| /* | 
 |  * Copyright 2019 Google Inc. | 
 |  * | 
 |  * Use of this source code is governed by a BSD-style license that can be | 
 |  * found in the LICENSE file. | 
 |  */ | 
 |  | 
 | #ifndef SKVX_DEFINED | 
 | #define SKVX_DEFINED | 
 |  | 
 | // skvx::Vec<N,T> are SIMD vectors of N T's, a v1.5 successor to SkNx<N,T>. | 
 | // | 
 | // This time we're leaning a bit less on platform-specific intrinsics and a bit | 
 | // more on Clang/GCC vector extensions, but still keeping the option open to | 
 | // drop in platform-specific intrinsics, actually more easily than before. | 
 | // | 
 | // We've also fixed a few of the caveats that used to make SkNx awkward to work | 
 | // with across translation units.  skvx::Vec<N,T> always has N*sizeof(T) size | 
 | // and alignment[1][2] and is safe to use across translation units freely. | 
 | // | 
 | // [1] Ideally we'd only align to T, but that tanks ARMv7 NEON codegen. | 
 | // [2] Some compilers barf if we try to use N*sizeof(T), so instead we leave them at T. | 
 |  | 
 | // Please try to keep this file independent of Skia headers. | 
 | #include <algorithm>         // std::min, std::max | 
 | #include <cmath>             // std::ceil, std::floor, std::trunc, std::round, std::sqrt, etc. | 
 | #include <cstdint>           // intXX_t | 
 | #include <cstring>           // memcpy() | 
 | #include <initializer_list>  // std::initializer_list | 
 |  | 
 | #if defined(__SSE__) | 
 |     #include <immintrin.h> | 
 | #elif defined(__ARM_NEON) | 
 |     #include <arm_neon.h> | 
 | #endif | 
 |  | 
 | #if !defined(__clang__) && defined(__GNUC__) && defined(__mips64) | 
 |     // GCC 7 hits an internal compiler error when targeting MIPS64. | 
 |     #define SKVX_ALIGNMENT | 
 | #elif !defined(__clang__) && defined(_MSC_VER) && defined(_M_IX86) | 
 |     // Our SkVx unit tests fail when built by MSVC for 32-bit x86. | 
 |     #define SKVX_ALIGNMENT | 
 | #else | 
 |     #define SKVX_ALIGNMENT alignas(N * sizeof(T)) | 
 | #endif | 
 |  | 
 |  | 
 | namespace skvx { | 
 |  | 
 | // All Vec have the same simple memory layout, the same as `T vec[N]`. | 
 | // This gives Vec a consistent ABI, letting them pass between files compiled with | 
 | // different instruction sets (e.g. SSE2 and AVX2) without fear of ODR violation. | 
 | template <int N, typename T> | 
 | struct SKVX_ALIGNMENT Vec { | 
 |     static_assert((N & (N-1)) == 0,        "N must be a power of 2."); | 
 |     static_assert(sizeof(T) >= alignof(T), "What kind of crazy T is this?"); | 
 |  | 
 |     Vec<N/2,T> lo, hi; | 
 |  | 
 |     // Methods belong here in the class declaration of Vec only if: | 
 |     //   - they must be here, like constructors or operator[]; | 
 |     //   - they'll definitely never want a specialized implementation. | 
 |     // Other operations on Vec should be defined outside the type. | 
 |  | 
 |     Vec() = default; | 
 |  | 
 |     template <typename U, | 
 |               typename=typename std::enable_if<std::is_convertible<U,T>::value>::type> | 
 |     Vec(U x) : lo(x), hi(x) {} | 
 |  | 
 |     Vec(std::initializer_list<T> xs) { | 
 |         T vals[N] = {0}; | 
 |         memcpy(vals, xs.begin(), std::min(xs.size(), (size_t)N)*sizeof(T)); | 
 |  | 
 |         lo = Vec<N/2,T>::Load(vals +   0); | 
 |         hi = Vec<N/2,T>::Load(vals + N/2); | 
 |     } | 
 |  | 
 |     T  operator[](int i) const { return i < N/2 ? lo[i] : hi[i-N/2]; } | 
