path: root/lib/libc/include/any-macos-any/simd/geometry.h

/*  Copyright (c) 2014-2017 Apple, Inc. All rights reserved.
 *
 *  The interfaces declared in this header provide operations for mathematical
 *  vectors; these functions and macros operate on vectors of floating-point
 *  data only.
 *
 *      Function                    Result
 *      ------------------------------------------------------------------
 *      simd_dot(x,y)               The dot product of x and y.
 *
 *      simd_project(x,y)           x projected onto y.  There are two variants
 *                                  of this function, simd_precise_project
 *                                  and simd_fast_project.  simd_project
 *                                  is equivalent to simd_precise_project
 *                                  unless you are compiling with -ffast-math
 *                                  specified, in which case it is equivalent
 *                                  to simd_fast_project.
 *
 *      simd_length(x)              The length (two-norm) of x.  Undefined if
 *                                  x is poorly scaled such that an
 *                                  intermediate computation overflows or
 *                                  underflows.  There are two variants
 *                                  of this function, simd_precise_length
 *                                  and simd_fast_length.  simd_length
 *                                  is equivalent to simd_precise_length
 *                                  unless you are compiling with -ffast-math
 *                                  specified, in which case it is equivalent
 *                                  to simd_fast_length.
 *
 *      simd_length_squared(x)      The square of the length of x.  If you
 *                                  simply need to compare relative magnitudes,
 *                                  use this instead of simd_length; it is
 *                                  faster than simd_fast_length and as
 *                                  accurate as simd_precise_length.
 *
 *      simd_norm_one(x)            The one-norm (sum of absolute values) of x.
 *
 *      simd_norm_inf(x)            The inf-norm (max absolute value) of x.
 *
 *      simd_distance(x,y)          The distance between x and y. Undefined if
 *                                  x and y are poorly scaled such that an
 *                                  intermediate computation overflows
 *                                  or underflows.  There are two variants
 *                                  of this function, simd_precise_distance
 *                                  and simd_fast_distance.  simd_distance
 *                                  is equivalent to simd_precise_distance
 *                                  unless you are compiling with -ffast-math
 *                                  specified, in which case it is equivalent
 *                                  to simd_fast_distance.
 *
 *      simd_distance_squared(x,y)  The square of the distance between x and y.
 *
 *      simd_normalize(x)           A vector pointing in the direction of x
 *                                  with length 1.0.  Undefined if x is
 *                                  the zero vector, or if x is poorly scaled
 *                                  such that an intermediate computation
 *                                  overflows or underflows.  There are two
 *                                  variants of this function,
 *                                  simd_precise_normalize and
 *                                  simd_fast_normalize.  simd_normalize
 *                                  is equivalent to simd_precise_normalize
 *                                  unless you are compiling with -ffast-math
 *                                  specified, in which case it is equivalent
 *                                  to simd_fast_normalize.
 *
 *      simd_cross(x,y)             If x and y are vectors of dimension 3,
 *                                  the cross-product of x and y.
 *
 *                                  If x and y are vectors of dimension 2,
 *                                  the cross-product of x and y interpreted as
 *                                  vectors in the z == 0 plane of a three-
 *                                  dimensional space.
 *
 *                                  If x and y are vectors with a length that
 *                                  is neither 2 nor 3, this operation is not
 *                                  available.
 *
 *      simd_reflect(x,n)           Reflects x through the plane perpendicular
 *                                  to the normal vector n.  Only available
 *                                  for vectors of length 2, 3, or 4.
 *
 *      simd_refract(x,n,eta)       Calculates the refraction direction given
 *                                  unit incident vector x, unit normal vector
 *                                  n, and index of refraction eta.  If the
 *                                  angle between the incident vector and the
 *                                  surface normal is too great for the
 *                                  specified index of refraction, zero is
 *                                  returned.
 *                                  Available for vectors of length 2, 3, or 4.
 *
 *     simd_orient(x,y,...)         Return a positive value if the origin and
 *                                  their ordered arguments determine a positively
 *                                  oriented parallelepiped, zero if it is degenerate,
 *                                  and a negative value if it is negatively oriented.
 *
 *  In C++ the following geometric functions are available in the simd::
 *  namespace:
 *
 *      C++ Function                    Equivalent C Function
 *      -----------------------------------------------------------
 *      simd::dot(x,y)                  simd_dot(x,y)
 *      simd::project(x,y)              simd_project(x,y)
 *      simd::length_squared(x)         simd_length_squared(x)
 *      simd::length(x)                 simd_length(x)
 *      simd::distance_squared(x,y)     simd_distance_squared(x,y)
 *      simd::norm_one(x)               simd_norm_one(x)
 *      simd::norm_inf(x)               simd_norm_inf(x)
 *      simd::distance(x,y)             simd_distance(x,y)
 *      simd::normalize(x)              simd_normalize(x)
 *      simd::cross(x,y)                simd_cross(x,y)
 *      simd::reflect(x,n)              simd_reflect(x,n)
 *      simd::refract(x,n,eta)          simd_refract(x,n,eta)
 *      simd::orient(x,y,...)           simd_orient(x,y,...)
 *
 *      simd::precise::project(x,y)     simd_precise_project(x,y)
 *      simd::precise::length(x)        simd_precise_length(x)
 *      simd::precise::distance(x,y)    simd_precise_distance(x,y)
 *      simd::precise::normalize(x)     simd_precise_normalize(x)
 *
 *      simd::fast::project(x,y)        simd_fast_project(x,y)
 *      simd::fast::length(x)           simd_fast_length(x)
 *      simd::fast::distance(x,y)       simd_fast_distance(x,y)
 *      simd::fast::normalize(x)        simd_fast_normalize(x)
 */

#ifndef __SIMD_GEOMETRY_HEADER__
#define __SIMD_GEOMETRY_HEADER__

#include <simd/base.h>
#if SIMD_COMPILER_HAS_REQUIRED_FEATURES
#include <simd/vector_types.h>
#include <simd/common.h>
#include <simd/extern.h>

#ifdef __cplusplus
extern "C" {
#endif
  
static _Float16 SIMD_CFUNC simd_dot(simd_half2  __x, simd_half2  __y);
static _Float16 SIMD_CFUNC simd_dot(simd_half3  __x, simd_half3  __y);
static _Float16 SIMD_CFUNC simd_dot(simd_half4  __x, simd_half4  __y);
static _Float16 SIMD_CFUNC simd_dot(simd_half8  __x, simd_half8  __y);
static _Float16 SIMD_CFUNC simd_dot(simd_half16 __x, simd_half16 __y);
static _Float16 SIMD_CFUNC simd_dot(simd_half32 __x, simd_half32 __y);
static float  SIMD_CFUNC simd_dot(simd_float2  __x, simd_float2  __y);
static float  SIMD_CFUNC simd_dot(simd_float3  __x, simd_float3  __y);
static float  SIMD_CFUNC simd_dot(simd_float4  __x, simd_float4  __y);
static float  SIMD_CFUNC simd_dot(simd_float8  __x, simd_float8  __y);
static float  SIMD_CFUNC simd_dot(simd_float16 __x, simd_float16 __y);
static double SIMD_CFUNC simd_dot(simd_double2 __x, simd_double2 __y);
static double SIMD_CFUNC simd_dot(simd_double3 __x, simd_double3 __y);
static double SIMD_CFUNC simd_dot(simd_double4 __x, simd_double4 __y);
static double SIMD_CFUNC simd_dot(simd_double8 __x, simd_double8 __y);
#define vector_dot simd_dot

static simd_half2   SIMD_CFUNC simd_precise_project(simd_half2   __x, simd_half2   __y);
static simd_half3   SIMD_CFUNC simd_precise_project(simd_half3   __x, simd_half3   __y);
static simd_half4   SIMD_CFUNC simd_precise_project(simd_half4   __x, simd_half4   __y);
static simd_half8   SIMD_CFUNC simd_precise_project(simd_half8   __x, simd_half8   __y);
static simd_half16  SIMD_CFUNC simd_precise_project(simd_half16  __x, simd_half16  __y);
static simd_half32  SIMD_CFUNC simd_precise_project(simd_half32  __x, simd_half32  __y);
static simd_float2  SIMD_CFUNC simd_precise_project(simd_float2  __x, simd_float2  __y);
static simd_float3  SIMD_CFUNC simd_precise_project(simd_float3  __x, simd_float3  __y);
static simd_float4  SIMD_CFUNC simd_precise_project(simd_float4  __x, simd_float4  __y);
static simd_float8  SIMD_CFUNC simd_precise_project(simd_float8  __x, simd_float8  __y);
static simd_float16 SIMD_CFUNC simd_precise_project(simd_float16 __x, simd_float16 __y);
static simd_double2 SIMD_CFUNC simd_precise_project(simd_double2 __x, simd_double2 __y);
static simd_double3 SIMD_CFUNC simd_precise_project(simd_double3 __x, simd_double3 __y);
static simd_double4 SIMD_CFUNC simd_precise_project(simd_double4 __x, simd_double4 __y);
static simd_double8 SIMD_CFUNC simd_precise_project(simd_double8 __x, simd_double8 __y);
#define vector_precise_project simd_precise_project

static simd_half2   SIMD_CFUNC simd_fast_project(simd_half2   __x, simd_half2   __y);
static simd_half3   SIMD_CFUNC simd_fast_project(simd_half3   __x, simd_half3   __y);
static simd_half4   SIMD_CFUNC simd_fast_project(simd_half4   __x, simd_half4   __y);
static simd_half8   SIMD_CFUNC simd_fast_project(simd_half8   __x, simd_half8   __y);
static simd_half16  SIMD_CFUNC simd_fast_project(simd_half16  __x, simd_half16  __y);
static simd_half32  SIMD_CFUNC simd_fast_project(simd_half32  __x, simd_half32  __y);
static simd_float2  SIMD_CFUNC simd_fast_project(simd_float2  __x, simd_float2  __y);
static simd_float3  SIMD_CFUNC simd_fast_project(simd_float3  __x, simd_float3  __y);
static simd_float4  SIMD_CFUNC simd_fast_project(simd_float4  __x, simd_float4  __y);
static simd_float8  SIMD_CFUNC simd_fast_project(simd_float8  __x, simd_float8  __y);
static simd_float16 SIMD_CFUNC simd_fast_project(simd_float16 __x, simd_float16 __y);
static simd_double2 SIMD_CFUNC simd_fast_project(simd_double2 __x, simd_double2 __y);
static simd_double3 SIMD_CFUNC simd_fast_project(simd_double3 __x, simd_double3 __y);
static simd_double4 SIMD_CFUNC simd_fast_project(simd_double4 __x, simd_double4 __y);
static simd_double8 SIMD_CFUNC simd_fast_project(simd_double8 __x, simd_double8 __y);
#define vector_fast_project simd_fast_project

static simd_half2   SIMD_CFUNC simd_project(simd_half2   __x, simd_half2   __y);
static simd_half3   SIMD_CFUNC simd_project(simd_half3   __x, simd_half3   __y);
static simd_half4   SIMD_CFUNC simd_project(simd_half4   __x, simd_half4   __y);
static simd_half8   SIMD_CFUNC simd_project(simd_half8   __x, simd_half8   __y);
static simd_half16  SIMD_CFUNC simd_project(simd_half16  __x, simd_half16  __y);
static simd_half32  SIMD_CFUNC simd_project(simd_half32  __x, simd_half32  __y);
static simd_float2  SIMD_CFUNC simd_project(simd_float2  __x, simd_float2  __y);
static simd_float3  SIMD_CFUNC simd_project(simd_float3  __x, simd_float3  __y);
static simd_float4  SIMD_CFUNC simd_project(simd_float4  __x, simd_float4  __y);
static simd_float8  SIMD_CFUNC simd_project(simd_float8  __x, simd_float8  __y);
static simd_float16 SIMD_CFUNC simd_project(simd_float16 __x, simd_float16 __y);
static simd_double2 SIMD_CFUNC simd_project(simd_double2 __x, simd_double2 __y);
static simd_double3 SIMD_CFUNC simd_project(simd_double3 __x, simd_double3 __y);
static simd_double4 SIMD_CFUNC simd_project(simd_double4 __x, simd_double4 __y);
static simd_double8 SIMD_CFUNC simd_project(simd_double8 __x, simd_double8 __y);
#define vector_project simd_project

