; /* lvalue */
811        XVec4<T,0x3103> const wyxw, agra, qtsq;
812        XVec4<T,0x3110> const wyyx, aggr, qtts;
813        XVec4<T,0x3111> const wyyy, aggg, qttt;
814        XVec4<T,0x3112> const wyyz, aggb, qttp;
815        XVec4<T,0x3113> const wyyw, agga, qttq;
816        XVec4<T,0x3120> const wyzx, agbr, qtps; /* lvalue */
817        XVec4<T,0x3121> const wyzy, agbg, qtpt;
818        XVec4<T,0x3122> const wyzz, agbb, qtpp;
819        XVec4<T,0x3123> const wyzw, agba, qtpq;
820        XVec4<T,0x3130> const wywx, agar, qtqs;
821        XVec4<T,0x3131> const wywy, agag, qtqt;
822        XVec4<T,0x3132> const wywz, agab, qtqp;
823        XVec4<T,0x3133> const wyww, agaa, qtqq;
824        XVec4<T,0x3200> const wzxx, abrr, qpss;
825        XVec4<T,0x3201> const wzxy, abrg, qpst; /* lvalue */
826        XVec4<T,0x3202> const wzxz, abrb, qpsp;
827        XVec4<T,0x3203> const wzxw, abra, qpsq;
828        XVec4<T,0x3210> const wzyx, abgr, qpts; /* lvalue */
829        XVec4<T,0x3211> const wzyy, abgg, qptt;
830        XVec4<T,0x3212> const wzyz, abgb, qptp;
831        XVec4<T,0x3213> const wzyw, abga, qptq;
832        XVec4<T,0x3220> const wzzx, abbr, qpps;
833        XVec4<T,0x3221> const wzzy, abbg, qppt;
834        XVec4<T,0x3222> const wzzz, abbb, qppp;
835        XVec4<T,0x3223> const wzzw, abba, qppq;
836        XVec4<T,0x3230> const wzwx, abar, qpqs;
837        XVec4<T,0x3231> const wzwy, abag, qpqt;
838        XVec4<T,0x3232> const wzwz, abab, qpqp;
839        XVec4<T,0x3233> const wzww, abaa, qpqq;
840        XVec4<T,0x3300> const wwxx, aarr, qqss;
841        XVec4<T,0x3301> const wwxy, aarg, qqst;
842        XVec4<T,0x3302> const wwxz, aarb, qqsp;
843        XVec4<T,0x3303> const wwxw, aara, qqsq;
844        XVec4<T,0x3310> const wwyx, aagr, qqts;
845        XVec4<T,0x3311> const wwyy, aagg, qqtt;
846        XVec4<T,0x3312> const wwyz, aagb, qqtp;
847        XVec4<T,0x3313> const wwyw, aaga, qqtq;
848        XVec4<T,0x3320> const wwzx, aabr, qqps;
849        XVec4<T,0x3321> const wwzy, aabg, qqpt;
850        XVec4<T,0x3322> const wwzz, aabb, qqpp;
851        XVec4<T,0x3323> const wwzw, aaba, qqpq;
852        XVec4<T,0x3330> const wwwx, aaar, qqqs;
853        XVec4<T,0x3331> const wwwy, aaag, qqqt;
854        XVec4<T,0x3332> const wwwz, aaab, qqqp;
855        XVec4<T,0x3333> const wwww, aaaa, qqqq;
856#if LOL_NO_CONST_MEMBERS_IN_ANONYMOUS_UNIONS
857#   undef const
858#endif
859    };
860};
861
862template <> struct BVec4<half>
863{
864    explicit inline BVec4() {}
865    explicit inline BVec4(half X, half Y, half Z, half W)
866     : x(X), y(Y), z(Z), w(W) {}
867
868    half x, y, z, w;
869};
870
871template <> struct BVec4<real>
872{
873    explicit inline BVec4() {}
874    explicit inline BVec4(real X, real Y, real Z, real W)
875     : x(X), y(Y), z(Z), w(W) {}
876
877    real x, y, z, w;
878};
879
880template <typename T> struct Vec4 : BVec4<T>
881{
882    inline Vec4() {}
883    inline Vec4(T X, T Y, T Z, T W) : BVec4<T>(X, Y, Z, W) {}
884    inline Vec4(Vec2<T> XY, T Z, T W) : BVec4<T>(XY.x, XY.y, Z, W) {}
885    inline Vec4(T X, Vec2<T> YZ, T W) : BVec4<T>(X, YZ.x, YZ.y, W) {}
886    inline Vec4(T X, T Y, Vec2<T> ZW) : BVec4<T>(X, Y, ZW.x, ZW.y) {}
887    inline Vec4(Vec2<T> XY, Vec2<T> ZW) : BVec4<T>(XY.x, XY.y, ZW.x, ZW.y) {}
888    inline Vec4(Vec3<T> XYZ, T W) : BVec4<T>(XYZ.x, XYZ.y, XYZ.z, W) {}
889    inline Vec4(T X, Vec3<T> YZW) : BVec4<T>(X, YZW.x, YZW.y, YZW.z) {}
890
891    explicit inline Vec4(T X) : BVec4<T>(X, X, X, X) {}
892
893    template<int N>
894    inline Vec4(XVec4<T, N> const &v)
895      : BVec4<T>(v[0], v[1], v[2], v[3]) {}
896
897    template<typename U, int N>
898    explicit inline Vec4(XVec4<U, N> const &v)
899      : BVec4<T>(v[0], v[1], v[2], v[3]) {}
900
901    DECLARE_MEMBER_OPS(Vec4)
902
903#if !defined __ANDROID__
904    template<typename U>
905    friend std::ostream &operator<<(std::ostream &stream, Vec4<U> const &v);
906#endif
907};
908
909/*
910 * 4-element quaternions
911 */
912
913template <typename T> struct Quat
914{
915    inline Quat() {}
916    inline Quat(T W) : x(0), y(0), z(0), w(W) {}
