• Home
  • Line#
  • Scopes#
  • Navigate#
  • Raw
  • Download
1 /*
2  * Copyright 2019 Google Inc.
3  *
4  * Use of this source code is governed by a BSD-style license that can be
5  * found in the LICENSE file.
6  */
7 
8 #ifndef SKVX_DEFINED
9 #define SKVX_DEFINED
10 
11 // skvx::Vec<N,T> are SIMD vectors of N T's, a v1.5 successor to SkNx<N,T>.
12 //
13 // This time we're leaning a bit less on platform-specific intrinsics and a bit
14 // more on Clang/GCC vector extensions, but still keeping the option open to
15 // drop in platform-specific intrinsics, actually more easily than before.
16 //
17 // We've also fixed a few of the caveats that used to make SkNx awkward to work
18 // with across translation units.  skvx::Vec<N,T> always has N*sizeof(T) size
19 // and alignment[1][2] and is safe to use across translation units freely.
20 //
21 // [1] Ideally we'd only align to T, but that tanks ARMv7 NEON codegen.
22 // [2] Some compilers barf if we try to use N*sizeof(T), so instead we leave them at T.
23 
24 // Please try to keep this file independent of Skia headers.
25 #include <algorithm>         // std::min, std::max
26 #include <cmath>             // std::ceil, std::floor, std::trunc, std::round, std::sqrt, etc.
27 #include <cstdint>           // intXX_t
28 #include <cstring>           // memcpy()
29 #include <initializer_list>  // std::initializer_list
30 
31 #if defined(__SSE__)
32     #include <immintrin.h>
33 #elif defined(__ARM_NEON)
34     #include <arm_neon.h>
35 #endif
36 
37 #if !defined(__clang__) && defined(__GNUC__) && defined(__mips64)
38     // GCC 7 hits an internal compiler error when targeting MIPS64.
39     #define SKVX_ALIGNMENT
40 #elif !defined(__clang__) && defined(_MSC_VER) && defined(_M_IX86)
41     // Our SkVx unit tests fail when built by MSVC for 32-bit x86.
42     #define SKVX_ALIGNMENT
43 #else
44     #define SKVX_ALIGNMENT alignas(N * sizeof(T))
45 #endif
46 
47 
48 namespace skvx {
49 
50 // All Vec have the same simple memory layout, the same as `T vec[N]`.
51 // This gives Vec a consistent ABI, letting them pass between files compiled with
52 // different instruction sets (e.g. SSE2 and AVX2) without fear of ODR violation.
53 template <int N, typename T>
54 struct SKVX_ALIGNMENT Vec {
55     static_assert((N & (N-1)) == 0,        "N must be a power of 2.");
56     static_assert(sizeof(T) >= alignof(T), "What kind of crazy T is this?");
57 
58     Vec<N/2,T> lo, hi;
59 
60     // Methods belong here in the class declaration of Vec only if:
61     //   - they must be here, like constructors or operator[];
62     //   - they'll definitely never want a specialized implementation.
63     // Other operations on Vec should be defined outside the type.
64 
65     Vec() = default;
66 
67     template <typename U,
68               typename=typename std::enable_if<std::is_convertible<U,T>::value>::type>
VecVec69     Vec(U x) : lo(x), hi(x) {}
70 
VecVec71     Vec(std::initializer_list<T> xs) {
72         T vals[N] = {0};
73         memcpy(vals, xs.begin(), std::min(xs.size(), (size_t)N)*sizeof(T));
74 
75         lo = Vec<N/2,T>::Load(vals +   0);
76         hi = Vec<N/2,T>::Load(vals + N/2);
77     }
78 
79     T  operator[](int i) const { return i < N/2 ? lo[i] : hi[i-N/2]; }
80     T& operator[](int i)       { return i < N/2 ? lo[i] : hi[i-N/2]; }
81 
LoadVec82     static Vec Load(const void* ptr) {
83         Vec v;
84         memcpy(&v, ptr, sizeof(Vec));
85         return v;
86     }
storeVec87     void store(void* ptr) const {
88         memcpy(ptr, this, sizeof(Vec));
89     }
90 };
91 
92 template <typename T>
93 struct Vec<1,T> {
94     T val;
95 
96     Vec() = default;
97 
98     template <typename U,
99               typename=typename std::enable_if<std::is_convertible<U,T>::value>::type>
100     Vec(U x) : val(x) {}
101 
102     Vec(std::initializer_list<T> xs) : val(xs.size() ? *xs.begin() : 0) {}
103 
104     T  operator[](int) const { return val; }
105     T& operator[](int)       { return val; }
106 
107     static Vec Load(const void* ptr) {
108         Vec v;
109         memcpy(&v, ptr, sizeof(Vec));
110         return v;
111     }
112     void store(void* ptr) const {
113         memcpy(ptr, this, sizeof(Vec));
114     }
115 };
116 
117 #if defined(__GNUC__) && !defined(__clang__) && defined(__SSE__)
118     // GCC warns about ABI changes when returning >= 32 byte vectors when -mavx is not enabled.