 |     T& operator[](int i)       { return i < N/2 ? lo[i] : hi[i-N/2]; } | 
 |  | 
 |     static Vec Load(const void* ptr) { | 
 |         Vec v; | 
 |         memcpy(&v, ptr, sizeof(Vec)); | 
 |         return v; | 
 |     } | 
 |     void store(void* ptr) const { | 
 |         memcpy(ptr, this, sizeof(Vec)); | 
 |     } | 
 | }; | 
 |  | 
 | template <typename T> | 
 | struct Vec<1,T> { | 
 |     T val; | 
 |  | 
 |     Vec() = default; | 
 |  | 
 |     template <typename U, | 
 |               typename=typename std::enable_if<std::is_convertible<U,T>::value>::type> | 
 |     Vec(U x) : val(x) {} | 
 |  | 
 |     Vec(std::initializer_list<T> xs) : val(xs.size() ? *xs.begin() : 0) {} | 
 |  | 
 |     T  operator[](int) const { return val; } | 
 |     T& operator[](int)       { return val; } | 
 |  | 
 |     static Vec Load(const void* ptr) { | 
 |         Vec v; | 
 |         memcpy(&v, ptr, sizeof(Vec)); | 
 |         return v; | 
 |     } | 
 |     void store(void* ptr) const { | 
 |         memcpy(ptr, this, sizeof(Vec)); | 
 |     } | 
 | }; | 
 |  | 
 | #if defined(__GNUC__) && !defined(__clang__) && defined(__SSE__) | 
 |     // GCC warns about ABI changes when returning >= 32 byte vectors when -mavx is not enabled. | 
 |     // This only happens for types like VExt whose ABI we don't care about, not for Vec itself. | 
 |     #pragma GCC diagnostic ignored "-Wpsabi" | 
 | #endif | 
 |  | 
 | // Helps tamp down on the repetitive boilerplate. | 
 | #define SIT   template <       typename T> static inline | 
 | #define SINT  template <int N, typename T> static inline | 
 | #define SINTU template <int N, typename T, typename U, \ | 
 |                         typename=typename std::enable_if<std::is_convertible<U,T>::value>::type> \ | 
 |               static inline | 
 |  | 
 | template <typename D, typename S> | 
 | static inline D bit_pun(const S& s) { | 
 |     static_assert(sizeof(D) == sizeof(S), ""); | 
 |     D d; | 
 |     memcpy(&d, &s, sizeof(D)); | 
 |     return d; | 
 | } | 
 |  | 
 | // Translate from a value type T to its corresponding Mask, the result of a comparison. | 
 | template <typename T> struct Mask { using type = T; }; | 
 | template <> struct Mask<float > { using type = int32_t; }; | 
 | template <> struct Mask<double> { using type = int64_t; }; | 
 | template <typename T> using M = typename Mask<T>::type; | 
 |  | 
 | // Join two Vec<N,T> into one Vec<2N,T>. | 
 | SINT Vec<2*N,T> join(const Vec<N,T>& lo, const Vec<N,T>& hi) { | 
 |     Vec<2*N,T> v; | 
 |     v.lo = lo; | 
 |     v.hi = hi; | 
 |     return v; | 
 | } | 
 |  | 
 | // We have two default strategies for implementing most operations: | 
 | //    1) lean on Clang/GCC vector extensions when available; | 
 | //    2) recurse to scalar portable implementations when not. | 
 | // At the end we can drop in platform-specific implementations that override either default. | 
 |  | 
 | #if !defined(SKNX_NO_SIMD) && (defined(__clang__) || defined(__GNUC__)) | 
 |  | 
 |     // VExt<N,T> types have the same size as Vec<N,T> and support most operations directly. | 
 |     // N.B. VExt<N,T> alignment is N*alignof(T), stricter than Vec<N,T>'s alignof(T). | 
 |     #if defined(__clang__) | 
 |         template <int N, typename T> | 
 |         using VExt = T __attribute__((ext_vector_type(N))); | 
 |  | 
 |     #elif defined(__GNUC__) | 
 |         template <int N, typename T> | 
 |         struct VExtHelper { | 
 |             typedef T __attribute__((vector_size(N*sizeof(T)))) type; | 
