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Signed-off-by: Slendi <slendi@socopon.com>
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Slendi
2025-08-24 19:20:40 +03:00
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[Bb]uild*
.cache

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cmake_minimum_required(VERSION 3.15)
project(SmathExamples CXX)
set(CMAKE_CXX_STANDARD 23)
set(CMAKE_CXX_STANDARD_REQUIRED ON)
add_library(smath INTERFACE)
target_include_directories(smath INTERFACE ${CMAKE_SOURCE_DIR}/include)
add_library(smath::smath ALIAS smath)
option(BUILD_EXAMPLES "Build example programs" ON)
if(BUILD_EXAMPLES)
file(GLOB EXAMPLE_SOURCES "${CMAKE_SOURCE_DIR}/examples/*.cpp")
foreach(EXAMPLE_FILE ${EXAMPLE_SOURCES})
get_filename_component(EXAMPLE_NAME ${EXAMPLE_FILE} NAME_WE)
add_executable(${EXAMPLE_NAME} ${EXAMPLE_FILE})
target_link_libraries(${EXAMPLE_NAME} PRIVATE smath::smath)
endforeach()
endif()

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Apache License
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http://www.apache.org/licenses/
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README.md Normal file
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# smath
Single-file linear algebra math library for C++23.

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/* Copyright 2025 Slendi <slendi@socopon.com>
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <print>
// #define SMATH_IMPLICIT_CONVERSIONS
#include <smath.hpp>
int main() {
using namespace smath;
Vec3 v{1, 2, 3};
std::println("v: {}", v);
auto v2 = swizzle<"zyx">(v);
std::println("v2: {}", v2);
std::println("+: {}", v + v2);
std::println("-: {}", v - v2);
std::println("*: {}", v * v2);
std::println("/: {}", v / v2);
std::println("dot: {}", v.dot(v2));
std::println("rrggbb: {}", swizzle<"rrggbb">(v));
std::println("Magnitude: {}", v.magnitude());
std::println("Normalized: {}", v.normalized());
std::println("(alias) Unit: {}", v.unit());
std::println("(alias) Normalize: {}", v.normalize());
std::println("(alias) Length: {}", v.length());
std::println("std::get<1>(v): {}", std::get<1>(v));
auto [x, y, z] = v;
std::println("Bindings: [{}, {}, {}]", x, y, z);
// Let's mix and match!
Vec<6> v3(v, 7, swizzle<"zy">(v2));
std::println("{{v, 7, XZ(v2)}}: {}", v3);
// Scalar operations
std::println("v + 3: {}", v + 3);
std::println("v - 3: {}", v - 3);
std::println("v * 3: {}", v * 3);
std::println("v / 3: {}", v / 3);
std::println("3 + v: {}", 3 + v);
std::println("3 - v: {}", 3 - v);
std::println("3 * v: {}", 3 * v);
std::println("3 / v: {}", 3 / v);
// Casting
auto v4 = static_cast<Vec3d>(v);
#ifdef SMATH_IMPLICIT_CONVERSIONS
Vec3d v5 = v;
#else
Vec3d v5 = static_cast<Vec3d>(v);
#endif // SMATH_IMPLICIT_CONVERSIONS
std::println("Are v4 and v5 same? {}", v4 == v5);
}

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{
"nodes": {
"flake-utils": {
"inputs": {
"systems": "systems"
},
"locked": {
"lastModified": 1731533236,
"narHash": "sha256-l0KFg5HjrsfsO/JpG+r7fRrqm12kzFHyUHqHCVpMMbI=",
"owner": "numtide",
"repo": "flake-utils",
"rev": "11707dc2f618dd54ca8739b309ec4fc024de578b",
"type": "github"
},
"original": {
"owner": "numtide",
"repo": "flake-utils",
"type": "github"
}
},
"nixpkgs": {
"locked": {
"lastModified": 1755615617,
"narHash": "sha256-HMwfAJBdrr8wXAkbGhtcby1zGFvs+StOp19xNsbqdOg=",
"owner": "NixOS",
"repo": "nixpkgs",
"rev": "20075955deac2583bb12f07151c2df830ef346b4",
"type": "github"
},
"original": {
"owner": "NixOS",
"ref": "nixos-unstable",
"repo": "nixpkgs",
"type": "github"
}
},
"root": {
"inputs": {
"flake-utils": "flake-utils",
"nixpkgs": "nixpkgs"
}
},
"systems": {
"locked": {
"lastModified": 1681028828,
"narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
"owner": "nix-systems",