119     // This only happens for types like VExt whose ABI we don't care about, not for Vec itself.
120     #pragma GCC diagnostic ignored "-Wpsabi"
121 #endif
122 
123 // Helps tamp down on the repetitive boilerplate.
124 #define SIT   template <       typename T> static inline
125 #define SINT  template <int N, typename T> static inline
126 #define SINTU template <int N, typename T, typename U, \
127                         typename=typename std::enable_if<std::is_convertible<U,T>::value>::type> \
128               static inline
129 
130 template <typename D, typename S>
131 static inline D bit_pun(const S& s) {
132     static_assert(sizeof(D) == sizeof(S), "");
133     D d;
134     memcpy(&d, &s, sizeof(D));
135     return d;
136 }
137 
138 // Translate from a value type T to its corresponding Mask, the result of a comparison.
139 template <typename T> struct Mask { using type = T; };
140 template <> struct Mask<float > { using type = int32_t; };
141 template <> struct Mask<double> { using type = int64_t; };
142 template <typename T> using M = typename Mask<T>::type;
143 
144 // Join two Vec<N,T> into one Vec<2N,T>.
145 SINT Vec<2*N,T> join(const Vec<N,T>& lo, const Vec<N,T>& hi) {
146     Vec<2*N,T> v;
147     v.lo = lo;
148     v.hi = hi;
149     return v;
150 }
151 
152 // We have two default strategies for implementing most operations:
153 //    1) lean on Clang/GCC vector extensions when available;
154 //    2) recurse to scalar portable implementations when not.
155 // At the end we can drop in platform-specific implementations that override either default.
156 
157 #if !defined(SKNX_NO_SIMD) && (defined(__clang__) || defined(__GNUC__))
158 
159     // VExt<N,T> types have the same size as Vec<N,T> and support most operations directly.
160     // N.B. VExt<N,T> alignment is N*alignof(T), stricter than Vec<N,T>'s alignof(T).
161     #if defined(__clang__)
162         template <int N, typename T>
163         using VExt = T __attribute__((ext_vector_type(N)));
164 
165     #elif defined(__GNUC__)
166         template <int N, typename T>
167         struct VExtHelper {
168             typedef T __attribute__((vector_size(N*sizeof(T)))) type;
169         };
170 
171         template <int N, typename T>
172         using VExt = typename VExtHelper<N,T>::type;
173 
174         // For some reason some (new!) versions of GCC cannot seem to deduce N in the generic
175         // to_vec<N,T>() below for N=4 and T=float.  This workaround seems to help...