 |         }; | 
 |  | 
 |         template <int N, typename T> | 
 |         using VExt = typename VExtHelper<N,T>::type; | 
 |  | 
 |         // For some reason some (new!) versions of GCC cannot seem to deduce N in the generic | 
 |         // to_vec<N,T>() below for N=4 and T=float.  This workaround seems to help... | 
 |         static inline Vec<4,float> to_vec(VExt<4,float> v) { return bit_pun<Vec<4,float>>(v); } | 
 |     #endif | 
 |  | 
 |     SINT VExt<N,T> to_vext(const Vec<N,T>& v) { return bit_pun<VExt<N,T>>(v); } | 
 |     SINT Vec <N,T> to_vec(const VExt<N,T>& v) { return bit_pun<Vec <N,T>>(v); } | 
 |  | 
 |     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)); } | 
 |     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)); } | 
 |     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)); } | 
 |     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)); } | 
 |  | 
 |     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)); } | 
 |     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)); } | 
 |     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)); } | 
 |  | 
 |     SINT Vec<N,T> operator!(const Vec<N,T>& x) { return to_vec<N,T>(!to_vext(x)); } | 
 |     SINT Vec<N,T> operator-(const Vec<N,T>& x) { return to_vec<N,T>(-to_vext(x)); } | 
 |     SINT Vec<N,T> operator~(const Vec<N,T>& x) { return to_vec<N,T>(~to_vext(x)); } | 
 |  | 
 |     SINT Vec<N,T> operator<<(const Vec<N,T>& x, int bits) { return to_vec<N,T>(to_vext(x) << bits); } | 
 |     SINT Vec<N,T> operator>>(const Vec<N,T>& x, int bits) { return to_vec<N,T>(to_vext(x) >> bits); } | 
 |  | 
 |     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)); } | 
 |     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)); } | 
 |     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)); } | 
 |     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)); } | 
 |     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)); } | 
 |     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)); } | 
 |  | 
 | #else | 
 |  | 
 |     // Either SKNX_NO_SIMD is defined, or Clang/GCC vector extensions are not available. | 
 |     // We'll implement things portably, in a way that should be easily autovectorizable. | 
 |  | 
 |     // N == 1 scalar implementations. | 
 |     SIT Vec<1,T> operator+(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val + y.val; } | 
 |     SIT Vec<1,T> operator-(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val - y.val; } | 
 |     SIT Vec<1,T> operator*(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val * y.val; } | 
 |     SIT Vec<1,T> operator/(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val / y.val; } | 
 |  | 
 |     SIT Vec<1,T> operator^(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val ^ y.val; } | 
 |     SIT Vec<1,T> operator&(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val & y.val; } | 
 |     SIT Vec<1,T> operator|(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val | y.val; } | 
 |  | 
 |     SIT Vec<1,T> operator!(const Vec<1,T>& x) { return !x.val; } | 
 |     SIT Vec<1,T> operator-(const Vec<1,T>& x) { return -x.val; } | 
 |     SIT Vec<1,T> operator~(const Vec<1,T>& x) { return ~x.val; } | 
 |  | 
 |     SIT Vec<1,T> operator<<(const Vec<1,T>& x, int bits) { return x.val << bits; } | 
 |     SIT Vec<1,T> operator>>(const Vec<1,T>& x, int bits) { return x.val >> bits; } | 
 |  | 