917    inline Quat(T W, T X, T Y, T Z) : x(X), y(Y), z(Z), w(W) {}
918
919    Quat(Mat3<T> const &m);
920    Quat(Mat4<T> const &m);
921
922    DECLARE_MEMBER_OPS(Quat)
923
924    static Quat<T> rotate(T angle, T x, T y, T z);
925    static Quat<T> rotate(T angle, Vec3<T> const &v);
926    static Quat<T> fromeuler(T x, T y, T z);
927    static Quat<T> fromeuler(Vec3<T> const &v);
928
929    inline Quat<T> operator *(Quat<T> const &val) const
930    {
931        Quat<T> ret;
932        Vec3<T> v1(x, y, z);
933        Vec3<T> v2(val.x, val.y, val.z);
934        Vec3<T> v3 = cross(v1, v2) + w * v2 + val.w * v1;
935        return Quat<T>(w * val.w - dot(v1, v2), v3.x, v3.y, v3.z);
936    }
937
938    inline Quat<T> operator *=(Quat<T> const &val)
939    {
940        return *this = (*this) * val;
941    }
942
943    inline Quat<T> operator ~() const
944    {
945        return Quat<T>(w, -x, -y, -z);
946    }
947
948#if !defined __ANDROID__
949    template<typename U>
950    friend std::ostream &operator<<(std::ostream &stream, Quat<U> const &v);
951#endif
952
953    /* Storage order is still xyzw because operator[] uses &this->x */
954    T x, y, z, w;
955};
956
957template<typename T>
958inline T norm(Quat<T> const &val)
959{
960    return sqlen(val);
961}
962
963template<typename T>
964static inline Quat<T> re(Quat<T> const &val)
965{
966    return ~val / norm(val);
967}
968
969template<typename T>
970static inline Quat<T> operator /(T x, Quat<T> const &y)
971{
972    return x * re(y);
973}
974
975template<typename T>
976static inline Quat<T> operator /(Quat<T> x, Quat<T> const &y)
977{
978    return x * re(y);
979}
980
981/*
982 * Common operators for all vector types, including quaternions
983 */
984
985/*
986 * vec +(vec, vec)   (also complex & quaternion)
987 * vec -(vec, vec)   (also complex & quaternion)
988 * vec *(vec, vec)
989 * vec /(vec, vec)
990 */
991#define DECLARE_VECTOR_VECTOR_COERCE_OP(tname, op, tprefix, t1, t2, tf) \
992    tprefix \
993    inline tname<tf> operator op(tname<t1> const &a, tname<t2> const &b) \
994    { \
995        tname<tf> ret; \
996        for (size_t n = 0; n < sizeof(a) / sizeof(t1); n++) \
997            ret[n] = a[n] op b[n]; \
998        return ret; \
999    }
1000
1001/*
1002 * vec +=(vec, vec)   (also complex & quaternion)
1003 * vec -=(vec, vec)   (also complex & quaternion)
1004 * vec *=(vec, vec)
1005 * vec /=(vec, vec)
1006 */
1007#define DECLARE_VECTOR_VECTOR_OP(tname, op, tprefix, type) \
1008    tprefix \
1009    inline tname<type> operator op##=(tname<type> &a, tname<type> const &b) \
1010    { \
1011        return a = a op b; \
1012    }
1013
1014/*
1015 * vec min(vec, vec)     (also max)
1016 * vec min(vec, scalar)  (also max)
1017 * vec min(scalar, vec)  (also max)
1018 */
1019#define DECLARE_VECTOR_MINMAX_OP(tname, op, tprefix, type) \
1020    tprefix \
1021    inline tname<type> op(tname<type> const &a, tname<type> const &b) \
1022    { \
1023        using std::op; \
1024        tname<type> ret; \
1025        for (size_t n = 0; n < sizeof(a) / sizeof(type); n++) \
1026            ret[n] = op(a[n], b[n]); \
1027        return ret; \
1028    } \
1029    \
1030    tprefix \
1031    inline tname<type> op(tname<type> const &a, type const &b) \
1032    { \
1033        using std::op; \
1034        tname<type> ret; \
1035        for (size_t n = 0; n < sizeof(a) / sizeof(type); n++) \
1036            ret[n] = op(a[n], b); \
1037        return ret; \
1038    } \
1039    \
1040    tprefix \
1041    inline tname<type> op(type const &a, tname<type> const &b) \
1042    { \
1043        using std::op; \
1044        tname<type> ret; \
1045        for (size_t n = 0; n < sizeof(b) / sizeof(type); n++) \
1046            ret[n] = op(a, b[n]); \
1047        return ret; \
1048    }
1049
1050/*
1051 * vec clamp(vec, vec, vec)
1052 * vec clamp(vec, vec, scalar)
1053 * vec clamp(vec, scalar, vec)
1054 */
1055#define DECLARE_VECTOR_CLAMP_OP(tname, tprefix, type) \
1056    tprefix \
1057    inline tname<type> clamp(tname<type> const &x, \
1058                             tname<type> const &a, tname<type> const &b) \
1059    { \
1060        return max(min(x, b), a); \