"repo": "default",
"rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
"type": "github"
},
"original": {
"owner": "nix-systems",
"repo": "default",
"type": "github"
}
}
},
"root": "root",
"version": 7
}

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{
inputs = {
nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
flake-utils.url = "github:numtide/flake-utils";
};
outputs =
{
self,
nixpkgs,
flake-utils,
}:
flake-utils.lib.eachDefaultSystem (
system:
let
pkgs = import nixpkgs {
system = system;
};
in
{
devShells.default = pkgs.mkShell {
packages = with pkgs; [
cmake
ninja
clang-tools
lldb
pkg-config
];
};
}
);
}

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#pragma once
/* Copyright 2025 Slendi <slendi@socopon.com>
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* You can define the following macros to change functionality:
* - SMATH_IMPLICIT_CONVERSIONS
*/
#include <array>
#include <cmath>
#include <cstddef>
#include <format>
#include <type_traits>
namespace smath {
template <std::size_t N, typename T>
requires std::is_arithmetic_v<T>
struct VecV;
namespace detail {
template <std::size_t N> struct FixedString {
char data[N]{};
static constexpr std::size_t size = N - 1;
constexpr FixedString(char const (&s)[N]) {
for (std::size_t i = 0; i < N; ++i)
data[i] = s[i];
}
constexpr char operator[](std::size_t i) const { return data[i]; }
};
template <class X> struct is_vecv : std::false_type {};
template <std::size_t M, class U>
struct is_vecv<VecV<M, U>> : std::true_type {};
template <class X>
inline constexpr bool is_vecv_v = is_vecv<std::remove_cvref_t<X>>::value;
template <class X>
inline constexpr bool is_scalar_v =
std::is_arithmetic_v<std::remove_cvref_t<X>>;
template <class X> struct vecv_size;
template <std::size_t M, class U>
struct vecv_size<VecV<M, U>> : std::integral_constant<std::size_t, M> {};
} // namespace detail
template <std::size_t N, typename T = float>
requires std::is_arithmetic_v<T>
struct VecV : std::array<T, N> {
private:
template <class X> static consteval std::size_t extent() {
if constexpr (detail::is_vecv_v<X>)
return detail::vecv_size<std::remove_cvref_t<X>>::value;
else if constexpr (detail::is_scalar_v<X>)
return 1;
else
return 0; // Should be unreachable
}
template <class... Args> static consteval std::size_t total_extent() {
return (extent<Args>() + ... + 0);
}
public:
// Constructors
constexpr VecV() noexcept {
for (auto &v : *this)
v = T(0);
}
explicit constexpr VecV(T const &s) noexcept {
for (auto &v : *this)
v = s;
}
template <typename... Args>
requires((detail::is_scalar_v<Args> || detail::is_vecv_v<Args>) && ...) &&
(total_extent<Args...>() == N) &&
(!(sizeof...(Args) == 1 && (detail::is_vecv_v<Args> && ...)))
constexpr VecV(Args &&...args) noexcept {
std::size_t i = 0;
(fill_one(i, std::forward<Args>(args)), ...);
}
// Member accesses
// NOTE: This can (probably) be improved with C++26 reflection in the future.
#define VEC_ACC(component, req, idx) \
constexpr auto component() noexcept -> T &requires(N >= req) { \
return (*this)[idx]; \
} constexpr auto component() const->T const & \
requires(N >= req) \
{ \
return (*this)[idx]; \
}
VEC_ACC(r, 1, 0)
VEC_ACC(g, 2, 1)
VEC_ACC(b, 3, 2)
VEC_ACC(a, 4, 3)
VEC_ACC(x, 1, 0)
VEC_ACC(y, 2, 1)
VEC_ACC(z, 3, 2)
VEC_ACC(w, 4, 3)
VEC_ACC(s, 1, 0)
VEC_ACC(t, 2, 1)
VEC_ACC(p, 3, 2)
VEC_ACC(q, 4, 3)
VEC_ACC(u, 1, 0)
VEC_ACC(v, 2, 1)
#undef VEC_ACC
// RHS operations
friend constexpr auto operator+(T s, VecV const &v) noexcept -> VecV {
return v + s;
}
friend constexpr auto operator-(T s, VecV const &v) noexcept -> VecV {
return VecV(s) - v;
}
friend constexpr auto operator*(T s, VecV const &v) noexcept -> VecV {
return v * s;
}
friend constexpr auto operator/(T s, VecV const &v) noexcept -> VecV {
VecV r{};
for (std::size_t i = 0; i < N; ++i)