 |     SIT Vec<1,M<T>> operator==(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val == y.val ? ~0 : 0; } | 
 |     SIT Vec<1,M<T>> operator!=(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val != y.val ? ~0 : 0; } | 
 |     SIT Vec<1,M<T>> operator<=(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val <= y.val ? ~0 : 0; } | 
 |     SIT Vec<1,M<T>> operator>=(const Vec<1,T>& x, const Vec<1,T>& y) { return x.val >= y.val ? ~0 : 0; } | 
 |     SIT Vec<1,M<T>> operator< (const Vec<1,T>& x, const Vec<1,T>& y) { return x.val <  y.val ? ~0 : 0; } | 
 |     SIT Vec<1,M<T>> operator> (const Vec<1,T>& x, const Vec<1,T>& y) { return x.val >  y.val ? ~0 : 0; } | 
 |  | 
 |     // All default N != 1 implementations just recurse on lo and hi halves. | 
 |     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); } | 
 |     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); } | 
 |     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); } | 
 |     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); } | 
 |  | 
 |     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); } | 
 |     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); } | 
 |     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); } | 
 |  | 
 |     SINT Vec<N,T> operator!(const Vec<N,T>& x) { return join(!x.lo, !x.hi); } | 
 |     SINT Vec<N,T> operator-(const Vec<N,T>& x) { return join(-x.lo, -x.hi); } | 
 |     SINT Vec<N,T> operator~(const Vec<N,T>& x) { return join(~x.lo, ~x.hi); } | 
 |  | 
 |     SINT Vec<N,T> operator<<(const Vec<N,T>& x, int bits) { return join(x.lo << bits, x.hi << bits); } | 
 |     SINT Vec<N,T> operator>>(const Vec<N,T>& x, int bits) { return join(x.lo >> bits, x.hi >> bits); } | 
 |  | 
 |     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); } | 
 |     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); } | 
 |     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); } | 
 |     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); } | 
 |     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); } | 
 |     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); } | 
 | #endif | 
 |  | 
 | // Some operations we want are not expressible with Clang/GCC vector | 
 | // extensions, so we implement them using the recursive approach. | 
 |  | 
 | // N == 1 scalar implementations. | 
 | SIT Vec<1,T> if_then_else(const Vec<1,M<T>>& cond, const Vec<1,T>& t, const Vec<1,T>& e) { | 
 |     auto t_bits = bit_pun<M<T>>(t), | 
 |          e_bits = bit_pun<M<T>>(e); | 
 |     return bit_pun<T>( (cond.val & t_bits) | (~cond.val & e_bits) ); | 
 | } | 
 |  | 
 | SIT bool any(const Vec<1,T>& x) { return x.val != 0; } | 
 | SIT bool all(const Vec<1,T>& x) { return x.val != 0; } | 
 |  | 
 | SIT T min(const Vec<1,T>& x) { return x.val; } | 
 | SIT T max(const Vec<1,T>& x) { return x.val; } | 
 |  | 
 | SIT Vec<1,T> min(const Vec<1,T>& x, const Vec<1,T>& y) { return std::min(x.val, y.val); } | 
 | SIT Vec<1,T> max(const Vec<1,T>& x, const Vec<1,T>& y) { return std::max(x.val, y.val); } | 
 |  | 
 | SIT Vec<1,T>  ceil(const Vec<1,T>& x) { return std:: ceil(x.val); } | 
 | SIT Vec<1,T> floor(const Vec<1,T>& x) { return std::floor(x.val); } | 
 | SIT Vec<1,T> trunc(const Vec<1,T>& x) { return std::trunc(x.val); } | 
 | SIT Vec<1,T> round(const Vec<1,T>& x) { return std::round(x.val); } | 
 | SIT Vec<1,T>  sqrt(const Vec<1,T>& x) { return std:: sqrt(x.val); } | 
