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/* graphene-simd4x4f.h: 4x4 float vector operations
*
* SPDX-License-Identifier: MIT
*
* Copyright 2014 Emmanuele Bassi
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#pragma once
#include "graphene-simd4f.h"
#include <math.h>
#include <float.h>
GRAPHENE_BEGIN_DECLS
/**
* graphene_simd4x4f_t:
*
* A SIMD-based matrix type that uses four #graphene_simd4f_t vectors.
*
* The matrix is treated as row-major, i.e. the x, y, z, and w vectors
* are rows, and elements of each vector are a column:
*
* |[<!-- language="C" -->
* graphene_simd4x4f_t = {
* x.x, x.y, x.z, x.w,
* y.x, y.y, y.z, y.w,
* z.x, z.y, z.z, z.w,
* w.x, w.y, w.z, w.w
* }
* ]|
*
* The contents of the #graphene_simd4x4f_t type are private and
* cannot be accessed directly; use the provided API instead.
*
* Since: 1.0
*/
/**
* graphene_simd4x4f_init:
* @x: a #graphene_simd4f_t for the first row
* @y: a #graphene_simd4f_t for the second row
* @z: a #graphene_simd4f_t for the third row
* @w: a #graphene_simd4f_t for the fourth row
*
* Creates a new #graphene_simd4x4f_t using the given row vectors
* to initialize it.
*
* Returns: the newly created #graphene_simd4x4f_t
*
* Since: 1.0
*/
static inline graphene_simd4x4f_t GRAPHENE_VECTORCALL
graphene_simd4x4f_init (graphene_simd4f_t x,
graphene_simd4f_t y,
graphene_simd4f_t z,
graphene_simd4f_t w)
{
graphene_simd4x4f_t s;
s.x = x;
s.y = y;
s.z = z;
s.w = w;
return s;
}
/**
* graphene_simd4x4f_init_identity:
* @m: a #graphene_simd4x4f_t
*
* Initializes @m to be the identity matrix.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_init_identity (graphene_simd4x4f_t *m)
{
*m = graphene_simd4x4f_init (graphene_simd4f_init (1.0f, 0.0f, 0.0f, 0.0f),
graphene_simd4f_init (0.0f, 1.0f, 0.0f, 0.0f),
graphene_simd4f_init (0.0f, 0.0f, 1.0f, 0.0f),
graphene_simd4f_init (0.0f, 0.0f, 0.0f, 1.0f));
}
/**
* graphene_simd4x4f_init_from_float:
* @m: a #graphene_simd4x4f_t
* @f: (array fixed-size=16): an array of 16 floating point values
*
* Initializes a #graphene_simd4x4f_t with the given array
* of floating point values.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_init_from_float (graphene_simd4x4f_t *m,
const float *f)
{
m->x = graphene_simd4f_init_4f (f + 0);
m->y = graphene_simd4f_init_4f (f + 4);
m->z = graphene_simd4f_init_4f (f + 8);
m->w = graphene_simd4f_init_4f (f + 12);
}
/**
* graphene_simd4x4f_to_float:
* @m: a #graphene_sidm4x4f_t
* @v: (out caller-allocates) (array fixed-size=16): a floating
* point values vector capable of holding at least 16 values
*
* Copies the content of @m in a float array.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_to_float (const graphene_simd4x4f_t *m,
float *v)
{
graphene_simd4f_dup_4f (m->x, v + 0);
graphene_simd4f_dup_4f (m->y, v + 4);
graphene_simd4f_dup_4f (m->z, v + 8);
graphene_simd4f_dup_4f (m->w, v + 12);
}
GRAPHENE_AVAILABLE_IN_1_0
void graphene_simd4x4f_transpose_in_place (graphene_simd4x4f_t *s);
#if defined(GRAPHENE_USE_SSE)
#ifdef __GNUC__
#define graphene_simd4x4f_transpose_in_place(s) \
(__extension__ ({ \
_MM_TRANSPOSE4_PS ((s)->x, (s)->y, (s)->z, (s)->w); \
}))
#elif defined (_MSC_VER)
#define graphene_simd4x4f_transpose_in_place(s) \
_MM_TRANSPOSE4_PS ((s)->x, (s)->y, (s)->z, (s)->w)
#endif
#elif defined(GRAPHENE_USE_GCC)
#define graphene_simd4x4f_transpose_in_place(s) \
(__extension__ ({ \
const graphene_simd4f_t sx = (s)->x; \
const graphene_simd4f_t sy = (s)->y; \
const graphene_simd4f_t sz = (s)->z; \
const graphene_simd4f_t sw = (s)->w; \
(s)->x = graphene_simd4f_init (sx[0], sy[0], sz[0], sw[0]); \
(s)->y = graphene_simd4f_init (sx[1], sy[1], sz[1], sw[1]); \
(s)->z = graphene_simd4f_init (sx[2], sy[2], sz[2], sw[2]); \
(s)->w = graphene_simd4f_init (sx[3], sy[3], sz[3], sw[3]); \
}))
#elif defined(GRAPHENE_USE_ARM_NEON)
# ifdef __GNUC__
#define graphene_simd4x4f_transpose_in_place(s) \
(__extension__ ({ \
const graphene_simd4f_union_t sx = { (s)->x }; \
const graphene_simd4f_union_t sy = { (s)->y }; \
const graphene_simd4f_union_t sz = { (s)->z }; \
const graphene_simd4f_union_t sw = { (s)->w }; \
(s)->x = graphene_simd4f_init (sx.f[0], sy.f[0], sz.f[0], sw.f[0]); \
(s)->y = graphene_simd4f_init (sx.f[1], sy.f[1], sz.f[1], sw.f[1]); \
(s)->z = graphene_simd4f_init (sx.f[2], sy.f[2], sz.f[2], sw.f[2]); \
(s)->w = graphene_simd4f_init (sx.f[3], sy.f[3], sz.f[3], sw.f[3]); \
}))
# elif defined (_MSC_VER)
#define graphene_simd4x4f_transpose_in_place(s) _simd4x4f_transpose_in_place(s)
static inline void
_simd4x4f_transpose_in_place (graphene_simd4x4f_t *s)
{
const graphene_simd4f_union_t sx = { (s)->x };
const graphene_simd4f_union_t sy = { (s)->y };
const graphene_simd4f_union_t sz = { (s)->z };
const graphene_simd4f_union_t sw = { (s)->w };
(s)->x = graphene_simd4f_init (sx.f[0], sy.f[0], sz.f[0], sw.f[0]);
(s)->y = graphene_simd4f_init (sx.f[1], sy.f[1], sz.f[1], sw.f[1]);
(s)->z = graphene_simd4f_init (sx.f[2], sy.f[2], sz.f[2], sw.f[2]);
(s)->w = graphene_simd4f_init (sx.f[3], sy.f[3], sz.f[3], sw.f[3]);
}
# endif
#elif defined(GRAPHENE_USE_SCALAR)
#define graphene_simd4x4f_transpose_in_place(s) \
(graphene_simd4x4f_transpose_in_place ((graphene_simd4x4f_t *) (s)))