#if SIMD_LIBRARY_VERSION >= 6
static _Float16 SIMD_CFUNC simd_precise_length(simd_half2  __x);
static _Float16 SIMD_CFUNC simd_precise_length(simd_half3  __x);
static _Float16 SIMD_CFUNC simd_precise_length(simd_half4  __x);
static _Float16 SIMD_CFUNC simd_precise_length(simd_half8  __x);
static _Float16 SIMD_CFUNC simd_precise_length(simd_half16 __x);
static _Float16 SIMD_CFUNC simd_precise_length(simd_half32 __x);
#endif // SIMD_LIBRARY_VERSION >= 6
static float  SIMD_CFUNC simd_precise_length(simd_float2  __x);
static float  SIMD_CFUNC simd_precise_length(simd_float3  __x);
static float  SIMD_CFUNC simd_precise_length(simd_float4  __x);
static float  SIMD_CFUNC simd_precise_length(simd_float8  __x);
static float  SIMD_CFUNC simd_precise_length(simd_float16 __x);
static double SIMD_CFUNC simd_precise_length(simd_double2 __x);
static double SIMD_CFUNC simd_precise_length(simd_double3 __x);
static double SIMD_CFUNC simd_precise_length(simd_double4 __x);
static double SIMD_CFUNC simd_precise_length(simd_double8 __x);
#define vector_precise_length simd_precise_length

static _Float16 SIMD_CFUNC simd_fast_length(simd_half2  __x);
static _Float16 SIMD_CFUNC simd_fast_length(simd_half3  __x);
static _Float16 SIMD_CFUNC simd_fast_length(simd_half4  __x);
static _Float16 SIMD_CFUNC simd_fast_length(simd_half8  __x);
static _Float16 SIMD_CFUNC simd_fast_length(simd_half16 __x);
static _Float16 SIMD_CFUNC simd_fast_length(simd_half32 __x);
static float  SIMD_CFUNC simd_fast_length(simd_float2  __x);
static float  SIMD_CFUNC simd_fast_length(simd_float3  __x);
static float  SIMD_CFUNC simd_fast_length(simd_float4  __x);
static float  SIMD_CFUNC simd_fast_length(simd_float8  __x);
static float  SIMD_CFUNC simd_fast_length(simd_float16 __x);
static double SIMD_CFUNC simd_fast_length(simd_double2 __x);
static double SIMD_CFUNC simd_fast_length(simd_double3 __x);
static double SIMD_CFUNC simd_fast_length(simd_double4 __x);
static double SIMD_CFUNC simd_fast_length(simd_double8 __x);
#define vector_fast_length simd_fast_length

static _Float16 SIMD_CFUNC simd_length(simd_half2  __x);
static _Float16 SIMD_CFUNC simd_length(simd_half3  __x);
static _Float16 SIMD_CFUNC simd_length(simd_half4  __x);
static _Float16 SIMD_CFUNC simd_length(simd_half8  __x);
static _Float16 SIMD_CFUNC simd_length(simd_half16 __x);
static _Float16 SIMD_CFUNC simd_length(simd_half32 __x);
static float  SIMD_CFUNC simd_length(simd_float2  __x);
static float  SIMD_CFUNC simd_length(simd_float3  __x);
static float  SIMD_CFUNC simd_length(simd_float4  __x);
static float  SIMD_CFUNC simd_length(simd_float8  __x);
static float  SIMD_CFUNC simd_length(simd_float16 __x);
static double SIMD_CFUNC simd_length(simd_double2 __x);
static double SIMD_CFUNC simd_length(simd_double3 __x);
static double SIMD_CFUNC simd_length(simd_double4 __x);
static double SIMD_CFUNC simd_length(simd_double8 __x);
#define vector_length simd_length

static _Float16 SIMD_CFUNC simd_length_squared(simd_half2  __x);
static _Float16 SIMD_CFUNC simd_length_squared(simd_half3  __x);
static _Float16 SIMD_CFUNC simd_length_squared(simd_half4  __x);
static _Float16 SIMD_CFUNC simd_length_squared(simd_half8  __x);
static _Float16 SIMD_CFUNC simd_length_squared(simd_half16 __x);
static _Float16 SIMD_CFUNC simd_length_squared(simd_half32 __x);
static float  SIMD_CFUNC simd_length_squared(simd_float2  __x);
static float  SIMD_CFUNC simd_length_squared(simd_float3  __x);
static float  SIMD_CFUNC simd_length_squared(simd_float4  __x);
static float  SIMD_CFUNC simd_length_squared(simd_float8  __x);
static float  SIMD_CFUNC simd_length_squared(simd_float16 __x);
static double SIMD_CFUNC simd_length_squared(simd_double2 __x);
static double SIMD_CFUNC simd_length_squared(simd_double3 __x);
static double SIMD_CFUNC simd_length_squared(simd_double4 __x);
static double SIMD_CFUNC simd_length_squared(simd_double8 __x);
#define vector_length_squared simd_length_squared

static _Float16 SIMD_CFUNC simd_norm_one(simd_half2 __x);
static _Float16 SIMD_CFUNC simd_norm_one(simd_half3 __x);
static _Float16 SIMD_CFUNC simd_norm_one(simd_half4 __x);
static _Float16 SIMD_CFUNC simd_norm_one(simd_half8 __x);
static _Float16 SIMD_CFUNC simd_norm_one(simd_half16 __x);
static _Float16 SIMD_CFUNC simd_norm_one(simd_half32 __x);
static float SIMD_CFUNC simd_norm_one(simd_float2 __x);
static float SIMD_CFUNC simd_norm_one(simd_float3 __x);
static float SIMD_CFUNC simd_norm_one(simd_float4 __x);
static float SIMD_CFUNC simd_norm_one(simd_float8 __x);
static float SIMD_CFUNC simd_norm_one(simd_float16 __x);
static double SIMD_CFUNC simd_norm_one(simd_double2 __x);
static double SIMD_CFUNC simd_norm_one(simd_double3 __x);
static double SIMD_CFUNC simd_norm_one(simd_double4 __x);
static double SIMD_CFUNC simd_norm_one(simd_double8 __x);
#define vector_norm_one simd_norm_one

static _Float16 SIMD_CFUNC simd_norm_inf(simd_half2 __x);
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half3 __x);
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half4 __x);
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half8 __x);
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half16 __x);
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half32 __x);
static float SIMD_CFUNC simd_norm_inf(simd_float2 __x);
static float SIMD_CFUNC simd_norm_inf(simd_float3 __x);
static float SIMD_CFUNC simd_norm_inf(simd_float4 __x);
static float SIMD_CFUNC simd_norm_inf(simd_float8 __x);
static float SIMD_CFUNC simd_norm_inf(simd_float16 __x);
static double SIMD_CFUNC simd_norm_inf(simd_double2 __x);
static double SIMD_CFUNC simd_norm_inf(simd_double3 __x);
static double SIMD_CFUNC simd_norm_inf(simd_double4 __x);
static double SIMD_CFUNC simd_norm_inf(simd_double8 __x);
#define vector_norm_inf simd_norm_inf

static _Float16 SIMD_CFUNC simd_precise_distance(simd_half2  __x, simd_half2  __y);
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half3  __x, simd_half3  __y);
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half4  __x, simd_half4  __y);
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half8  __x, simd_half8  __y);
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half16 __x, simd_half16 __y);
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half32 __x, simd_half32 __y);
static float  SIMD_CFUNC simd_precise_distance(simd_float2  __x, simd_float2  __y);
static float  SIMD_CFUNC simd_precise_distance(simd_float3  __x, simd_float3  __y);
static float  SIMD_CFUNC simd_precise_distance(simd_float4  __x, simd_float4  __y);
static float  SIMD_CFUNC simd_precise_distance(simd_float8  __x, simd_float8  __y);
static float  SIMD_CFUNC simd_precise_distance(simd_float16 __x, simd_float16 __y);
static double SIMD_CFUNC simd_precise_distance(simd_double2 __x, simd_double2 __y);
static double SIMD_CFUNC simd_precise_distance(simd_double3 __x, simd_double3 __y);
static double SIMD_CFUNC simd_precise_distance(simd_double4 __x, simd_double4 __y);
static double SIMD_CFUNC simd_precise_distance(simd_double8 __x, simd_double8 __y);
#define vector_precise_distance simd_precise_distance

static _Float16 SIMD_CFUNC simd_fast_distance(simd_half2  __x, simd_half2  __y);
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half3  __x, simd_half3  __y);
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half4  __x, simd_half4  __y);
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half8  __x, simd_half8  __y);
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half16 __x, simd_half16 __y);
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half32 __x, simd_half32 __y);
static float  SIMD_CFUNC simd_fast_distance(simd_float2  __x, simd_float2  __y);
static float  SIMD_CFUNC simd_fast_distance(simd_float3  __x, simd_float3  __y);
static float  SIMD_CFUNC simd_fast_distance(simd_float4  __x, simd_float4  __y);
static float  SIMD_CFUNC simd_fast_distance(simd_float8  __x, simd_float8  __y);
static float  SIMD_CFUNC simd_fast_distance(simd_float16 __x, simd_float16 __y);
static double SIMD_CFUNC simd_fast_distance(simd_double2 __x, simd_double2 __y);
static double SIMD_CFUNC simd_fast_distance(simd_double3 __x, simd_double3 __y);
static double SIMD_CFUNC simd_fast_distance(simd_double4 __x, simd_double4 __y);
static double SIMD_CFUNC simd_fast_distance(simd_double8 __x, simd_double8 __y);
#define vector_fast_distance simd_fast_distance

static _Float16 SIMD_CFUNC simd_distance(simd_half2  __x, simd_half2  __y);
static _Float16 SIMD_CFUNC simd_distance(simd_half3  __x, simd_half3  __y);
static _Float16 SIMD_CFUNC simd_distance(simd_half4  __x, simd_half4  __y);
static _Float16 SIMD_CFUNC simd_distance(simd_half8  __x, simd_half8  __y);
static _Float16 SIMD_CFUNC simd_distance(simd_half16 __x, simd_half16 __y);
static _Float16 SIMD_CFUNC simd_distance(simd_half32 __x, simd_half32 __y);
static float  SIMD_CFUNC simd_distance(simd_float2  __x, simd_float2  __y);
static float  SIMD_CFUNC simd_distance(simd_float3  __x, simd_float3  __y);
static float  SIMD_CFUNC simd_distance(simd_float4  __x, simd_float4  __y);
static float  SIMD_CFUNC simd_distance(simd_float8  __x, simd_float8  __y);
static float  SIMD_CFUNC simd_distance(simd_float16 __x, simd_float16 __y);
static double SIMD_CFUNC simd_distance(simd_double2 __x, simd_double2 __y);
static double SIMD_CFUNC simd_distance(simd_double3 __x, simd_double3 __y);
static double SIMD_CFUNC simd_distance(simd_double4 __x, simd_double4 __y);
static double SIMD_CFUNC simd_distance(simd_double8 __x, simd_double8 __y);
#define vector_distance simd_distance

static _Float16 SIMD_CFUNC simd_distance_squared(simd_half2  __x, simd_half2  __y);
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half3  __x, simd_half3  __y);
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half4  __x, simd_half4  __y);
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half8  __x, simd_half8  __y);
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half16 __x, simd_half16 __y);
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half32 __x, simd_half32 __y);
static float  SIMD_CFUNC simd_distance_squared(simd_float2  __x, simd_float2  __y);
static float  SIMD_CFUNC simd_distance_squared(simd_float3  __x, simd_float3  __y);
static float  SIMD_CFUNC simd_distance_squared(simd_float4  __x, simd_float4  __y);
static float  SIMD_CFUNC simd_distance_squared(simd_float8  __x, simd_float8  __y);
static float  SIMD_CFUNC simd_distance_squared(simd_float16 __x, simd_float16 __y);
static double SIMD_CFUNC simd_distance_squared(simd_double2 __x, simd_double2 __y);
static double SIMD_CFUNC simd_distance_squared(simd_double3 __x, simd_double3 __y);
static double SIMD_CFUNC simd_distance_squared(simd_double4 __x, simd_double4 __y);
static double SIMD_CFUNC simd_distance_squared(simd_double8 __x, simd_double8 __y);
#define vector_distance_squared simd_distance_squared

static simd_half2   SIMD_CFUNC simd_precise_normalize(simd_half2   __x);
static simd_half3   SIMD_CFUNC simd_precise_normalize(simd_half3   __x);
static simd_half4   SIMD_CFUNC simd_precise_normalize(simd_half4   __x);
static simd_half8   SIMD_CFUNC simd_precise_normalize(simd_half8   __x);
static simd_half16  SIMD_CFUNC simd_precise_normalize(simd_half16  __x);
static simd_half32  SIMD_CFUNC simd_precise_normalize(simd_half32  __x);
static simd_float2  SIMD_CFUNC simd_precise_normalize(simd_float2  __x);
static simd_float3  SIMD_CFUNC simd_precise_normalize(simd_float3  __x);
static simd_float4  SIMD_CFUNC simd_precise_normalize(simd_float4  __x);
static simd_float8  SIMD_CFUNC simd_precise_normalize(simd_float8  __x);
static simd_float16 SIMD_CFUNC simd_precise_normalize(simd_float16 __x);
static simd_double2 SIMD_CFUNC simd_precise_normalize(simd_double2 __x);
static simd_double3 SIMD_CFUNC simd_precise_normalize(simd_double3 __x);
static simd_double4 SIMD_CFUNC simd_precise_normalize(simd_double4 __x);
static simd_double8 SIMD_CFUNC simd_precise_normalize(simd_double8 __x);
#define vector_precise_normalize simd_precise_normalize