1061    } \
1062    \
1063    tprefix \
1064    inline tname<type> clamp(tname<type> const &x, \
1065                             type const &a, tname<type> const &b) \
1066    { \
1067        return max(min(x, b), a); \
1068    } \
1069    \
1070    tprefix \
1071    inline tname<type> clamp(tname<type> const &x, \
1072                             tname<type> const &a, type const &b) \
1073    { \
1074        return max(min(x, b), a); \
1075    }
1076
1077/*
1078 * bool ==(vec, vec)   (also complex & quaternion)
1079 * bool !=(vec, vec)   (also complex & quaternion)
1080 * bool >=(vec, vec)
1081 * bool <=(vec, vec)
1082 * bool >(vec, vec)
1083 * bool <(vec, vec)
1084 */
1085#define DECLARE_VECTOR_VECTOR_BOOLOP(tname, op, op2, ret, tprefix, t1, t2) \
1086    tprefix \
1087    inline bool operator op(tname<t1> const &a, tname<t2> const &b) \
1088    { \
1089        for (size_t n = 0; n < sizeof(a) / sizeof(t1); n++) \
1090            if (!(a[n] op2 b[n])) \
1091                return !ret; \
1092        return ret; \
1093    }
1094
1095/*
1096 * vec *(vec, scalar)   (also complex & quaternion)
1097 * vec *(scalar, vec)   (also complex & quaternion)
1098 * vec /(vec, scalar)   (also complex & quaternion)
1099 * vec /(scalar, vec)   (also complex & quaternion)
1100 */
1101#define DECLARE_VECTOR_SCALAR_COERCE_OP(tname, op, tprefix, t1, t2, tf) \
1102    tprefix \
1103    inline tname<tf> operator op(tname<t1> const &a, t2 const &val) \
1104    { \
1105        tname<tf> ret; \
1106        for (size_t n = 0; n < sizeof(a) / sizeof(t1); n++) \
1107            ret[n] = a[n] op val; \
1108        return ret; \
1109    } \
1110    \
1111    tprefix \
1112    inline tname<tf> operator op(t1 const &val, tname<t2> const &a) \
1113    { \
1114        tname<tf> ret; \
1115        for (size_t n = 0; n < sizeof(a) / sizeof(t2); n++) \
1116            ret[n] = a[n] op val; \
1117        return ret; \
1118    }
1119
1120/*
1121 * vec *=(vec, scalar)   (also complex & quaternion)
1122 * vec /=(vec, scalar)   (also complex & quaternion)
1123 */
1124#define DECLARE_VECTOR_SCALAR_OP(tname, op, tprefix, type) \
1125    tprefix \
1126    inline tname<type> operator op##=(tname<type> &a, type const &val) \
1127    { \
1128        return a = a op val; \
1129    }
1130
1131#define DECLARE_UNARY_OPS(tname, tprefix, type) \
1132    tprefix \
1133    inline tname<type> operator -(tname<type> const &a) \
1134    { \
1135        tname<type> ret; \
1136        for (size_t n = 0; n < sizeof(a) / sizeof(type); n++) \
1137            ret[n] = -a[n]; \
1138        return ret; \
1139    } \
1140    \
1141    tprefix \
1142    inline type sqlen(tname<type> const &a) \
1143    { \
1144        type acc = 0; \
1145        for (size_t n = 0; n < sizeof(a) / sizeof(type); n++) \
1146            acc += a[n] * a[n]; \
1147        return acc; \
1148    } \
1149    \
1150    tprefix \
1151    inline double len(tname<type> const &a) \
1152    { \
1153        using std::sqrt; \
1154        return sqrt((double)sqlen(a)); \
1155    } \
1156    \
1157    tprefix \
1158    inline tname<type> normalize(tname<type> const &val) \
1159    { \
1160        type norm = (type)len(val); \
1161        return norm ? val / norm : val * (type)0; \
1162    }
1163
1164#define DECLARE_BINARY_COERCE_OPS(tname, tprefix, t1, t2, tf) \
1165    DECLARE_VECTOR_SCALAR_COERCE_OP(tname, *, tprefix, t1, t2, tf) \
1166    DECLARE_VECTOR_SCALAR_COERCE_OP(tname, /, tprefix, t1, t2, tf) \
1167    \
1168    DECLARE_VECTOR_VECTOR_COERCE_OP(tname, -, tprefix, t1, t2, tf) \
1169    DECLARE_VECTOR_VECTOR_COERCE_OP(tname, +, tprefix, t1, t2, tf) \
1170    \
1171    DECLARE_VECTOR_VECTOR_BOOLOP(tname, ==, ==, true, tprefix, t1, t2) \
1172    DECLARE_VECTOR_VECTOR_BOOLOP(tname, !=, ==, false, tprefix, t1, t2) \
1173    \
1174    tprefix \
1175    inline tf dot(tname<t1> const &a, tname<t2> const &b) \
1176    { \
1177        tf ret = 0; \
1178        for (size_t n = 0; n < sizeof(a) / sizeof(t1); n++) \
1179            ret += a[n] * b[n]; \
1180        return ret; \
1181    }
1182
1183#define DECLARE_VEC_3_COERCE_OPS(tname, tprefix, t1, t2, tf) \