#else
# error "No implementation for graphene_simd4x4f_t defined."
#endif
/**
* graphene_simd4x4f_sum:
* @a: a #graphene_simd4f_t
* @res: (out): return location for the sum vector
*
* Adds all the row vectors of @a.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_sum (const graphene_simd4x4f_t *a,
graphene_simd4f_t *res)
{
graphene_simd4f_t s = graphene_simd4f_add (a->x, a->y);
s = graphene_simd4f_add (s, a->z);
s = graphene_simd4f_add (s, a->w);
*res = s;
}
/**
* graphene_simd4x4f_vec4_mul:
* @a: a #graphene_simd4x4f_t
* @b: a #graphene_simd4f_t
* @res: (out): return location for a #graphene_simd4f_t
*
* Left multiplies the given #graphene_simd4x4f_t with the given
* #graphene_simd4f_t row vector using a dot product:
*
* |[<!-- language="plain" -->
* res = b × A
*
* = ⎡x⎤ ⎛ x.x x.y x.z x.w ⎞
* ⎜y⎟ ⎜ y.x y.y y.z y.w ⎟
* ⎜z⎟ ⎜ z.x z.y z.z z.w ⎟
* ⎣w⎦ ⎝ w.x w.y w.z w.w ⎠
*
* = [ x.x × x x.y × x x.z × x x.w × x ]
* + + + +
* [ y.x × y y.y × y y.z × y y.w × y ]
* + + + +
* [ z.x × z z.y × z z.z × z z.w × z ]
* + + + +
* [ w.x × w w.y × w w.z × w w.w × w ]
*
* = ⎡ x.x × x + y.x × y + z.x × z + w.x × w ⎤
* ⎜ x.y × x + y.y × y + z.y × z + w.y × w ⎟
* ⎜ x.z × x + y.z × y + z.z × z + w.z × w ⎟
* ⎣ x.w × x + y.w × y + z.w × z + w.w × w ⎦
* ]|
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_vec4_mul (const graphene_simd4x4f_t *a,
const graphene_simd4f_t *b,
graphene_simd4f_t *res)
{
const graphene_simd4f_t v = *b;
const graphene_simd4f_t v_x = graphene_simd4f_splat_x (v);
const graphene_simd4f_t v_y = graphene_simd4f_splat_y (v);
const graphene_simd4f_t v_z = graphene_simd4f_splat_z (v);
const graphene_simd4f_t v_w = graphene_simd4f_splat_w (v);
*res = graphene_simd4f_add (graphene_simd4f_add (graphene_simd4f_mul (a->x, v_x),
graphene_simd4f_mul (a->y, v_y)),
graphene_simd4f_add (graphene_simd4f_mul (a->z, v_z),
graphene_simd4f_mul (a->w, v_w)));
}
/**
* graphene_simd4x4f_vec3_mul:
* @m: a #graphene_simd4x4f_t
* @v: a #graphene_simd4f_t
* @res: (out): return location for a #graphene_simd4f_t
*
* Left multiplies the given #graphene_simd4x4f_t with the given
* #graphene_simd4f_t, using only the first three row vectors
* of the matrix, and the first three components of the vector;
* the W components of the matrix and vector are ignored:
*
* |[<!-- language="plain" -->
* res = b × A
*
* = ⎡x⎤ ⎛ x.x x.y x.z ⎞
* ⎜y⎟ ⎜ y.x y.y y.z ⎟
* ⎣z⎦ ⎝ z.x z.y z.z ⎠
*
* = [ x.x × x x.y × x x.z × x ]
* + + +
* [ y.x × y y.y × y y.z × y ]
* + + +
* [ z.x × z z.y × z z.z × z ]
*
* = ⎡ x.x × x + y.x × y + z.x × z ⎤
* ⎜ x.y × x + y.y × y + z.y × z ⎟
* ⎜ x.z × x + y.z × y + z.z × z ⎟
* ⎣ 0 ⎦
* ]|
*
* See also: graphene_simd4x4f_vec4_mul(), graphene_simd4x4f_point3_mul()
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_vec3_mul (const graphene_simd4x4f_t *m,
const graphene_simd4f_t *v,
graphene_simd4f_t *res)
{
const graphene_simd4f_t v_x = graphene_simd4f_splat_x (*v);
const graphene_simd4f_t v_y = graphene_simd4f_splat_y (*v);
const graphene_simd4f_t v_z = graphene_simd4f_splat_z (*v);
graphene_simd4f_t r;
r = graphene_simd4f_add (graphene_simd4f_add (graphene_simd4f_mul (m->x, v_x),
graphene_simd4f_mul (m->y, v_y)),
graphene_simd4f_mul (m->z, v_z));
*res = graphene_simd4f_zero_w (r);
}
/**
* graphene_simd4x4f_point3_mul:
* @m: a #graphene_simd4x4f_t
* @p: a #graphene_simd4f_t
* @res: (out): return location for a #graphene_simd4f_t
*
* Multiplies the given #graphene_simd4x4f_t with the given
* #graphene_simd4f_t.