static simd_half2   SIMD_CFUNC simd_fast_normalize(simd_half2   __x);
static simd_half3   SIMD_CFUNC simd_fast_normalize(simd_half3   __x);
static simd_half4   SIMD_CFUNC simd_fast_normalize(simd_half4   __x);
static simd_half8   SIMD_CFUNC simd_fast_normalize(simd_half8   __x);
static simd_half16  SIMD_CFUNC simd_fast_normalize(simd_half16  __x);
static simd_half32  SIMD_CFUNC simd_fast_normalize(simd_half32  __x);
static simd_float2  SIMD_CFUNC simd_fast_normalize(simd_float2  __x);
static simd_float3  SIMD_CFUNC simd_fast_normalize(simd_float3  __x);
static simd_float4  SIMD_CFUNC simd_fast_normalize(simd_float4  __x);
static simd_float8  SIMD_CFUNC simd_fast_normalize(simd_float8  __x);
static simd_float16 SIMD_CFUNC simd_fast_normalize(simd_float16 __x);
static simd_double2 SIMD_CFUNC simd_fast_normalize(simd_double2 __x);
static simd_double3 SIMD_CFUNC simd_fast_normalize(simd_double3 __x);
static simd_double4 SIMD_CFUNC simd_fast_normalize(simd_double4 __x);
static simd_double8 SIMD_CFUNC simd_fast_normalize(simd_double8 __x);
#define vector_fast_normalize simd_fast_normalize

static simd_half2   SIMD_CFUNC simd_normalize(simd_half2   __x);
static simd_half3   SIMD_CFUNC simd_normalize(simd_half3   __x);
static simd_half4   SIMD_CFUNC simd_normalize(simd_half4   __x);
static simd_half8   SIMD_CFUNC simd_normalize(simd_half8   __x);
static simd_half16  SIMD_CFUNC simd_normalize(simd_half16  __x);
static simd_half32  SIMD_CFUNC simd_normalize(simd_half32  __x);
static simd_float2  SIMD_CFUNC simd_normalize(simd_float2  __x);
static simd_float3  SIMD_CFUNC simd_normalize(simd_float3  __x);
static simd_float4  SIMD_CFUNC simd_normalize(simd_float4  __x);
static simd_float8  SIMD_CFUNC simd_normalize(simd_float8  __x);
static simd_float16 SIMD_CFUNC simd_normalize(simd_float16 __x);
static simd_double2 SIMD_CFUNC simd_normalize(simd_double2 __x);
static simd_double3 SIMD_CFUNC simd_normalize(simd_double3 __x);
static simd_double4 SIMD_CFUNC simd_normalize(simd_double4 __x);
static simd_double8 SIMD_CFUNC simd_normalize(simd_double8 __x);
#define vector_normalize simd_normalize

static simd_half3   SIMD_CFUNC simd_cross(simd_half2   __x, simd_half2   __y);
static simd_half3   SIMD_CFUNC simd_cross(simd_half3   __x, simd_half3   __y);
static simd_float3  SIMD_CFUNC simd_cross(simd_float2  __x, simd_float2  __y);
static simd_float3  SIMD_CFUNC simd_cross(simd_float3  __x, simd_float3  __y);
static simd_double3 SIMD_CFUNC simd_cross(simd_double2 __x, simd_double2 __y);
static simd_double3 SIMD_CFUNC simd_cross(simd_double3 __x, simd_double3 __y);
#define vector_cross simd_cross

static simd_half2   SIMD_CFUNC simd_reflect(simd_half2   __x, simd_half2   __n);
static simd_half3   SIMD_CFUNC simd_reflect(simd_half3   __x, simd_half3   __n);
static simd_half4   SIMD_CFUNC simd_reflect(simd_half4   __x, simd_half4   __n);
static simd_float2  SIMD_CFUNC simd_reflect(simd_float2  __x, simd_float2  __n);
static simd_float3  SIMD_CFUNC simd_reflect(simd_float3  __x, simd_float3  __n);
static simd_float4  SIMD_CFUNC simd_reflect(simd_float4  __x, simd_float4  __n);
static simd_double2 SIMD_CFUNC simd_reflect(simd_double2 __x, simd_double2 __n);
static simd_double3 SIMD_CFUNC simd_reflect(simd_double3 __x, simd_double3 __n);
static simd_double4 SIMD_CFUNC simd_reflect(simd_double4 __x, simd_double4 __n);
#define vector_reflect simd_reflect

#if SIMD_LIBRARY_VERSION >= 6
static simd_half2   SIMD_CFUNC simd_refract(simd_half2   __x, simd_half2   __n, _Float16 __eta);
static simd_half3   SIMD_CFUNC simd_refract(simd_half3   __x, simd_half3   __n, _Float16 __eta);
static simd_half4   SIMD_CFUNC simd_refract(simd_half4   __x, simd_half4   __n, _Float16 __eta);
#endif // SIMD_LIBRARY_VERSION >= 6
static simd_float2  SIMD_CFUNC simd_refract(simd_float2  __x, simd_float2  __n, float __eta);
static simd_float3  SIMD_CFUNC simd_refract(simd_float3  __x, simd_float3  __n, float __eta);
static simd_float4  SIMD_CFUNC simd_refract(simd_float4  __x, simd_float4  __n, float __eta);
static simd_double2 SIMD_CFUNC simd_refract(simd_double2 __x, simd_double2 __n, double __eta);
static simd_double3 SIMD_CFUNC simd_refract(simd_double3 __x, simd_double3 __n, double __eta);
static simd_double4 SIMD_CFUNC simd_refract(simd_double4 __x, simd_double4 __n, double __eta);
#define vector_refract simd_refract

#if SIMD_LIBRARY_VERSION >= 2
/*  These functions require that you are building for OS X 10.12 or later,
 *  iOS 10.0 or later, watchOS 3.0 or later, and tvOS 10.0 or later.  On
 *  earlier OS versions, the library functions that implement these
 *  operations are not available.                                             */

/*! @functiongroup vector orientation
 *
 *  @discussion These functions return a positive value if the origin and
 *  their ordered arguments determine a positively oriented parallelepiped,
 *  zero if it is degenerate, and a negative value if it is negatively
 *  oriented.  This is equivalent to saying that the matrix with rows equal
 *  to the vectors has a positive, zero, or negative determinant,
 *  respectively.
 *
 *  Naive evaluation of the determinant is prone to producing incorrect
 *  results if the vectors are nearly degenerate (e.g. floating-point
 *  rounding might cause the determinant to be zero or negative when
 *  the points are very nearly coplanar but positively oriented).  If
 *  the vectors are very large or small, computing the determininat is
 *  also prone to premature overflow, which may cause the result to be
 *  NaN even though the vectors contain normal floating-point numbers.
 *
 *  These routines take care to avoid those issues and always return a
 *  result with correct sign, even when the problem is very ill-
 *  conditioned.                                                              */

/*! @abstract Test the orientation of two 2d vectors.
 *
 *  @param __x The first vector.
 *  @param __y The second vector.
 *
 *  @result Positive if (x, y) are positively oriented, zero if they are
 *  colinear, and negative if they are negatively oriented.
 *
 *  @discussion For two-dimensional vectors, "positively oriented" is
 *  equivalent to the ordering (0, x, y) proceeding counter-clockwise
 *  when viewed down the z axis, or to the cross product of x and y
 *  extended to three-dimensions having positive z-component.                 */
static float SIMD_CFUNC simd_orient(simd_float2 __x, simd_float2 __y);

/*! @abstract Test the orientation of two 2d vectors.
 *
 *  @param __x The first vector.
 *  @param __y The second vector.
 *
 *  @result Positive if (x, y) are positively oriented, zero if they are
 *  colinear, and negative if they are negatively oriented.
 *
 *  @discussion For two-dimensional vectors, "positively oriented" is
 *  equivalent to the ordering (0, x, y) proceeding counter- clockwise
 *  when viewed down the z axis, or to the cross product of x and y
 *  extended to three-dimensions having positive z-component.                 */
static double SIMD_CFUNC simd_orient(simd_double2 __x, simd_double2 __y);

/*! @abstract Test the orientation of three 3d vectors.
 *
 *  @param __x The first vector.
 *  @param __y The second vector.
 *  @param __z The third vector.
 *
 *  @result Positive if (x, y, z) are positively oriented, zero if they
 *  are coplanar, and negative if they are negatively oriented.
 *
 *  @discussion For three-dimensional vectors, "positively oriented" is
 *  equivalent to the ordering (x, y, z) following the "right hand rule",
 *  or to the dot product of z with the cross product of x and y being
 *  positive.                                                                 */
static float SIMD_CFUNC simd_orient(simd_float3 __x, simd_float3 __y, simd_float3 __z);

/*! @abstract Test the orientation of three 3d vectors.
 *
 *  @param __x The first vector.
 *  @param __y The second vector.
 *  @param __z The third vector.
 *
 *  @result Positive if (x, y, c) are positively oriented, zero if they
 *  are coplanar, and negative if they are negatively oriented.
 *
 *  @discussion For three-dimensional vectors, "positively oriented" is
 *  equivalent to the ordering (x, y, z) following the "right hand rule",
 *  or to the dot product of z with the cross product of x and y being
 *  positive.                                                                 */
static double SIMD_CFUNC simd_orient(simd_double3 __x, simd_double3 __y, simd_double3 __z);

/*! @functiongroup point (affine) orientation
 *
 *  @discussion These functions return a positive value if their ordered
 *  arguments determine a positively oriented parallelepiped, zero if it
 *  is degenerate, and a negative value if it is negatively oriented.
 *
 *  simd_orient(a, b, c) is formally equivalent to simd_orient(b-a, c-a),
 *  but it is not effected by rounding error from subtraction of points,
 *  as that implementation would be.  Care is taken so that the sign of
 *  the result is always correct, even if the problem is ill-conditioned.     */

/*! @abstract Test the orientation of a triangle in 2d.
 *
 *  @param __a The first point of the triangle.
 *  @param __b The second point of the triangle.
 *  @param __c The third point of the triangle.
 *
 *  @result Positive if the triangle is positively oriented, zero if it
 *  is degenerate (three points in a line), and negative if it is negatively
 *  oriented.
 *
 *  @discussion "Positively oriented" is equivalent to the ordering
 *  (a, b, c) proceeding counter-clockwise when viewed down the z axis,
 *  or to the cross product of a-c and b-c extended to three-dimensions
 *  having positive z-component.                                              */
static float SIMD_CFUNC simd_orient(simd_float2 __a, simd_float2 __b, simd_float2 __c);

/*! @abstract Test the orientation of a triangle in 2d.
 *
 *  @param __a The first point of the triangle.
 *  @param __b The second point of the triangle.
 *  @param __c The third point of the triangle.
 *
 *  @result Positive if the triangle is positively oriented, zero if it
 *  is degenerate (three points in a line), and negative if it is negatively
 *  oriented.
 *
 *  @discussion "Positively oriented" is equivalent to the ordering
 *  (a, b, c) proceeding counter-clockwise when viewed down the z axis,
 *  or to the cross product of a-c and b-c extended to three-dimensions
 *  having positive z-component.                                              */
static double SIMD_CFUNC simd_orient(simd_double2 __a, simd_double2 __b, simd_double2 __c);

/*! @abstract Test the orientation of a tetrahedron in 3d.
 *
 *  @param __a The first point of the tetrahedron.
 *  @param __b The second point of the tetrahedron.
 *  @param __c The third point of the tetrahedron.
 *  @param __d The fourth point of the tetrahedron.
 *
 *  @result Positive if the tetrahedron is positively oriented, zero if it
 *  is degenerate (four points in a plane), and negative if it is negatively
 *  oriented.
 *
 *  @discussion "Positively oriented" is equivalent to the vectors
 *  (a-d, b-d, c-d) following the "right hand rule", or to the dot product
 *  of c-d with the the cross product of a-d and b-d being positive.          */
static float SIMD_CFUNC simd_orient(simd_float3 __a, simd_float3 __b, simd_float3 __c, simd_float3 __d);

/*! @abstract Test the orientation of a tetrahedron in 3d.
 *
 *  @param __a The first point of the tetrahedron.
 *  @param __b The second point of the tetrahedron.
 *  @param __c The third point of the tetrahedron.
 *  @param __d The fourth point of the tetrahedron.
 *
 *  @result Positive if the tetrahedron is positively oriented, zero if it
 *  is degenerate (four points in a plane), and negative if it is negatively
 *  oriented.
 *
 *  @discussion "Positively oriented" is equivalent to the vectors
 *  (a-d, b-d, c-d) following the "right hand rule", or to the dot product
 *  of c-d with the the cross product of a-d and b-d being positive.          */
static double SIMD_CFUNC simd_orient(simd_double3 __a, simd_double3 __b, simd_double3 __c, simd_double3 __d);

/*! @functiongroup incircle (points) tests
 *
 *  @discussion These functions determine whether the point x is inside, on,
 *  or outside the circle or sphere passing through a group of points.  If
 *  x is inside the circle, the result is positive; if x is on the circle,
 *  the result is zero; if x is outside the circle the result is negative.
 *
 *  These functions are always exact, even if the problem is ill-
 *  conditioned (meaning that the points are nearly co-linear or
 *  co-planar).
 *
 *  If the points are negatively-oriented, the the notions of "inside" and
 *  "outside" are flipped.  If the points are degenerate, then the result
 *  is undefined.                                                             */

