libarrow

Introduction
Status
Reference

Introduction

This library implements a small set of fixed-size spatial data types, namely vectors, matrices and quaternions, along with common linear algebra routines for each of them. The source code is fully ANSI C compatible, thus portable across most compilers.

The following table lists the data types available in this library:

Type name	Description
`vec2f`	2D single-precision vector.
`vec2d`	2D double-precision vector.
`vec3f`	3D single-precision vector.
`vec3d`	3D double-precision vector.
`vec4f`	4D single-precision vector.
`vec4d`	4D double-precision vector.
`mat2f`	2x2 single-precision matrix.
`mat2d`	2x2 double-precision matrix.
`mat3f`	3x3 single-precision matrix.
`mat3d`	3x3 double-precision matrix.
`mat4f`	4x4 single-precision matrix.
`mat4d`	4x4 double-precision matrix.
`quatf`	Single-precision quaternion.
`quatd`	Double-precision quaternion.

Those using Clang or GCC may pass an additional compilation flag, -D_ARROW_VECTORIZED, to enable the library to take advantage of the compiler's vector extension capabilities to produce faster code. See Clang's or GCC's respective documentation pages for more information about vectorized data types.

Status

The vector and matrix modules are nearing completion while the quaternion module is still well underway. No comprehensive tests and benchmarks have been written either. I would not recommend using this library yet.

Reference

Vector

#include "arrow/vector.h"

Vector types

Type name	Description	Size (standard)	Size (vectorized)
`vec2f`	2D single-precision vector.	8	8 (Clang), 16 (GCC)
`vec2d`	2D double-precision vector.	16	16
`vec3f`	3D single-precision vector.	12	16
`vec3d`	3D double-precision vector.	24	32
`vec4f`	4D single-precision vector.	16	16
`vec4d`	4D double-precision vector.	32	32

Vector indexing macros

Macro definition	Description
`vec_x(v)`	Index to the x-component of a vector.
`vec_y(v)`	Index to the y-component of a vector.
`vec_z(v)`	Index to the z-component of a vector.
`vec_w(v)`	Index to the w-component of a vector.

Vector constructors

Function prototype	Return value	Description
`vec2f_make(float, float)`	`vec2f`	Constructs a 2D single-precision vector.
`vec2d_make(double, double)`	`vec2d`	Constructs a 2D double-precision vector.
`vec3f_make(float, float, float)`	`vec3f`	Constructs a 3D single-precision vector.
`vec3d_make(double, double, double)`	`vec3d`	Constructs a 3D double-precision vector.
`vec4f_make(float, float, float, float)`	`vec4f`	Constructs a 4D single-precision vector.
`vec4d_make(double, double, double, double)`	`vec4d`	Constructs a 4D double-precision vector.
`vec2f_with(float)`	`vec2f`	Constructs a 2D single-precision vector with an initial value.
`vec2d_with(double)`	`vec2d`	Constructs a 2D double-precision vector with an initial value.
`vec3f_with(float)`	`vec3f`	Constructs a 3D single-precision vector with an initial value.
`vec3d_with(double)`	`vec3d`	Constructs a 3D double-precision vector with an initial value.
`vec4f_with(float)`	`vec4f`	Constructs a 4D single-precision vector with an initial value.
`vec4d_with(double)`	`vec4d`	Constructs a 4D double-precision vector with an initial value.
`vec2f_zero(void)`	`vec2f`	Constructs a zero 2D single-precision vector.
`vec2d_zero(void)`	`vec2d`	Constructs a zero 2D double-precision vector.
`vec3f_zero(void)`	`vec3f`	Constructs a zero 3D single-precision vector.
`vec3d_zero(void)`	`vec3d`	Constructs a zero 3D double-precision vector.
`vec4f_zero(void)`	`vec4f`	Constructs a zero 4D single-precision vector.
`vec4d_zero(void)`	`vec4d`	Constructs a zero 4D double-precision vector.