*
* Unlike graphene_simd4x4f_vec3_mul(), this function will
* use the W components of the matrix:
*
* |[<!-- language="plain" -->
* res = b × A
*
* = ⎡x⎤ ⎛ x.x x.y x.z x.w ⎞
* ⎜y⎟ ⎜ y.x y.y y.z y.w ⎟
* ⎜z⎟ ⎜ z.x z.y z.z z.w ⎟
* ⎣w⎦ ⎝ w.x w.y w.z w.w ⎠
*
* = [ x.x × x x.y × x x.z × x x.w × x ]
* + + + +
* [ y.x × y y.y × y y.z × y y.w × y ]
* + + + +
* [ z.x × z z.y × z z.z × z z.w × z ]
* + + + +
* [ w.x w.y w.z w.w ]
*
* = ⎡ x.x × x + y.x × y + z.x × z + w.x ⎤
* ⎜ x.y × x + y.y × y + z.y × z + w.y ⎟
* ⎜ x.z × x + y.z × y + z.z × z + w.z ⎟
* ⎣ x.w × x + y.w × y + z.w × z + w.w ⎦
* ]|
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_point3_mul (const graphene_simd4x4f_t *m,
const graphene_simd4f_t *p,
graphene_simd4f_t *res)
{
const graphene_simd4f_t v = *p;
const graphene_simd4f_t v_x = graphene_simd4f_splat_x (v);
const graphene_simd4f_t v_y = graphene_simd4f_splat_y (v);
const graphene_simd4f_t v_z = graphene_simd4f_splat_z (v);
*res = graphene_simd4f_add (graphene_simd4f_add (graphene_simd4f_mul (m->x, v_x),
graphene_simd4f_mul (m->y, v_y)),
graphene_simd4f_add (graphene_simd4f_mul (m->z, v_z),
m->w));
}
/**
* graphene_simd4x4f_transpose:
* @s: a #graphene_simd4x4f_t
* @res: (out): return location for the transposed matrix
*
* Transposes the given #graphene_simd4x4f_t.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_transpose (const graphene_simd4x4f_t *s,
graphene_simd4x4f_t *res)
{
*res = *s;
graphene_simd4x4f_transpose_in_place (res);
}
/**
* graphene_simd4x4f_inv_ortho_vec3_mul:
* @a: a #graphene_simd4x4f_t
* @b: a #graphene_simd4f_t
* @res: (out): return location for the transformed vector
*
* Performs the inverse orthographic transformation of the first
* three components in the given vector, using the first three
* row vectors of the given SIMD matrix.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_inv_ortho_vec3_mul (const graphene_simd4x4f_t *a,
const graphene_simd4f_t *b,
graphene_simd4f_t *res)
{
graphene_simd4x4f_t transpose = *a;
graphene_simd4f_t translation = *b;
transpose.w = graphene_simd4f_init (0.f, 0.f, 0.f, 0.f);
graphene_simd4x4f_transpose_in_place (&transpose);
graphene_simd4x4f_vec3_mul (&transpose, &translation, res);
}
/**
* graphene_simd4x4f_inv_ortho_point3_mul:
* @a: a #graphene_simd4x4f_t
* @b: a #graphene_simd4x4f_t
* @res: (out): return location for the result vector
*
* Performs the inverse orthographic transformation of the first
* three components in the given vector, using the given SIMD
* matrix.
*
* Unlike graphene_simd4x4f_inv_ortho_vec3_mul(), this function
* will also use the fourth row vector of the SIMD matrix.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_inv_ortho_point3_mul (const graphene_simd4x4f_t *a,
const graphene_simd4f_t *b,
graphene_simd4f_t *res)
{
graphene_simd4f_t translation = graphene_simd4f_sub (*b, a->w);
graphene_simd4x4f_t transpose = *a;
transpose.w = graphene_simd4f_init (0.f, 0.f, 0.f, 0.f);
graphene_simd4x4f_transpose_in_place (&transpose);
graphene_simd4x4f_point3_mul (&transpose, &translation, res);
}
/**
* graphene_simd4x4f_matrix_mul:
* @a: a #graphene_simd4x4f_t
* @b: a #graphene_simd4x4f_t
* @res: (out): return location for the result
*
* Multiplies the two matrices, following the convention:
*
* |[<!-- language="plain" -->
* res = A × B
*
* = ⎡ A.x × B ⎤
* ⎜ A.y × B ⎟
* ⎜ A.z × B ⎟
* ⎣ A.w × B ⎦
*
* = ⎡ res.x ⎤
* ⎜ res.y ⎟
* ⎜ res.z ⎟
* ⎣ res.w ⎦
* ]|
*
* See also: graphene_simd4x4f_vec4_mul()
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_matrix_mul (const graphene_simd4x4f_t *a,
const graphene_simd4x4f_t *b,
graphene_simd4x4f_t *res)
{
#if 0
/* this is the classic naive A*B implementation of the row * column
* matrix product. using a SIMD scalar implementation, it's fairly
* slow at 329ns per multiplication; the SSE implementation makes it
* about 10x faster, at 32ns; the GCC vector implementation is only
* 5x faster, at 66ns. the biggest culprits are the transpose operation
* and the multiple, one lane reads to compute the scalar sum.