/*! @abstract Test if x lies inside, on, or outside the circle passing
 *  through a, b, and c.
 *
 *  @param __x The point being tested.
 *  @param __a The first point determining the circle.
 *  @param __b The second point determining the circle.
 *  @param __c The third point determining the circle.
 *
 *  @result Assuming that (a,b,c) are positively-oriented, positive if x is
 *  inside the circle, zero if x is on the circle, and negative if x is
 *  outside the circle.  The sign of the result is flipped if (a,b,c) are
 *  negatively-oriented.                                                      */
static float SIMD_CFUNC simd_incircle(simd_float2 __x, simd_float2 __a, simd_float2 __b, simd_float2 __c);

/*! @abstract Test if x lies inside, on, or outside the circle passing
 *  through a, b, and c.
 *
 *  @param __x The point being tested.
 *  @param __a The first point determining the circle.
 *  @param __b The second point determining the circle.
 *  @param __c The third point determining the circle.
 *
 *  @result Assuming that (a,b,c) are positively-oriented, positive if x is
 *  inside the circle, zero if x is on the circle, and negative if x is
 *  outside the circle.  The sign of the result is flipped if (a,b,c) are
 *  negatively-oriented.                                                      */
static double SIMD_CFUNC simd_incircle(simd_double2 __x, simd_double2 __a, simd_double2 __b, simd_double2 __c);

/*! @abstract Test if x lies inside, on, or outside the sphere passing
 *  through a, b, c, and d.
 *
 *  @param __x The point being tested.
 *  @param __a The first point determining the sphere.
 *  @param __b The second point determining the sphere.
 *  @param __c The third point determining the sphere.
 *  @param __d The fourth point determining the sphere.
 *
 *  @result Assuming that the points are positively-oriented, positive if x
 *  is inside the sphere, zero if x is on the sphere, and negative if x is
 *  outside the sphere.  The sign of the result is flipped if the points are
 *  negatively-oriented.                                                      */
static float SIMD_CFUNC simd_insphere(simd_float3 __x, simd_float3 __a, simd_float3 __b, simd_float3 __c, simd_float3 __d);

/*! @abstract Test if x lies inside, on, or outside the sphere passing
 *  through a, b, c, and d.
 *
 *  @param __x The point being tested.
 *  @param __a The first point determining the sphere.
 *  @param __b The second point determining the sphere.
 *  @param __c The third point determining the sphere.
 *  @param __d The fourth point determining the sphere.
 *
 *  @result Assuming that the points are positively-oriented, positive if x
 *  is inside the sphere, zero if x is on the sphere, and negative if x is
 *  outside the sphere.  The sign of the result is flipped if the points are
 *  negatively-oriented.                                                      */
static double SIMD_CFUNC simd_insphere(simd_double3 __x, simd_double3 __a, simd_double3 __b, simd_double3 __c, simd_double3 __d);
#endif /* SIMD_LIBRARY_VERSION */

#if SIMD_LIBRARY_VERSION >= 6
/*  fp16 support requires that you are building for OS X 15.0 or later,
 *  iOS 18.0 or later, watchOS 11.0 or later, and tvOS 18.0 or later.  On
 *  earlier OS versions, the library functions that implement these
 *  operations are not available.                                             */

  static _Float16 SIMD_CFUNC simd_orient(simd_half2 __x, simd_half2 __y);
  static _Float16 SIMD_CFUNC simd_orient(simd_half3 __x, simd_half3 __y, simd_half3 __z);
  static _Float16 SIMD_CFUNC simd_orient(simd_half2 __a, simd_half2 __b, simd_half2 __c);
  static _Float16 SIMD_CFUNC simd_orient(simd_half3 __a, simd_half3 __b, simd_half3 __c, simd_half3 __d);
  static _Float16 SIMD_CFUNC simd_incircle(simd_half2 __x, simd_half2 __a, simd_half2 __b, simd_half2 __c);
  static _Float16 SIMD_CFUNC simd_insphere(simd_half3 __x, simd_half3 __a, simd_half3 __b, simd_half3 __c, simd_half3 __d);
#endif /* SIMD_LIBRARY_VERSION */

#ifdef __cplusplus
} /* extern "C" */

namespace simd {
  static SIMD_CPPFUNC _Float16 dot(const half2  x, const half2  y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC _Float16 dot(const half3  x, const half3  y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC _Float16 dot(const half4  x, const half4  y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC _Float16 dot(const half8  x, const half8  y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC _Float16 dot(const half16 x, const half16 y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC _Float16 dot(const half32 x, const half32 y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC float  dot(const float2  x, const float2  y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC float  dot(const float3  x, const float3  y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC float  dot(const float4  x, const float4  y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC float  dot(const float8  x, const float8  y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC float  dot(const float16 x, const float16 y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC double dot(const double2 x, const double2 y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC double dot(const double3 x, const double3 y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC double dot(const double4 x, const double4 y) { return ::simd_dot(x, y); }
  static SIMD_CPPFUNC double dot(const double8 x, const double8 y) { return ::simd_dot(x, y); }
  
  static SIMD_CPPFUNC half2   project(const half2   x, const half2   y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC half3   project(const half3   x, const half3   y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC half4   project(const half4   x, const half4   y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC half8   project(const half8   x, const half8   y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC half16  project(const half16  x, const half16  y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC half32  project(const half32  x, const half32  y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC float2  project(const float2  x, const float2  y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC float3  project(const float3  x, const float3  y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC float4  project(const float4  x, const float4  y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC float8  project(const float8  x, const float8  y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC float16 project(const float16 x, const float16 y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC double2 project(const double2 x, const double2 y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC double3 project(const double3 x, const double3 y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC double4 project(const double4 x, const double4 y) { return ::simd_project(x, y); }
  static SIMD_CPPFUNC double8 project(const double8 x, const double8 y) { return ::simd_project(x, y); }
  
  static SIMD_CPPFUNC _Float16 length_squared(const half2  x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC _Float16 length_squared(const half3  x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC _Float16 length_squared(const half4  x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC _Float16 length_squared(const half8  x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC _Float16 length_squared(const half16 x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC _Float16 length_squared(const half32 x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC float  length_squared(const float2  x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC float  length_squared(const float3  x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC float  length_squared(const float4  x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC float  length_squared(const float8  x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC float  length_squared(const float16 x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC double length_squared(const double2 x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC double length_squared(const double3 x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC double length_squared(const double4 x) { return ::simd_length_squared(x); }
  static SIMD_CPPFUNC double length_squared(const double8 x) { return ::simd_length_squared(x); }
  
  static SIMD_CPPFUNC _Float16 norm_one(const half2  x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC _Float16 norm_one(const half3  x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC _Float16 norm_one(const half4  x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC _Float16 norm_one(const half8  x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC _Float16 norm_one(const half16 x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC _Float16 norm_one(const half32 x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC float  norm_one(const float2  x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC float  norm_one(const float3  x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC float  norm_one(const float4  x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC float  norm_one(const float8  x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC float  norm_one(const float16 x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC double norm_one(const double2 x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC double norm_one(const double3 x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC double norm_one(const double4 x) { return ::simd_norm_one(x); }
  static SIMD_CPPFUNC double norm_one(const double8 x) { return ::simd_norm_one(x); }
  
  static SIMD_CPPFUNC _Float16 norm_inf(const half2  x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC _Float16 norm_inf(const half3  x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC _Float16 norm_inf(const half4  x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC _Float16 norm_inf(const half8  x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC _Float16 norm_inf(const half16 x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC _Float16 norm_inf(const half32 x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC float  norm_inf(const float2  x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC float  norm_inf(const float3  x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC float  norm_inf(const float4  x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC float  norm_inf(const float8  x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC float  norm_inf(const float16 x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC double norm_inf(const double2 x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC double norm_inf(const double3 x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC double norm_inf(const double4 x) { return ::simd_norm_inf(x); }
  static SIMD_CPPFUNC double norm_inf(const double8 x) { return ::simd_norm_inf(x); }
  
  static SIMD_CPPFUNC _Float16 length(const half2  x) { return ::simd_length(x); }
  static SIMD_CPPFUNC _Float16 length(const half3  x) { return ::simd_length(x); }
  static SIMD_CPPFUNC _Float16 length(const half4  x) { return ::simd_length(x); }
  static SIMD_CPPFUNC _Float16 length(const half8  x) { return ::simd_length(x); }
  static SIMD_CPPFUNC _Float16 length(const half16 x) { return ::simd_length(x); }
  static SIMD_CPPFUNC _Float16 length(const half32 x) { return ::simd_length(x); }
  static SIMD_CPPFUNC float  length(const float2  x) { return ::simd_length(x); }
  static SIMD_CPPFUNC float  length(const float3  x) { return ::simd_length(x); }
  static SIMD_CPPFUNC float  length(const float4  x) { return ::simd_length(x); }
  static SIMD_CPPFUNC float  length(const float8  x) { return ::simd_length(x); }
  static SIMD_CPPFUNC float  length(const float16 x) { return ::simd_length(x); }
  static SIMD_CPPFUNC double length(const double2 x) { return ::simd_length(x); }
  static SIMD_CPPFUNC double length(const double3 x) { return ::simd_length(x); }
  static SIMD_CPPFUNC double length(const double4 x) { return ::simd_length(x); }
  static SIMD_CPPFUNC double length(const double8 x) { return ::simd_length(x); }
  
  static SIMD_CPPFUNC _Float16 distance_squared(const half2  x, const half2  y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC _Float16 distance_squared(const half3  x, const half3  y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC _Float16 distance_squared(const half4  x, const half4  y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC _Float16 distance_squared(const half8  x, const half8  y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC _Float16 distance_squared(const half16 x, const half16 y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC _Float16 distance_squared(const half32 x, const half32 y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC float  distance_squared(const float2  x, const float2  y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC float  distance_squared(const float3  x, const float3  y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC float  distance_squared(const float4  x, const float4  y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC float  distance_squared(const float8  x, const float8  y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC float  distance_squared(const float16 x, const float16 y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC double distance_squared(const double2 x, const double2 y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC double distance_squared(const double3 x, const double3 y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC double distance_squared(const double4 x, const double4 y) { return ::simd_distance_squared(x, y); }
  static SIMD_CPPFUNC double distance_squared(const double8 x, const double8 y) { return ::simd_distance_squared(x, y); }
  
  static SIMD_CPPFUNC _Float16 distance(const half2  x, const half2  y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC _Float16 distance(const half3  x, const half3  y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC _Float16 distance(const half4  x, const half4  y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC _Float16 distance(const half8  x, const half8  y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC _Float16 distance(const half16 x, const half16 y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC _Float16 distance(const half32 x, const half32 y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC float  distance(const float2  x, const float2  y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC float  distance(const float3  x, const float3  y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC float  distance(const float4  x, const float4  y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC float  distance(const float8  x, const float8  y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC float  distance(const float16 x, const float16 y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC double distance(const double2 x, const double2 y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC double distance(const double3 x, const double3 y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC double distance(const double4 x, const double4 y) { return ::simd_distance(x, y); }
  static SIMD_CPPFUNC double distance(const double8 x, const double8 y) { return ::simd_distance(x, y); }
  
  static SIMD_CPPFUNC half2   normalize(const half2   x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC half3   normalize(const half3   x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC half4   normalize(const half4   x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC half8   normalize(const half8   x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC half16  normalize(const half16  x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC half32  normalize(const half32  x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC float2  normalize(const float2  x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC float3  normalize(const float3  x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC float4  normalize(const float4  x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC float8  normalize(const float8  x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC float16 normalize(const float16 x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC double2 normalize(const double2 x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC double3 normalize(const double3 x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC double4 normalize(const double4 x) { return ::simd_normalize(x); }
  static SIMD_CPPFUNC double8 normalize(const double8 x) { return ::simd_normalize(x); }
  
  static SIMD_CPPFUNC half3   cross(const half2   x, const half2   y) { return ::simd_cross(x,y); }
  static SIMD_CPPFUNC half3   cross(const half3   x, const half3   y) { return ::simd_cross(x,y); }
  static SIMD_CPPFUNC float3  cross(const float2  x, const float2  y) { return ::simd_cross(x,y); }
  static SIMD_CPPFUNC float3  cross(const float3  x, const float3  y) { return ::simd_cross(x,y); }
  static SIMD_CPPFUNC double3 cross(const double2 x, const double2 y) { return ::simd_cross(x,y); }
  static SIMD_CPPFUNC double3 cross(const double3 x, const double3 y) { return ::simd_cross(x,y); }
  
  static SIMD_CPPFUNC half2   reflect(const half2   x, const half2   n) { return ::simd_reflect(x,n); }
  static SIMD_CPPFUNC half3   reflect(const half3   x, const half3   n) { return ::simd_reflect(x,n); }
  static SIMD_CPPFUNC half4   reflect(const half4   x, const half4   n) { return ::simd_reflect(x,n); }
  static SIMD_CPPFUNC float2  reflect(const float2  x, const float2  n) { return ::simd_reflect(x,n); }
  static SIMD_CPPFUNC float3  reflect(const float3  x, const float3  n) { return ::simd_reflect(x,n); }
  static SIMD_CPPFUNC float4  reflect(const float4  x, const float4  n) { return ::simd_reflect(x,n); }
  static SIMD_CPPFUNC double2 reflect(const double2 x, const double2 n) { return ::simd_reflect(x,n); }
  static SIMD_CPPFUNC double3 reflect(const double3 x, const double3 n) { return ::simd_reflect(x,n); }
  static SIMD_CPPFUNC double4 reflect(const double4 x, const double4 n) { return ::simd_reflect(x,n); }