1184    tprefix \
1185    inline tname<tf> cross(tname<t1> const &a, tname<t2> const &b) \
1186    { \
1187        return tname<tf>((tf)(a.y * b.z) - (tf)(a.z * b.y), \
1188                         (tf)(a.z * b.x) - (tf)(a.x * b.z), \
1189                         (tf)(a.x * b.y) - (tf)(a.y * b.x)); \
1190    }
1191
1192#define DECLARE_BINARY_OPS(tname, tprefix, type) \
1193    DECLARE_BINARY_COERCE_OPS(tname, tprefix, type, type, type) \
1194    \
1195    DECLARE_VECTOR_SCALAR_OP(tname, *, tprefix, type) \
1196    DECLARE_VECTOR_SCALAR_OP(tname, /, tprefix, type) \
1197    \
1198    DECLARE_VECTOR_VECTOR_OP(tname, -, tprefix, type) \
1199    DECLARE_VECTOR_VECTOR_OP(tname, +, tprefix, type) \
1200    \
1201    DECLARE_VECTOR_MINMAX_OP(tname, min, tprefix, type) \
1202    DECLARE_VECTOR_MINMAX_OP(tname, max, tprefix, type) \
1203    DECLARE_VECTOR_CLAMP_OP(tname, tprefix, type)
1204
1205#define DECLARE_VECTOR_COERCE_OPS(tname, tprefix, t1, t2, tf) \
1206    DECLARE_VECTOR_VECTOR_COERCE_OP(tname, *, tprefix, t1, t2, tf) \
1207    DECLARE_VECTOR_VECTOR_COERCE_OP(tname, /, tprefix, t1, t2, tf) \
1208    \
1209    DECLARE_VECTOR_VECTOR_BOOLOP(tname, <=, <=, true, tprefix, t1, t2) \
1210    DECLARE_VECTOR_VECTOR_BOOLOP(tname, >=, >=, true, tprefix, t1, t2) \
1211    DECLARE_VECTOR_VECTOR_BOOLOP(tname, <, <, true, tprefix, t1, t2) \
1212    DECLARE_VECTOR_VECTOR_BOOLOP(tname, >, >, true, tprefix, t1, t2)
1213
1214#define DECLARE_VECTOR_OPS(tname, tprefix, type) \
1215    DECLARE_VECTOR_COERCE_OPS(tname, static, type, type, type) \
1216    \
1217    DECLARE_VECTOR_VECTOR_OP(tname, *, tprefix, type) \
1218    DECLARE_VECTOR_VECTOR_OP(tname, /, tprefix, type)
1219
1220#define DECLARE_ALL_NONVECTOR_OPS(tname) \
1221    DECLARE_BINARY_OPS(tname, template<typename T> static, T) \
1222    DECLARE_UNARY_OPS(tname, template<typename T> static, T)
1223
1224#define DECLARE_ALL_VECTOR_OPS_INNER(tname, type) \
1225    DECLARE_BINARY_OPS(tname, static, type) \
1226    DECLARE_UNARY_OPS(tname, static, type) \
1227    DECLARE_VECTOR_OPS(tname, static, type) \
1228
1229#define DECLARE_ALL_VECTOR_OPS(type) \
1230    DECLARE_ALL_VECTOR_OPS_INNER(Vec2, type) \
1231    DECLARE_ALL_VECTOR_OPS_INNER(Vec3, type) \
1232    DECLARE_ALL_VECTOR_OPS_INNER(Vec4, type) \
1233    \
1234    DECLARE_VEC_3_COERCE_OPS(Vec3, static, type, type, type)
1235
1236#define DECLARE_VEC_ANY_COERCE_OPS(tname, tlow, thigh) \
1237    DECLARE_BINARY_COERCE_OPS(tname, static, tlow, thigh, thigh) \
1238    DECLARE_BINARY_COERCE_OPS(tname, static, thigh, tlow, thigh) \
1239    \
1240    DECLARE_VECTOR_COERCE_OPS(tname, static, tlow, thigh, thigh) \
1241    DECLARE_VECTOR_COERCE_OPS(tname, static, thigh, tlow, thigh)
1242
1243#define DECLARE_ALL_VECTOR_COERCE_OPS(tlow, thigh) \
1244    DECLARE_VEC_ANY_COERCE_OPS(Vec2, tlow, thigh) \
1245    DECLARE_VEC_ANY_COERCE_OPS(Vec3, tlow, thigh) \
1246    DECLARE_VEC_ANY_COERCE_OPS(Vec4, tlow, thigh) \
1247    \
1248    DECLARE_VEC_3_COERCE_OPS(Vec3, static, tlow, thigh, thigh) \
1249    DECLARE_VEC_3_COERCE_OPS(Vec3, static, thigh, tlow, thigh)
1250
1251DECLARE_ALL_NONVECTOR_OPS(Cmplx)
1252DECLARE_ALL_NONVECTOR_OPS(Quat)
1253
1254/* Disable warning about unary operator applied to unsigned type */
1255#if defined _MSC_VER
1256#   pragma warning(push)
1257#   pragma warning(disable: 4146)
1258#endif
1259
1260DECLARE_ALL_VECTOR_OPS(half)
1261DECLARE_ALL_VECTOR_OPS(float)
1262DECLARE_ALL_VECTOR_OPS(double)
1263DECLARE_ALL_VECTOR_OPS(int8_t)
1264DECLARE_ALL_VECTOR_OPS(uint8_t)
1265DECLARE_ALL_VECTOR_OPS(int16_t)
1266DECLARE_ALL_VECTOR_OPS(uint16_t)
1267DECLARE_ALL_VECTOR_OPS(int32_t)
1268DECLARE_ALL_VECTOR_OPS(uint32_t)
1269DECLARE_ALL_VECTOR_OPS(int64_t)
1270DECLARE_ALL_VECTOR_OPS(uint64_t)
1271
1272#if defined _MSC_VER
1273#   pragma warning(pop)
1274#endif
1275
1276/* Disable warnings in the >= > etc. operators about comparing signed and
1277 * unsigned. Ideally we would like to get these warnings only when the
1278 * inlined operators are actually used, but they seem to be triggered at
1279 * the code parsing step, so the compiler does not yet know whether they
1280 * will be used.