*/
graphene_simd4x4f_t t;
graphene_simd4x4f_transpose (b, &t);
res->x =
graphene_simd4f_init (graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->x, t.x)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->x, t.y)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->x, t.z)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->x, t.w)));
res->y =
graphene_simd4f_init (graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->y, t.x)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->y, t.y)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->y, t.z)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->y, t.w)));
res->z =
graphene_simd4f_init (graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->z, t.x)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->z, t.y)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->z, t.z)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->z, t.w)));
res->w =
graphene_simd4f_init (graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->w, t.x)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->w, t.y)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->w, t.z)),
graphene_simd4f_sum_scalar (graphene_simd4f_mul (a->w, t.w)));
#else
/* this is an optimized version of the matrix multiplication, using
* four dot products for each row vector. this yields drastically
* better numbers while retaining the same correct results as above:
* the scalar implementation now clocks at 91ns; the GCC vector
* implementation is 19ns; and the SSE implementation is 16ns.
*
* the order is correct if we want to multiply A with B; remember
* that matrix multiplication is non-commutative.
*/
graphene_simd4f_t x, y, z, w;
graphene_simd4x4f_vec4_mul (b, &a->x, &x);
graphene_simd4x4f_vec4_mul (b, &a->y, &y);
graphene_simd4x4f_vec4_mul (b, &a->z, &z);
graphene_simd4x4f_vec4_mul (b, &a->w, &w);
*res = graphene_simd4x4f_init (x, y, z, w);
#endif
}
/**
* graphene_simd4x4f_init_perspective:
* @m: a #graphene_simd4x4f_t
* @fovy_rad: the angle of the field of vision, in radians
* @aspect: the aspect value
* @z_near: the depth of the near clipping plane
* @z_far: the depth of the far clipping plane
*
* Initializes a #graphene_simd4x4f_t with a perspective projection.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_init_perspective (graphene_simd4x4f_t *m,
float fovy_rad,
float aspect,
float z_near,
float z_far)
{
float delta_z = z_far - z_near;
float cotangent = tanf (GRAPHENE_PI_2 - fovy_rad * 0.5f);
float a = cotangent / aspect;
float b = cotangent;
float c = -(z_far + z_near) / delta_z;
float d = -2 * z_near * z_far / delta_z;
m->x = graphene_simd4f_init ( a, 0.0f, 0.0f, 0.0f);
m->y = graphene_simd4f_init (0.0f, b, 0.0f, 0.0f);
m->z = graphene_simd4f_init (0.0f, 0.0f, c, -1.0f);
m->w = graphene_simd4f_init (0.0f, 0.0f, d, 0.0f);
}
/**
* graphene_simd4x4f_init_ortho:
* @m: a #graphene_simd4x4f_t
* @left: edge of the left clipping plane
* @right: edge of the right clipping plane
* @bottom: edge of the bottom clipping plane
* @top: edge of the top clipping plane
* @z_near: depth of the near clipping plane
* @z_far: depth of the far clipping plane
*
* Initializes the given SIMD matrix with an orthographic projection.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_init_ortho (graphene_simd4x4f_t *m,
float left,
float right,
float bottom,
float top,
float z_near,
float z_far)
{
float delta_x = right - left;
float delta_y = top - bottom;
float delta_z = z_far - z_near;
float a = 2.0f / delta_x;
float b = -(right + left) / delta_x;
float c = 2.0f / delta_y;
float d = -(top + bottom) / delta_y;
float e = -2.0f / delta_z;
float f = -(z_far + z_near) / delta_z;
m->x = graphene_simd4f_init ( a, 0.0f, 0.0f, 0.0f);
m->y = graphene_simd4f_init (0.0f, c, 0.0f, 0.0f);
m->z = graphene_simd4f_init (0.0f, 0.0f, e, 0.0f);
m->w = graphene_simd4f_init ( b, d, f, 1.0f);
}
/**
* graphene_simd4x4f_init_look_at:
* @m: a #graphene_simd4x4f_t
* @eye: vector for the camera coordinates
* @center: vector for the object coordinates
* @up: vector for the upwards direction
*
* Initializes a SIMD matrix with the projection necessary for
* the camera at the @eye coordinates to look at the object at
* the @center coordinates. The top of the camera is aligned to
* the @up vector.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_init_look_at (graphene_simd4x4f_t *m,
graphene_simd4f_t eye,
graphene_simd4f_t center,
graphene_simd4f_t up)
{
const graphene_simd4f_t direction = graphene_simd4f_sub (center, eye);
graphene_simd4f_t cross;
graphene_simd4f_t z_axis;
graphene_simd4f_t x_axis;
graphene_simd4f_t y_axis;
float eye_v[4];
if (graphene_simd4f_get_x (graphene_simd4f_dot3 (direction, direction)) < FLT_EPSILON)
/* eye and center are in the same position */
z_axis = graphene_simd4f_init (0, 0, 1, 0);
else
z_axis = graphene_simd4f_normalize3 (direction);
cross = graphene_simd4f_cross3 (z_axis, up);
if (graphene_simd4f_get_x (graphene_simd4f_dot3 (cross, cross)) < FLT_EPSILON)
{
graphene_simd4f_t tweak_z;
/* up and z_axis are parallel */
if (fabs (graphene_simd4f_get_z (up) - 1.0) < FLT_EPSILON)
tweak_z = graphene_simd4f_init (0.0001f, 0, 0, 0);
else
tweak_z = graphene_simd4f_init (0, 0, 0.0001f, 0);
z_axis = graphene_simd4f_add (z_axis, tweak_z);
z_axis = graphene_simd4f_normalize3 (z_axis);
cross = graphene_simd4f_cross3 (z_axis, up);
}
x_axis = graphene_simd4f_normalize3 (cross);
y_axis = graphene_simd4f_cross3 (x_axis, z_axis);
graphene_simd4f_dup_4f (eye, eye_v);
m->x = x_axis;
m->y = y_axis;
m->z = graphene_simd4f_neg (z_axis);
m->w = graphene_simd4f_init (-eye_v[0], -eye_v[1], -eye_v[2], 1.f);
}
/**
* graphene_simd4x4f_init_frustum:
* @m: a #graphene_simd4x4f_t
* @left: distance of the left clipping plane
* @right: distance of the right clipping plane
* @bottom: distance of the bottom clipping plane
* @top: distance of the top clipping plane
* @z_near: distance of the near clipping plane
* @z_far: distance of the far clipping plane
*
* Initializes a SIMD matrix with a frustum described by the distances
* of six clipping planes.