 | SIT Vec<1,T>   abs(const Vec<1,T>& x) { return std::  abs(x.val); } | 
 |  | 
 | SIT Vec<1,T>   rcp(const Vec<1,T>& x) { return 1 / x.val; } | 
 | SIT Vec<1,T> rsqrt(const Vec<1,T>& x) { return rcp(sqrt(x)); } | 
 | SIT Vec<1,T>   mad(const Vec<1,T>& f, | 
 |                    const Vec<1,T>& m, | 
 |                    const Vec<1,T>& a) { return f*m+a; } | 
 |  | 
 | // All default N != 1 implementations just recurse on lo and hi halves. | 
 | SINT Vec<N,T> if_then_else(const Vec<N,M<T>>& cond, const Vec<N,T>& t, const Vec<N,T>& e) { | 
 |     return join(if_then_else(cond.lo, t.lo, e.lo), | 
 |                 if_then_else(cond.hi, t.hi, e.hi)); | 
 | } | 
 |  | 
 | SINT bool any(const Vec<N,T>& x) { return any(x.lo) || any(x.hi); } | 
 | SINT bool all(const Vec<N,T>& x) { return all(x.lo) && all(x.hi); } | 
 |  | 
 | SINT T min(const Vec<N,T>& x) { return std::min(min(x.lo), min(x.hi)); } | 
 | SINT T max(const Vec<N,T>& x) { return std::max(max(x.lo), max(x.hi)); } | 
 |  | 
 | 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)); } | 
 | 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)); } | 
 |  | 
 | SINT Vec<N,T>  ceil(const Vec<N,T>& x) { return join( ceil(x.lo),  ceil(x.hi)); } | 
 | SINT Vec<N,T> floor(const Vec<N,T>& x) { return join(floor(x.lo), floor(x.hi)); } | 
 | SINT Vec<N,T> trunc(const Vec<N,T>& x) { return join(trunc(x.lo), trunc(x.hi)); } | 
 | SINT Vec<N,T> round(const Vec<N,T>& x) { return join(round(x.lo), round(x.hi)); } | 
 | SINT Vec<N,T>  sqrt(const Vec<N,T>& x) { return join( sqrt(x.lo),  sqrt(x.hi)); } | 
 | SINT Vec<N,T>   abs(const Vec<N,T>& x) { return join(  abs(x.lo),   abs(x.hi)); } | 
 |  | 
 | SINT Vec<N,T>   rcp(const Vec<N,T>& x) { return join(  rcp(x.lo),   rcp(x.hi)); } | 
 | SINT Vec<N,T> rsqrt(const Vec<N,T>& x) { return join(rsqrt(x.lo), rsqrt(x.hi)); } | 
 | SINT Vec<N,T>   mad(const Vec<N,T>& f, | 
 |                     const Vec<N,T>& m, | 
 |                     const Vec<N,T>& a) { return join(mad(f.lo, m.lo, a.lo), mad(f.hi, m.hi, a.hi)); } | 
 |  | 
 |  | 
 | // Scalar/vector operations just splat the scalar to a vector... | 
 | SINTU Vec<N,T>    operator+ (U x, const Vec<N,T>& y) { return Vec<N,T>(x) +  y; } | 
 | SINTU Vec<N,T>    operator- (U x, const Vec<N,T>& y) { return Vec<N,T>(x) -  y; } | 
 | SINTU Vec<N,T>    operator* (U x, const Vec<N,T>& y) { return Vec<N,T>(x) *  y; } | 
 | SINTU Vec<N,T>    operator/ (U x, const Vec<N,T>& y) { return Vec<N,T>(x) /  y; } | 
 | SINTU Vec<N,T>    operator^ (U x, const Vec<N,T>& y) { return Vec<N,T>(x) ^  y; } | 
 | SINTU Vec<N,T>    operator& (U x, const Vec<N,T>& y) { return Vec<N,T>(x) &  y; } | 
 | SINTU Vec<N,T>    operator| (U x, const Vec<N,T>& y) { return Vec<N,T>(x) |  y; } | 
 | SINTU Vec<N,M<T>> operator==(U x, const Vec<N,T>& y) { return Vec<N,T>(x) == y; } | 
 | SINTU Vec<N,M<T>> operator!=(U x, const Vec<N,T>& y) { return Vec<N,T>(x) != y; } | 
 | SINTU Vec<N,M<T>> operator<=(U x, const Vec<N,T>& y) { return Vec<N,T>(x) <= y; } | 
 | SINTU Vec<N,M<T>> operator>=(U x, const Vec<N,T>& y) { return Vec<N,T>(x) >= y; } | 
 | SINTU Vec<N,M<T>> operator< (U x, const Vec<N,T>& y) { return Vec<N,T>(x) <  y; } | 
 | SINTU Vec<N,M<T>> operator> (U x, const Vec<N,T>& y) { return Vec<N,T>(x) >  y; } | 
 | SINTU Vec<N,T>           min(U x, const Vec<N,T>& y) { return min(Vec<N,T>(x), y); } | 
 | SINTU Vec<N,T>           max(U x, const Vec<N,T>& y) { return max(Vec<N,T>(x), y); } | 
 |  | 