Element-wise vector arithmetic

Function prototype	Return value	Description
`vec2f_add(vec2f, vec2f)`	`vec2f`	Returns the sum vector of two 2D single-precision vectors.
`vec2d_add(vec2d, vec2d)`	`vec2d`	Returns the sum vector of two 2D double-precision vectors.
`vec3f_add(vec3f, vec3f)`	`vec3f`	Returns the sum vector of two 3D single-precision vectors.
`vec3d_add(vec3d, vec3d)`	`vec3d`	Returns the sum vector of two 3D double-precision vectors.
`vec4f_add(vec4f, vec4f)`	`vec4f`	Returns the sum vector of two 4D single-precision vectors.
`vec4d_add(vec4d, vec4d)`	`vec4d`	Returns the sum vector of two 4D double-precision vectors.
`vec2f_sub(vec2f, vec2f)`	`vec2f`	Returns the difference vector between two 2D single-precision vectors.
`vec2d_sub(vec2d, vec2d)`	`vec2d`	Returns the difference vector between two 2D double-precision vectors.
`vec3f_sub(vec3f, vec3f)`	`vec3f`	Returns the difference vector between two 3D single-precision vectors.
`vec3d_sub(vec3d, vec3d)`	`vec3d`	Returns the difference vector between two 3D double-precision vectors.
`vec4f_sub(vec4f, vec4f)`	`vec4f`	Returns the difference vector between two 4D single-precision vectors.
`vec4d_sub(vec4d, vec4d)`	`vec4d`	Returns the difference vector between two 4D double-precision vectors.
`vec2f_mul(vec2f, vec2f)`	`vec2f`	Returns the product vector of two 2D single-precision vectors.
`vec2d_mul(vec2d, vec2d)`	`vec2d`	Returns the product vector of two 2D double-precision vectors.
`vec3f_mul(vec3f, vec3f)`	`vec3f`	Returns the product vector of two 3D single-precision vectors.
`vec3d_mul(vec3d, vec3d)`	`vec3d`	Returns the product vector of two 3D double-precision vectors.
`vec4f_mul(vec4f, vec4f)`	`vec4f`	Returns the product vector of two 4D single-precision vectors.
`vec4d_mul(vec4d, vec4d)`	`vec4d`	Returns the product vector of two 4D double-precision vectors.
`vec2f_div(vec2f, vec2f)`	`vec2f`	Returns the quotient vector between two 2D single-precision vectors.
`vec2d_div(vec2d, vec2d)`	`vec2d`	Returns the quotient vector between two 2D double-precision vectors.
`vec3f_div(vec3f, vec3f)`	`vec3f`	Returns the quotient vector between two 3D single-precision vectors.
`vec3d_div(vec3d, vec3d)`	`vec3d`	Returns the quotient vector between two 3D double-precision vectors.
`vec4f_div(vec4f, vec4f)`	`vec4f`	Returns the quotient vector between two 4D single-precision vectors.
`vec4d_div(vec4d, vec4d)`	`vec4d`	Returns the quotient vector between two 4D double-precision vectors.
`vec2f_add_scalar(vec2f, vec2f)`	`vec2f`	Returns the sum vector of a 2D single-precision vector and a scalar.
`vec2d_add_scalar(vec2d, vec2d)`	`vec2d`	Returns the sum vector of a 2D double-precision vector and a scalar.
`vec3f_add_scalar(vec3f, vec3f)`	`vec3f`	Returns the sum vector of a 3D single-precision vector and a scalar.
`vec3d_add_scalar(vec3d, vec3d)`	`vec3d`	Returns the sum vector of a 3D double-precision vector and a scalar.
`vec4f_add_scalar(vec4f, vec4f)`	`vec4f`	Returns the sum vector of a 4D single-precision vector and a scalar.
`vec4d_add_scalar(vec4d, vec4d)`	`vec4d`	Returns the sum vector of a 4D double-precision vector and a scalar.
`vec2f_sub_scalar(vec2f, vec2f)`	`vec2f`	Returns the difference vector between a 2D single-precision vector and a scalar.
`vec2d_sub_scalar(vec2d, vec2d)`	`vec2d`	Returns the difference vector between a 2D double-precision vector and a scalar.
`vec3f_sub_scalar(vec3f, vec3f)`	`vec3f`	Returns the difference vector between a 3D single-precision vector and a scalar.
`vec3d_sub_scalar(vec3d, vec3d)`	`vec3d`	Returns the difference vector between a 3D double-precision vector and a scalar.
`vec4f_sub_scalar(vec4f, vec4f)`	`vec4f`	Returns the difference vector between a 4D single-precision vector and a scalar.
`vec4d_sub_scalar(vec4d, vec4d)`	`vec4d`	Returns the difference vector between a 4D double-precision vector and a scalar.
`vec2f_mul_scalar(vec2f, vec2f)`	`vec2f`	Returns the product vector of a 2D single-precision vector and a scalar.
`vec2d_mul_scalar(vec2d, vec2d)`	`vec2d`	Returns the product vector of a 2D double-precision vector and a scalar.
`vec3f_mul_scalar(vec3f, vec3f)`	`vec3f`	Returns the product vector of a 3D single-precision vector and a scalar.
`vec3d_mul_scalar(vec3d, vec3d)`	`vec3d`	Returns the product vector of a 3D double-precision vector and a scalar.
`vec4f_mul_scalar(vec4f, vec4f)`	`vec4f`	Returns the product vector of a 4D single-precision vector and a scalar.
`vec4d_mul_scalar(vec4d, vec4d)`	`vec4d`	Returns the product vector of a 4D double-precision vector and a scalar.
`vec2f_div_scalar(vec2f, vec2f)`	`vec2f`	Returns the quotient vector between a 2D single-precision vector and a scalar.
`vec2d_div_scalar(vec2d, vec2d)`	`vec2d`	Returns the quotient vector between a 2D double-precision vector and a scalar.
`vec3f_div_scalar(vec3f, vec3f)`	`vec3f`	Returns the quotient vector between a 3D single-precision vector and a scalar.
`vec3d_div_scalar(vec3d, vec3d)`	`vec3d`	Returns the quotient vector between a 3D double-precision vector and a scalar.
`vec4f_div_scalar(vec4f, vec4f)`	`vec4f`	Returns the quotient vector between a 4D single-precision vector and a scalar.
`vec4d_div_scalar(vec4d, vec4d)`	`vec4d`	Returns the quotient vector between a 4D double-precision vector and a scalar.