*
* Since: 1.2
*/
static inline void
graphene_simd4x4f_init_frustum (graphene_simd4x4f_t *m,
float left,
float right,
float bottom,
float top,
float z_near,
float z_far)
{
float x = 2.f * z_near / (right - left);
float y = 2.f * z_near / (top - bottom);
float a = (right + left) / (right - left);
float b = (top + bottom) / (top - bottom);
float c = -1.f * (z_far + z_near) / (z_far - z_near);
float d = -2.f * z_far * z_near / (z_far - z_near);
m->x = graphene_simd4f_init ( x, 0.f, 0.f, 0.f);
m->y = graphene_simd4f_init (0.f, y, 0.f, 0.f);
m->z = graphene_simd4f_init ( a, b, c, -1.f);
m->w = graphene_simd4f_init (0.f, 0.f, d, 0.f);
}
/**
* graphene_simd4x4f_perspective:
* @m: a #graphene_simd4x4f_t
* @depth: depth of the perspective
*
* Adds a perspective transformation for the given @depth.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_perspective (graphene_simd4x4f_t *m,
float depth)
{
#if 1
const float m_xw = graphene_simd4f_get_w (m->x);
const float m_yw = graphene_simd4f_get_w (m->y);
const float m_zw = graphene_simd4f_get_w (m->z);
const float m_ww = graphene_simd4f_get_w (m->w);
const float p0 = graphene_simd4f_get_z (m->x) + -1.0f / depth * m_xw;
const float p1 = graphene_simd4f_get_z (m->y) + -1.0f / depth * m_yw;
const float p2 = graphene_simd4f_get_z (m->z) + -1.0f / depth * m_zw;
const float p3 = graphene_simd4f_get_z (m->w) + -1.0f / depth * m_ww;
const graphene_simd4f_t p_x = graphene_simd4f_merge_w (m->x, m_xw + p0);
const graphene_simd4f_t p_y = graphene_simd4f_merge_w (m->y, m_yw + p1);
const graphene_simd4f_t p_z = graphene_simd4f_merge_w (m->z, m_zw + p2);
const graphene_simd4f_t p_w = graphene_simd4f_merge_w (m->w, m_ww + p3);
#else
/* this is equivalent to the operations above, but trying to inline
* them into SIMD registers as much as possible by transposing the
* original matrix and operating on the resulting column vectors. it
* should warrant a micro benchmark, because while the above code is
* dominated by single channel reads, the code below has a transpose
* operation.
*/
graphene_simd4x4f_t t;
const graphene_simd4f_t f, p;
const graphene_simd4f_t p_x, p_y, p_z, p_w;
graphene_simd4x4f_transpose (m, &t);
f = graphene_simd4f_neg (graphene_simd4f_reciprocal (graphene_simd4f_splat (depth)));
p = graphene_simd4f_sum (t.w, graphene_simd4f_sum (t.z, graphene_simd4f_mul (f, t.w)));
p_x = graphene_simd4f_merge_w (m->x, graphene_simd4f_get_x (p));
p_y = graphene_simd4f_merge_w (m->y, graphene_simd4f_get_y (p));
p_z = graphene_simd4f_merge_w (m->z, graphene_simd4f_get_z (p));
p_w = graphene_simd4f_merge_w (m->w, graphene_simd4f_get_w (p));
#endif
*m = graphene_simd4x4f_init (p_x, p_y, p_z, p_w);
}
/**
* graphene_simd4x4f_translation:
* @m: a #graphene_simd4x4f_t
* @x: coordinate of the X translation
* @y: coordinate of the Y translation
* @z: coordinate of the Z translation
*
* Initializes @m to contain a translation to the given coordinates.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_translation (graphene_simd4x4f_t *m,
float x,
float y,
float z)
{
*m = graphene_simd4x4f_init (graphene_simd4f_init (1.0f, 0.0f, 0.0f, 0.0f),
graphene_simd4f_init (0.0f, 1.0f, 0.0f, 0.0f),
graphene_simd4f_init (0.0f, 0.0f, 1.0f, 0.0f),
graphene_simd4f_init ( x, y, z, 1.0f));
}
/**
* graphene_simd4x4f_scale:
* @m: a #graphene_simd4x4f_t
* @x: scaling factor on the X axis
* @y: scaling factor on the Y axis
* @z: scaling factor on the Z axis
*
* Initializes @m to contain a scaling transformation with the
* given factors.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_scale (graphene_simd4x4f_t *m,
float x,
float y,
float z)
{
*m = graphene_simd4x4f_init (graphene_simd4f_init ( x, 0.0f, 0.0f, 0.0f),
graphene_simd4f_init (0.0f, y, 0.0f, 0.0f),
graphene_simd4f_init (0.0f, 0.0f, z, 0.0f),