#if SIMD_LIBRARY_VERSION >= 6
  static SIMD_CPPFUNC half2   refract(const half2   x, const half2   n, const _Float16 eta) { return ::simd_refract(x,n,eta); }
  static SIMD_CPPFUNC half3   refract(const half3   x, const half3   n, const _Float16 eta) { return ::simd_refract(x,n,eta); }
  static SIMD_CPPFUNC half4   refract(const half4   x, const half4   n, const _Float16 eta) { return ::simd_refract(x,n,eta); }
#endif // SIMD_LIBRARY_VERSION >= 6
  static SIMD_CPPFUNC float2  refract(const float2  x, const float2  n, const float eta) { return ::simd_refract(x,n,eta); }
  static SIMD_CPPFUNC float3  refract(const float3  x, const float3  n, const float eta) { return ::simd_refract(x,n,eta); }
  static SIMD_CPPFUNC float4  refract(const float4  x, const float4  n, const float eta) { return ::simd_refract(x,n,eta); }
  static SIMD_CPPFUNC double2 refract(const double2 x, const double2 n, const float eta) { return ::simd_refract(x,n,eta); }
  static SIMD_CPPFUNC double3 refract(const double3 x, const double3 n, const float eta) { return ::simd_refract(x,n,eta); }
  static SIMD_CPPFUNC double4 refract(const double4 x, const double4 n, const float eta) { return ::simd_refract(x,n,eta); }
  
#if SIMD_LIBRARY_VERSION >= 2
  static SIMD_CPPFUNC float  orient(const float2  x, const float2 y) { return ::simd_orient(x,y); }
  static SIMD_CPPFUNC float  orient(const float2  a, const float2 b, const float2 c) { return ::simd_orient(a,b,c); }
  static SIMD_CPPFUNC float  orient(const float3  x, const float3 y, const float3 z) { return ::simd_orient(x,y,z); }
  static SIMD_CPPFUNC float  orient(const float3  a, const float3 b, const float3 c, const float3 d) { return ::simd_orient(a,b,c,d); }
  static SIMD_CPPFUNC double orient(const double2 x, const double2 y) { return ::simd_orient(x,y); }
  static SIMD_CPPFUNC double orient(const double2 a, const double2 b, const double2 c) { return ::simd_orient(a,b,c); }
  static SIMD_CPPFUNC double orient(const double3 x, const double3 y, const double3 z) { return ::simd_orient(x,y,z); }
  static SIMD_CPPFUNC double orient(const double3 a, const double3 b, const double3 c, const double3 d) { return ::simd_orient(a,b,c,d); }
#endif

#if SIMD_LIBRARY_VERSION >= 6
  static SIMD_CPPFUNC _Float16  orient(const half2  x, const half2 y) { return ::simd_orient(x,y); }
  static SIMD_CPPFUNC _Float16  orient(const half2  a, const half2 b, const half2 c) { return ::simd_orient(a,b,c); }
  static SIMD_CPPFUNC _Float16  orient(const half3  x, const half3 y, const half3 z) { return ::simd_orient(x,y,z); }
  static SIMD_CPPFUNC _Float16  orient(const half3  a, const half3 b, const half3 c, const half3 d) { return ::simd_orient(a,b,c,d); }
#endif

  /* precise and fast sub-namespaces                                        */
  namespace precise {
    static SIMD_CPPFUNC half2   project(const half2   x, const half2   y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC half3   project(const half3   x, const half3   y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC half4   project(const half4   x, const half4   y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC half8   project(const half8   x, const half8   y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC half16  project(const half16  x, const half16  y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC half32  project(const half32  x, const half32  y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC float2  project(const float2  x, const float2  y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC float3  project(const float3  x, const float3  y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC float4  project(const float4  x, const float4  y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC float8  project(const float8  x, const float8  y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC float16 project(const float16 x, const float16 y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC double2 project(const double2 x, const double2 y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC double3 project(const double3 x, const double3 y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC double4 project(const double4 x, const double4 y) { return ::simd_precise_project(x, y); }
    static SIMD_CPPFUNC double8 project(const double8 x, const double8 y) { return ::simd_precise_project(x, y); }

#if SIMD_LIBRARY_VERSION >= 6
    static SIMD_CPPFUNC _Float16 length(const half2  x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half3  x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half4  x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half8  x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half16 x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half32 x) { return ::simd_precise_length(x); }
#endif // #if SIMD_LIBRARY_VERSION >= 6
    static SIMD_CPPFUNC float  length(const float2  x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC float  length(const float3  x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC float  length(const float4  x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC float  length(const float8  x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC float  length(const float16 x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC double length(const double2 x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC double length(const double3 x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC double length(const double4 x) { return ::simd_precise_length(x); }
    static SIMD_CPPFUNC double length(const double8 x) { return ::simd_precise_length(x); }
    
    static SIMD_CPPFUNC _Float16 distance(const half2  x, const half2  y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half3  x, const half3  y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half4  x, const half4  y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half8  x, const half8  y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half16 x, const half16 y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half32 x, const half32 y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float2  x, const float2  y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float3  x, const float3  y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float4  x, const float4  y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float8  x, const float8  y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float16 x, const float16 y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC double distance(const double2 x, const double2 y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC double distance(const double3 x, const double3 y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC double distance(const double4 x, const double4 y) { return ::simd_precise_distance(x, y); }
    static SIMD_CPPFUNC double distance(const double8 x, const double8 y) { return ::simd_precise_distance(x, y); }
    
    static SIMD_CPPFUNC half2   normalize(const half2   x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC half3   normalize(const half3   x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC half4   normalize(const half4   x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC half8   normalize(const half8   x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC half16  normalize(const half16  x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC half32  normalize(const half32  x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC float2  normalize(const float2  x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC float3  normalize(const float3  x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC float4  normalize(const float4  x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC float8  normalize(const float8  x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC float16 normalize(const float16 x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC double2 normalize(const double2 x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC double3 normalize(const double3 x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC double4 normalize(const double4 x) { return ::simd_precise_normalize(x); }
    static SIMD_CPPFUNC double8 normalize(const double8 x) { return ::simd_precise_normalize(x); }
  }
  
  namespace fast {
    static SIMD_CPPFUNC half2   project(const half2   x, const half2   y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC half3   project(const half3   x, const half3   y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC half4   project(const half4   x, const half4   y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC half8   project(const half8   x, const half8   y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC half16  project(const half16  x, const half16  y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC half32  project(const half32  x, const half32  y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC float2  project(const float2  x, const float2  y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC float3  project(const float3  x, const float3  y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC float4  project(const float4  x, const float4  y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC float8  project(const float8  x, const float8  y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC float16 project(const float16 x, const float16 y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC double2 project(const double2 x, const double2 y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC double3 project(const double3 x, const double3 y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC double4 project(const double4 x, const double4 y) { return ::simd_fast_project(x, y); }
    static SIMD_CPPFUNC double8 project(const double8 x, const double8 y) { return ::simd_fast_project(x, y); }
    
    static SIMD_CPPFUNC _Float16 length(const half2  x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half3  x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half4  x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half8  x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half16 x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC _Float16 length(const half32 x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC float  length(const float2  x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC float  length(const float3  x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC float  length(const float4  x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC float  length(const float8  x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC float  length(const float16 x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC double length(const double2 x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC double length(const double3 x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC double length(const double4 x) { return ::simd_fast_length(x); }
    static SIMD_CPPFUNC double length(const double8 x) { return ::simd_fast_length(x); }
    
    static SIMD_CPPFUNC _Float16 distance(const half2  x, const half2  y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half3  x, const half3  y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half4  x, const half4  y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half8  x, const half8  y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half16 x, const half16 y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC _Float16 distance(const half32 x, const half32 y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float2  x, const float2  y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float3  x, const float3  y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float4  x, const float4  y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float8  x, const float8  y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC float  distance(const float16 x, const float16 y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC double distance(const double2 x, const double2 y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC double distance(const double3 x, const double3 y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC double distance(const double4 x, const double4 y) { return ::simd_fast_distance(x, y); }
    static SIMD_CPPFUNC double distance(const double8 x, const double8 y) { return ::simd_fast_distance(x, y); }
    
    static SIMD_CPPFUNC half2   normalize(const half2   x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC half3   normalize(const half3   x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC half4   normalize(const half4   x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC half8   normalize(const half8   x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC half16  normalize(const half16  x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC half32  normalize(const half32  x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC float2  normalize(const float2  x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC float3  normalize(const float3  x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC float4  normalize(const float4  x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC float8  normalize(const float8  x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC float16 normalize(const float16 x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC double2 normalize(const double2 x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC double3 normalize(const double3 x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC double4 normalize(const double4 x) { return ::simd_fast_normalize(x); }
    static SIMD_CPPFUNC double8 normalize(const double8 x) { return ::simd_fast_normalize(x); }
  }
}

extern "C" {
#endif /* __cplusplus */
  
#pragma mark - Implementation

static _Float16 SIMD_CFUNC simd_dot(simd_half2  __x, simd_half2  __y) { return simd_reduce_add(__x*__y); }
static _Float16 SIMD_CFUNC simd_dot(simd_half3  __x, simd_half3  __y) { return simd_reduce_add(__x*__y); }
static _Float16 SIMD_CFUNC simd_dot(simd_half4  __x, simd_half4  __y) { return simd_reduce_add(__x*__y); }
static _Float16 SIMD_CFUNC simd_dot(simd_half8  __x, simd_half8  __y) { return simd_reduce_add(__x*__y); }
static _Float16 SIMD_CFUNC simd_dot(simd_half16 __x, simd_half16 __y) { return simd_reduce_add(__x*__y); }
static _Float16 SIMD_CFUNC simd_dot(simd_half32 __x, simd_half32 __y) { return simd_reduce_add(__x*__y); }
static float  SIMD_CFUNC simd_dot(simd_float2  __x, simd_float2  __y) { return simd_reduce_add(__x*__y); }
static float  SIMD_CFUNC simd_dot(simd_float3  __x, simd_float3  __y) { return simd_reduce_add(__x*__y); }
static float  SIMD_CFUNC simd_dot(simd_float4  __x, simd_float4  __y) { return simd_reduce_add(__x*__y); }
static float  SIMD_CFUNC simd_dot(simd_float8  __x, simd_float8  __y) { return simd_reduce_add(__x*__y); }
static float  SIMD_CFUNC simd_dot(simd_float16 __x, simd_float16 __y) { return simd_reduce_add(__x*__y); }
static double SIMD_CFUNC simd_dot(simd_double2 __x, simd_double2 __y) { return simd_reduce_add(__x*__y); }
static double SIMD_CFUNC simd_dot(simd_double3 __x, simd_double3 __y) { return simd_reduce_add(__x*__y); }
static double SIMD_CFUNC simd_dot(simd_double4 __x, simd_double4 __y) { return simd_reduce_add(__x*__y); }
static double SIMD_CFUNC simd_dot(simd_double8 __x, simd_double8 __y) { return simd_reduce_add(__x*__y); }

static simd_half2   SIMD_CFUNC simd_precise_project(simd_half2   __x, simd_half2   __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_half3   SIMD_CFUNC simd_precise_project(simd_half3   __x, simd_half3   __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_half4   SIMD_CFUNC simd_precise_project(simd_half4   __x, simd_half4   __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_half8   SIMD_CFUNC simd_precise_project(simd_half8   __x, simd_half8   __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_half16  SIMD_CFUNC simd_precise_project(simd_half16  __x, simd_half16  __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_half32  SIMD_CFUNC simd_precise_project(simd_half32  __x, simd_half32  __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_float2  SIMD_CFUNC simd_precise_project(simd_float2  __x, simd_float2  __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_float3  SIMD_CFUNC simd_precise_project(simd_float3  __x, simd_float3  __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_float4  SIMD_CFUNC simd_precise_project(simd_float4  __x, simd_float4  __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_float8  SIMD_CFUNC simd_precise_project(simd_float8  __x, simd_float8  __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_float16 SIMD_CFUNC simd_precise_project(simd_float16 __x, simd_float16 __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_double2 SIMD_CFUNC simd_precise_project(simd_double2 __x, simd_double2 __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_double3 SIMD_CFUNC simd_precise_project(simd_double3 __x, simd_double3 __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_double4 SIMD_CFUNC simd_precise_project(simd_double4 __x, simd_double4 __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }
static simd_double8 SIMD_CFUNC simd_precise_project(simd_double8 __x, simd_double8 __y) { return simd_dot(__x,__y)/simd_dot(__y,__y)*__y; }

static simd_half2   SIMD_CFUNC simd_fast_project(simd_half2   __x, simd_half2   __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_half3   SIMD_CFUNC simd_fast_project(simd_half3   __x, simd_half3   __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_half4   SIMD_CFUNC simd_fast_project(simd_half4   __x, simd_half4   __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_half8   SIMD_CFUNC simd_fast_project(simd_half8   __x, simd_half8   __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_half16  SIMD_CFUNC simd_fast_project(simd_half16  __x, simd_half16  __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_half32  SIMD_CFUNC simd_fast_project(simd_half32  __x, simd_half32  __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_float2  SIMD_CFUNC simd_fast_project(simd_float2  __x, simd_float2  __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_float3  SIMD_CFUNC simd_fast_project(simd_float3  __x, simd_float3  __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_float4  SIMD_CFUNC simd_fast_project(simd_float4  __x, simd_float4  __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_float8  SIMD_CFUNC simd_fast_project(simd_float8  __x, simd_float8  __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_float16 SIMD_CFUNC simd_fast_project(simd_float16 __x, simd_float16 __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_double2 SIMD_CFUNC simd_fast_project(simd_double2 __x, simd_double2 __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_double3 SIMD_CFUNC simd_fast_project(simd_double3 __x, simd_double3 __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_double4 SIMD_CFUNC simd_fast_project(simd_double4 __x, simd_double4 __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }
static simd_double8 SIMD_CFUNC simd_fast_project(simd_double8 __x, simd_double8 __y) { return __y*simd_dot(__x,__y)*simd_fast_recip(simd_dot(__y,__y)); }