r[i] = s / v[i];
return r;
}
// Members
#define VEC_OP(op) \
constexpr auto operator op(VecV const &rhs) const noexcept -> VecV { \
VecV result{}; \
for (std::size_t i = 0; i < N; ++i) { \
result[i] = (*this)[i] op rhs[i]; \
} \
return result; \
} \
constexpr auto operator op(T const &rhs) const noexcept -> VecV { \
VecV result{}; \
for (std::size_t i = 0; i < N; ++i) { \
result[i] = (*this)[i] op rhs; \
} \
return result; \
}
VEC_OP(+)
VEC_OP(-)
VEC_OP(*)
VEC_OP(/)
#undef VEC_OP
#define VEC_OP_ASSIGN(sym) \
constexpr VecV &operator sym##=(VecV const &rhs) noexcept { \
for (std::size_t i = 0; i < N; ++i) \
(*this)[i] sym## = rhs[i]; \
return *this; \
} \
constexpr VecV &operator sym##=(T const &s) noexcept { \
for (std::size_t i = 0; i < N; ++i) \
(*this)[i] sym## = s; \
return *this; \
}
VEC_OP_ASSIGN(+)
VEC_OP_ASSIGN(-)
VEC_OP_ASSIGN(*)
VEC_OP_ASSIGN(/)
#undef VEC_OP_ASSIGN
constexpr auto magnitude() const noexcept -> T {
T total = 0;
for (auto const &v : *this)
total += v * v;
return std::sqrt(total);
}
constexpr auto length() const noexcept -> T { return this->magnitude(); }
constexpr VecV normalized_safe(T eps = eps_default) const noexcept {
auto m = magnitude();
return (m > eps) ? (*this) / m : VecV{};
}
constexpr VecV normalize_safe(T eps = eps_default) const noexcept {
return normalized_safe(eps);
}
[[nodiscard]] constexpr auto normalized() noexcept -> VecV<N, T> const {
return (*this) / this->magnitude();
}
[[nodiscard]] constexpr auto normalize() noexcept -> VecV<N, T> const {
return this->normalized();
}
[[nodiscard]] constexpr auto unit() noexcept -> VecV<N, T> const {
return this->normalized();
}
[[nodiscard]] constexpr auto dot(VecV<N, T> const &other) noexcept -> T {
T res = 0;
for (std::size_t i = 0; i < N; ++i) {
res += (*this)[i] * other[i];
}
return res;
}
static constexpr T eps_default = T(1e-6);
template <class U = T>
[[nodiscard]] constexpr auto
approx_equal(VecV const &rhs, U eps = eps_default) const noexcept {
using F = std::conditional_t<std::is_floating_point_v<U>, U, double>;
for (size_t i = 0; i < N; ++i)
if (std::abs(F((*this)[i] - rhs[i])) > F(eps))
return false;
return true;
}
template <class U = T> constexpr auto magnitude_promoted() const noexcept {
using F = std::conditional_t<std::is_floating_point_v<U>, U, double>;
F s = 0;
for (auto v : *this)
s += F(v) * F(v);
return std::sqrt(s);
}
template <typename U = T>
requires(N == 3)
constexpr VecV cross(const VecV &r) const noexcept {
return {(*this)[1] * r[2] - (*this)[2] * r[1],
(*this)[2] * r[0] - (*this)[0] * r[2],
(*this)[0] * r[1] - (*this)[1] * r[0]};
}
constexpr T distance(VecV const &r) const noexcept {
return (*this - r).magnitude();
}
constexpr VecV project_onto(VecV const &n) const noexcept {
auto d = this->dot(n);
auto nn = n.dot(n);
return (nn ? (d / nn) * n : VecV());
}
template <class U>
requires(std::is_arithmetic_v<U> && N >= 1)
constexpr explicit(!std::is_convertible_v<U, T>)
VecV(VecV<N, U> const &other) noexcept {
for (std::size_t i = 0; i < N; ++i)
this->operator[](i) = static_cast<T>(other[i]);
}
template <class U>
requires(std::is_arithmetic_v<U> && N >= 1)
constexpr explicit(!std::is_convertible_v<T, U>)
operator VecV<N, U>() const noexcept {
VecV<N, U> r{};
for (std::size_t i = 0; i < N; ++i)
r[i] = static_cast<U>((*this)[i]);
return r;
}
template <class U>
requires(std::is_arithmetic_v<U> && !std::is_same_v<U, T>)
constexpr VecV &operator=(VecV<N, U> const &rhs) noexcept {
for (std::size_t i = 0; i < N; ++i)
(*this)[i] = static_cast<T>(rhs[i]);
return *this;
}
private:
constexpr void fill_one(std::size_t &i, const T &v) noexcept {
(*this)[i++] = v;
}
#ifdef SMATH_IMPLICIT_CONVERSIONS
template <class U>
requires std::is_arithmetic_v<U> && (!std::is_same_v<U, T>)
constexpr void fill_one(std::size_t &i, const U &v) noexcept {