176         static inline Vec<4,float> to_vec(VExt<4,float> v) { return bit_pun<Vec<4,float>>(v); }
177     #endif
178 
179     SINT VExt<N,T> to_vext(const Vec<N,T>& v) { return bit_pun<VExt<N,T>>(v); }
180     SINT Vec <N,T> to_vec(const VExt<N,T>& v) { return bit_pun<Vec <N,T>>(v); }
181 
182     SINT Vec<N,T> operator+(const Vec<N,T>& x, const Vec<N,T>& y) { return to_vec<N,T>(to_vext(x) + to_vext(y)); }
183     SINT Vec<N,T> operator-(const Vec<N,T>& x, const Vec<N,T>& y) { return to_vec<N,T>(to_vext(x) - to_vext(y)); }
184     SINT Vec<N,T> operator*(const Vec<N,T>& x, const Vec<N,T>& y) { return to_vec<N,T>(to_vext(x) * to_vext(y)); }
185     SINT Vec<N,T> operator/(const Vec<N,T>& x, const Vec<N,T>& y) { return to_vec<N,T>(to_vext(x) / to_vext(y)); }
186 
187     SINT Vec<N,T> operator^(const Vec<N,T>& x, const Vec<N,T>& y) { return to_vec<N,T>(to_vext(x) ^ to_vext(y)); }
188     SINT Vec<N,T> operator&(const Vec<N,T>& x, const Vec<N,T>& y) { return to_vec<N,T>(to_vext(x) & to_vext(y)); }
189     SINT Vec<N,T> operator|(const Vec<N,T>& x, const Vec<N,T>& y) { return to_vec<N,T>(to_vext(x) | to_vext(y)); }
190 
191     SINT Vec<N,T> operator!(const Vec<N,T>& x) { return to_vec<N,T>(!to_vext(x)); }
192     SINT Vec<N,T> operator-(const Vec<N,T>& x) { return to_vec<N,T>(-to_vext(x)); }
193     SINT Vec<N,T> operator~(const Vec<N,T>& x) { return to_vec<N,T>(~to_vext(x)); }
194 
195     SINT Vec<N,T> operator<<(const Vec<N,T>& x, int bits) { return to_vec<N,T>(to_vext(x) << bits); }
196     SINT Vec<N,T> operator>>(const Vec<N,T>& x, int bits) { return to_vec<N,T>(to_vext(x) >> bits); }
197 
198     SINT Vec<N,M<T>> operator==(const Vec<N,T>& x, const Vec<N,T>& y) { return bit_pun<Vec<N,M<T>>>(to_vext(x) == to_vext(y)); }
199     SINT Vec<N,M<T>> operator!=(const Vec<N,T>& x, const Vec<N,T>& y) { return bit_pun<Vec<N,M<T>>>(to_vext(x) != to_vext(y)); }
200     SINT Vec<N,M<T>> operator<=(const Vec<N,T>& x, const Vec<N,T>& y) { return bit_pun<Vec<N,M<T>>>(to_vext(x) <= to_vext(y)); }
201     SINT Vec<N,M<T>> operator>=(const Vec<N,T>& x, const Vec<N,T>& y) { return bit_pun<Vec<N,M<T>>>(to_vext(x) >= to_vext(y)); }
202     SINT Vec<N,M<T>> operator< (const Vec<N,T>& x, const Vec<N,T>& y) { return bit_pun<Vec<N,M<T>>>(to_vext(x) <  to_vext(y)); }
203     SINT Vec<N,M<T>> operator> (const Vec<N,T>& x, const Vec<N,T>& y) { return bit_pun<Vec<N,M<T>>>(to_vext(x) >  to_vext(y)); }
204 
205 #else
206 
207     // Either SKNX_NO_SIMD is defined, or Clang/GCC vector extensions are not available.
208     // We'll implement things portably, in a way that should be easily autovectorizable.
209 
210     // N == 1 scalar implementations.
211     SIT Vec<1,T> operator+(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val + y.val; }
212     SIT Vec<1,T> operator-(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val - y.val; }
213     SIT Vec<1,T> operator*(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val * y.val; }
214     SIT Vec<1,T> operator/(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val / y.val; }
215 
216     SIT Vec<1,T> operator^(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val ^ y.val; }
217     SIT Vec<1,T> operator&(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val & y.val; }
218     SIT Vec<1,T> operator|(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val | y.val; }
219 
220     SIT Vec<1,T> operator!(const Vec<1,T>& x) { return !x.val; }
221     SIT Vec<1,T> operator-(const Vec<1,T>& x) { return -x.val; }
222     SIT Vec<1,T> operator~(const Vec<1,T>& x) { return ~x.val; }
223 
224     SIT Vec<1,T> operator<<(const Vec<1,T>& x, int bits) { return x.val << bits; }
225     SIT Vec<1,T> operator>>(const Vec<1,T>& x, int bits) { return x.val >> bits; }
226 
227     SIT Vec<1,M<T>> operator==(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val == y.val ? ~0 : 0; }
228     SIT Vec<1,M<T>> operator!=(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val != y.val ? ~0 : 0; }
229     SIT Vec<1,M<T>> operator<=(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val <= y.val ? ~0 : 0; }
230     SIT Vec<1,M<T>> operator>=(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val >= y.val ? ~0 : 0; }
231     SIT Vec<1,M<T>> operator< (const Vec<1,T>& x, const Vec<1,T>& y) { return x.val <  y.val ? ~0 : 0; }
232     SIT Vec<1,M<T>> operator> (const Vec<1,T>& x, const Vec<1,T>& y) { return x.val >  y.val ? ~0 : 0; }
233 
234     // All default N != 1 implementations just recurse on lo and hi halves.