General vector functions

Function prototype	Return value	Description
`vec2f_dot(vec2f, vec2f)`	`float`	Returns the dot product of two 2D single-precision vectors.
`vec2d_dot(vec2d, vec2d)`	`double`	Returns the dot product of two 2D double-precision vectors.
`vec3f_dot(vec3f, vec3f)`	`float`	Returns the dot product of two 3D single-precision vectors.
`vec3d_dot(vec3d, vec3d)`	`double`	Returns the dot product of two 3D double-precision vectors.
`vec4f_dot(vec4f, vec4f)`	`float`	Returns the dot product of two 4D single-precision vectors.
`vec4d_dot(vec4d, vec4d)`	`double`	Returns the dot product of two 4D double-precision vectors.
`vec2f_norm(vec2f)`	`float`	Returns the length of a 2D single-precision vector.
`vec2d_norm(vec2d)`	`double`	Returns the length of a 2D double-precision vector.
`vec3f_norm(vec3f)`	`float`	Returns the length of a 3D single-precision vector.
`vec3d_norm(vec3d)`	`double`	Returns the length of a 3D double-precision vector.
`vec4f_norm(vec4f)`	`float`	Returns the length of a 4D single-precision vector.
`vec4d_norm(vec4d)`	`double`	Returns the length of a 4D double-precision vector.
`vec2f_unit(vec2f)`	`vec2f`	Returns a normalized vector from a 2D single-precision vector.
`vec2d_unit(vec2d)`	`vec2d`	Returns a normalized vector from a 2D double-precision vector.
`vec3f_unit(vec3f)`	`vec3f`	Returns a normalized vector from a 3D single-precision vector.
`vec3d_unit(vec3d)`	`vec3d`	Returns a normalized vector from a 3D double-precision vector.
`vec4f_unit(vec4f)`	`vec4f`	Returns a normalized vector from a 4D single-precision vector.
`vec4d_unit(vec4d)`	`vec4d`	Returns a normalized vector from a 4D double-precision vector.
`vec2f_angle(vec2f, vec2f)`	`float`	Returns the angle between two 2D single-precision vectors.
`vec2d_angle(vec2d, vec2d)`	`double`	Returns the angle between two 2D double-precision vectors.
`vec3f_angle(vec3f, vec3f)`	`float`	Returns the angle between two 3D single-precision vectors.
`vec3d_angle(vec3d, vec3d)`	`double`	Returns the angle between two 3D double-precision vectors.
`vec4f_angle(vec4f, vec4f)`	`float`	Returns the angle between two 4D single-precision vectors.
`vec4d_angle(vec4d, vec4d)`	`double`	Returns the angle between two 4D double-precision vectors.
`vec2f_vproject(vec2f, vec2f)`	`vec2f`	Returns the vector projection of the first 2D single-precision vector onto the second.
`vec2d_vproject(vec2d, vec2d)`	`vec2d`	Returns the vector projection of the first 2D double-precision vector onto the second.
`vec3f_vproject(vec3f, vec3f)`	`vec3f`	Returns the vector projection of the first 3D single-precision vector onto the second.
`vec3d_vproject(vec3d, vec3d)`	`vec3d`	Returns the vector projection of the first 3D double-precision vector onto the second.
`vec4f_vproject(vec4f, vec4f)`	`vec4f`	Returns the vector projection of the first 4D single-precision vector onto the second.
`vec4d_vproject(vec4d, vec4d)`	`vec4d`	Returns the vector projection of the first 4D double-precision vector onto the second.
`vec2f_sproject(vec2f, vec2f)`	`float`	Returns the scalar projection of the first 2D single-precision vector onto the second.
`vec2d_sproject(vec2d, vec2d)`	`double`	Returns the scalar projection of the first 2D double-precision vector onto the second.
`vec3f_sproject(vec3f, vec3f)`	`float`	Returns the scalar projection of the first 3D single-precision vector onto the second.
`vec3d_sproject(vec3d, vec3d)`	`double`	Returns the scalar projection of the first 3D double-precision vector onto the second.
`vec4f_sproject(vec4f, vec4f)`	`float`	Returns the scalar projection of the first 4D single-precision vector onto the second.
`vec4d_sproject(vec4d, vec4d)`	`double`	Returns the scalar projection of the first 4D double-precision vector onto the second.

2D vector functions

Function prototype	Return value	Description
`vec2f_rotate(vec2f, float)`	`vec2f`	Returns the 2D single-precision vector rotated by an angle around the origin.
`vec2d_rotate(vec2d, double)`	`vec2d`	Returns the 2D double-precision vector rotated by an angle around the origin.
`vec2f_perp(vec2f)`	`vec2f`	Returns the vector counter-clockwise perpendicular to a 2D single-precision vector.
`vec2d_perp(vec2d)`	`vec2d`	Returns the vector counter-clockwise perpendicular to a 2D double-precision vector.
`vec2f_cperp(vec2f)`	`vec2f`	Returns the vector clockwise perpendicular to a 2D single-precision vector.
`vec2d_cperp(vec2d)`	`vec2d`	Returns the vector clockwise perpendicular to a 2D double-precision vector.

3D vector functions

Function prototype	Return value	Description
`vec3f_cross(vec3f, vec3f)`	`vec3f`	Returns the cross product of two 3D single-precision vectors.
`vec3d_cross(vec3d, vec3d)`	`vec3d`	Returns the cross product of two 3D double-precision vectors.
`vec3f_stp(vec3f, vec3f, vec3f)`	`float`	Returns the scalar triple product of three 3D single-precision vectors.
`vec3d_stp(vec3d, vec3d, vec3d)`	`double`	Returns the scalar triple product of three 3D double-precision vectors.

Vector type conversion functions

Function prototype	Return value	Description
`vec2d_to_f(vec2d)`	`vec2f`	Converts a 2D vector from double- to single-precision.
`vec2f_to_d(vec2f)`	`vec2d`	Converts a 2D vector from single- to double-precision.
`vec3d_to_f(vec3d)`	`vec3f`	Converts a 3D vector from double- to single-precision.
`vec3f_to_d(vec3f)`	`vec3d`	Converts a 3D vector from single- to double-precision.
`vec4d_to_f(vec4d)`	`vec4f`	Converts a 4D vector from double- to single-precision.
`vec4f_to_d(vec4f)`	`vec4d`	Converts a 4D vector from single- to double-precision.

Vector size conversion functions

Function prototype	Return value	Description
`vec3f_to_2(vec3f)`	`vec2f`	Converts a 3D single-precision vector to a 2D vector.
`vec4f_to_2(vec4f)`	`vec2f`	Converts a 4D single-precision vector to a 2D vector.
`vec3d_to_2(vec3d)`	`vec2d`	Converts a 3D double-precision vector to a 2D vector.
`vec4d_to_2(vec4d)`	`vec2d`	Converts a 4D double-precision vector to a 2D vector.
`vec2f_to_3(vec2f)`	`vec3f`	Converts a 2D single-precision vector to a 3D vector.
`vec4f_to_3(vec4f)`	`vec3f`	Converts a 4D single-precision vector to a 3D vector.
`vec2d_to_3(vec2d)`	`vec3d`	Converts a 2D double-precision vector to a 3D vector.
`vec4d_to_3(vec4d)`	`vec3d`	Converts a 4D double-precision vector to a 3D vector.
`vec2f_to_4(vec2f)`	`vec4f`	Converts a 2D single-precision vector to a 4D vector.
`vec3f_to_4(vec3f)`	`vec4f`	Converts a 3D single-precision vector to a 4D vector.
`vec2d_to_4(vec2d)`	`vec4d`	Converts a 2D double-precision vector to a 4D vector.
`vec3d_to_4(vec3d)`	`vec4d`	Converts a 3D double-precision vector to a 4D vector.