 | // ... and same deal for vector/scalar operations. | 
 | SINTU Vec<N,T>    operator+ (const Vec<N,T>& x, U y) { return x +  Vec<N,T>(y); } | 
 | SINTU Vec<N,T>    operator- (const Vec<N,T>& x, U y) { return x -  Vec<N,T>(y); } | 
 | SINTU Vec<N,T>    operator* (const Vec<N,T>& x, U y) { return x *  Vec<N,T>(y); } | 
 | SINTU Vec<N,T>    operator/ (const Vec<N,T>& x, U y) { return x /  Vec<N,T>(y); } | 
 | SINTU Vec<N,T>    operator^ (const Vec<N,T>& x, U y) { return x ^  Vec<N,T>(y); } | 
 | SINTU Vec<N,T>    operator& (const Vec<N,T>& x, U y) { return x &  Vec<N,T>(y); } | 
 | SINTU Vec<N,T>    operator| (const Vec<N,T>& x, U y) { return x |  Vec<N,T>(y); } | 
 | SINTU Vec<N,M<T>> operator==(const Vec<N,T>& x, U y) { return x == Vec<N,T>(y); } | 
 | SINTU Vec<N,M<T>> operator!=(const Vec<N,T>& x, U y) { return x != Vec<N,T>(y); } | 
 | SINTU Vec<N,M<T>> operator<=(const Vec<N,T>& x, U y) { return x <= Vec<N,T>(y); } | 
 | SINTU Vec<N,M<T>> operator>=(const Vec<N,T>& x, U y) { return x >= Vec<N,T>(y); } | 
 | SINTU Vec<N,M<T>> operator< (const Vec<N,T>& x, U y) { return x <  Vec<N,T>(y); } | 
 | SINTU Vec<N,M<T>> operator> (const Vec<N,T>& x, U y) { return x >  Vec<N,T>(y); } | 
 | SINTU Vec<N,T>           min(const Vec<N,T>& x, U y) { return min(x, Vec<N,T>(y)); } | 
 | SINTU Vec<N,T>           max(const Vec<N,T>& x, U y) { return max(x, Vec<N,T>(y)); } | 
 |  | 
 | // All vector/scalar combinations for mad() with at least one vector. | 
 | SINTU Vec<N,T> mad(U f, const Vec<N,T>& m, const Vec<N,T>& a) { return Vec<N,T>(f)*m + a; } | 
 | SINTU Vec<N,T> mad(const Vec<N,T>& f, U m, const Vec<N,T>& a) { return f*Vec<N,T>(m) + a; } | 
 | SINTU Vec<N,T> mad(const Vec<N,T>& f, const Vec<N,T>& m, U a) { return f*m + Vec<N,T>(a); } | 
 | SINTU Vec<N,T> mad(const Vec<N,T>& f, U m, U a) { return f*Vec<N,T>(m) + Vec<N,T>(a); } | 
 | SINTU Vec<N,T> mad(U f, const Vec<N,T>& m, U a) { return Vec<N,T>(f)*m + Vec<N,T>(a); } | 
 | SINTU Vec<N,T> mad(U f, U m, const Vec<N,T>& a) { return Vec<N,T>(f)*Vec<N,T>(m) + a; } | 
 |  | 
 | // The various op= operators, for vectors... | 
 | SINT Vec<N,T>& operator+=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x + y); } | 
 | SINT Vec<N,T>& operator-=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x - y); } | 
 | SINT Vec<N,T>& operator*=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x * y); } | 
 | SINT Vec<N,T>& operator/=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x / y); } | 
 | SINT Vec<N,T>& operator^=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x ^ y); } | 
 | SINT Vec<N,T>& operator&=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x & y); } | 
 | SINT Vec<N,T>& operator|=(Vec<N,T>& x, const Vec<N,T>& y) { return (x = x | y); } | 
 |  | 
 | // ... for scalars... | 
 | SINTU Vec<N,T>& operator+=(Vec<N,T>& x, U y) { return (x = x + Vec<N,T>(y)); } | 
 | SINTU Vec<N,T>& operator-=(Vec<N,T>& x, U y) { return (x = x - Vec<N,T>(y)); } | 
 | SINTU Vec<N,T>& operator*=(Vec<N,T>& x, U y) { return (x = x * Vec<N,T>(y)); } | 
 | SINTU Vec<N,T>& operator/=(Vec<N,T>& x, U y) { return (x = x / Vec<N,T>(y)); } | 
 | SINTU Vec<N,T>& operator^=(Vec<N,T>& x, U y) { return (x = x ^ Vec<N,T>(y)); } | 
 | SINTU Vec<N,T>& operator&=(Vec<N,T>& x, U y) { return (x = x & Vec<N,T>(y)); } | 
 | SINTU Vec<N,T>& operator|=(Vec<N,T>& x, U y) { return (x = x | Vec<N,T>(y)); } | 
 |  | 
 | // ... and for shifts. | 
 | SINT Vec<N,T>& operator<<=(Vec<N,T>& x, int bits) { return (x = x << bits); } | 