235     SINT Vec<N,T> operator+(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo + y.lo, x.hi + y.hi); }
236     SINT Vec<N,T> operator-(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo - y.lo, x.hi - y.hi); }
237     SINT Vec<N,T> operator*(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo * y.lo, x.hi * y.hi); }
238     SINT Vec<N,T> operator/(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo / y.lo, x.hi / y.hi); }
239 
240     SINT Vec<N,T> operator^(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo ^ y.lo, x.hi ^ y.hi); }
241     SINT Vec<N,T> operator&(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo & y.lo, x.hi & y.hi); }
242     SINT Vec<N,T> operator|(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo | y.lo, x.hi | y.hi); }
243 
244     SINT Vec<N,T> operator!(const Vec<N,T>& x) { return join(!x.lo, !x.hi); }
245     SINT Vec<N,T> operator-(const Vec<N,T>& x) { return join(-x.lo, -x.hi); }
246     SINT Vec<N,T> operator~(const Vec<N,T>& x) { return join(~x.lo, ~x.hi); }
247 
248     SINT Vec<N,T> operator<<(const Vec<N,T>& x, int bits) { return join(x.lo << bits, x.hi << bits); }
249     SINT Vec<N,T> operator>>(const Vec<N,T>& x, int bits) { return join(x.lo >> bits, x.hi >> bits); }
250 
251     SINT Vec<N,M<T>> operator==(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo == y.lo, x.hi == y.hi); }
252     SINT Vec<N,M<T>> operator!=(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo != y.lo, x.hi != y.hi); }
253     SINT Vec<N,M<T>> operator<=(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo <= y.lo, x.hi <= y.hi); }
254     SINT Vec<N,M<T>> operator>=(const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo >= y.lo, x.hi >= y.hi); }
255     SINT Vec<N,M<T>> operator< (const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo <  y.lo, x.hi <  y.hi); }
256     SINT Vec<N,M<T>> operator> (const Vec<N,T>& x, const Vec<N,T>& y) { return join(x.lo >  y.lo, x.hi >  y.hi); }
257 #endif
258 
259 // Some operations we want are not expressible with Clang/GCC vector
260 // extensions, so we implement them using the recursive approach.
261 
262 // N == 1 scalar implementations.
263 SIT Vec<1,T> if_then_else(const Vec<1,M<T>>& cond, const Vec<1,T>& t, const Vec<1,T>& e) {
264     auto t_bits = bit_pun<M<T>>(t),
265          e_bits = bit_pun<M<T>>(e);
266     return bit_pun<T>( (cond.val & t_bits) | (~cond.val & e_bits) );
267 }
268 
269 SIT bool any(const Vec<1,T>& x) { return x.val != 0; }
270 SIT bool all(const Vec<1,T>& x) { return x.val != 0; }
271 
272 SIT T min(const Vec<1,T>& x) { return x.val; }
273 SIT T max(const Vec<1,T>& x) { return x.val; }
274 
275 SIT Vec<1,T> min(const Vec<1,T>& x, const Vec<1,T>& y) { return std::min(x.val, y.val); }
276 SIT Vec<1,T> max(const Vec<1,T>& x, const Vec<1,T>& y) { return std::max(x.val, y.val); }
277 
278 SIT Vec<1,T>  ceil(const Vec<1,T>& x) { return std:: ceil(x.val); }
279 SIT Vec<1,T> floor(const Vec<1,T>& x) { return std::floor(x.val); }
280 SIT Vec<1,T> trunc(const Vec<1,T>& x) { return std::trunc(x.val); }
281 SIT Vec<1,T> round(const Vec<1,T>& x) { return std::round(x.val); }
282 SIT Vec<1,T>  sqrt(const Vec<1,T>& x) { return std:: sqrt(x.val); }
283 SIT Vec<1,T>   abs(const Vec<1,T>& x) { return std::  abs(x.val); }
284 
285 SIT Vec<1,T>   rcp(const Vec<1,T>& x) { return 1 / x.val; }
286 SIT Vec<1,T> rsqrt(const Vec<1,T>& x) { return rcp(sqrt(x)); }
287 SIT Vec<1,T>   mad(const Vec<1,T>& f,
288                    const Vec<1,T>& m,
289                    const Vec<1,T>& a) { return f*m+a; }
290 
291 // All default N != 1 implementations just recurse on lo and hi halves.