Matrix

#include "arrow/matrix.h"

Matrix types

Type name	Description	Size (standard)	Size (vectorized)
`mat2f`	2x2 single-precision matrix.	16	16
`mat2d`	2x2 double-precision matrix.	32	32
`mat3f`	3x3 single-precision matrix.	36	64
`mat3d`	3x3 double-precision matrix.	72	128
`mat4f`	4x4 single-precision matrix.	64	64
`mat4d`	4x4 double-precision matrix.	128	128

General matrix indexing macros

Macro definition	Description
`mat_i(m, i)`	Index to the value at cell `i` in an arbitrarily sized row-major ordered matrix `m`.

2x2 matrix indexing macros

Macro definition	Description
`mat2_rc(m, r, c)`	Index to the value at row `r`, column `c` in a 2x2 matrix `m`.
`mat2_11(m)`	Index to the value at row 1, column 1 in a 2x2 matrix `m`.
`mat2_12(m)`	Index to the value at row 1, column 2 in a 2x2 matrix `m`.
`mat2_21(m)`	Index to the value at row 2, column 1 in a 2x2 matrix `m`.
`mat2_22(m)`	Index to the value at row 2, column 2 in a 2x2 matrix `m`.

3x3 matrix indexing macros

Macro definition	Description
`mat3_rc(m, r, c)`	Index to the value at row `r`, column `c` in a 3x3 matrix `m`.
`mat3_11(m)`	Index to the value at row 1, column 1 in a 3x3 matrix `m`.
`mat3_12(m)`	Index to the value at row 1, column 2 in a 3x3 matrix `m`.
`mat3_13(m)`	Index to the value at row 1, column 3 in a 3x3 matrix `m`.
`mat3_21(m)`	Index to the value at row 2, column 1 in a 3x3 matrix `m`.
`mat3_22(m)`	Index to the value at row 2, column 2 in a 3x3 matrix `m`.
`mat3_23(m)`	Index to the value at row 2, column 3 in a 3x3 matrix `m`.
`mat3_31(m)`	Index to the value at row 3, column 1 in a 3x3 matrix `m`.
`mat3_32(m)`	Index to the value at row 3, column 2 in a 3x3 matrix `m`.
`mat3_33(m)`	Index to the value at row 3, column 3 in a 3x3 matrix `m`.

4x4 matrix indexing macros

Macro definition	Description
`mat4_rc(m, r, c)`	Index to the value at row `r`, column `c` in a 4x4 matrix `m`.
`mat4_11(m)`	Index to the value at row 1, column 1 in a 4x4 matrix `m`.
`mat4_12(m)`	Index to the value at row 1, column 2 in a 4x4 matrix `m`.
`mat4_13(m)`	Index to the value at row 1, column 3 in a 4x4 matrix `m`.
`mat4_14(m)`	Index to the value at row 1, column 4 in a 4x4 matrix `m`.
`mat4_21(m)`	Index to the value at row 2, column 1 in a 4x4 matrix `m`.
`mat4_22(m)`	Index to the value at row 2, column 2 in a 4x4 matrix `m`.
`mat4_23(m)`	Index to the value at row 2, column 3 in a 4x4 matrix `m`.
`mat4_24(m)`	Index to the value at row 2, column 4 in a 4x4 matrix `m`.
`mat4_31(m)`	Index to the value at row 3, column 1 in a 4x4 matrix `m`.
`mat4_32(m)`	Index to the value at row 3, column 2 in a 4x4 matrix `m`.
`mat4_33(m)`	Index to the value at row 3, column 3 in a 4x4 matrix `m`.
`mat4_34(m)`	Index to the value at row 3, column 4 in a 4x4 matrix `m`.
`mat4_41(m)`	Index to the value at row 4, column 1 in a 4x4 matrix `m`.
`mat4_42(m)`	Index to the value at row 4, column 2 in a 4x4 matrix `m`.
`mat4_43(m)`	Index to the value at row 4, column 3 in a 4x4 matrix `m`.
`mat4_44(m)`	Index to the value at row 4, column 4 in a 4x4 matrix `m`.

