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/*
* Copyright (c), Zeriph Enterprises
* All rights reserved.
*
* Contributor(s):
* Zechariah Perez, omni (at) zeriph (dot) com
*
* THIS SOFTWARE IS PROVIDED BY ZERIPH AND CONTRIBUTORS "AS IS" AND ANY
* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL ZERIPH AND CONTRIBUTORS BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#if !defined(OMNI_MATH_DEF_HPP)
#define OMNI_MATH_DEF_HPP 1
#define OMNI_MATH_MAX_ROUND_DIGITS_FW 15
#define OMNI_MATH_ROUND_LIMIT_FW 1e16
// float
#if !defined(OMNI_E_F)
#if (defined(OMNI_USE_M_E_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_E)
#define OMNI_E_F static_cast<float>(M_E)
#else
#define OMNI_E_F 2.7182818F
#endif
#endif
#if !defined(OMNI_PI_F)
#if (defined(OMNI_USE_M_PI_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PI)
#define OMNI_PI_F static_cast<float>(M_PI)
#else
#define OMNI_PI_F 3.1415926F
#endif
#define OMNI_PI_F_180 0.0174533F
#define OMNI_180_PI_F 57.2957805F
#define OMNI_PI_F_X2 6.2831853F
#define OMNI_PI_F_X4 12.5663706F
#endif
#if !defined(OMNI_PI_2_F)
#if (defined(OMNI_USE_M_PI_2_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PI_2)
#define OMNI_PI_2_F static_cast<float>(M_PI_2)
#else
#define OMNI_PI_2_F 1.5707963F
#endif
#endif
#if !defined(OMNI_PI_4_F)
#if (defined(OMNI_USE_M_PI_4_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PI_4)
#define OMNI_PI_4_F static_cast<float>(M_PI_4)
#else
#define OMNI_PI_4_F 0.7853981F
#endif
#endif
#if !defined(OMNI_1_PI_F)
#if (defined(OMNI_USE_M_1_PI_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_1_PI)
#define OMNI_1_PI_F static_cast<float>(M_1_PI)
#else
#define OMNI_1_PI_F 0.3183098F
#endif
#endif
#if !defined(OMNI_2_PI_F)
#if (defined(OMNI_USE_M_2_PI_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_2_PI)
#define OMNI_2_PI_F static_cast<float>(M_2_PI)
#else
#define OMNI_2_PI_F 0.6366197F
#endif
#endif
#if !defined(OMNI_2_SQRTPI_F)
#if (defined(OMNI_USE_M_2_SQRTPI_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_2_SQRTPI)
#define OMNI_2_SQRTPI_F static_cast<float>(M_2_SQRTPI)
#else
#define OMNI_2_SQRTPI_F 1.1283791F
#endif
#endif
#if !defined(OMNI_TAU_F)
#define OMNI_TAU_F OMNI_PI_F_X2
#endif
#if !defined(OMNI_LOG2E_F)
#if (defined(OMNI_USE_M_LOG2E_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LOG2E)
#define OMNI_LOG2E_F static_cast<float>(M_LOG2E)
#else
#define OMNI_LOG2E_F 1.4426950F
#endif
#endif
#if !defined(OMNI_LOG10E_F)
#if (defined(OMNI_USE_M_LOG10E_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LOG10E)
#define OMNI_LOG10E_F static_cast<float>(M_LOG10E)
#else
#define OMNI_LOG10E_F 0.4342944F
#endif
#endif
#if !defined(OMNI_LN2_F)
#if (defined(OMNI_USE_M_LN2_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LN2)
#define OMNI_LN2_F static_cast<float>(M_LN2)
#else
#define OMNI_LN2_F 0.6931471F
#endif
#endif
#if !defined(OMNI_LN10_F)
#if (defined(OMNI_USE_M_LN10_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LN10)
#define OMNI_LN10_F static_cast<float>(M_LN10)
#else
#define OMNI_LN10_F 2.3025850F
#endif
#endif
#if !defined(OMNI_SQRT2_F)
#if (defined(OMNI_USE_M_SQRT2_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_SQRT2)