1281 * Also we do this for the whole block of declarations, because GCC prior
1282 * to 4.6.3 does not appear to support _Pragma() inside a macro. */
1283#if defined __GNUC__ && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
1284#   pragma GCC diagnostic push
1285#   pragma GCC diagnostic ignored "-Wsign-compare"
1286#elif defined _MSC_VER
1287#   pragma warning(push)
1288#   pragma warning(disable: 4018)
1289#endif
1290
1291/* Apply the same coercion rules as in the C++ standard. However, instead
1292 * of always promoting smaller types to int, we allow int8_t op int16_t to
1293 * return an int16_t. */
1294DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, uint8_t)
1295DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, int16_t)
1296DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, uint16_t)
1297DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, int32_t)
1298DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, uint32_t)
1299DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, int64_t)
1300DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, uint64_t)
1301DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, float)
1302DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, double)
1303DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, long double)
1304
1305DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, int16_t)
1306DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, uint16_t)
1307DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, int32_t)
1308DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, uint32_t)
1309DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, int64_t)
1310DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, uint64_t)
1311DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, float)
1312DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, double)
1313DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, long double)
1314
1315DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, uint16_t)
1316DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, int32_t)
1317DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, uint32_t)
1318DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, int64_t)
1319DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, uint64_t)
1320DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, float)
1321DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, double)
1322DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, long double)
1323
1324DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, int32_t)
1325DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, uint32_t)
1326DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, int64_t)
1327DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, uint64_t)
1328DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, float)
1329DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, double)
1330DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, long double)
1331
1332DECLARE_ALL_VECTOR_COERCE_OPS(int32_t, uint32_t)
1333DECLARE_ALL_VECTOR_COERCE_OPS(int32_t, int64_t)
1334DECLARE_ALL_VECTOR_COERCE_OPS(int32_t, uint64_t)
1335DECLARE_ALL_VECTOR_COERCE_OPS(int32_t, float)
1336DECLARE_ALL_VECTOR_COERCE_OPS(int32_t, double)
1337DECLARE_ALL_VECTOR_COERCE_OPS(int32_t, long double)
1338
1339DECLARE_ALL_VECTOR_COERCE_OPS(uint32_t, int64_t)
1340DECLARE_ALL_VECTOR_COERCE_OPS(uint32_t, uint64_t)
1341DECLARE_ALL_VECTOR_COERCE_OPS(uint32_t, float)
1342DECLARE_ALL_VECTOR_COERCE_OPS(uint32_t, double)
1343DECLARE_ALL_VECTOR_COERCE_OPS(uint32_t, long double)
1344
1345DECLARE_ALL_VECTOR_COERCE_OPS(int64_t, uint64_t)
1346DECLARE_ALL_VECTOR_COERCE_OPS(int64_t, float)
1347DECLARE_ALL_VECTOR_COERCE_OPS(int64_t, double)
1348DECLARE_ALL_VECTOR_COERCE_OPS(int64_t, long double)
1349
1350DECLARE_ALL_VECTOR_COERCE_OPS(uint64_t, float)
1351DECLARE_ALL_VECTOR_COERCE_OPS(uint64_t, double)
1352DECLARE_ALL_VECTOR_COERCE_OPS(uint64_t, long double)
1353
1354DECLARE_ALL_VECTOR_COERCE_OPS(float, double)
1355DECLARE_ALL_VECTOR_COERCE_OPS(float, long double)
1356
1357DECLARE_ALL_VECTOR_COERCE_OPS(double, long double)
1358
1359/* FIXME: vectors of "half" are deactivated for now, because they
1360 * induce extremely long compilation times (about 17 seconds per TU). */
1361
1362#if 0
1363/* All integer types are promoted to half; all floating point types
1364 * cause half to be promoted. */
1365DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, half)
1366DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, half)
1367DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, half)
1368DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, half)
1369DECLARE_ALL_VECTOR_COERCE_OPS(int32_t, half)
1370DECLARE_ALL_VECTOR_COERCE_OPS(uint32_t, half)
1371DECLARE_ALL_VECTOR_COERCE_OPS(int64_t, half)
1372DECLARE_ALL_VECTOR_COERCE_OPS(uint64_t, half)
1373
1374DECLARE_ALL_VECTOR_COERCE_OPS(half, float)
1375DECLARE_ALL_VECTOR_COERCE_OPS(half, double)
1376DECLARE_ALL_VECTOR_COERCE_OPS(half, long double)
1377#endif
1378
1379/* FIXME: vectors of "real" are deactivated for now, because we do
1380 * not implement all combinations of operators for these types yet. */
1381
1382#if 0
1383/* All types are promoted to real */
1384DECLARE_ALL_VECTOR_COERCE_OPS(int8_t, real)
1385DECLARE_ALL_VECTOR_COERCE_OPS(uint8_t, real)
1386DECLARE_ALL_VECTOR_COERCE_OPS(int16_t, real)
1387DECLARE_ALL_VECTOR_COERCE_OPS(uint16_t, real)
1388DECLARE_ALL_VECTOR_COERCE_OPS(int32_t, real)
1389DECLARE_ALL_VECTOR_COERCE_OPS(uint32_t, real)
1390DECLARE_ALL_VECTOR_COERCE_OPS(int64_t, real)
1391DECLARE_ALL_VECTOR_COERCE_OPS(uint64_t, real)
1392DECLARE_ALL_VECTOR_COERCE_OPS(half, real)
1393DECLARE_ALL_VECTOR_COERCE_OPS(float, real)
1394DECLARE_ALL_VECTOR_COERCE_OPS(double, real)
1395DECLARE_ALL_VECTOR_COERCE_OPS(long double, real)
1396#endif
1397
1398#if defined __GNUC__ && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6))
1399#   pragma GCC diagnostic pop
1400#elif defined _MSC_VER
1401#   pragma warning(pop)
1402#endif
1403
1404#undef DECLARE_VECTOR_TYPEDEFS
1405#undef DECLARE_MEMBER_OPS
1406#undef DECLARE_VECTOR_VECTOR_OP
1407#undef DECLARE_VECTOR_VECTOR_BOOLOP
1408#undef DECLARE_VECTOR_SCALAR_OP
1409#undef DECLARE_BINARY_OPS
1410#undef DECLARE_UNARY_OPS
1411#undef DECLARE_ALL_NONVECTOR_OPS
1412#undef DECLARE_ALL_VECTOR_OPS_INNER
1413#undef DECLARE_ALL_VECTOR_OPS
1414
1415/*
1416 * Magic vector swizzling (part 2/2)
1417 * Unfortunately these assignment operators cannot be used for now, because
1418 * we would also need to override the default copy assignment operator, and
1419 * in C++98 unions cannot contain such objects. This is why all the swizzling
1420 * magic objects are marked 'const' even those that could be lvalues.
