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Medusa Slockbower
2026-01-12 00:36:39 -05:00
parent 450f725cab
commit ed381c4178
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include/fennec/math/ext/constants.h
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@@ -546,81 +546,81 @@ namespace fennec
// Rational Constants ==================================================================================================
template<typename genType> constexpr genType zero() { return genType(0); } ///< \returns The value of \f$0\f$
template<typename genType> constexpr genType one() { return genType(1); } ///< \returns The value of \f$1\f$
template<typename genType> constexpr genType one_half() { return genType(0.5); } ///< \returns The value of \f$\frac{1}{2}\f$
template<typename genType> constexpr genType three_over_two() { return genType(1.5); } ///< \returns The value of \f$\frac{3}{2}\f$
template<typename genType> constexpr genType zero() { return genType(0); } //!< \returns The value of \f$0\f$
template<typename genType> constexpr genType one() { return genType(1); } //!< \returns The value of \f$1\f$
template<typename genType> constexpr genType one_half() { return genType(0.5); } //!< \returns The value of \f$\frac{1}{2}\f$
template<typename genType> constexpr genType three_over_two() { return genType(1.5); } //!< \returns The value of \f$\frac{3}{2}\f$
// Irrational Constants ================================================================================================
template<typename genType> constexpr genType one_third() { return 0.33333333333333333333333333333333333333333333333333; } ///< \returns The value of \f$\frac{1}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_thirds() { return 0.66666666666666666666666666666666666666666666666666; } ///< \returns The value of \f$\frac{2}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_two() { return 1.41421356237309504880168872420969807856967187537694; } ///< \returns The value of \f$\sqrt{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_three() { return 1.73205080756887729352744634150587236694280525381038; } ///< \returns The value of \f$\sqrt{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_five() { return 2.23606797749978969640917366873127623544061835961152; } ///< \returns The value of \f$\sqrt{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_seven() { return 2.64575131106459059050161575363926042571025918308245; } ///< \returns The value of \f$\sqrt{7}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_ten() { return 3.16227766016837933199889354443271853371955513932521; } ///< \returns The value of \f$\sqrt{10}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_over_sqrt_two() { return 0.70710678118654752440084436210484903928483593768847; } ///< \returns The value of \f$\frac{1}{\sqrt{2}}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_over_sqrt_three() { return 0.57735026918962576450914878050195745564760175127012; } ///< \returns The value of \f$\frac{1}{\sqrt{3}}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_over_sqrt_five() { return 0.44721359549995793928183473374625524708812367192230; } ///< \returns The value of \f$\frac{1}{\sqrt{5}}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType cbrt_two() { return 1.25992104989487316476721060727822835057025146470150; } ///< \returns The value of \f$\sqrt[3]{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType qdrt_two() { return 1.18920711500272106671749997056047591529297209246381; } ///< \returns The value of \f$\sqrt[4]{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_raised_sqrt_two() { return 2.66514414269022518865029724987313984827421131371465; } ///< \returns The value of \f${2}^{\sqrt{2}}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_third() { return 0.33333333333333333333333333333333333333333333333333; } //!< \returns The value of \f$\frac{1}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_thirds() { return 0.66666666666666666666666666666666666666666666666666; } //!< \returns The value of \f$\frac{2}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_two() { return 1.41421356237309504880168872420969807856967187537694; } //!< \returns The value of \f$\sqrt{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_three() { return 1.73205080756887729352744634150587236694280525381038; } //!< \returns The value of \f$\sqrt{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_five() { return 2.23606797749978969640917366873127623544061835961152; } //!< \returns The value of \f$\sqrt{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_seven() { return 2.64575131106459059050161575363926042571025918308245; } //!< \returns The value of \f$\sqrt{7}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_ten() { return 3.16227766016837933199889354443271853371955513932521; } //!< \returns The value of \f$\sqrt{10}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_over_sqrt_two() { return 0.70710678118654752440084436210484903928483593768847; } //!< \returns The value of \f$\frac{1}{\sqrt{2}}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_over_sqrt_three() { return 0.57735026918962576450914878050195745564760175127012; } //!< \returns The value of \f$\frac{1}{\sqrt{3}}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_over_sqrt_five() { return 0.44721359549995793928183473374625524708812367192230; } //!< \returns The value of \f$\frac{1}{\sqrt{5}}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType cbrt_two() { return 1.25992104989487316476721060727822835057025146470150; } //!< \returns The value of \f$\sqrt[3]{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType qdrt_two() { return 1.18920711500272106671749997056047591529297209246381; } //!< \returns The value of \f$\sqrt[4]{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_raised_sqrt_two() { return 2.66514414269022518865029724987313984827421131371465; } //!< \returns The value of \f${2}^{\sqrt{2}}\f$ with the highest precision for \f$genType\f$