#define OMNI_SQRT2_F static_cast<float>(M_SQRT2)
#else
#define OMNI_SQRT2_F 1.4142135F
#endif
#endif
#if !defined(OMNI_SQRT1_2_F)
#if (defined(OMNI_USE_M_SQRT1_2_F) || defined(OMNI_USE_MATH_DEFS)) && defined(M_SQRT1_2)
#define OMNI_SQRT1_2_F static_cast<float>(M_SQRT1_2)
#else
#define OMNI_SQRT1_2_F 0.7071067F
#endif
#endif
// double
#if !defined(OMNI_E)
#if (defined(OMNI_USE_M_E) || defined(OMNI_USE_MATH_DEFS)) && defined(M_E)
#define OMNI_E M_E
#else
#define OMNI_E 2.71828182845904523536
#endif
#endif
#if !defined(OMNI_PI)
#if (defined(OMNI_USE_M_PI) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PI)
#define OMNI_PI M_PI
#else
#define OMNI_PI 3.14159265358979323846
#endif
#define OMNI_PI_180 0.01745329251994329577
#define OMNI_180_PI 57.29577951308232087684
#define OMNI_PI_X2 6.28318530717958647692
#define OMNI_PI_X4 12.56637061435917295385
#endif
#if !defined(OMNI_PI_2)
#if (defined(OMNI_USE_M_PI_2) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PI_2)
#define OMNI_PI_2 M_PI_2
#else
#define OMNI_PI_2 1.57079632679489661923
#endif
#endif
#if !defined(OMNI_PI_4)
#if (defined(OMNI_USE_M_PI_4) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PI_4)
#define OMNI_PI_4 M_PI_4
#else
#define OMNI_PI_4 0.78539816339744830961
#endif
#endif
#if !defined(OMNI_1_PI)
#if (defined(OMNI_USE_M_1_PI) || defined(OMNI_USE_MATH_DEFS)) && defined(M_1_PI)
#define OMNI_1_PI M_1_PI
#else
#define OMNI_1_PI 0.31830988618379067153
#endif
#endif
#if !defined(OMNI_2_PI)
#if (defined(OMNI_USE_M_2_PI) || defined(OMNI_USE_MATH_DEFS)) && defined(M_2_PI)
#define OMNI_2_PI M_2_PI
#else
#define OMNI_2_PI 0.63661977236758134307
#endif
#endif
#if !defined(OMNI_2_SQRTPI)
#if (defined(OMNI_USE_M_2_SQRTPI) || defined(OMNI_USE_MATH_DEFS)) && defined(M_2_SQRTPI)
#define OMNI_2_SQRTPI M_2_SQRTPI
#else
#define OMNI_2_SQRTPI 1.12837916709551257389
#endif
#endif
#if !defined(OMNI_TAU)
#define OMNI_TAU OMNI_PI_X2
#endif
#if !defined(OMNI_LOG2E)
#if (defined(OMNI_USE_M_LOG2E) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LOG2E)
#define OMNI_LOG2E M_LOG2E
#else
#define OMNI_LOG2E 1.44269504088896340735
#endif
#endif
#if !defined(OMNI_LOG10E)
#if (defined(OMNI_USE_M_LOG10E) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LOG10E)
#define OMNI_LOG10E M_LOG10E
#else
#define OMNI_LOG10E 0.43429448190325182765
#endif
#endif
#if !defined(OMNI_LN2)
#if (defined(OMNI_USE_M_LN2) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LN2)
#define OMNI_LN2 M_LN2
#else
#define OMNI_LN2 0.69314718055994530941
#endif
#endif
#if !defined(OMNI_LN10)
#if (defined(OMNI_USE_M_LN10) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LN10)
#define OMNI_LN10 M_LN10
#else
#define OMNI_LN10 2.30258509299404568401
#endif
#endif
#if !defined(OMNI_SQRT2)
#if (defined(OMNI_USE_M_SQRT2) || defined(OMNI_USE_MATH_DEFS)) && defined(M_SQRT2)
#define OMNI_SQRT2 M_SQRT2
#else
#define OMNI_SQRT2 1.41421356237309504880
#endif
#endif
#if !defined(OMNI_SQRT1_2)
#if (defined(OMNI_USE_M_SQRT1_2) || defined(OMNI_USE_MATH_DEFS)) && defined(M_SQRT1_2)
#define OMNI_SQRT1_2 M_SQRT1_2
#else
#define OMNI_SQRT1_2 0.70710678118654752440
#endif
#endif
// long double
#if !defined(OMNI_E_L)