 | SINT Vec<N,T>& operator>>=(Vec<N,T>& x, int bits) { return (x = x >> bits); } | 
 |  | 
 | // cast() Vec<N,S> to Vec<N,D>, as if applying a C-cast to each lane. | 
 | template <typename D, typename S> | 
 | static inline Vec<1,D> cast(const Vec<1,S>& src) { return (D)src.val; } | 
 |  | 
 | template <typename D, int N, typename S> | 
 | static inline Vec<N,D> cast(const Vec<N,S>& src) { | 
 | #if !defined(SKNX_NO_SIMD) && defined(__clang__) | 
 |     return to_vec(__builtin_convertvector(to_vext(src), VExt<N,D>)); | 
 | #else | 
 |     return join(cast<D>(src.lo), cast<D>(src.hi)); | 
 | #endif | 
 | } | 
 |  | 
 | // Shuffle values from a vector pretty arbitrarily: | 
 | //    skvx::Vec<4,float> rgba = {R,G,B,A}; | 
 | //    shuffle<2,1,0,3>        (rgba) ~> {B,G,R,A} | 
 | //    shuffle<2,1>            (rgba) ~> {B,G} | 
 | //    shuffle<2,1,2,1,2,1,2,1>(rgba) ~> {B,G,B,G,B,G,B,G} | 
 | //    shuffle<3,3,3,3>        (rgba) ~> {A,A,A,A} | 
 | // The only real restriction is that the output also be a legal N=power-of-two sknx::Vec. | 
 | template <int... Ix, int N, typename T> | 
 | static inline Vec<sizeof...(Ix),T> shuffle(const Vec<N,T>& x) { | 
 | #if !defined(SKNX_NO_SIMD) && defined(__clang__) | 
 |     return to_vec<sizeof...(Ix),T>(__builtin_shufflevector(to_vext(x), to_vext(x), Ix...)); | 
 | #else | 
 |     return { x[Ix]... }; | 
 | #endif | 
 | } | 
 |  | 
 | // div255(x) = (x + 127) / 255 is a bit-exact rounding divide-by-255, packing down to 8-bit. | 
 | template <int N> | 
 | static inline Vec<N,uint8_t> div255(const Vec<N,uint16_t>& x) { | 
 |     return cast<uint8_t>( (x+127)/255 ); | 
 | } | 
 |  | 
 | // approx_scale(x,y) approximates div255(cast<uint16_t>(x)*cast<uint16_t>(y)) within a bit, | 
 | // and is always perfect when x or y is 0 or 255. | 
 | template <int N> | 
 | static inline Vec<N,uint8_t> approx_scale(const Vec<N,uint8_t>& x, const Vec<N,uint8_t>& y) { | 
 |     // All of (x*y+x)/256, (x*y+y)/256, and (x*y+255)/256 meet the criteria above. | 
 |     // We happen to have historically picked (x*y+x)/256. | 
 |     auto X = cast<uint16_t>(x), | 
 |          Y = cast<uint16_t>(y); | 
 |     return cast<uint8_t>( (X*Y+X)/256 ); | 
 | } | 
 |  | 
 | #if !defined(SKNX_NO_SIMD) && defined(__ARM_NEON) | 
 |     // With NEON we can do eight u8*u8 -> u16 in one instruction, vmull_u8 (read, mul-long). | 
 |     static inline Vec<8,uint16_t> mull(const Vec<8,uint8_t>& x, | 
 |                                        const Vec<8,uint8_t>& y) { | 
 |         return to_vec<8,uint16_t>(vmull_u8(to_vext(x), | 
 |                                            to_vext(y))); | 
 |     } | 
 |  | 
 |     template <int N> | 
 |     static inline typename std::enable_if<(N < 8), | 
 |     Vec<N,uint16_t>>::type mull(const Vec<N,uint8_t>& x, | 
 |                                 const Vec<N,uint8_t>& y) { | 
 |         // N < 8 --> double up data until N == 8, returning the part we need. | 
 |         return mull(join(x,x), | 
 |                     join(y,y)).lo; | 
 |     } | 
 |  | 
 |     template <int N> | 
 |     static inline typename std::enable_if<(N > 8), | 
 |     Vec<N,uint16_t>>::type mull(const Vec<N,uint8_t>& x, | 
 |                                 const Vec<N,uint8_t>& y) { | 
 |         // N > 8 --> usual join(lo,hi) strategy to recurse down to N == 8. | 
 |         return join(mull(x.lo, y.lo), | 
 |                     mull(x.hi, y.hi)); | 
 |     } | 
 | #else | 