#if defined __FAST_MATH__
static simd_half2   SIMD_CFUNC simd_project(simd_half2   __x, simd_half2   __y) { return simd_fast_project(__x,__y); }
static simd_half3   SIMD_CFUNC simd_project(simd_half3   __x, simd_half3   __y) { return simd_fast_project(__x,__y); }
static simd_half4   SIMD_CFUNC simd_project(simd_half4   __x, simd_half4   __y) { return simd_fast_project(__x,__y); }
static simd_half8   SIMD_CFUNC simd_project(simd_half8   __x, simd_half8   __y) { return simd_fast_project(__x,__y); }
static simd_half16  SIMD_CFUNC simd_project(simd_half16  __x, simd_half16  __y) { return simd_fast_project(__x,__y); }
static simd_half32  SIMD_CFUNC simd_project(simd_half32  __x, simd_half32  __y) { return simd_fast_project(__x,__y); }
static simd_float2  SIMD_CFUNC simd_project(simd_float2  __x, simd_float2  __y) { return simd_fast_project(__x,__y); }
static simd_float3  SIMD_CFUNC simd_project(simd_float3  __x, simd_float3  __y) { return simd_fast_project(__x,__y); }
static simd_float4  SIMD_CFUNC simd_project(simd_float4  __x, simd_float4  __y) { return simd_fast_project(__x,__y); }
static simd_float8  SIMD_CFUNC simd_project(simd_float8  __x, simd_float8  __y) { return simd_fast_project(__x,__y); }
static simd_float16 SIMD_CFUNC simd_project(simd_float16 __x, simd_float16 __y) { return simd_fast_project(__x,__y); }
static simd_double2 SIMD_CFUNC simd_project(simd_double2 __x, simd_double2 __y) { return simd_fast_project(__x,__y); }
static simd_double3 SIMD_CFUNC simd_project(simd_double3 __x, simd_double3 __y) { return simd_fast_project(__x,__y); }
static simd_double4 SIMD_CFUNC simd_project(simd_double4 __x, simd_double4 __y) { return simd_fast_project(__x,__y); }
static simd_double8 SIMD_CFUNC simd_project(simd_double8 __x, simd_double8 __y) { return simd_fast_project(__x,__y); }
#else
static simd_half2   SIMD_CFUNC simd_project(simd_half2   __x, simd_half2   __y) { return simd_precise_project(__x,__y); }
static simd_half3   SIMD_CFUNC simd_project(simd_half3   __x, simd_half3   __y) { return simd_precise_project(__x,__y); }
static simd_half4   SIMD_CFUNC simd_project(simd_half4   __x, simd_half4   __y) { return simd_precise_project(__x,__y); }
static simd_half8   SIMD_CFUNC simd_project(simd_half8   __x, simd_half8   __y) { return simd_precise_project(__x,__y); }
static simd_half16  SIMD_CFUNC simd_project(simd_half16  __x, simd_half16  __y) { return simd_precise_project(__x,__y); }
static simd_half32  SIMD_CFUNC simd_project(simd_half32  __x, simd_half32  __y) { return simd_precise_project(__x,__y); }
static simd_float2  SIMD_CFUNC simd_project(simd_float2  __x, simd_float2  __y) { return simd_precise_project(__x,__y); }
static simd_float3  SIMD_CFUNC simd_project(simd_float3  __x, simd_float3  __y) { return simd_precise_project(__x,__y); }
static simd_float4  SIMD_CFUNC simd_project(simd_float4  __x, simd_float4  __y) { return simd_precise_project(__x,__y); }
static simd_float8  SIMD_CFUNC simd_project(simd_float8  __x, simd_float8  __y) { return simd_precise_project(__x,__y); }
static simd_float16 SIMD_CFUNC simd_project(simd_float16 __x, simd_float16 __y) { return simd_precise_project(__x,__y); }
static simd_double2 SIMD_CFUNC simd_project(simd_double2 __x, simd_double2 __y) { return simd_precise_project(__x,__y); }
static simd_double3 SIMD_CFUNC simd_project(simd_double3 __x, simd_double3 __y) { return simd_precise_project(__x,__y); }
static simd_double4 SIMD_CFUNC simd_project(simd_double4 __x, simd_double4 __y) { return simd_precise_project(__x,__y); }
static simd_double8 SIMD_CFUNC simd_project(simd_double8 __x, simd_double8 __y) { return simd_precise_project(__x,__y); }
#endif

#if SIMD_LIBRARY_VERSION >= 6
static _Float16 SIMD_CFUNC simd_precise_length(simd_half2  __x) { return __sqrtf16(simd_length_squared(__x)); }
static _Float16 SIMD_CFUNC simd_precise_length(simd_half3  __x) { return __sqrtf16(simd_length_squared(__x)); }
static _Float16 SIMD_CFUNC simd_precise_length(simd_half4  __x) { return __sqrtf16(simd_length_squared(__x)); }
static _Float16 SIMD_CFUNC simd_precise_length(simd_half8  __x) { return __sqrtf16(simd_length_squared(__x)); }
static _Float16 SIMD_CFUNC simd_precise_length(simd_half16 __x) { return __sqrtf16(simd_length_squared(__x)); }
static _Float16 SIMD_CFUNC simd_precise_length(simd_half32 __x) { return __sqrtf16(simd_length_squared(__x)); }
#endif // SIMD_LIBRARY_VERSION >= 6
static float  SIMD_CFUNC simd_precise_length(simd_float2  __x) { return sqrtf(simd_length_squared(__x)); }
static float  SIMD_CFUNC simd_precise_length(simd_float3  __x) { return sqrtf(simd_length_squared(__x)); }
static float  SIMD_CFUNC simd_precise_length(simd_float4  __x) { return sqrtf(simd_length_squared(__x)); }
static float  SIMD_CFUNC simd_precise_length(simd_float8  __x) { return sqrtf(simd_length_squared(__x)); }
static float  SIMD_CFUNC simd_precise_length(simd_float16 __x) { return sqrtf(simd_length_squared(__x)); }
static double SIMD_CFUNC simd_precise_length(simd_double2 __x) { return sqrt(simd_length_squared(__x)); }
static double SIMD_CFUNC simd_precise_length(simd_double3 __x) { return sqrt(simd_length_squared(__x)); }
static double SIMD_CFUNC simd_precise_length(simd_double4 __x) { return sqrt(simd_length_squared(__x)); }
static double SIMD_CFUNC simd_precise_length(simd_double8 __x) { return sqrt(simd_length_squared(__x)); }
#if SIMD_LIBRARY_VERSION >= 6
static _Float16 SIMD_CFUNC simd_fast_length(simd_half2  __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_fast_length(simd_half3  __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_fast_length(simd_half4  __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_fast_length(simd_half8  __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_fast_length(simd_half16 __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_fast_length(simd_half32 __x) { return simd_precise_length(__x); }
#endif // SIMD_LIBRARY_VERSION >= 6
static float  SIMD_CFUNC simd_fast_length(simd_float2  __x) { return simd_precise_length(__x); }
static float  SIMD_CFUNC simd_fast_length(simd_float3  __x) { return simd_precise_length(__x); }
static float  SIMD_CFUNC simd_fast_length(simd_float4  __x) { return simd_precise_length(__x); }
static float  SIMD_CFUNC simd_fast_length(simd_float8  __x) { return simd_precise_length(__x); }
static float  SIMD_CFUNC simd_fast_length(simd_float16 __x) { return simd_precise_length(__x); }
static double SIMD_CFUNC simd_fast_length(simd_double2 __x) { return simd_precise_length(__x); }
static double SIMD_CFUNC simd_fast_length(simd_double3 __x) { return simd_precise_length(__x); }
static double SIMD_CFUNC simd_fast_length(simd_double4 __x) { return simd_precise_length(__x); }
static double SIMD_CFUNC simd_fast_length(simd_double8 __x) { return simd_precise_length(__x); }

#if defined __FAST_MATH__
static _Float16 SIMD_CFUNC simd_length(simd_half2  __x) { return simd_fast_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half3  __x) { return simd_fast_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half4  __x) { return simd_fast_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half8  __x) { return simd_fast_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half16 __x) { return simd_fast_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half32 __x) { return simd_fast_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float2  __x) { return simd_fast_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float3  __x) { return simd_fast_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float4  __x) { return simd_fast_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float8  __x) { return simd_fast_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float16 __x) { return simd_fast_length(__x); }
static double SIMD_CFUNC simd_length(simd_double2 __x) { return simd_fast_length(__x); }
static double SIMD_CFUNC simd_length(simd_double3 __x) { return simd_fast_length(__x); }
static double SIMD_CFUNC simd_length(simd_double4 __x) { return simd_fast_length(__x); }
static double SIMD_CFUNC simd_length(simd_double8 __x) { return simd_fast_length(__x); }
#else
#if SIMD_LIBRARY_VERSION >= 6
static _Float16 SIMD_CFUNC simd_length(simd_half2  __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half3  __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half4  __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half8  __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half16 __x) { return simd_precise_length(__x); }
static _Float16 SIMD_CFUNC simd_length(simd_half32 __x) { return simd_precise_length(__x); }
#endif // SIMD_LIBRARY_VERSION >= 6
static float  SIMD_CFUNC simd_length(simd_float2  __x) { return simd_precise_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float3  __x) { return simd_precise_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float4  __x) { return simd_precise_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float8  __x) { return simd_precise_length(__x); }
static float  SIMD_CFUNC simd_length(simd_float16 __x) { return simd_precise_length(__x); }
static double SIMD_CFUNC simd_length(simd_double2 __x) { return simd_precise_length(__x); }
static double SIMD_CFUNC simd_length(simd_double3 __x) { return simd_precise_length(__x); }
static double SIMD_CFUNC simd_length(simd_double4 __x) { return simd_precise_length(__x); }
static double SIMD_CFUNC simd_length(simd_double8 __x) { return simd_precise_length(__x); }
#endif

static _Float16 SIMD_CFUNC simd_length_squared(simd_half2  __x) { return simd_dot(__x,__x); }
static _Float16 SIMD_CFUNC simd_length_squared(simd_half3  __x) { return simd_dot(__x,__x); }
static _Float16 SIMD_CFUNC simd_length_squared(simd_half4  __x) { return simd_dot(__x,__x); }
static _Float16 SIMD_CFUNC simd_length_squared(simd_half8  __x) { return simd_dot(__x,__x); }
static _Float16 SIMD_CFUNC simd_length_squared(simd_half16 __x) { return simd_dot(__x,__x); }
static _Float16 SIMD_CFUNC simd_length_squared(simd_half32 __x) { return simd_dot(__x,__x); }
static float  SIMD_CFUNC simd_length_squared(simd_float2  __x) { return simd_dot(__x,__x); }
static float  SIMD_CFUNC simd_length_squared(simd_float3  __x) { return simd_dot(__x,__x); }
static float  SIMD_CFUNC simd_length_squared(simd_float4  __x) { return simd_dot(__x,__x); }
static float  SIMD_CFUNC simd_length_squared(simd_float8  __x) { return simd_dot(__x,__x); }
static float  SIMD_CFUNC simd_length_squared(simd_float16 __x) { return simd_dot(__x,__x); }
static double SIMD_CFUNC simd_length_squared(simd_double2 __x) { return simd_dot(__x,__x); }
static double SIMD_CFUNC simd_length_squared(simd_double3 __x) { return simd_dot(__x,__x); }
static double SIMD_CFUNC simd_length_squared(simd_double4 __x) { return simd_dot(__x,__x); }
static double SIMD_CFUNC simd_length_squared(simd_double8 __x) { return simd_dot(__x,__x); }

static _Float16 SIMD_CFUNC simd_norm_one(simd_half2  __x) { return simd_reduce_add(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_one(simd_half3  __x) { return simd_reduce_add(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_one(simd_half4  __x) { return simd_reduce_add(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_one(simd_half8  __x) { return simd_reduce_add(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_one(simd_half16 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_one(simd_half32 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_one(simd_float2 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_one(simd_float3 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_one(simd_float4 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_one(simd_float8 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_one(simd_float16 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static double SIMD_CFUNC simd_norm_one(simd_double2 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static double SIMD_CFUNC simd_norm_one(simd_double3 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static double SIMD_CFUNC simd_norm_one(simd_double4 __x) { return simd_reduce_add(__tg_fabs(__x)); }
static double SIMD_CFUNC simd_norm_one(simd_double8 __x) { return simd_reduce_add(__tg_fabs(__x)); }

static _Float16 SIMD_CFUNC simd_norm_inf(simd_half2  __x) { return simd_reduce_max(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half3  __x) { return simd_reduce_max(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half4  __x) { return simd_reduce_max(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half8  __x) { return simd_reduce_max(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half16 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static _Float16 SIMD_CFUNC simd_norm_inf(simd_half32 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_inf(simd_float2 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_inf(simd_float3 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_inf(simd_float4 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_inf(simd_float8 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static float SIMD_CFUNC simd_norm_inf(simd_float16 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static double SIMD_CFUNC simd_norm_inf(simd_double2 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static double SIMD_CFUNC simd_norm_inf(simd_double3 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static double SIMD_CFUNC simd_norm_inf(simd_double4 __x) { return simd_reduce_max(__tg_fabs(__x)); }
static double SIMD_CFUNC simd_norm_inf(simd_double8 __x) { return simd_reduce_max(__tg_fabs(__x)); }