#if (defined(OMNI_USE_M_E_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_El)
#define OMNI_E_L M_El
#else
#define OMNI_E_L 2.71828182845904523536028747135266250L
#endif
#endif
#if !defined(OMNI_PI_L)
#if (defined(OMNI_USE_M_PI_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PIl)
#define OMNI_PI_L M_PIl
#else
#define OMNI_PI_L 3.141592653589793238462643383279502884L
#endif
#define OMNI_PI_L_180 0.017453292519943295769236907684886127L
#define OMNI_180_PI_L 57.295779513082320876798154814105170336L
#define OMNI_PI_L_X2 6.283185307179586476925286766559005768L
#define OMNI_PI_L_X4 12.566370614359172953850573533118011536L
#endif
#if !defined(OMNI_PI_2_L)
#if (defined(OMNI_USE_M_PI_2_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PI_2l)
#define OMNI_PI_2_L M_PI_2l
#else
#define OMNI_PI_2_L 1.57079632679489661923132169163975144L
#endif
#endif
#if !defined(OMNI_PI_4_L)
#if (defined(OMNI_USE_M_PI_4_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_PI_4l)
#define OMNI_PI_4_L M_PI_4l
#else
#define OMNI_PI_4_L 0.785398163397448309615660845819875721L
#endif
#endif
#if !defined(OMNI_1_PI_L)
#if (defined(OMNI_USE_M_1_PI_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_1_PIl)
#define OMNI_1_PI_L M_1_PIl
#else
#define OMNI_1_PI_L 0.318309886183790671537767526745028724L
#endif
#endif
#if !defined(OMNI_2_PI_L)
#if (defined(OMNI_USE_M_2_PI_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_2_PIl)
#define OMNI_2_PI_L M_2_PIl
#else
#define OMNI_2_PI_L 0.636619772367581343075535053490057448L
#endif
#endif
#if !defined(OMNI_2_SQRTPI_L)
#if (defined(OMNI_USE_M_2_SQRTPI_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_2_SQRTPIl)
#define OMNI_2_SQRTPI_L M_2_SQRTPIl
#else
#define OMNI_2_SQRTPI_L 1.12837916709551257389615890312154517L
#endif
#endif
#if !defined(OMNI_TAU_L)
#define OMNI_TAU_L OMNI_PI_L_X2
#endif
#if !defined(OMNI_LOG2E_L)
#if (defined(OMNI_USE_M_LOG2E_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LOG2El)
#define OMNI_LOG2E_L M_LOG2El
#else
#define OMNI_LOG2E_L 1.44269504088896340735992468100189214L
#endif
#endif
#if !defined(OMNI_LOG10E_L)
#if (defined(OMNI_USE_M_LOG10E_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LOG10El)
#define OMNI_LOG10E_L M_LOG10El
#else
#define OMNI_LOG10E_L 0.434294481903251827651128918916605082L
#endif
#endif
#if !defined(OMNI_LN2_L)
#if (defined(OMNI_USE_M_LN2_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LN2l)
#define OMNI_LN2_L M_LN2l
#else
#define OMNI_LN2_L 0.693147180559945309417232121458176568L
#endif
#endif
#if !defined(OMNI_LN10_L)
#if (defined(OMNI_USE_M_LN10_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_LN10l)
#define OMNI_LN10_L M_LN10l
#else
#define OMNI_LN10_L 2.30258509299404568401799145468436421L
#endif
#endif
#if !defined(OMNI_SQRT2_L)
#if (defined(OMNI_USE_M_SQRT2_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_SQRT2l)
#define OMNI_SQRT2_L M_SQRT2l
#else
#define OMNI_SQRT2_L 1.41421356237309504880168872420969808L
#endif
#endif
#if !defined(OMNI_SQRT1_2_L)
#if (defined(OMNI_USE_M_SQRT1_2_L) || defined(OMNI_USE_MATH_DEFS)) && defined(M_SQRT1_2l)
#define OMNI_SQRT1_2_L M_SQRT1_2l
#else
#define OMNI_SQRT1_2_L 0.707106781186547524400844362104849039L
#endif
#endif
/*