 |     // Nothing special when we don't have NEON... just cast up to 16-bit and multiply. | 
 |     template <int N> | 
 |     static inline Vec<N,uint16_t> mull(const Vec<N,uint8_t>& x, | 
 |                                        const Vec<N,uint8_t>& y) { | 
 |         return cast<uint16_t>(x) | 
 |              * cast<uint16_t>(y); | 
 |     } | 
 | #endif | 
 |  | 
 | #if !defined(SKNX_NO_SIMD) | 
 |  | 
 |     // Platform-specific specializations and overloads can now drop in here. | 
 |  | 
 |     #if defined(__SSE__) | 
 |         static inline Vec<4,float> sqrt(const Vec<4,float>& x) { | 
 |             return bit_pun<Vec<4,float>>(_mm_sqrt_ps(bit_pun<__m128>(x))); | 
 |         } | 
 |         static inline Vec<4,float> rsqrt(const Vec<4,float>& x) { | 
 |             return bit_pun<Vec<4,float>>(_mm_rsqrt_ps(bit_pun<__m128>(x))); | 
 |         } | 
 |         static inline Vec<4,float> rcp(const Vec<4,float>& x) { | 
 |             return bit_pun<Vec<4,float>>(_mm_rcp_ps(bit_pun<__m128>(x))); | 
 |         } | 
 |  | 
 |         static inline Vec<2,float>  sqrt(const Vec<2,float>& x) { | 
 |             return shuffle<0,1>( sqrt(shuffle<0,1,0,1>(x))); | 
 |         } | 
 |         static inline Vec<2,float> rsqrt(const Vec<2,float>& x) { | 
 |             return shuffle<0,1>(rsqrt(shuffle<0,1,0,1>(x))); | 
 |         } | 
 |         static inline Vec<2,float>   rcp(const Vec<2,float>& x) { | 
 |             return shuffle<0,1>(  rcp(shuffle<0,1,0,1>(x))); | 
 |         } | 
 |     #endif | 
 |  | 
 |     #if defined(__SSE4_1__) | 
 |         static inline Vec<4,float> if_then_else(const Vec<4,int  >& c, | 
 |                                                 const Vec<4,float>& t, | 
 |                                                 const Vec<4,float>& e) { | 
 |             return bit_pun<Vec<4,float>>(_mm_blendv_ps(bit_pun<__m128>(e), | 
 |                                                        bit_pun<__m128>(t), | 
 |                                                        bit_pun<__m128>(c))); | 
 |         } | 
 |     #elif defined(__SSE__) | 
 |         static inline Vec<4,float> if_then_else(const Vec<4,int  >& c, | 
 |                                                 const Vec<4,float>& t, | 
 |                                                 const Vec<4,float>& e) { | 
 |             return bit_pun<Vec<4,float>>(_mm_or_ps(_mm_and_ps   (bit_pun<__m128>(c), | 
 |                                                                  bit_pun<__m128>(t)), | 
 |                                                    _mm_andnot_ps(bit_pun<__m128>(c), | 
 |                                                                  bit_pun<__m128>(e)))); | 
 |         } | 
 |     #elif defined(__ARM_NEON) | 
 |         static inline Vec<4,float> if_then_else(const Vec<4,int  >& c, | 
 |                                                 const Vec<4,float>& t, | 
 |                                                 const Vec<4,float>& e) { | 
 |             return bit_pun<Vec<4,float>>(vbslq_f32(bit_pun<uint32x4_t> (c), | 
 |                                                    bit_pun<float32x4_t>(t), | 
 |                                                    bit_pun<float32x4_t>(e))); | 
 |         } | 
 |     #endif | 
 |  | 
 | #endif // !defined(SKNX_NO_SIMD) | 
 |  | 
 | }  // namespace skvx | 
 |  | 
 | #undef SINTU | 
 | #undef SINT | 
 | #undef SIT | 
 | #undef SKVX_ALIGNMENT | 
 |  | 
 | #endif//SKVX_DEFINED |