Matrix constructors

Function prototype	Return value	Description
`mat2f_make(float...)`	`mat2f`	Constructs a 2x2 single-precision matrix from 4 floats.
`mat2d_make(double...)`	`mat2d`	Constructs a 2x2 double-precision matrix from 4 doubles.
`mat3f_make(float...)`	`mat3f`	Constructs a 3x3 single-precision matrix from 9 floats.
`mat3d_make(double...)`	`mat3d`	Constructs a 3x3 double-precision matrix from 9 doubles.
`mat4f_make(float...)`	`mat4f`	Constructs a 4x4 single-precision matrix from 16 floats.
`mat4d_make(double...)`	`mat4d`	Constructs a 4x4 double-precision matrix from 16 doubles.
`mat2f_with(float)`	`mat2f`	Constructs a 2x2 single-precision matrix with an initial value.
`mat2d_with(double)`	`mat2d`	Constructs a 2x2 double-precision matrix with an initial value.
`mat3f_with(float)`	`mat3f`	Constructs a 3x3 single-precision matrix with an initial value.
`mat3d_with(double)`	`mat3d`	Constructs a 3x3 double-precision matrix with an initial value.
`mat4f_with(float)`	`mat4f`	Constructs a 4x4 single-precision matrix with an initial value.
`mat4d_with(double)`	`mat4d`	Constructs a 4x4 double-precision matrix with an initial value.
`mat2f_from_rows(vec2f, vec2f)`	`mat2f`	Constructs a 2x2 single-precision matrix from two row vectors.
`mat2d_from_rows(vec2d, vec2d)`	`mat2d`	Constructs a 2x2 double-precision matrix from two row vectors.
`mat3f_from_rows(vec3f, vec3f, vec3f)`	`mat3f`	Constructs a 3x3 single-precision matrix from three row vectors.
`mat3d_from_rows(vec3d, vec3d, vec3d)`	`mat3d`	Constructs a 3x3 double-precision matrix from three row vectors.
`mat4f_from_rows(vec4f, vec4f, vec4f, vec4f)`	`mat4f`	Constructs a 4x4 single-precision matrix from four row vectors.
`mat4d_from_rows(vec4d, vec4d, vec4d, vec4d)`	`mat4d`	Constructs a 4x4 double-precision matrix from four row vectors.
`mat2f_from_columns(vec2f, vec2f)`	`mat2f`	Constructs a 2x2 single-precision matrix from two column vectors.
`mat2d_from_columns(vec2d, vec2d)`	`mat2d`	Constructs a 2x2 double-precision matrix from two column vectors.
`mat3f_from_columns(vec3f, vec3f, vec3f)`	`mat3f`	Constructs a 3x3 single-precision matrix from three column vectors.
`mat3d_from_columns(vec3d, vec3d, vec3d)`	`mat3d`	Constructs a 3x3 double-precision matrix from three column vectors.
`mat4f_from_columns(vec4f, vec4f, vec4f, vec4f)`	`mat4f`	Constructs a 4x4 single-precision matrix from four column vectors.
`mat4d_from_columns(vec4d, vec4d, vec4d, vec4d)`	`mat4d`	Constructs a 4x4 double-precision matrix from four column vectors.
`mat2f_zero(void)`	`mat2f`	Constructs a zero 2x2 single-precision matrix.
`mat2d_zero(void)`	`mat2d`	Constructs a zero 2x2 double-precision matrix.
`mat3f_zero(void)`	`mat3f`	Constructs a zero 3x3 single-precision matrix.
`mat3d_zero(void)`	`mat3d`	Constructs a zero 3x3 double-precision matrix.
`mat4f_zero(void)`	`mat4f`	Constructs a zero 4x4 single-precision matrix.
`mat4d_zero(void)`	`mat4d`	Constructs a zero 4x4 double-precision matrix.
`mat2f_ident(void)`	`mat2f`	Constructs a 2x2 single-precision identity matrix.
`mat2d_ident(void)`	`mat2d`	Constructs a 2x2 double-precision identity matrix.
`mat3f_ident(void)`	`mat3f`	Constructs a 3x3 single-precision identity matrix.
`mat3d_ident(void)`	`mat3d`	Constructs a 3x3 double-precision identity matrix.
`mat4f_ident(void)`	`mat4f`	Constructs a 4x4 single-precision identity matrix.
`mat4d_ident(void)`	`mat4d`	Constructs a 4x4 double-precision identity matrix.