(*this)[i++] = static_cast<T>(v);
}
template <std::size_t M, class U>
constexpr void fill_one(std::size_t &i, const VecV<M, U> &v) noexcept {
for (std::size_t k = 0; k < M; ++k)
(*this)[i++] = static_cast<T>(v[k]);
}
#endif // SMATH_IMPLICIT_CONVERSIONS
template <std::size_t M>
constexpr void fill_one(std::size_t &i, const VecV<M, T> &v) noexcept {
for (std::size_t k = 0; k < M; ++k)
(*this)[i++] = static_cast<T>(v[k]);
}
};
template <size_t I, size_t N, class T>
constexpr T &get(VecV<N, T> &v) noexcept {
static_assert(I < N);
return v[I];
}
template <size_t I, size_t N, class T>
constexpr const T &get(const VecV<N, T> &v) noexcept {
static_assert(I < N);
return v[I];
}
template <size_t I, size_t N, class T>
constexpr T &&get(VecV<N, T> &&v) noexcept {
static_assert(I < N);
return std::move(v[I]);
}
template <size_t I, size_t N, class T>
constexpr const T &&get(const VecV<N, T> &&v) noexcept {
static_assert(I < N);
return std::move(v[I]);
}
template <std::size_t N, typename T = float>
requires std::is_arithmetic_v<T>
using Vec = std::conditional_t<N == 1, T, VecV<N, T>>;
namespace detail {
consteval auto char_to_idx(char c) -> std::size_t {
if (c == 'r' || c == 'x' || c == 's' || c == 'u')
return 0;
else if (c == 'g' || c == 'y' || c == 't' || c == 'v')
return 1;
else if (c == 'b' || c == 'z' || c == 'p')
return 2;
else if (c == 'a' || c == 'w' || c == 'q')
return 3;
return static_cast<std::size_t>(-1);
}
constexpr auto is_valid(char c) -> bool {
switch (c) {
case 'r':
case 'g':
case 'b':
case 'a':
case 'x':
case 'y':
case 'z':
case 'w':
case 's':
case 't':
case 'p':
case 'q':
case 'u':
case 'v':
return true;
}
return false;
}
template <detail::FixedString S, std::size_t N, typename T, std::size_t... I>
constexpr auto swizzle_impl(VecV<N, T> const &v, std::index_sequence<I...>)
-> Vec<S.size, T> {
static_assert(((is_valid(S[I])) && ...), "Invalid swizzle component");
static_assert(((char_to_idx(S[I]) < N) && ...),
"Pattern index out of bounds");
Vec<S.size, T> out{};
std::size_t i = 0;
((out[i++] = v[char_to_idx(S[I])]), ...);
return out;
}
template <FixedString S>
concept SwizzleCharsOK = []<std::size_t... I>(std::index_sequence<I...>) {
return ((is_valid(S[I])) && ...);
}(std::make_index_sequence<S.size>{});
template <FixedString S, std::size_t N>
concept SwizzleInBounds = []<std::size_t... I>(std::index_sequence<I...>) {
return ((char_to_idx(S[I]) < N) && ...);
}(std::make_index_sequence<S.size>{});
template <FixedString S, std::size_t N>
concept ValidSwizzle =
(S.size > 0) && SwizzleCharsOK<S> && SwizzleInBounds<S, N>;
} // namespace detail
template <detail::FixedString S, std::size_t N, typename T>
requires detail::ValidSwizzle<S, N>
constexpr auto swizzle(VecV<N, T> const &v) -> Vec<S.size, T> {
return detail::swizzle_impl<S>(v, std::make_index_sequence<S.size>{});
}
using Vec2 = VecV<2>;
using Vec3 = VecV<3>;
using Vec4 = VecV<4>;
using Vec2d = VecV<2, double>;
using Vec3d = VecV<3, double>;
using Vec4d = VecV<4, double>;
} // namespace smath
template <std::size_t N, typename T>
requires std::formattable<T, char>
struct std::formatter<smath::VecV<N, T>> : std::formatter<T> {
constexpr auto parse(std::format_parse_context &ctx) {
return std::formatter<T>::parse(ctx);
}
template <typename Ctx>
auto format(smath::VecV<N, T> const &v, Ctx &ctx) const {
auto out = ctx.out();
*out++ = '{';
for (std::size_t i = 0; i < N; ++i) {
if (i) {
*out++ = ',';
*out++ = ' ';
}
out = std::formatter<T>::format(v[i], ctx);
}
*out++ = '}';
return out;
}
};
namespace std {
template <size_t N, class T>
struct tuple_size<smath::VecV<N, T>> : std::integral_constant<size_t, N> {};
template <size_t I, size_t N, class T>
struct tuple_element<I, smath::VecV<N, T>> {
static_assert(I < N);
using type = T;
};
} // namespace std