#if SIMD_LIBRARY_VERSION >= 6
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half2  __x, simd_half2  __y) { return simd_precise_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half3  __x, simd_half3  __y) { return simd_precise_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half4  __x, simd_half4  __y) { return simd_precise_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half8  __x, simd_half8  __y) { return simd_precise_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half16 __x, simd_half16 __y) { return simd_precise_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_precise_distance(simd_half32 __x, simd_half32 __y) { return simd_precise_length(__x - __y); }
#endif // SIMD_LIBRARY_VERSION >= 6
static float  SIMD_CFUNC simd_precise_distance(simd_float2  __x, simd_float2  __y) { return simd_precise_length(__x - __y); }
static float  SIMD_CFUNC simd_precise_distance(simd_float3  __x, simd_float3  __y) { return simd_precise_length(__x - __y); }
static float  SIMD_CFUNC simd_precise_distance(simd_float4  __x, simd_float4  __y) { return simd_precise_length(__x - __y); }
static float  SIMD_CFUNC simd_precise_distance(simd_float8  __x, simd_float8  __y) { return simd_precise_length(__x - __y); }
static float  SIMD_CFUNC simd_precise_distance(simd_float16 __x, simd_float16 __y) { return simd_precise_length(__x - __y); }
static double SIMD_CFUNC simd_precise_distance(simd_double2 __x, simd_double2 __y) { return simd_precise_length(__x - __y); }
static double SIMD_CFUNC simd_precise_distance(simd_double3 __x, simd_double3 __y) { return simd_precise_length(__x - __y); }
static double SIMD_CFUNC simd_precise_distance(simd_double4 __x, simd_double4 __y) { return simd_precise_length(__x - __y); }
static double SIMD_CFUNC simd_precise_distance(simd_double8 __x, simd_double8 __y) { return simd_precise_length(__x - __y); }

static _Float16 SIMD_CFUNC simd_fast_distance(simd_half2  __x, simd_half2  __y) { return simd_fast_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half3  __x, simd_half3  __y) { return simd_fast_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half4  __x, simd_half4  __y) { return simd_fast_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half8  __x, simd_half8  __y) { return simd_fast_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half16 __x, simd_half16 __y) { return simd_fast_length(__x - __y); }
static _Float16 SIMD_CFUNC simd_fast_distance(simd_half32 __x, simd_half32 __y) { return simd_fast_length(__x - __y); }
static float  SIMD_CFUNC simd_fast_distance(simd_float2  __x, simd_float2  __y) { return simd_fast_length(__x - __y); }
static float  SIMD_CFUNC simd_fast_distance(simd_float3  __x, simd_float3  __y) { return simd_fast_length(__x - __y); }
static float  SIMD_CFUNC simd_fast_distance(simd_float4  __x, simd_float4  __y) { return simd_fast_length(__x - __y); }
static float  SIMD_CFUNC simd_fast_distance(simd_float8  __x, simd_float8  __y) { return simd_fast_length(__x - __y); }
static float  SIMD_CFUNC simd_fast_distance(simd_float16 __x, simd_float16 __y) { return simd_fast_length(__x - __y); }
static double SIMD_CFUNC simd_fast_distance(simd_double2 __x, simd_double2 __y) { return simd_fast_length(__x - __y); }
static double SIMD_CFUNC simd_fast_distance(simd_double3 __x, simd_double3 __y) { return simd_fast_length(__x - __y); }
static double SIMD_CFUNC simd_fast_distance(simd_double4 __x, simd_double4 __y) { return simd_fast_length(__x - __y); }
static double SIMD_CFUNC simd_fast_distance(simd_double8 __x, simd_double8 __y) { return simd_fast_length(__x - __y); }

#if defined __FAST_MATH__
static _Float16 SIMD_CFUNC simd_distance(simd_half2  __x, simd_half2  __y) { return simd_fast_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half3  __x, simd_half3  __y) { return simd_fast_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half4  __x, simd_half4  __y) { return simd_fast_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half8  __x, simd_half8  __y) { return simd_fast_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half16 __x, simd_half16 __y) { return simd_fast_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half32 __x, simd_half32 __y) { return simd_fast_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float2  __x, simd_float2  __y) { return simd_fast_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float3  __x, simd_float3  __y) { return simd_fast_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float4  __x, simd_float4  __y) { return simd_fast_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float8  __x, simd_float8  __y) { return simd_fast_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float16 __x, simd_float16 __y) { return simd_fast_distance(__x,__y); }
static double SIMD_CFUNC simd_distance(simd_double2 __x, simd_double2 __y) { return simd_fast_distance(__x,__y); }
static double SIMD_CFUNC simd_distance(simd_double3 __x, simd_double3 __y) { return simd_fast_distance(__x,__y); }
static double SIMD_CFUNC simd_distance(simd_double4 __x, simd_double4 __y) { return simd_fast_distance(__x,__y); }
static double SIMD_CFUNC simd_distance(simd_double8 __x, simd_double8 __y) { return simd_fast_distance(__x,__y); }
#else
static _Float16 SIMD_CFUNC simd_distance(simd_half2  __x, simd_half2  __y) { return simd_precise_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half3  __x, simd_half3  __y) { return simd_precise_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half4  __x, simd_half4  __y) { return simd_precise_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half8  __x, simd_half8  __y) { return simd_precise_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half16 __x, simd_half16 __y) { return simd_precise_distance(__x,__y); }
static _Float16 SIMD_CFUNC simd_distance(simd_half32 __x, simd_half32 __y) { return simd_precise_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float2  __x, simd_float2  __y) { return simd_precise_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float3  __x, simd_float3  __y) { return simd_precise_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float4  __x, simd_float4  __y) { return simd_precise_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float8  __x, simd_float8  __y) { return simd_precise_distance(__x,__y); }
static float  SIMD_CFUNC simd_distance(simd_float16 __x, simd_float16 __y) { return simd_precise_distance(__x,__y); }
static double SIMD_CFUNC simd_distance(simd_double2 __x, simd_double2 __y) { return simd_precise_distance(__x,__y); }
static double SIMD_CFUNC simd_distance(simd_double3 __x, simd_double3 __y) { return simd_precise_distance(__x,__y); }
static double SIMD_CFUNC simd_distance(simd_double4 __x, simd_double4 __y) { return simd_precise_distance(__x,__y); }
static double SIMD_CFUNC simd_distance(simd_double8 __x, simd_double8 __y) { return simd_precise_distance(__x,__y); }
#endif

static _Float16 SIMD_CFUNC simd_distance_squared(simd_half2  __x, simd_half2  __y) { return simd_length_squared(__x - __y); }
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half3  __x, simd_half3  __y) { return simd_length_squared(__x - __y); }
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half4  __x, simd_half4  __y) { return simd_length_squared(__x - __y); }
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half8  __x, simd_half8  __y) { return simd_length_squared(__x - __y); }
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half16 __x, simd_half16 __y) { return simd_length_squared(__x - __y); }
static _Float16 SIMD_CFUNC simd_distance_squared(simd_half32 __x, simd_half32 __y) { return simd_length_squared(__x - __y); }
static float  SIMD_CFUNC simd_distance_squared(simd_float2  __x, simd_float2  __y) { return simd_length_squared(__x - __y); }
static float  SIMD_CFUNC simd_distance_squared(simd_float3  __x, simd_float3  __y) { return simd_length_squared(__x - __y); }
static float  SIMD_CFUNC simd_distance_squared(simd_float4  __x, simd_float4  __y) { return simd_length_squared(__x - __y); }
static float  SIMD_CFUNC simd_distance_squared(simd_float8  __x, simd_float8  __y) { return simd_length_squared(__x - __y); }
static float  SIMD_CFUNC simd_distance_squared(simd_float16 __x, simd_float16 __y) { return simd_length_squared(__x - __y); }
static double SIMD_CFUNC simd_distance_squared(simd_double2 __x, simd_double2 __y) { return simd_length_squared(__x - __y); }
static double SIMD_CFUNC simd_distance_squared(simd_double3 __x, simd_double3 __y) { return simd_length_squared(__x - __y); }
static double SIMD_CFUNC simd_distance_squared(simd_double4 __x, simd_double4 __y) { return simd_length_squared(__x - __y); }
static double SIMD_CFUNC simd_distance_squared(simd_double8 __x, simd_double8 __y) { return simd_length_squared(__x - __y); }

static simd_half2   SIMD_CFUNC simd_precise_normalize(simd_half2   __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_half3   SIMD_CFUNC simd_precise_normalize(simd_half3   __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_half4   SIMD_CFUNC simd_precise_normalize(simd_half4   __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_half8   SIMD_CFUNC simd_precise_normalize(simd_half8   __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_half16  SIMD_CFUNC simd_precise_normalize(simd_half16  __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_half32  SIMD_CFUNC simd_precise_normalize(simd_half32  __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_float2  SIMD_CFUNC simd_precise_normalize(simd_float2  __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_float3  SIMD_CFUNC simd_precise_normalize(simd_float3  __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_float4  SIMD_CFUNC simd_precise_normalize(simd_float4  __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_float8  SIMD_CFUNC simd_precise_normalize(simd_float8  __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_float16 SIMD_CFUNC simd_precise_normalize(simd_float16 __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_double2 SIMD_CFUNC simd_precise_normalize(simd_double2 __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_double3 SIMD_CFUNC simd_precise_normalize(simd_double3 __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_double4 SIMD_CFUNC simd_precise_normalize(simd_double4 __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }
static simd_double8 SIMD_CFUNC simd_precise_normalize(simd_double8 __x) { return __x * simd_precise_rsqrt(simd_length_squared(__x)); }

static simd_half2   SIMD_CFUNC simd_fast_normalize(simd_half2   __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_half3   SIMD_CFUNC simd_fast_normalize(simd_half3   __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_half4   SIMD_CFUNC simd_fast_normalize(simd_half4   __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_half8   SIMD_CFUNC simd_fast_normalize(simd_half8   __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_half16  SIMD_CFUNC simd_fast_normalize(simd_half16  __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_half32  SIMD_CFUNC simd_fast_normalize(simd_half32  __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_float2  SIMD_CFUNC simd_fast_normalize(simd_float2  __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_float3  SIMD_CFUNC simd_fast_normalize(simd_float3  __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_float4  SIMD_CFUNC simd_fast_normalize(simd_float4  __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_float8  SIMD_CFUNC simd_fast_normalize(simd_float8  __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_float16 SIMD_CFUNC simd_fast_normalize(simd_float16 __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_double2 SIMD_CFUNC simd_fast_normalize(simd_double2 __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_double3 SIMD_CFUNC simd_fast_normalize(simd_double3 __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_double4 SIMD_CFUNC simd_fast_normalize(simd_double4 __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }
static simd_double8 SIMD_CFUNC simd_fast_normalize(simd_double8 __x) { return __x * simd_fast_rsqrt(simd_length_squared(__x)); }