graphene_simd4f_init (0.0f, 0.0f, 0.0f, 1.0f));
}
/**
* graphene_simd4x4f_rotation:
* @m: a #graphene_simd4x4f_t
* @rad: the rotation, in radians
* @axis: the vector of the axis of rotation
*
* Initializes @m to contain a rotation of the given angle
* along the given axis.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_rotation (graphene_simd4x4f_t *m,
float rad,
graphene_simd4f_t axis)
{
float sine, cosine;
float x, y, z;
float ab, bc, ca;
float tx, ty, tz;
graphene_simd4f_t i, j, k;
rad = -rad;
axis = graphene_simd4f_normalize3 (axis);
/* We cannot use graphene_sincos() because it's a private function, whereas
* graphene-simd4x4f.h is a public header
*/
sine = sinf (rad);
cosine = cosf (rad);
x = graphene_simd4f_get_x (axis);
y = graphene_simd4f_get_y (axis);
z = graphene_simd4f_get_z (axis);
ab = x * y * (1.0f - cosine);
bc = y * z * (1.0f - cosine);
ca = z * x * (1.0f - cosine);
tx = x * x;
ty = y * y;
tz = z * z;
i = graphene_simd4f_init (tx + cosine * (1.0f - tx), ab - z * sine, ca + y * sine, 0.f);
j = graphene_simd4f_init (ab + z * sine, ty + cosine * (1.0f - ty), bc - x * sine, 0.f);
k = graphene_simd4f_init (ca - y * sine, bc + x * sine, tz + cosine * (1.0f - tz), 0.f);
*m = graphene_simd4x4f_init (i, j, k, graphene_simd4f_init (0.0f, 0.0f, 0.0f, 1.0f));
}
/**
* graphene_simd4x4f_add:
* @a: a #graphene_simd4x4f_t
* @b: a #graphene_simd4x4f_t
* @res: (out caller-allocates): return location for a #graphene_simd4x4f_t
*
* Adds each row vector of @a and @b and places the results in @res.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_add (const graphene_simd4x4f_t *a,
const graphene_simd4x4f_t *b,
graphene_simd4x4f_t *res)
{
res->x = graphene_simd4f_add (a->x, b->x);
res->y = graphene_simd4f_add (a->y, b->y);
res->z = graphene_simd4f_add (a->z, b->z);
res->w = graphene_simd4f_add (a->w, b->w);
}
/**
* graphene_simd4x4f_sub:
* @a: a #graphene_simd4x4f_t
* @b: a #graphene_simd4x4f_t
* @res: (out caller-allocates): return location for a #graphene_simd4x4f_t
*
* Subtracts each row vector of @a and @b and places the results in @res.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_sub (const graphene_simd4x4f_t *a,
const graphene_simd4x4f_t *b,
graphene_simd4x4f_t *res)
{
res->x = graphene_simd4f_sub (a->x, b->x);
res->y = graphene_simd4f_sub (a->y, b->y);
res->z = graphene_simd4f_sub (a->z, b->z);
res->w = graphene_simd4f_sub (a->w, b->w);
}
/**
* graphene_simd4x4f_mul:
* @a: a #graphene_simd4x4f_t
* @b: a #graphene_simd4x4f_t
* @res: (out caller-allocates): return location for a #graphene_simd4x4f_t
*
* Multiplies each row vector of @a and @b and places the results in @res.
*
* You most likely want graphene_simd4x4f_matrix_mul() instead.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_mul (const graphene_simd4x4f_t *a,
const graphene_simd4x4f_t *b,
graphene_simd4x4f_t *res)
{
res->x = graphene_simd4f_mul (a->x, b->x);
res->y = graphene_simd4f_mul (a->y, b->y);
res->z = graphene_simd4f_mul (a->z, b->z);
res->w = graphene_simd4f_mul (a->w, b->w);
}
/**
* graphene_simd4x4f_div:
* @a: a #graphene_simd4x4f_t
* @b: a #graphene_simd4x4f_t
* @res: (out caller-allocates): return location for a #graphene_simd4x4f_t
*
* Divides each row vector of @a and @b and places the results in @res.
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_div (const graphene_simd4x4f_t *a,
const graphene_simd4x4f_t *b,
graphene_simd4x4f_t *res)
{
res->x = graphene_simd4f_div (a->x, b->x);
res->y = graphene_simd4f_div (a->y, b->y);
res->z = graphene_simd4f_div (a->z, b->z);
res->w = graphene_simd4f_div (a->w, b->w);
}
/**
* graphene_simd4x4f_inverse:
* @m: a #graphene_simd4x4f_t
* @res: (out): return location for the inverse matrix
*
* Inverts the given #graphene_simd4x4f_t.