292 SINT Vec<N,T> if_then_else(const Vec<N,M<T>>& cond, const Vec<N,T>& t, const Vec<N,T>& e) {
293     return join(if_then_else(cond.lo, t.lo, e.lo),
294                 if_then_else(cond.hi, t.hi, e.hi));
295 }
296 
297 SINT bool any(const Vec<N,T>& x) { return any(x.lo) || any(x.hi); }
298 SINT bool all(const Vec<N,T>& x) { return all(x.lo) && all(x.hi); }
299 
300 SINT T min(const Vec<N,T>& x) { return std::min(min(x.lo), min(x.hi)); }
301 SINT T max(const Vec<N,T>& x) { return std::max(max(x.lo), max(x.hi)); }
302 
303 SINT Vec<N,T> min(const Vec<N,T>& x, const Vec<N,T>& y) { return join(min(x.lo, y.lo), min(x.hi, y.hi)); }
304 SINT Vec<N,T> max(const Vec<N,T>& x, const Vec<N,T>& y) { return join(max(x.lo, y.lo), max(x.hi, y.hi)); }
305 
306 SINT Vec<N,T>  ceil(const Vec<N,T>& x) { return join( ceil(x.lo),  ceil(x.hi)); }
307 SINT Vec<N,T> floor(const Vec<N,T>& x) { return join(floor(x.lo), floor(x.hi)); }
308 SINT Vec<N,T> trunc(const Vec<N,T>& x) { return join(trunc(x.lo), trunc(x.hi)); }
309 SINT Vec<N,T> round(const Vec<N,T>& x) { return join(round(x.lo), round(x.hi)); }
310 SINT Vec<N,T>  sqrt(const Vec<N,T>& x) { return join( sqrt(x.lo),  sqrt(x.hi)); }
311 SINT Vec<N,T>   abs(const Vec<N,T>& x) { return join(  abs(x.lo),   abs(x.hi)); }
312 
313 SINT Vec<N,T>   rcp(const Vec<N,T>& x) { return join(  rcp(x.lo),   rcp(x.hi)); }
314 SINT Vec<N,T> rsqrt(const Vec<N,T>& x) { return join(rsqrt(x.lo), rsqrt(x.hi)); }
315 SINT Vec<N,T>   mad(const Vec<N,T>& f,
316                     const Vec<N,T>& m,
317                     const Vec<N,T>& a) { return join(mad(f.lo, m.lo, a.lo), mad(f.hi, m.hi, a.hi)); }
318 
319 
320 // Scalar/vector operations just splat the scalar to a vector...
321 SINTU Vec<N,T>    operator+ (U x, const Vec<N,T>& y) { return Vec<N,T>(x) +  y; }
322 SINTU Vec<N,T>    operator- (U x, const Vec<N,T>& y) { return Vec<N,T>(x) -  y; }
323 SINTU Vec<N,T>    operator* (U x, const Vec<N,T>& y) { return Vec<N,T>(x) *  y; }
324 SINTU Vec<N,T>    operator/ (U x, const Vec<N,T>& y) { return Vec<N,T>(x) /  y; }
325 SINTU Vec<N,T>    operator^ (U x, const Vec<N,T>& y) { return Vec<N,T>(x) ^  y; }
326 SINTU Vec<N,T>    operator& (U x, const Vec<N,T>& y) { return Vec<N,T>(x) &  y; }
327 SINTU Vec<N,T>    operator| (U x, const Vec<N,T>& y) { return Vec<N,T>(x) |  y; }
328 SINTU Vec<N,M<T>> operator==(U x, const Vec<N,T>& y) { return Vec<N,T>(x) == y; }
329 SINTU Vec<N,M<T>> operator!=(U x, const Vec<N,T>& y) { return Vec<N,T>(x) != y; }
330 SINTU Vec<N,M<T>> operator<=(U x, const Vec<N,T>& y) { return Vec<N,T>(x) <= y; }
331 SINTU Vec<N,M<T>> operator>=(U x, const Vec<N,T>& y) { return Vec<N,T>(x) >= y; }
332 SINTU Vec<N,M<T>> operator< (U x, const Vec<N,T>& y) { return Vec<N,T>(x) <  y; }
333 SINTU Vec<N,M<T>> operator> (U x, const Vec<N,T>& y) { return Vec<N,T>(x) >  y; }
334 SINTU Vec<N,T>           min(U x, const Vec<N,T>& y) { return min(Vec<N,T>(x), y); }
335 SINTU Vec<N,T>           max(U x, const Vec<N,T>& y) { return max(Vec<N,T>(x), y); }
336 
337 // ... and same deal for vector/scalar operations.