1421 */
1422
1423template<typename T, int N>
1424inline Vec2<T> XVec2<T, N>::operator =(Vec2<T> const &that)
1425{
1426    for (int i = 0; i < 2; i++)
1427        *this[i] = that[i];
1428    return *this;
1429}
1430
1431template<typename T, int N>
1432inline Vec3<T> XVec3<T, N>::operator =(Vec3<T> const &that)
1433{
1434    for (int i = 0; i < 3; i++)
1435        *this[i] = that[i];
1436    return *this;
1437}
1438
1439template<typename T, int N>
1440inline Vec4<T> XVec4<T, N>::operator =(Vec4<T> const &that)
1441{
1442    for (int i = 0; i < 4; i++)
1443        *this[i] = that[i];
1444    return *this;
1445}
1446
1447/*
1448 * 2×2-element matrices
1449 */
1450
1451template <typename T> struct Mat2
1452{
1453    inline Mat2() {}
1454    inline Mat2(Vec2<T> V0, Vec2<T> V1)
1455      : v0(V0), v1(V1) {}
1456
1457    explicit inline Mat2(T val)
1458      : v0(val, (T)0),
1459        v1((T)0, val) {}
1460
1461    explicit inline Mat2(Mat4<T> const &mat)
1462      : v0(mat[0].xy),
1463        v1(mat[1].xy) {}
1464
1465    inline Vec2<T>& operator[](size_t n) { return (&v0)[n]; }
1466    inline Vec2<T> const& operator[](size_t n) const { return (&v0)[n]; }
1467
1468    /* Helpers for transformation matrices */
1469    static Mat2<T> rotate(T angle);
1470
1471    static inline Mat2<T> rotate(Mat2<T> mat, T angle)
1472    {
1473        return rotate(angle) * mat;
1474    }
1475
1476    void printf() const;
1477
1478#if !defined __ANDROID__
1479    template<class U>
1480    friend std::ostream &operator<<(std::ostream &stream, Mat2<U> const &m);
1481#endif
1482
1483    inline Mat2<T> operator +(Mat2<T> const m) const
1484    {
1485        return Mat2<T>(v0 + m[0], v1 + m[1]);
1486    }
1487
1488    inline Mat2<T> operator +=(Mat2<T> const m)
1489    {
1490        return *this = *this + m;
1491    }
1492
1493    inline Mat2<T> operator -(Mat2<T> const m) const
1494    {
1495        return Mat2<T>(v0 - m[0], v1 - m[1]);
1496    }
1497
1498    inline Mat2<T> operator -=(Mat2<T> const m)
1499    {
1500        return *this = *this - m;
1501    }
1502
1503    inline Mat2<T> operator *(Mat2<T> const m) const
1504    {
1505        return Mat2<T>(*this * m[0], *this * m[1]);
1506    }
1507
1508    inline Mat2<T> operator *=(Mat2<T> const m)
1509    {
1510        return *this = *this * m;
1511    }
1512
1513    inline Vec2<T> operator *(Vec2<T> const m) const
1514    {
1515        Vec2<T> ret;
1516        for (int j = 0; j < 2; j++)
1517        {
1518            T tmp = 0;
1519            for (int k = 0; k < 2; k++)
1520                tmp += (*this)[k][j] * m[k];
1521            ret[j] = tmp;
1522        }
1523        return ret;
1524    }
1525
1526    Vec2<T> v0, v1;
1527};
1528
1529/*
1530 * 3×3-element matrices
1531 */
1532
1533template <typename T> struct Mat3
1534{
1535    inline Mat3() {}
1536    inline Mat3(Vec3<T> V0, Vec3<T> V1, Vec3<T> V2)
1537      : v0(V0), v1(V1), v2(V2) {}
1538
1539    explicit inline Mat3(T val)
1540      : v0(val, (T)0, (T)0),
1541        v1((T)0, val, (T)0),
1542        v2((T)0, (T)0, val) {}
1543
1544    explicit inline Mat3(Mat2<T> mat)
1545      : v0(mat[0], (T)0),
1546        v1(mat[1], (T)0),
1547        v2((T)0, (T)0, (T)0) {}
1548
1549    explicit inline Mat3(Mat2<T> mat, T val)
1550      : v0(Vec3<T>(mat[0], (T)0)),
1551        v1(Vec3<T>(mat[1], (T)0)),
1552        v2((T)0, (T)0, val) {}
1553
1554    explicit inline Mat3(Mat4<T> const &mat)
1555      : v0(mat[0].xyz),
1556        v1(mat[1].xyz),
1557        v2(mat[2].xyz) {}
1558
1559    inline Vec3<T>& operator[](size_t n) { return (&v0)[n]; }
1560    inline Vec3<T> const& operator[](size_t n) const { return (&v0)[n]; }
1561
1562    /* Helpers for transformation matrices */
1563    static Mat3<T> scale(T x, T y, T z);
1564    static Mat3<T> scale(Vec3<T> v);
1565    static Mat3<T> rotate(T angle, T x, T y, T z);
1566    static Mat3<T> rotate(T angle, Vec3<T> v);
1567    static Mat3<T> rotate(Quat<T> q);
1568
1569    static inline Mat3<T> rotate(Mat3<T> mat, T angle, Vec3<T> v)
1570    {
1571        return rotate(angle, v) * mat;
1572    }
1573
1574    void printf() const;
1575
1576#if !defined __ANDROID__
1577    template<class U>
1578    friend std::ostream &operator<<(std::ostream &stream, Mat3<U> const &m);