#if defined __FAST_MATH__
static simd_half2   SIMD_CFUNC simd_normalize(simd_half2   __x) { return simd_fast_normalize(__x); }
static simd_half3   SIMD_CFUNC simd_normalize(simd_half3   __x) { return simd_fast_normalize(__x); }
static simd_half4   SIMD_CFUNC simd_normalize(simd_half4   __x) { return simd_fast_normalize(__x); }
static simd_half8   SIMD_CFUNC simd_normalize(simd_half8   __x) { return simd_fast_normalize(__x); }
static simd_half16  SIMD_CFUNC simd_normalize(simd_half16  __x) { return simd_fast_normalize(__x); }
static simd_half32  SIMD_CFUNC simd_normalize(simd_half32  __x) { return simd_fast_normalize(__x); }
static simd_float2  SIMD_CFUNC simd_normalize(simd_float2  __x) { return simd_fast_normalize(__x); }
static simd_float3  SIMD_CFUNC simd_normalize(simd_float3  __x) { return simd_fast_normalize(__x); }
static simd_float4  SIMD_CFUNC simd_normalize(simd_float4  __x) { return simd_fast_normalize(__x); }
static simd_float8  SIMD_CFUNC simd_normalize(simd_float8  __x) { return simd_fast_normalize(__x); }
static simd_float16 SIMD_CFUNC simd_normalize(simd_float16 __x) { return simd_fast_normalize(__x); }
static simd_double2 SIMD_CFUNC simd_normalize(simd_double2 __x) { return simd_fast_normalize(__x); }
static simd_double3 SIMD_CFUNC simd_normalize(simd_double3 __x) { return simd_fast_normalize(__x); }
static simd_double4 SIMD_CFUNC simd_normalize(simd_double4 __x) { return simd_fast_normalize(__x); }
static simd_double8 SIMD_CFUNC simd_normalize(simd_double8 __x) { return simd_fast_normalize(__x); }
#else
static simd_half2   SIMD_CFUNC simd_normalize(simd_half2   __x) { return simd_precise_normalize(__x); }
static simd_half3   SIMD_CFUNC simd_normalize(simd_half3   __x) { return simd_precise_normalize(__x); }
static simd_half4   SIMD_CFUNC simd_normalize(simd_half4   __x) { return simd_precise_normalize(__x); }
static simd_half8   SIMD_CFUNC simd_normalize(simd_half8   __x) { return simd_precise_normalize(__x); }
static simd_half16  SIMD_CFUNC simd_normalize(simd_half16  __x) { return simd_precise_normalize(__x); }
static simd_half32  SIMD_CFUNC simd_normalize(simd_half32  __x) { return simd_precise_normalize(__x); }
static simd_float2  SIMD_CFUNC simd_normalize(simd_float2  __x) { return simd_precise_normalize(__x); }
static simd_float3  SIMD_CFUNC simd_normalize(simd_float3  __x) { return simd_precise_normalize(__x); }
static simd_float4  SIMD_CFUNC simd_normalize(simd_float4  __x) { return simd_precise_normalize(__x); }
static simd_float8  SIMD_CFUNC simd_normalize(simd_float8  __x) { return simd_precise_normalize(__x); }
static simd_float16 SIMD_CFUNC simd_normalize(simd_float16 __x) { return simd_precise_normalize(__x); }
static simd_double2 SIMD_CFUNC simd_normalize(simd_double2 __x) { return simd_precise_normalize(__x); }
static simd_double3 SIMD_CFUNC simd_normalize(simd_double3 __x) { return simd_precise_normalize(__x); }
static simd_double4 SIMD_CFUNC simd_normalize(simd_double4 __x) { return simd_precise_normalize(__x); }
static simd_double8 SIMD_CFUNC simd_normalize(simd_double8 __x) { return simd_precise_normalize(__x); }
#endif

static simd_half3   SIMD_CFUNC simd_cross(simd_half2   __x, simd_half2   __y) { return (simd_half3){ 0, 0, __x.x*__y.y - __x.y*__y.x }; }
static simd_half3   SIMD_CFUNC simd_cross(simd_half3   __x, simd_half3   __y) { return (__x.zxy*__y - __x*__y.zxy).zxy; }
static simd_float3  SIMD_CFUNC simd_cross(simd_float2  __x, simd_float2  __y) { return (simd_float3){ 0, 0, __x.x*__y.y - __x.y*__y.x }; }
static simd_float3  SIMD_CFUNC simd_cross(simd_float3  __x, simd_float3  __y) { return (__x.zxy*__y - __x*__y.zxy).zxy; }
static simd_double3 SIMD_CFUNC simd_cross(simd_double2 __x, simd_double2 __y) { return (simd_double3){ 0, 0, __x.x*__y.y - __x.y*__y.x }; }
static simd_double3 SIMD_CFUNC simd_cross(simd_double3 __x, simd_double3 __y) { return (__x.zxy*__y - __x*__y.zxy).zxy; }

static simd_half2   SIMD_CFUNC simd_reflect(simd_half2   __x, simd_half2   __n) { return __x - 2*simd_dot(__x,__n)*__n; }
static simd_half3   SIMD_CFUNC simd_reflect(simd_half3   __x, simd_half3   __n) { return __x - 2*simd_dot(__x,__n)*__n; }
static simd_half4   SIMD_CFUNC simd_reflect(simd_half4   __x, simd_half4   __n) { return __x - 2*simd_dot(__x,__n)*__n; }
static simd_float2  SIMD_CFUNC simd_reflect(simd_float2  __x, simd_float2  __n) { return __x - 2*simd_dot(__x,__n)*__n; }
static simd_float3  SIMD_CFUNC simd_reflect(simd_float3  __x, simd_float3  __n) { return __x - 2*simd_dot(__x,__n)*__n; }
static simd_float4  SIMD_CFUNC simd_reflect(simd_float4  __x, simd_float4  __n) { return __x - 2*simd_dot(__x,__n)*__n; }
static simd_double2 SIMD_CFUNC simd_reflect(simd_double2 __x, simd_double2 __n) { return __x - 2*simd_dot(__x,__n)*__n; }
static simd_double3 SIMD_CFUNC simd_reflect(simd_double3 __x, simd_double3 __n) { return __x - 2*simd_dot(__x,__n)*__n; }
static simd_double4 SIMD_CFUNC simd_reflect(simd_double4 __x, simd_double4 __n) { return __x - 2*simd_dot(__x,__n)*__n; }

#if SIMD_LIBRARY_VERSION >= 6
static simd_half2  SIMD_CFUNC simd_refract(simd_half2  __x, simd_half2  __n, _Float16 __eta) {
  const _Float16 __k = 1.0f16 - __eta*__eta*(1.0f16 - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0f16) ? __eta*__x - (__eta*simd_dot(__x,__n) + __sqrtf16(__k))*__n : (simd_half2)0.0f16;
}
static simd_half3  SIMD_CFUNC simd_refract(simd_half3  __x, simd_half3  __n, _Float16 __eta) {
  const _Float16 __k = 1.0f16 - __eta*__eta*(1.0f16 - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0f16) ? __eta*__x - (__eta*simd_dot(__x,__n) + __sqrtf16(__k))*__n : (simd_half3)0.0f16;
}
static simd_half4  SIMD_CFUNC simd_refract(simd_half4  __x, simd_half4  __n, _Float16 __eta) {
  const _Float16 __k = 1.0f16 - __eta*__eta*(1.0f16 - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0f16) ? __eta*__x - (__eta*simd_dot(__x,__n) + __sqrtf16(__k))*__n : (simd_half4)0.0f16;
}
#endif // SIMD_LIBRARY_VERSION >= 6
static simd_float2  SIMD_CFUNC simd_refract(simd_float2  __x, simd_float2  __n, float __eta) {
  const float __k = 1.0f - __eta*__eta*(1.0f - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0f) ? __eta*__x - (__eta*simd_dot(__x,__n) + sqrt(__k))*__n : (simd_float2)0.0f;
}
static simd_float3  SIMD_CFUNC simd_refract(simd_float3  __x, simd_float3  __n, float __eta) {
  const float __k = 1.0f - __eta*__eta*(1.0f - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0f) ? __eta*__x - (__eta*simd_dot(__x,__n) + sqrt(__k))*__n : (simd_float3)0.0f;
}
static simd_float4  SIMD_CFUNC simd_refract(simd_float4  __x, simd_float4  __n, float __eta) {
  const float __k = 1.0f - __eta*__eta*(1.0f - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0f) ? __eta*__x - (__eta*simd_dot(__x,__n) + sqrt(__k))*__n : (simd_float4)0.0f;
}
static simd_double2 SIMD_CFUNC simd_refract(simd_double2 __x, simd_double2 __n, double __eta) {
  const double __k = 1.0 - __eta*__eta*(1.0 - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0) ? __eta*__x - (__eta*simd_dot(__x,__n) + sqrt(__k))*__n : (simd_double2)0.0;
}
static simd_double3 SIMD_CFUNC simd_refract(simd_double3 __x, simd_double3 __n, double __eta) {
  const double __k = 1.0 - __eta*__eta*(1.0 - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0) ? __eta*__x - (__eta*simd_dot(__x,__n) + sqrt(__k))*__n : (simd_double3)0.0;
}
static simd_double4 SIMD_CFUNC simd_refract(simd_double4 __x, simd_double4 __n, double __eta) {
  const double __k = 1.0 - __eta*__eta*(1.0 - simd_dot(__x,__n)*simd_dot(__x,__n));
  return (__k >= 0.0) ? __eta*__x - (__eta*simd_dot(__x,__n) + sqrt(__k))*__n : (simd_double4)0.0;
}

#if SIMD_LIBRARY_VERSION >= 2
static float SIMD_CFUNC simd_orient(simd_float2 __x, simd_float2 __y) {
  return _simd_orient_vf2(__x, __y);
}
static double SIMD_CFUNC simd_orient(simd_double2 __x, simd_double2 __y) {
  return _simd_orient_vd2(__x, __y);
}
static float SIMD_CFUNC simd_orient(simd_float3 __x, simd_float3 __y, simd_float3 __z) {
  return _simd_orient_vf3(__x, __y, __z);
}
static double SIMD_CFUNC simd_orient(simd_double3 __x, simd_double3 __y, simd_double3 __z) {
  simd_double3 __args[3] = { __x, __y, __z };
  return _simd_orient_vd3((const double *)__args);
}

static float SIMD_CFUNC simd_orient(simd_float2 __a, simd_float2 __b, simd_float2 __c) {
  return _simd_orient_pf2(__a, __b, __c);
}
static double SIMD_CFUNC simd_orient(simd_double2 __a, simd_double2 __b, simd_double2 __c) {
  return _simd_orient_pd2(__a, __b, __c);
}
static float SIMD_CFUNC simd_orient(simd_float3 __a, simd_float3 __b, simd_float3 __c, simd_float3 __d) {
  return _simd_orient_pf3(__a, __b, __c, __d);
}
static double SIMD_CFUNC simd_orient(simd_double3 __a, simd_double3 __b, simd_double3 __c, simd_double3 __d) {
  simd_double3 __args[4] = { __a, __b, __c, __d };
  return _simd_orient_pd3((const double *)__args);
}

static float SIMD_CFUNC simd_incircle(simd_float2 __x, simd_float2 __a, simd_float2 __b, simd_float2 __c) {
  return _simd_incircle_pf2(__x, __a, __b, __c);
}
static double SIMD_CFUNC simd_incircle(simd_double2 __x, simd_double2 __a, simd_double2 __b, simd_double2 __c) {
  return _simd_incircle_pd2(__x, __a, __b, __c);
}
static float SIMD_CFUNC simd_insphere(simd_float3 __x, simd_float3 __a, simd_float3 __b, simd_float3 __c, simd_float3 __d) {
  return _simd_insphere_pf3(__x, __a, __b, __c, __d);
}
static double SIMD_CFUNC simd_insphere(simd_double3 __x, simd_double3 __a, simd_double3 __b, simd_double3 __c, simd_double3 __d) {
  simd_double3 __args[5] = { __x, __a, __b, __c, __d };
  return _simd_insphere_pd3((const double *)__args);
}
#endif /* SIMD_LIBRARY_VERSION */

#if SIMD_LIBRARY_VERSION >= 6
static _Float16 SIMD_CFUNC simd_orient(simd_half2 __x, simd_half2 __y) {
  return _simd_orient_vh2(__x, __y);
}
static _Float16 SIMD_CFUNC simd_orient(simd_half3 __x, simd_half3 __y, simd_half3 __z) {
  return _simd_orient_vh3(__x, __y, __z);
}

static _Float16 SIMD_CFUNC simd_orient(simd_half2 __a, simd_half2 __b, simd_half2 __c) {
  return _simd_orient_ph2(__a, __b, __c);
}
static _Float16 SIMD_CFUNC simd_orient(simd_half3 __a, simd_half3 __b, simd_half3 __c, simd_half3 __d) {
  return _simd_orient_ph3(__a, __b, __c, __d);
}

static _Float16 SIMD_CFUNC simd_incircle(simd_half2 __x, simd_half2 __a, simd_half2 __b, simd_half2 __c) {
  return _simd_incircle_ph2(__x, __a, __b, __c);
}
static _Float16 SIMD_CFUNC simd_insphere(simd_half3 __x, simd_half3 __a, simd_half3 __b, simd_half3 __c, simd_half3 __d) {
  return _simd_insphere_ph3(__x, __a, __b, __c, __d);
}
#endif /* SIMD_LIBRARY_VERSION */

#ifdef __cplusplus
}
#endif
#endif /* SIMD_COMPILER_HAS_REQUIRED_FEATURES */
#endif /* __SIMD_COMMON_HEADER__ */