338 SINTU Vec<N,T>    operator+ (const Vec<N,T>& x, U y) { return x +  Vec<N,T>(y); }
339 SINTU Vec<N,T>    operator- (const Vec<N,T>& x, U y) { return x -  Vec<N,T>(y); }
340 SINTU Vec<N,T>    operator* (const Vec<N,T>& x, U y) { return x *  Vec<N,T>(y); }
341 SINTU Vec<N,T>    operator/ (const Vec<N,T>& x, U y) { return x /  Vec<N,T>(y); }
342 SINTU Vec<N,T>    operator^ (const Vec<N,T>& x, U y) { return x ^  Vec<N,T>(y); }
343 SINTU Vec<N,T>    operator& (const Vec<N,T>& x, U y) { return x &  Vec<N,T>(y); }
344 SINTU Vec<N,T>    operator| (const Vec<N,T>& x, U y) { return x |  Vec<N,T>(y); }
345 SINTU Vec<N,M<T>> operator==(const Vec<N,T>& x, U y) { return x == Vec<N,T>(y); }
346 SINTU Vec<N,M<T>> operator!=(const Vec<N,T>& x, U y) { return x != Vec<N,T>(y); }
347 SINTU Vec<N,M<T>> operator<=(const Vec<N,T>& x, U y) { return x <= Vec<N,T>(y); }
348 SINTU Vec<N,M<T>> operator>=(const Vec<N,T>& x, U y) { return x >= Vec<N,T>(y); }
349 SINTU Vec<N,M<T>> operator< (const Vec<N,T>& x, U y) { return x <  Vec<N,T>(y); }
350 SINTU Vec<N,M<T>> operator> (const Vec<N,T>& x, U y) { return x >  Vec<N,T>(y); }
351 SINTU Vec<N,T>           min(const Vec<N,T>& x, U y) { return min(x, Vec<N,T>(y)); }
352 SINTU Vec<N,T>           max(const Vec<N,T>& x, U y) { return max(x, Vec<N,T>(y)); }
353 
354 // All vector/scalar combinations for mad() with at least one vector.
355 SINTU Vec<N,T> mad(U f, const Vec<N,T>& m, const Vec<N,T>& a) { return Vec<N,T>(f)*m + a; }
356 SINTU Vec<N,T> mad(const Vec<N,T>& f, U m, const Vec<N,T>& a) { return f*Vec<N,T>(m) + a; }
357 SINTU Vec<N,T> mad(const Vec<N,T>& f, const Vec<N,T>& m, U a) { return f*m + Vec<N,T>(a); }
358 SINTU Vec<N,T> mad(const Vec<N,T>& f, U m, U a) { return f*Vec<N,T>(m) + Vec<N,T>(a); }
359 SINTU Vec<N,T> mad(U f, const Vec<N,T>& m, U a) { return Vec<N,T>(f)*m + Vec<N,T>(a); }
360 SINTU Vec<N,T> mad(U f, U m, const Vec<N,T>& a) { return Vec<N,T>(f)*Vec<N,T>(m) + a; }
361 
362 // The various op= operators, for vectors...
363 SINT Vec<N,T>& operator+=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x + y); }
364 SINT Vec<N,T>& operator-=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x - y); }
365 SINT Vec<N,T>& operator*=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x * y); }
366 SINT Vec<N,T>& operator/=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x / y); }
367 SINT Vec<N,T>& operator^=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x ^ y); }
368 SINT Vec<N,T>& operator&=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x & y); }
369 SINT Vec<N,T>& operator|=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x | y); }
370 
371 // ... for scalars...