1579#endif
1580
1581    inline Mat3<T> operator +(Mat3<T> const m) const
1582    {
1583        return Mat3<T>(v0 + m[0], v1 + m[1], v2 + m[2]);
1584    }
1585
1586    inline Mat3<T> operator +=(Mat3<T> const m)
1587    {
1588        return *this = *this + m;
1589    }
1590
1591    inline Mat3<T> operator -(Mat3<T> const m) const
1592    {
1593        return Mat3<T>(v0 - m[0], v1 - m[1], v2 - m[2]);
1594    }
1595
1596    inline Mat3<T> operator -=(Mat3<T> const m)
1597    {
1598        return *this = *this - m;
1599    }
1600
1601    inline Mat3<T> operator *(Mat3<T> const m) const
1602    {
1603        return Mat3<T>(*this * m[0], *this * m[1], *this * m[2]);
1604    }
1605
1606    inline Mat3<T> operator *=(Mat3<T> const m)
1607    {
1608        return *this = *this * m;
1609    }
1610
1611    inline Vec3<T> operator *(Vec3<T> const m) const
1612    {
1613        Vec3<T> ret;
1614        for (int j = 0; j < 3; j++)
1615        {
1616            T tmp = 0;
1617            for (int k = 0; k < 3; k++)
1618                tmp += (*this)[k][j] * m[k];
1619            ret[j] = tmp;
1620        }
1621        return ret;
1622    }
1623
1624    Vec3<T> v0, v1, v2;
1625};
1626
1627/*
1628 * 4×4-element matrices
1629 */
1630
1631template <typename T> struct Mat4
1632{
1633    inline Mat4() {}
1634    inline Mat4(Vec4<T> V0, Vec4<T> V1, Vec4<T> V2, Vec4<T> V3)
1635      : v0(V0), v1(V1), v2(V2), v3(V3) {}
1636
1637    explicit inline Mat4(T val)
1638      : v0(val, (T)0, (T)0, (T)0),
1639        v1((T)0, val, (T)0, (T)0),
1640        v2((T)0, (T)0, val, (T)0),
1641        v3((T)0, (T)0, (T)0, val) {}
1642
1643    explicit inline Mat4(Mat2<T> mat)
1644      : v0(mat[0], (T)0, (T)0),
1645        v1(mat[1], (T)0, (T)0),
1646        v2((T)0, (T)0, (T)0, (T)0),
1647        v3((T)0, (T)0, (T)0, (T)0) {}
1648
1649    explicit inline Mat4(Mat2<T> mat, T val1, T val2)
1650      : v0(mat[0], (T)0, (T)0),
1651        v1(mat[1], (T)0, (T)0),
1652        v2((T)0, (T)0, val1, (T)0),
1653        v3((T)0, (T)0, (T)0, val2) {}
1654
1655    explicit inline Mat4(Mat3<T> mat)
1656      : v0(mat[0], (T)0),
1657        v1(mat[1], (T)0),
1658        v2(mat[2], (T)0),
1659        v3((T)0, (T)0, (T)0, (T)0) {}
1660
1661    explicit inline Mat4(Mat3<T> mat, T val)
1662      : v0(mat[0], (T)0),
1663        v1(mat[1], (T)0),
1664        v2(mat[2], (T)0),
1665        v3((T)0, (T)0, (T)0, val) {}
1666
1667    inline Vec4<T>& operator[](size_t n) { return (&v0)[n]; }
1668    inline Vec4<T> const& operator[](size_t n) const { return (&v0)[n]; }
1669
1670    /* Helpers for transformation matrices */
1671    static Mat4<T> translate(T x, T y, T z);
1672    static Mat4<T> translate(Vec3<T> v);
1673
1674    static inline Mat4<T> scale(T x, T y, T z)
1675    {
1676        return Mat4<T>(Mat3<T>::scale(x, y, z), (T)1);
1677    }
1678
1679    static inline Mat4<T> scale(Vec3<T> v)
1680    {
1681        return Mat4<T>(Mat3<T>::scale(v), (T)1);
1682    }
1683
1684    static inline Mat4<T> translate(Mat4<T> const &mat, Vec3<T> v)
1685    {
1686        return translate(v) * mat;
1687    }
1688
1689    static inline Mat4<T> rotate(T angle, T x, T y, T z)
1690    {
1691        return Mat4<T>(Mat3<T>::rotate(angle, x, y, z), (T)1);
1692    }
1693
1694    static inline Mat4<T> rotate(T angle, Vec3<T> v)
1695    {
1696        return Mat4<T>(Mat3<T>::rotate(angle, v), (T)1);
1697    }
1698
1699    static inline Mat4<T> rotate(Quat<T> q)
1700    {
1701        return Mat4<T>(Mat3<T>::rotate(q), (T)1);
1702    }
1703
1704    static inline Mat4<T> rotate(Mat4<T> &mat, T angle, Vec3<T> v)
1705    {
1706        return rotate(angle, v) * mat;
1707    }
1708
1709    /* Helpers for view matrices */
1710    static Mat4<T> lookat(Vec3<T> eye, Vec3<T> center, Vec3<T> up);
1711
1712    /* Helpers for projection matrices */
1713    static Mat4<T> ortho(T left, T right, T bottom, T top, T near, T far);
1714    static Mat4<T> frustum(T left, T right, T bottom, T top, T near, T far);
1715    static Mat4<T> perspective(T fov_y, T width, T height, T near, T far);
1716
1717    void printf() const;
1718
1719#if !defined __ANDROID__
1720    template<class U>
1721    friend std::ostream &operator<<(std::ostream &stream, Mat4<U> const &m);
1722#endif
1723