Element-wise matrix arithmetic

Function prototype	Return value	Description
`mat2f_add(mat2f, mat2f)`	`mat2f`	Returns the sum matrix of two 2x2 single-precision matrices.
`mat2d_add(mat2d, mat2d)`	`mat2d`	Returns the sum matrix of two 2x2 double-precision matrices.
`mat3f_add(mat3f, mat3f)`	`mat3f`	Returns the sum matrix of two 3x3 single-precision matrices.
`mat3d_add(mat3d, mat3d)`	`mat3d`	Returns the sum matrix of two 3x3 double-precision matrices.
`mat4f_add(mat4f, mat4f)`	`mat4f`	Returns the sum matrix of two 4x4 single-precision matrices.
`mat4d_add(mat4d, mat4d)`	`mat4d`	Returns the sum matrix of two 4x4 double-precision matrices.
`mat2f_sub(mat2f, mat2f)`	`mat2f`	Returns the difference matrix between two 2x2 single-precision matrices.
`mat2d_sub(mat2d, mat2d)`	`mat2d`	Returns the difference matrix between two 2x2 double-precision matrices.
`mat3f_sub(mat3f, mat3f)`	`mat3f`	Returns the difference matrix between two 3x3 single-precision matrices.
`mat3d_sub(mat3d, mat3d)`	`mat3d`	Returns the difference matrix between two 3x3 double-precision matrices.
`mat4f_sub(mat4f, mat4f)`	`mat4f`	Returns the difference matrix between two 4x4 single-precision matrices.
`mat4d_sub(mat4d, mat4d)`	`mat4d`	Returns the difference matrix between two 4x4 double-precision matrices.
`mat2f_mul(mat2f, mat2f)`	`mat2f`	Returns the product matrix of two 2x2 single-precision matrices.
`mat2d_mul(mat2d, mat2d)`	`mat2d`	Returns the product matrix of two 2x2 double-precision matrices.
`mat3f_mul(mat3f, mat3f)`	`mat3f`	Returns the product matrix of two 3x3 single-precision matrices.
`mat3d_mul(mat3d, mat3d)`	`mat3d`	Returns the product matrix of two 3x3 double-precision matrices.
`mat4f_mul(mat4f, mat4f)`	`mat4f`	Returns the product matrix of two 4x4 single-precision matrices.
`mat4d_mul(mat4d, mat4d)`	`mat4d`	Returns the product matrix of two 4x4 double-precision matrices.
`mat2f_div(mat2f, mat2f)`	`mat2f`	Returns the quotient matrix between two 2x2 single-precision matrices.
`mat2d_div(mat2d, mat2d)`	`mat2d`	Returns the quotient matrix between two 2x2 double-precision matrices.
`mat3f_div(mat3f, mat3f)`	`mat3f`	Returns the quotient matrix between two 3x3 single-precision matrices.
`mat3d_div(mat3d, mat3d)`	`mat3d`	Returns the quotient matrix between two 3x3 double-precision matrices.
`mat4f_div(mat4f, mat4f)`	`mat4f`	Returns the quotient matrix between two 4x4 single-precision matrices.
`mat4d_div(mat4d, mat4d)`	`mat4d`	Returns the quotient matrix between two 4x4 double-precision matrices.
`mat2f_add_scalar(mat2f, mat2f)`	`mat2f`	Returns the sum matrix of a 2x2 single-precision matrix and a scalar.
`mat2d_add_scalar(mat2d, mat2d)`	`mat2d`	Returns the sum matrix of a 2x2 double-precision matrix and a scalar.
`mat3f_add_scalar(mat3f, mat3f)`	`mat3f`	Returns the sum matrix of a 3x3 single-precision matrix and a scalar.
`mat3d_add_scalar(mat3d, mat3d)`	`mat3d`	Returns the sum matrix of a 3x3 double-precision matrix and a scalar.
`mat4f_add_scalar(mat4f, mat4f)`	`mat4f`	Returns the sum matrix of a 4x4 single-precision matrix and a scalar.
`mat4d_add_scalar(mat4d, mat4d)`	`mat4d`	Returns the sum matrix of a 4x4 double-precision matrix and a scalar.
`mat2f_sub_scalar(mat2f, mat2f)`	`mat2f`	Returns the difference matrix between a 2x2 single-precision matrix and a scalar.
`mat2d_sub_scalar(mat2d, mat2d)`	`mat2d`	Returns the difference matrix between a 2x2 double-precision matrix and a scalar.
`mat3f_sub_scalar(mat3f, mat3f)`	`mat3f`	Returns the difference matrix between a 3x3 single-precision matrix and a scalar.
`mat3d_sub_scalar(mat3d, mat3d)`	`mat3d`	Returns the difference matrix between a 3x3 double-precision matrix and a scalar.
`mat4f_sub_scalar(mat4f, mat4f)`	`mat4f`	Returns the difference matrix between a 4x4 single-precision matrix and a scalar.
`mat4d_sub_scalar(mat4d, mat4d)`	`mat4d`	Returns the difference matrix between a 4x4 double-precision matrix and a scalar.
`mat2f_mul_scalar(mat2f, mat2f)`	`mat2f`	Returns the product matrix of a 2x2 single-precision matrix and a scalar.
`mat2d_mul_scalar(mat2d, mat2d)`	`mat2d`	Returns the product matrix of a 2x2 double-precision matrix and a scalar.
`mat3f_mul_scalar(mat3f, mat3f)`	`mat3f`	Returns the product matrix of a 3x3 single-precision matrix and a scalar.
`mat3d_mul_scalar(mat3d, mat3d)`	`mat3d`	Returns the product matrix of a 3x3 double-precision matrix and a scalar.
`mat4f_mul_scalar(mat4f, mat4f)`	`mat4f`	Returns the product matrix of a 4x4 single-precision matrix and a scalar.
`mat4d_mul_scalar(mat4d, mat4d)`	`mat4d`	Returns the product matrix of a 4x4 double-precision matrix and a scalar.
`mat2f_div_scalar(mat2f, mat2f)`	`mat2f`	Returns the quotient matrix between a 2x2 single-precision matrix and a scalar.
`mat2d_div_scalar(mat2d, mat2d)`	`mat2d`	Returns the quotient matrix between a 2x2 double-precision matrix and a scalar.
`mat3f_div_scalar(mat3f, mat3f)`	`mat3f`	Returns the quotient matrix between a 3x3 single-precision matrix and a scalar.
`mat3d_div_scalar(mat3d, mat3d)`	`mat3d`	Returns the quotient matrix between a 3x3 double-precision matrix and a scalar.
`mat4f_div_scalar(mat4f, mat4f)`	`mat4f`	Returns the quotient matrix between a 4x4 single-precision matrix and a scalar.
`mat4d_div_scalar(mat4d, mat4d)`	`mat4d`	Returns the quotient matrix between a 4x4 double-precision matrix and a scalar.

General matrix functions

Function prototype	Return value	Description
`mat2f_transpose(mat2f)`	`mat2f`	Returns the transpose of a 2x2 single-precision matrix.
`mat2d_transpose(mat2d)`	`mat2d`	Returns the transpose of a 2x2 double-precision matrix.
`mat3f_transpose(mat3f)`	`mat3f`	Returns the transpose of a 3x3 single-precision matrix.
`mat3d_transpose(mat3d)`	`mat3d`	Returns the transpose of a 3x3 double-precision matrix.
`mat4f_transpose(mat4f)`	`mat4f`	Returns the transpose of a 4x4 single-precision matrix.
`mat4d_transpose(mat4d)`	`mat4d`	Returns the transpose of a 4x4 double-precision matrix.
`mat2f_trace(mat2f)`	`float`	Returns the trace of a 2x2 single-precision matrix.
`mat2d_trace(mat2d)`	`double`	Returns the trace of a 2x2 double-precision matrix.
`mat3f_trace(mat3f)`	`float`	Returns the trace of a 3x3 single-precision matrix.
`mat3d_trace(mat3d)`	`double`	Returns the trace of a 3x3 double-precision matrix.
`mat4f_trace(mat4f)`	`float`	Returns the trace of a 4x4 single-precision matrix.
`mat4d_trace(mat4d)`	`double`	Returns the trace of a 4x4 double-precision matrix.
`mat2f_det(mat2f)`	`float`	Returns the determinant of a 2x2 single-precision matrix.
`mat2d_det(mat2d)`	`double`	Returns the determinant of a 2x2 double-precision matrix.
`mat3f_det(mat3f)`	`float`	Returns the determinant of a 3x3 single-precision matrix.
`mat3d_det(mat3d)`	`double`	Returns the determinant of a 3x3 double-precision matrix.
`mat4f_det(mat4f)`	`float`	Returns the determinant of a 4x4 single-precision matrix.
`mat4d_det(mat4d)`	`double`	Returns the determinant of a 4x4 double-precision matrix.