372 SINTU Vec<N,T>& operator+=(Vec<N,T>& x, U y) { return (x = x + Vec<N,T>(y)); }
373 SINTU Vec<N,T>& operator-=(Vec<N,T>& x, U y) { return (x = x - Vec<N,T>(y)); }
374 SINTU Vec<N,T>& operator*=(Vec<N,T>& x, U y) { return (x = x * Vec<N,T>(y)); }
375 SINTU Vec<N,T>& operator/=(Vec<N,T>& x, U y) { return (x = x / Vec<N,T>(y)); }
376 SINTU Vec<N,T>& operator^=(Vec<N,T>& x, U y) { return (x = x ^ Vec<N,T>(y)); }
377 SINTU Vec<N,T>& operator&=(Vec<N,T>& x, U y) { return (x = x & Vec<N,T>(y)); }
378 SINTU Vec<N,T>& operator|=(Vec<N,T>& x, U y) { return (x = x | Vec<N,T>(y)); }
379 
380 // ... and for shifts.
381 SINT Vec<N,T>& operator<<=(Vec<N,T>& x, int bits) { return (x = x << bits); }
382 SINT Vec<N,T>& operator>>=(Vec<N,T>& x, int bits) { return (x = x >> bits); }
383 
384 // cast() Vec<N,S> to Vec<N,D>, as if applying a C-cast to each lane.
385 template <typename D, typename S>
386 static inline Vec<1,D> cast(const Vec<1,S>& src) { return (D)src.val; }
387 
388 template <typename D, int N, typename S>
389 static inline Vec<N,D> cast(const Vec<N,S>& src) {
390 #if !defined(SKNX_NO_SIMD) && defined(__clang__)
391     return to_vec(__builtin_convertvector(to_vext(src), VExt<N,D>));
392 #else
393     return join(cast<D>(src.lo), cast<D>(src.hi));
394 #endif
395 }
396 
397 // Shuffle values from a vector pretty arbitrarily:
398 //    skvx::Vec<4,float> rgba = {R,G,B,A};
399 //    shuffle<2,1,0,3>        (rgba) ~> {B,G,R,A}
400 //    shuffle<2,1>            (rgba) ~> {B,G}
401 //    shuffle<2,1,2,1,2,1,2,1>(rgba) ~> {B,G,B,G,B,G,B,G}
402 //    shuffle<3,3,3,3>        (rgba) ~> {A,A,A,A}
403 // The only real restriction is that the output also be a legal N=power-of-two sknx::Vec.
404 template <int... Ix, int N, typename T>
405 static inline Vec<sizeof...(Ix),T> shuffle(const Vec<N,T>& x) {
406 #if !defined(SKNX_NO_SIMD) && defined(__clang__)
407     return to_vec<sizeof...(Ix),T>(__builtin_shufflevector(to_vext(x), to_vext(x), Ix...));
408 #else
409     return { x[Ix]... };
410 #endif
411 }
412 
413 // div255(x) = (x + 127) / 255 is a bit-exact rounding divide-by-255, packing down to 8-bit.
414 template <int N>
415 static inline Vec<N,uint8_t> div255(const Vec<N,uint16_t>& x) {
416     return cast<uint8_t>( (x+127)/255 );
417 }
418 
419 // approx_scale(x,y) approximates div255(cast<uint16_t>(x)*cast<uint16_t>(y)) within a bit,
420 // and is always perfect when x or y is 0 or 255.
421 template <int N>
422 static inline Vec<N,uint8_t> approx_scale(const Vec<N,uint8_t>& x, const Vec<N,uint8_t>& y) {
423     // All of (x*y+x)/256, (x*y+y)/256, and (x*y+255)/256 meet the criteria above.
424     // We happen to have historically picked (x*y+x)/256.
425     auto X = cast<uint16_t>(x),
426          Y = cast<uint16_t>(y);
427     return cast<uint8_t>( (X*Y+X)/256 );
428 }
429 
430 #if !defined(SKNX_NO_SIMD) && defined(__ARM_NEON)
431     // With NEON we can do eight u8*u8 -> u16 in one instruction, vmull_u8 (read, mul-long).