1724    inline Mat4<T> operator +(Mat4<T> const &m) const
1725    {
1726        return Mat4<T>(v0 + m[0], v1 + m[1], v2 + m[2], v3 + m[3]);
1727    }
1728
1729    inline Mat4<T> operator +=(Mat4<T> const &m)
1730    {
1731        return *this = *this + m;
1732    }
1733
1734    inline Mat4<T> operator -(Mat4<T> const &m) const
1735    {
1736        return Mat4<T>(v0 - m[0], v1 - m[1], v2 - m[2], v3 - m[3]);
1737    }
1738
1739    inline Mat4<T> operator -=(Mat4<T> const &m)
1740    {
1741        return *this = *this - m;
1742    }
1743
1744    inline Mat4<T> operator *(Mat4<T> const &m) const
1745    {
1746        return Mat4<T>(*this * m[0], *this * m[1], *this * m[2], *this * m[3]);
1747    }
1748
1749    inline Mat4<T> operator *=(Mat4<T> const &m)
1750    {
1751        return *this = *this * m;
1752    }
1753
1754    inline Vec4<T> operator *(Vec4<T> const &m) const
1755    {
1756        Vec4<T> ret;
1757        for (int j = 0; j < 4; j++)
1758        {
1759            T tmp = 0;
1760            for (int k = 0; k < 4; k++)
1761                tmp += (*this)[k][j] * m[k];
1762            ret[j] = tmp;
1763        }
1764        return ret;
1765    }
1766
1767    Vec4<T> v0, v1, v2, v3;
1768};
1769
1770template<typename T> T determinant(Mat2<T> const &);
1771template<typename T> T determinant(Mat3<T> const &);
1772template<typename T> T determinant(Mat4<T> const &);
1773
1774template<typename T> Mat2<T> transpose(Mat2<T> const &);
1775template<typename T> Mat3<T> transpose(Mat3<T> const &);
1776template<typename T> Mat4<T> transpose(Mat4<T> const &);
1777
1778template<typename T> Mat2<T> inverse(Mat2<T> const &);
1779template<typename T> Mat3<T> inverse(Mat3<T> const &);
1780template<typename T> Mat4<T> inverse(Mat4<T> const &);
1781
1782/*
1783 * Arbitrarily-sized square matrices; for now this only supports
1784 * naive inversion and is used for the Remez inversion method.
1785 */
1786
1787template<int N, typename T> struct Mat
1788{
1789    inline Mat<N, T>() {}
1790
1791    Mat(T x)
1792    {
1793        for (int j = 0; j < N; j++)
1794            for (int i = 0; i < N; i++)
1795                if (i == j)
1796                    m[i][j] = x;
1797                else
1798                    m[i][j] = 0;
1799    }
1800
1801    /* Naive matrix inversion */
1802    Mat<N, T> inv() const
1803    {
1804        Mat a = *this, b((T)1);
1805
1806        /* Inversion method: iterate through all columns and make sure
1807         * all the terms are 1 on the diagonal and 0 everywhere else */
1808        for (int i = 0; i < N; i++)
1809        {
1810            /* If the expected coefficient is zero, add one of
1811             * the other lines. The first we meet will do. */
1812            if (!a.m[i][i])
1813            {
1814                for (int j = i + 1; j < N; j++)
1815                {
1816                    if (!a.m[i][j])
1817                        continue;
1818                    /* Add row j to row i */
1819                    for (int n = 0; n < N; n++)
1820                    {
1821                        a.m[n][i] += a.m[n][j];
1822                        b.m[n][i] += b.m[n][j];
1823                    }
1824                    break;
1825                }
1826            }
1827
1828            /* Now we know the diagonal term is non-zero. Get its inverse
1829             * and use that to nullify all other terms in the column */
1830            T x = (T)1 / a.m[i][i];
1831            for (int j = 0; j < N; j++)
1832            {
1833                if (j == i)
1834                    continue;
1835                T mul = x * a.m[i][j];
1836                for (int n = 0; n < N; n++)
1837                {
1838                    a.m[n][j] -= mul * a.m[n][i];
1839                    b.m[n][j] -= mul * b.m[n][i];
1840                }
1841            }
1842
1843            /* Finally, ensure the diagonal term is 1 */
1844            for (int n = 0; n < N; n++)
1845            {
1846                a.m[n][i] *= x;
1847                b.m[n][i] *= x;
1848            }
1849        }
1850
1851        return b;
1852    }
1853
1854    T m[N][N];
1855};
1856
1857} /* namespace lol */
1858
1859#endif // __LOL_MATH_VECTOR_H__
1860
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