Matrix and vector product functions

Function prototype	Return value	Description
`mat2f_product(mat2f, mat2f)`	`mat2f`	Returns the product between two 2x2 single-precision matrices.
`mat2d_product(mat2d, mat2d)`	`mat2d`	Returns the product between two 2x2 double-precision matrices.
`mat3f_product(mat3f, mat3f)`	`mat3f`	Returns the product between two 3x3 single-precision matrices.
`mat3d_product(mat3d, mat3d)`	`mat3d`	Returns the product between two 3x3 double-precision matrices.
`mat4f_product(mat4f, mat4f)`	`mat4f`	Returns the product between two 4x4 single-precision matrices.
`mat4d_product(mat4d, mat4d)`	`mat4d`	Returns the product between two 4x4 double-precision matrices.
`mat2f_v_product(mat2f, vec2f)`	`vec2f`	Returns the product between a 2x2 single-precision matrix and a 2D vector.
`mat2d_v_product(mat2d, vec2d)`	`vec2d`	Returns the product between a 2x2 double-precision matrix and a 2D vector.
`mat3f_v_product(mat3f, vec3f)`	`vec3f`	Returns the product between a 3x3 single-precision matrix and a 3D vector.
`mat3d_v_product(mat3d, vec3d)`	`vec3d`	Returns the product between a 3x3 double-precision matrix and a 3D vector.
`mat4f_v_product(mat4f, vec4f)`	`vec4f`	Returns the product between a 4x4 single-precision matrix and a 4D vector.
`mat4d_v_product(mat4d, vec4d)`	`vec4d`	Returns the product between a 4x4 double-precision matrix and a 4D vector.
`mat2f_tensor(vec2f, vec2f)`	`mat2f`	Returns the tensor product between two 2D single-precision vectors.
`mat2d_tensor(vec2d, vec2d)`	`mat2d`	Returns the tensor product between two 2D double-precision vectors.
`mat3f_tensor(vec3f, vec3f)`	`mat3f`	Returns the tensor product between two 3D single-precision vectors.
`mat3d_tensor(vec3d, vec3d)`	`mat3d`	Returns the tensor product between two 3D double-precision vectors.
`mat4f_tensor(vec4f, vec4f)`	`mat4f`	Returns the tensor product between two 4D single-precision vectors.
`mat4d_tensor(vec4d, vec4d)`	`mat4d`	Returns the tensor product between two 4D double-precision vectors.

2x2 and 3x3 rotation matrix constructors

Function prototype	Return value	Description
`mat2f_rotation(float)`	`mat2f`	Returns a 2x2 single-precision rotation matrix by an angle.
`mat2d_rotation(double)`	`mat2d`	Returns a 2x2 double-precision rotation matrix by an angle.
`mat3f_x_rotation(float)`	`mat3f`	Returns a 3x3 single-precision rotation matrix about the x-axis by an angle.
`mat3d_x_rotation(float)`	`mat3d`	Returns a 3x3 double-precision rotation matrix about the x-axis by an angle.
`mat3f_y_rotation(float)`	`mat3f`	Returns a 3x3 single-precision rotation matrix about the y-axis by an angle.
`mat3d_y_rotation(float)`	`mat3d`	Returns a 3x3 double-precision rotation matrix about the y-axis by an angle.
`mat3f_z_rotation(float)`	`mat3f`	Returns a 3x3 single-precision rotation matrix about the z-axis by an angle.
`mat3d_z_rotation(float)`	`mat3d`	Returns a 3x3 double-precision rotation matrix about the z-axis by an angle.
`mat3f_v_rotation(vec3f, float)`	`mat3f`	Returns a 3x3 single-precision rotation matrix about an axis by an angle.
`mat3d_v_rotation(vec3d, double)`	`mat3d`	Returns a 3x3 double-precision rotation matrix about an axis by an angle.

Matrix type conversion functions

Function prototype	Return value	Description
`mat2d_to_f(mat2d)`	`mat2f`	Converts a 2x2 matrix from double- to single-precision.
`mat2f_to_d(mat2f)`	`mat2d`	Converts a 2x2 matrix from single- to double-precision.
`mat3d_to_f(mat3d)`	`mat3f`	Converts a 3x3 matrix from double- to single-precision.
`mat3f_to_d(mat3f)`	`mat3d`	Converts a 3x3 matrix from single- to double-precision.
`mat4d_to_f(mat4d)`	`mat4f`	Converts a 4x4 matrix from double- to single-precision.
`mat4f_to_d(mat4f)`	`mat4d`	Converts a 4x4 matrix from single- to double-precision.

Quaternion

#include "arrow/quaternion.h"

This library implements the quaternion as a 4D vector with the x-, y- and z-components corresponding to the imaginary part and the w-component equal to the real part.

Quaternion types

Type name	Description	Size (standard)	Size (vectorized)
`quatf`	Single-precision quaternion.	16	16
`quatd`	Double-precision quaternion.	32	32

Quaternion indexing macros

Macro definition	Description
`quat_x(q)`	Index to the x-component of a quaternion.
`quat_y(q)`	Index to the y-component of a quaternion.
`quat_z(q)`	Index to the z-component of a quaternion.
`quat_w(v)`	Index to the w-component of a quaternion.

Quaternion constructors

Function prototype	Return value	Description
`quatf_make(float, float, float, float)`	`quatf`	Constructs a single-precision quaternion.
`quatd_make(double, double, double, double)`	`quatd`	Constructs a double-precision quaternion.
`quatf_zero(void)`	`quatf`	Constructs a zero single-precision quaternion.
`quatd_zero(void)`	`quatd`	Constructs a zero double-precision quaternion.