*
* Returns: `true` if the matrix was invertible
*
* Since: 1.0
*/
static inline bool
graphene_simd4x4f_inverse (const graphene_simd4x4f_t *m,
graphene_simd4x4f_t *res)
{
/* split rows */
const graphene_simd4f_t r0 = m->x;
const graphene_simd4f_t r1 = m->y;
const graphene_simd4f_t r2 = m->z;
const graphene_simd4f_t r3 = m->w;
/* cofactors */
const graphene_simd4f_t r0_wxyz = graphene_simd4f_shuffle_wxyz (r0);
const graphene_simd4f_t r0_zwxy = graphene_simd4f_shuffle_zwxy (r0);
const graphene_simd4f_t r0_yzwx = graphene_simd4f_shuffle_yzwx (r0);
const graphene_simd4f_t r1_wxyz = graphene_simd4f_shuffle_wxyz (r1);
const graphene_simd4f_t r1_zwxy = graphene_simd4f_shuffle_zwxy (r1);
const graphene_simd4f_t r1_yzwx = graphene_simd4f_shuffle_yzwx (r1);
const graphene_simd4f_t r2_wxyz = graphene_simd4f_shuffle_wxyz (r2);
const graphene_simd4f_t r2_zwxy = graphene_simd4f_shuffle_zwxy (r2);
const graphene_simd4f_t r2_yzwx = graphene_simd4f_shuffle_yzwx (r2);
const graphene_simd4f_t r3_wxyz = graphene_simd4f_shuffle_wxyz (r3);
const graphene_simd4f_t r3_zwxy = graphene_simd4f_shuffle_zwxy (r3);
const graphene_simd4f_t r3_yzwx = graphene_simd4f_shuffle_yzwx (r3);
const graphene_simd4f_t r0_wxyz_x_r1 = graphene_simd4f_mul (r0_wxyz, r1);
const graphene_simd4f_t r0_wxyz_x_r1_yzwx = graphene_simd4f_mul (r0_wxyz, r1_yzwx);
const graphene_simd4f_t r0_wxyz_x_r1_zwxy = graphene_simd4f_mul (r0_wxyz, r1_zwxy);
const graphene_simd4f_t r2_wxyz_x_r3 = graphene_simd4f_mul (r2_wxyz, r3);
const graphene_simd4f_t r2_wxyz_x_r3_yzwx = graphene_simd4f_mul (r2_wxyz, r3_yzwx);
const graphene_simd4f_t r2_wxyz_x_r3_zwxy = graphene_simd4f_mul (r2_wxyz, r3_zwxy);
const graphene_simd4f_t ar1 = graphene_simd4f_sub (graphene_simd4f_shuffle_wxyz (r2_wxyz_x_r3_zwxy),
graphene_simd4f_shuffle_zwxy (r2_wxyz_x_r3));
const graphene_simd4f_t ar2 = graphene_simd4f_sub (graphene_simd4f_shuffle_zwxy (r2_wxyz_x_r3_yzwx),
r2_wxyz_x_r3_yzwx);
const graphene_simd4f_t ar3 = graphene_simd4f_sub (r2_wxyz_x_r3_zwxy,
graphene_simd4f_shuffle_wxyz (r2_wxyz_x_r3));
const graphene_simd4f_t br1 = graphene_simd4f_sub (graphene_simd4f_shuffle_wxyz (r0_wxyz_x_r1_zwxy),
graphene_simd4f_shuffle_zwxy (r0_wxyz_x_r1));
const graphene_simd4f_t br2 = graphene_simd4f_sub (graphene_simd4f_shuffle_zwxy (r0_wxyz_x_r1_yzwx),
r0_wxyz_x_r1_yzwx);
const graphene_simd4f_t br3 = graphene_simd4f_sub (r0_wxyz_x_r1_zwxy,
graphene_simd4f_shuffle_wxyz (r0_wxyz_x_r1));
const graphene_simd4f_t r0_sum =
graphene_simd4f_madd (r0_yzwx, ar3,
graphene_simd4f_madd (r0_zwxy, ar2,
graphene_simd4f_mul (r0_wxyz, ar1)));
const graphene_simd4f_t r1_sum =
graphene_simd4f_madd (r1_wxyz, ar1,
graphene_simd4f_madd (r1_zwxy, ar2,
graphene_simd4f_mul (r1_yzwx, ar3)));
const graphene_simd4f_t r2_sum =
graphene_simd4f_madd (r2_yzwx, br3,
graphene_simd4f_madd (r2_zwxy, br2,
graphene_simd4f_mul (r2_wxyz, br1)));
const graphene_simd4f_t r3_sum =
graphene_simd4f_madd (r3_yzwx, br3,
graphene_simd4f_madd (r3_zwxy, br2,
graphene_simd4f_mul (r3_wxyz, br1)));
/* determinant and its inverse */
const graphene_simd4f_t d0 = graphene_simd4f_mul (r1_sum, r0);
const graphene_simd4f_t d1 = graphene_simd4f_add (d0, graphene_simd4f_merge_high (d0, d0));
const graphene_simd4f_t det = graphene_simd4f_sub (d1, graphene_simd4f_splat_y (d1));
if (fabsf (graphene_simd4f_get_x (det)) >= FLT_EPSILON)
{
const graphene_simd4f_t invdet = graphene_simd4f_splat_x (graphene_simd4f_div (graphene_simd4f_splat (1.0f), det));
const graphene_simd4f_t o0 = graphene_simd4f_mul (graphene_simd4f_flip_sign_0101 (r1_sum), invdet);
const graphene_simd4f_t o1 = graphene_simd4f_mul (graphene_simd4f_flip_sign_1010 (r0_sum), invdet);
const graphene_simd4f_t o2 = graphene_simd4f_mul (graphene_simd4f_flip_sign_0101 (r3_sum), invdet);
const graphene_simd4f_t o3 = graphene_simd4f_mul (graphene_simd4f_flip_sign_1010 (r2_sum), invdet);
graphene_simd4x4f_t mt = graphene_simd4x4f_init (o0, o1, o2, o3);
/* transpose the resulting matrix */
graphene_simd4x4f_transpose (&mt, res);