// Pi ==================================================================================================================
// Pi & Tau
template<typename genType> constexpr genType pi() { return 3.14159265358979323846264338327950288419716939937510; } ///< \returns The value of \f$\pi\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType tau() { return 6.28318530717958647692528676655900576839433879875021; } ///< \returns The value of \f$\tau\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType pi() { return 3.14159265358979323846264338327950288419716939937510; } //!< \returns The value of \f$\pi\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType tau() { return 6.28318530717958647692528676655900576839433879875021; } //!< \returns The value of \f$\tau\f$ with the highest precision for \f$genType\f$
// Multiples of Pi
template<typename genType> constexpr genType two_pi() { return 6.28318530717958647692528676655900576839433879875021; } ///< \returns The value of \f$2\pi\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType three_pi() { return 9.42477796076937971538793014983850865259150819812531; } ///< \returns The value of \f$3\pi\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType four_pi() { return 12.56637061435917295385057353311801153678867759750042; } ///< \returns The value of \f$4\pi\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_pi() { return 6.28318530717958647692528676655900576839433879875021; } //!< \returns The value of \f$2\pi\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType three_pi() { return 9.42477796076937971538793014983850865259150819812531; } //!< \returns The value of \f$3\pi\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType four_pi() { return 12.56637061435917295385057353311801153678867759750042; } //!< \returns The value of \f$4\pi\f$ with the highest precision for \f$genType\f$
// Fractions of Pi
template<typename genType> constexpr genType half_pi() { return 1.57079632679489661923132169163975144209858469968755; } ///< \returns The value of \f$\frac{\pi}{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType three_halves_pi() { return 4.71238898038468985769396507491925432629575409906265; } ///< \returns The value of \f$\frac{3\pi}{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType half_pi() { return 1.57079632679489661923132169163975144209858469968755; } //!< \returns The value of \f$\frac{\pi}{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType three_halves_pi() { return 4.71238898038468985769396507491925432629575409906265; } //!< \returns The value of \f$\frac{3\pi}{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType third_pi() { return 1.04719755119659774615421446109316762806572313312503; } ///< \returns The value of \f$\frac{\pi}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_thirds_pi() { return 2.09439510239319549230842892218633525613144626625007; } ///< \returns The value of \f$\frac{2\pi}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType four_thirds_pi() { return 4.18879020478639098461685784437267051226289253250014; } ///< \returns The value of \f$\frac{4\pi}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType five_thirds_pi() { return 5.23598775598298873077107230546583814032861566562517; } ///< \returns The value of \f$\frac{5\pi}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType third_pi() { return 1.04719755119659774615421446109316762806572313312503; } //!< \returns The value of \f$\frac{\pi}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_thirds_pi() { return 2.09439510239319549230842892218633525613144626625007; } //!< \returns The value of \f$\frac{2\pi}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType four_thirds_pi() { return 4.18879020478639098461685784437267051226289253250014; } //!< \returns The value of \f$\frac{4\pi}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType five_thirds_pi() { return 5.23598775598298873077107230546583814032861566562517; } //!< \returns The value of \f$\frac{5\pi}{3}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType quarter_pi() { return 0.78539816339744830961566084581987572104929234984377; } ///< \returns The value of \f$\frac{\pi}{4}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType three_quarters_pi() { return 2.35619449019234492884698253745962716314787704953132; } ///< \returns The value of \f$\frac{3\pi}{4}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType five_quarters_pi() { return 3.92699081698724154807830422909937860524646174921888; } ///< \returns The value of \f$\frac{5\pi}{4}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType seven_quarters_pi() { return 5.49778714378213816730962592073913004734504644890643; } ///< \returns The value of \f$\frac{7\pi}{4}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType quarter_pi() { return 0.78539816339744830961566084581987572104929234984377; } //!< \returns The value of \f$\frac{\pi}{4}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType three_quarters_pi() { return 2.35619449019234492884698253745962716314787704953132; } //!< \returns The value of \f$\frac{3\pi}{4}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType five_quarters_pi() { return 3.92699081698724154807830422909937860524646174921888; } //!< \returns The value of \f$\frac{5\pi}{4}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType seven_quarters_pi() { return 5.49778714378213816730962592073913004734504644890643; } //!