Element-wise quaternion arithmetic

Function prototype	Return value	Description
`quatf_add(quatf, quatf)`	`quatf`	Returns the sum quaternion of two single-precision quaternions.
`quatd_add(quatd, quatd)`	`quatd`	Returns the sum quaternion of two double-precision quaternions.
`quatf_sub(quatf, quatf)`	`quatf`	Returns the difference quaternion between two single-precision quaternions.
`quatd_sub(quatd, quatd)`	`quatd`	Returns the difference quaternion between two double-precision quaternions.
`quatf_mul(quatf, quatf)`	`quatf`	Returns the product quaternion of two single-precision quaternions.
`quatd_mul(quatd, quatd)`	`quatd`	Returns the product quaternion of two double-precision quaternions.
`quatf_div(quatf, quatf)`	`quatf`	Returns the quotient quaternion between two single-precision quaternions.
`quatd_div(quatd, quatd)`	`quatd`	Returns the quotient quaternion between two double-precision quaternions.
`quatf_add_scalar(quatf, quatf)`	`quatf`	Returns the sum quaternion of a single-precision quaternion and a scalar.
`quatd_add_scalar(quatd, quatd)`	`quatd`	Returns the sum quaternion of a double-precision quaternion and a scalar.
`quatf_sub_scalar(quatf, quatf)`	`quatf`	Returns the difference quaternion between a single-precision quaternion and a scalar.
`quatd_sub_scalar(quatd, quatd)`	`quatd`	Returns the difference quaternion between a double-precision quaternion and a scalar.
`quatf_mul_scalar(quatf, quatf)`	`quatf`	Returns the product quaternion of a single-precision quaternion and a scalar.
`quatd_mul_scalar(quatd, quatd)`	`quatd`	Returns the product quaternion of a double-precision quaternion and a scalar.
`quatf_div_scalar(quatf, quatf)`	`quatf`	Returns the quotient quaternion between a single-precision quaternion and a scalar.
`quatd_div_scalar(quatd, quatd)`	`quatd`	Returns the quotient quaternion between a double-precision quaternion and a scalar.

General quaternion functions

Function prototype	Return value	Description
`quatf_dot(quatf)`	`float`	Returns the dot product of a single-precision quaternion.
`quatd_dot(quatd)`	`double`	Returns the dot product of a double-precision quaternion.
`quatf_conj(quatf)`	`quatf`	Returns the conjugate of a single-precision quaternion.
`quatd_conj(quatd)`	`quatd`	Returns the conjugate of a double-precision quaternion.
`quatf_inv(quatf)`	`quatf`	Returns the inverse of a single-precision quaternion.
`quatd_inv(quatd)`	`quatd`	Returns the inverse of a double-precision quaternion.
`quatf_norm(quatf)`	`float`	Returns the norm of a single-precision quaternion.
`quatd_norm(quatd)`	`double`	Returns the norm of a double-precision quaternion.
`quatf_unit(quatf)`	`quatf`	Returns a normalized quaternion from a single-precision quaternion.
`quatd_unit(quatd)`	`quatd`	Returns a normalized quaternion from a double-precision quaternion.
`quatf_product(quatf, quatf)`	`quatf`	Returns the product between two single-precision quaternions.
`quatd_product(quatd, quatd)`	`quatd`	Returns the product between two double-precision quaternions.
`quatf_exp(quatf)`	`quatf`	Returns the exponential of a single-precision quaternion. (UNAVAILABLE)
`quatd_exp(quatd)`	`quatd`	Returns the exponential of a double-precision quaternion. (UNAVAILABLE)
`quatf_log(quatf)`	`quatf`	Returns the logarithm of a single-precision quaternion. (UNAVAILABLE)
`quatd_log(quatd)`	`quatd`	Returns the logarithm of a double-precision quaternion. (UNAVAILABLE)
`quatf_pow(quatf, float)`	`quatf`	Returns a single-precision quaternion raised to an arbitrary real exponent. (UNAVAILABLE)
`quatd_pow(quatd, double)`	`quatd`	Returns a double-precision quaternion raised to an arbitrary real exponent. (UNAVAILABLE)

Quaternion size conversion functions

Function prototype	Return value	Description
`quatd_to_f(quatd)`	`quatd`	Converts a quaternion from double- to single-precision.
`quatf_to_d(quatf)`	`quatf`	Converts a quaternion from single- to double-precision.

Quaternion-vector conversion functions

Function prototype	Return value	Description
`quatf_to_vec3(quatf)`	`vec3f`	Converts a single-precision quaternion to a 3D vector.
`quatd_to_vec3(quatd)`	`vec3d`	Converts a double-precision quaternion to a 3D vector.
`quatf_to_vec4(quatf)`	`vec4f`	Converts a single-precision quaternion to a 4D vector.
`quatd_to_vec4(quatd)`	`vec4d`	Converts a double-precision quaternion to a 4D vector.
`vec3f_to_quat(vec3f)`	`quatf`	Converts a 3D single-precision vector to a quaternion.
`vec3d_to_quat(vec3d)`	`quatd`	Converts a 3D double-precision vector to a quaternion.
`vec4f_to_quat(vec4f)`	`quatf`	Converts a 4D single-precision vector to a quaternion.
`vec4d_to_quat(vec4d)`	`quatd`	Converts a 4D double-precision vector to a quaternion.

Name		Name	Last commit message	Last commit date
Latest commit History 80 Commits
.gitignore		.gitignore
LICENSE		LICENSE
Makefile		Makefile
README.md		README.md
basic.c		basic.c
basic.h		basic.h
matrix.c		matrix.c
matrix.h		matrix.h
quaternion.c		quaternion.c
quaternion.h		quaternion.h
types.h		types.h
types_standard.h		types_standard.h
types_vectorized.h		types_vectorized.h
vector.c		vector.c
vector.h		vector.h

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tkriik/libarrow

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