432     static inline Vec<8,uint16_t> mull(const Vec<8,uint8_t>& x,
433                                        const Vec<8,uint8_t>& y) {
434         return to_vec<8,uint16_t>(vmull_u8(to_vext(x),
435                                            to_vext(y)));
436     }
437 
438     template <int N>
439     static inline typename std::enable_if<(N < 8),
440     Vec<N,uint16_t>>::type mull(const Vec<N,uint8_t>& x,
441                                 const Vec<N,uint8_t>& y) {
442         // N < 8 --> double up data until N == 8, returning the part we need.
443         return mull(join(x,x),
444                     join(y,y)).lo;
445     }
446 
447     template <int N>
448     static inline typename std::enable_if<(N > 8),
449     Vec<N,uint16_t>>::type mull(const Vec<N,uint8_t>& x,
450                                 const Vec<N,uint8_t>& y) {
451         // N > 8 --> usual join(lo,hi) strategy to recurse down to N == 8.
452         return join(mull(x.lo, y.lo),
453                     mull(x.hi, y.hi));
454     }
455 #else
456     // Nothing special when we don't have NEON... just cast up to 16-bit and multiply.
457     template <int N>
458     static inline Vec<N,uint16_t> mull(const Vec<N,uint8_t>& x,
459                                        const Vec<N,uint8_t>& y) {
460         return cast<uint16_t>(x)
461              * cast<uint16_t>(y);
462     }
463 #endif
464 
465 #if !defined(SKNX_NO_SIMD)
466 
467     // Platform-specific specializations and overloads can now drop in here.
468 
469     #if defined(__SSE__)
470         static inline Vec<4,float> sqrt(const Vec<4,float>& x) {
471             return bit_pun<Vec<4,float>>(_mm_sqrt_ps(bit_pun<__m128>(x)));
472         }
473         static inline Vec<4,float> rsqrt(const Vec<4,float>& x) {
474             return bit_pun<Vec<4,float>>(_mm_rsqrt_ps(bit_pun<__m128>(x)));
475         }
476         static inline Vec<4,float> rcp(const Vec<4,float>& x) {
477             return bit_pun<Vec<4,float>>(_mm_rcp_ps(bit_pun<__m128>(x)));
478         }
479 
480         static inline Vec<2,float>  sqrt(const Vec<2,float>& x) {
481             return shuffle<0,1>( sqrt(shuffle<0,1,0,1>(x)));
482         }
483         static inline Vec<2,float> rsqrt(const Vec<2,float>& x) {
484             return shuffle<0,1>(rsqrt(shuffle<0,1,0,1>(x)));
485         }
486         static inline Vec<2,float>   rcp(const Vec<2,float>& x) {
487             return shuffle<0,1>(  rcp(shuffle<0,1,0,1>(x)));
488         }
489     #endif
490 
491     #if defined(__SSE4_1__)
492         static inline Vec<4,float> if_then_else(const Vec<4,int  >& c,
493                                                 const Vec<4,float>& t,
494                                                 const Vec<4,float>& e) {
495             return bit_pun<Vec<4,float>>(_mm_blendv_ps(bit_pun<__m128>(e),
496                                                        bit_pun<__m128>(t),
497                                                        bit_pun<__m128>(c)));
498         }
499     #elif defined(__SSE__)
500         static inline Vec<4,float> if_then_else(const Vec<4,int  >& c,
501                                                 const Vec<4,float>& t,
502                                                 const Vec<4,float>& e) {
503             return bit_pun<Vec<4,float>>(_mm_or_ps(_mm_and_ps   (bit_pun<__m128>(c),
504                                                                  bit_pun<__m128>(t)),
505                                                    _mm_andnot_ps(bit_pun<__m128>(c),
506                                                                  bit_pun<__m128>(e))));
507         }
508     #elif defined(__ARM_NEON)
509         static inline Vec<4,float> if_then_else(const Vec<4,int  >& c,
510                                                 const Vec<4,float>& t,
511                                                 const Vec<4,float>& e) {
512             return bit_pun<Vec<4,float>>(vbslq_f32(bit_pun<uint32x4_t> (c),
513                                                    bit_pun<float32x4_t>(t),
514                                                    bit_pun<float32x4_t>(e)));
515         }
516     #endif
517 
518 #endif // !defined(SKNX_NO_SIMD)
519 
520 }  // namespace skvx
521 
522 #undef SINTU
523 #undef SINT
524 #undef SIT
525 #undef SKVX_ALIGNMENT
526 
527 #endif//SKVX_DEFINED
528