< \returns The value of \f$\frac{7\pi}{4}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType fifth_pi() { return 0.62831853071795864769252867665590057683943387987502; } ///< \returns The value of \f$\frac{\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_fifths_pi() { return 1.25663706143591729538505735331180115367886775975004; } ///< \returns The value of \f$\frac{2\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType three_fifths_pi() { return 1.88495559215387594307758602996770173051830163962506; } ///< \returns The value of \f$\frac{3\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType four_fifths_pi() { return 2.51327412287183459077011470662360230735773551950008; } ///< \returns The value of \f$\frac{4\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType six_fifths_pi() { return 3.76991118430775188615517205993540346103660327925012; } ///< \returns The value of \f$\frac{6\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType seven_fifths_pi() { return 4.39822971502571053384770073659130403787603715912514; } ///< \returns The value of \f$\frac{7\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType eight_fifths_pi() { return 5.02654824574366918154022941324720461471547103900016; } ///< \returns The value of \f$\frac{8\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType nine_fifths_pi() { return 5.65486677646162782923275808990310519155490491887519; } ///< \returns The value of \f$\frac{9\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType fifth_pi() { return 0.62831853071795864769252867665590057683943387987502; } //!< \returns The value of \f$\frac{\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_fifths_pi() { return 1.25663706143591729538505735331180115367886775975004; } //!< \returns The value of \f$\frac{2\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType three_fifths_pi() { return 1.88495559215387594307758602996770173051830163962506; } //!< \returns The value of \f$\frac{3\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType four_fifths_pi() { return 2.51327412287183459077011470662360230735773551950008; } //!< \returns The value of \f$\frac{4\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType six_fifths_pi() { return 3.76991118430775188615517205993540346103660327925012; } //!< \returns The value of \f$\frac{6\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType seven_fifths_pi() { return 4.39822971502571053384770073659130403787603715912514; } //!< \returns The value of \f$\frac{7\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType eight_fifths_pi() { return 5.02654824574366918154022941324720461471547103900016; } //!< \returns The value of \f$\frac{8\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType nine_fifths_pi() { return 5.65486677646162782923275808990310519155490491887519; } //!< \returns The value of \f$\frac{9\pi}{5}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sixth_pi() { return 0.52359877559829887307710723054658381403286156656251; } ///< \returns The value of \f$\frac{\pi}{6}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType five_sixths_pi() { return 2.61799387799149436538553615273291907016430783281258; } ///< \returns The value of \f$\frac{5\pi}{6}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType seven_sixths_pi() { return 3.66519142918809211153975061382608669823003096593762; } ///< \returns The value of \f$\frac{7\pi}{6}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType eleven_sixths_pi() { return 5.75958653158128760384817953601242195436147723218769; } ///< \returns The value of \f$\frac{11\pi}{6}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sixth_pi() { return 0.52359877559829887307710723054658381403286156656251; } //!< \returns The value of \f$\frac{\pi}{6}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType five_sixths_pi() { return 2.61799387799149436538553615273291907016430783281258; } //!< \returns The value of \f$\frac{5\pi}{6}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType seven_sixths_pi() { return 3.66519142918809211153975061382608669823003096593762; } //!< \returns The value of \f$\frac{7\pi}{6}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType eleven_sixths_pi() { return 5.75958653158128760384817953601242195436147723218769; } //!< \returns The value of \f$\frac{11\pi}{6}\f$ with the highest precision for \f$genType\f$
// Reciprocals of Pi
template<typename genType> constexpr genType one_over_pi() { return 0.31830988618379067153776752674502872406891929148091; } ///< \returns The value of \f$\frac{1}{\pi}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_over_pi() { return 0.63661977236758134307553505349005744813783858296182; } ///< \returns The value of \f$\frac{2}{\pi}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_over_pi() { return 0.31830988618379067153776752674502872406891929148091; } //!< \returns The value of \f$\frac{1}{\pi}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType two_over_pi() { return 0.63661977236758134307553505349005744813783858296182; } //!< \returns The value of \f$\frac{2}{\pi}\f$ with the highest precision for \f$genType\f$
// Exponentiations Pi
template<typename genType> constexpr genType pi_sq() { return 9.86960440108935861883449099987615113531369940724079; } ///< \returns The value of \f${\pi}^{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType pi_cb() { return 31.00627668029982017547631506710139520222528856588510; } ///< \returns The value of \f${\pi}^{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType pi_sq() { return 9.86960440108935861883449099987615113531369940724079; } //!< \returns The value of \f${\pi}^{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType pi_cb() { return 31.00627668029982017547631506710139520222528856588510; } //!< \returns The value of \f${\pi}^{2}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_pi() { return 1.77245385090551602729816748334114518279754945612238; } ///< \returns The value of \f$\sqrt{\pi}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType one_over_sqrt_pi() { return 0.56418958354775628694807945156077258584405062932899; } ///< \returns The value of \f$\frac{1}{\sqrt{\pi}}\f$ with the highest precision for \f$genType\f$
template<typename genType> constexpr genType sqrt_two_pi() { return 1.77245385090551602729816748334114518279754945612238; } ///< \returns The value of \f$\sqrt{2\pi}\f$ with the highest precision for \f$genType\f$