return true;
}
return false;
}
/**
* graphene_simd4x4f_determinant:
* @m: a #graphene_simd4x4f_t
* @det_r: (out): return location for the matrix determinant
* @invdet_r: (out): return location for the inverse of the matrix
* determinant
*
* Computes the determinant (and its inverse) of the given matrix
*
* Since: 1.0
*/
static inline void
graphene_simd4x4f_determinant (const graphene_simd4x4f_t *m,
graphene_simd4f_t *det_r,
graphene_simd4f_t *invdet_r)
{
/* split rows */
const graphene_simd4f_t r0 = m->x;
const graphene_simd4f_t r1 = m->y;
const graphene_simd4f_t r2 = m->z;
const graphene_simd4f_t r3 = m->w;
/* cofactors */
const graphene_simd4f_t r1_wxyz = graphene_simd4f_shuffle_wxyz (r1);
const graphene_simd4f_t r1_zwxy = graphene_simd4f_shuffle_zwxy (r1);
const graphene_simd4f_t r1_yzwx = graphene_simd4f_shuffle_yzwx (r1);
const graphene_simd4f_t r2_wxyz = graphene_simd4f_shuffle_wxyz (r2);
const graphene_simd4f_t r3_zwxy = graphene_simd4f_shuffle_zwxy (r3);
const graphene_simd4f_t r3_yzwx = graphene_simd4f_shuffle_yzwx (r3);
const graphene_simd4f_t r2_wxyz_x_r3 = graphene_simd4f_mul (r2_wxyz, r3);
const graphene_simd4f_t r2_wxyz_x_r3_yzwx = graphene_simd4f_mul (r2_wxyz, r3_yzwx);
const graphene_simd4f_t r2_wxyz_x_r3_zwxy = graphene_simd4f_mul (r2_wxyz, r3_zwxy);
const graphene_simd4f_t ar1 = graphene_simd4f_sub (graphene_simd4f_shuffle_wxyz (r2_wxyz_x_r3_zwxy),
graphene_simd4f_shuffle_zwxy (r2_wxyz_x_r3));
const graphene_simd4f_t ar2 = graphene_simd4f_sub (graphene_simd4f_shuffle_zwxy (r2_wxyz_x_r3_yzwx),
r2_wxyz_x_r3_yzwx);
const graphene_simd4f_t ar3 = graphene_simd4f_sub (r2_wxyz_x_r3_zwxy,
graphene_simd4f_shuffle_wxyz (r2_wxyz_x_r3));
const graphene_simd4f_t r1_sum =
graphene_simd4f_madd (r1_wxyz, ar1,
graphene_simd4f_madd (r1_zwxy, ar2,
graphene_simd4f_mul (r1_yzwx, ar3)));
/* determinant and its inverse */
const graphene_simd4f_t d0 = graphene_simd4f_mul (r1_sum, r0);
const graphene_simd4f_t d1 = graphene_simd4f_add (d0, graphene_simd4f_merge_high (d0, d0));
const graphene_simd4f_t det = graphene_simd4f_sub (d1, graphene_simd4f_splat_y (d1));
const graphene_simd4f_t invdet = graphene_simd4f_splat_x (graphene_simd4f_div (graphene_simd4f_splat (1.0f), det));
if (det_r != NULL)
*det_r = det;
if (invdet_r != NULL)
*invdet_r = invdet;
}
/**
* graphene_simd4x4f_is_identity:
* @m: a #graphene_simd4x4f_t
*
* Checks whether the given matrix is the identity matrix.
*
* Returns: `true` if the matrix is the identity matrix
*
* Since: 1.0
*/
static inline bool
graphene_simd4x4f_is_identity (const graphene_simd4x4f_t *m)
{
const graphene_simd4f_t r0 = graphene_simd4f_init (1.0f, 0.0f, 0.0f, 0.0f);
const graphene_simd4f_t r1 = graphene_simd4f_init (0.0f, 1.0f, 0.0f, 0.0f);
const graphene_simd4f_t r2 = graphene_simd4f_init (0.0f, 0.0f, 1.0f, 0.0f);
const graphene_simd4f_t r3 = graphene_simd4f_init (0.0f, 0.0f, 0.0f, 1.0f);
return graphene_simd4f_cmp_eq (m->x, r0) &&
graphene_simd4f_cmp_eq (m->y, r1) &&
graphene_simd4f_cmp_eq (m->z, r2) &&
graphene_simd4f_cmp_eq (m->w, r3);
}
/**
* graphene_simd4x4f_is_2d:
* @m: a #graphene_simd4x4f_t
*
* Checks whether the given matrix is compatible with an affine
* transformation matrix.
*
* Returns: `true` if the matrix is compatible with an affine
* transformation matrix
*
* Since: 1.0
*/
static inline bool
graphene_simd4x4f_is_2d (const graphene_simd4x4f_t *m)
{
float f[4];
if (!(fabsf (graphene_simd4f_get_z (m->x)) < FLT_EPSILON && fabsf (graphene_simd4f_get_w (m->x)) < FLT_EPSILON))
return false;
if (!(fabsf (graphene_simd4f_get_z (m->y)) < FLT_EPSILON && fabsf (graphene_simd4f_get_w (m->y)) < FLT_EPSILON))
return false;
graphene_simd4f_dup_4f (m->z, f);
if (!(fabsf (f[0]) < FLT_EPSILON &&
fabsf (f[1]) < FLT_EPSILON &&
1.f - fabsf (f[2]) < FLT_EPSILON &&
fabsf (f[3]) < FLT_EPSILON))
return false;
if (!(fabsf (graphene_simd4f_get_z (m->w)) < FLT_EPSILON && 1.f - fabsf (graphene_simd4f_get_w (m->w)) < FLT_EPSILON))
return false;
return true;
}
GRAPHENE_END_DECLS