DEV_NOTE: these are the exact values from the .NET lib, links:
https://docs.microsoft.com/en-us/dotnet/api/system.math.pi?view=net-5.0
public const double PI = 3.1415926535897931;
https://docs.microsoft.com/en-us/dotnet/api/system.math.e?view=net-5.0
public const double E = 2.7182818284590451;
https://docs.microsoft.com/en-us/dotnet/api/system.math.tau?view=net-5.0
public const double Tau = 6.2831853071795862;
*/
#define OMNI_MATH_COMPAT_PI 3.1415926535897931
#define OMNI_MATH_COMPAT_E 2.7182818284590451
#define OMNI_MATH_COMPAT_TAU 6.2831853071795862
// radians = degrees * π / 180
#define OMNI_DEG_TO_RAD(deg) (deg) * OMNI_PI_180
// degrees = radians * 180 / π
#define OMNI_RAD_TO_DEG(rad) (rad) * OMNI_180_PI
#define OMNI_MATH_DELTA(a,b) ((a) - (b))
#define OMNI_MATH_GET_POINT_X_FW(T, center_pt, radius, angle) \
static_cast<T>((static_cast<double>(center_pt) + (static_cast<double>(radius) * std::sin(OMNI_DEG_TO_RAD(static_cast<double>(angle))))))
#define OMNI_MATH_GET_POINT_Y_FW(T, center_pt, radius, angle) \
static_cast<T>((static_cast<double>(center_pt) + (static_cast<double>(radius) * std::cos(OMNI_DEG_TO_RAD(static_cast<double>(angle))))))
#define OMNI_MATH_GET_POINT_X_INT_FW(T, center_pt, radius, angle) \
static_cast<T>(std::ceil((static_cast<double>(center_pt) + (static_cast<double>(radius) * std::sin(OMNI_DEG_TO_RAD(static_cast<double>(angle)))))))
#define OMNI_MATH_GET_POINT_Y_INT_FW(T, center_pt, radius, angle) \
static_cast<T>(std::ceil((static_cast<double>(center_pt) + (static_cast<double>(radius) * std::cos(OMNI_DEG_TO_RAD(static_cast<double>(angle)))))))
#define OMNI_MATH_ANGLE_ERR_FW(angle) if ((angle < 0) || (angle > 360)) { OMNI_ERR_FW("angle must be between 0-360 degrees", omni::exceptions::overflow_error("angle must be between 0-360 degrees")) }
#define OMNI_MATH_GET_POINT_FW(T, out_x, out_y, center_x, center_y, radius, angle) \
OMNI_MATH_ANGLE_ERR_FW(angle) \
out_x = OMNI_MATH_GET_POINT_X_FW(T, center_x, radius, angle); \
out_y = OMNI_MATH_GET_POINT_Y_FW(T, center_y, radius, angle)
#define OMNI_MATH_GET_POINT_INT_FW(T, out_x, out_y, center_x, center_y, radius, angle) \
OMNI_MATH_ANGLE_ERR_FW(angle) \
out_x = OMNI_MATH_GET_POINT_X_INT_FW(T, center_x, radius, angle); \
out_y = OMNI_MATH_GET_POINT_Y_INT_FW(T, center_y, radius, angle)
#define OMNI_RECT_XYWH_CONTAINS_FW(rx,ry,rw,rh,ox,oy) ((ox >= rx) && (ox <= (rx + rw)) && (oy >= ry) && (oy <= (ry + rh)))
#define OMNI_RECT_LTRB_CONTAINS_FW(left,top,right,bottom,ox,oy) ((ox >= left) && (ox <= right) && (oy >= top) && (oy <= bottom))
#define OMNI_CIRCLE_CONTAINS_POINT_FW(cx,cy,r,x,y,oc) (oc ? (((x - cx)*(x - cx)) + ((y - cy) * (y - cy))) <= (r * r) : (((x - cx) * (x - cx)) + ((y - cy) * (y - cy))) < (r * r))
#define OMNI_DISTANCE_2POINTS_2D_FW(start_x, start_y, end_x, end_y) (std::sqrt(static_cast<double>((start_x - end_x) * (start_x - end_x)) + static_cast<double>((start_y - end_y) * (start_y - end_y))))
#define OMNI_DISTANCE_2POINTS_3D_FW(start_x, start_y, start_z, end_x, end_y, end_z) (std::sqrt(static_cast<double>((start_x - end_x) * (start_x - end_x)) + static_cast<double>((start_y - end_y) * (start_y - end_y)) + static_cast<double>((start_z - end_z) * (start_z - end_z))))
#if defined(OMNI_ENABLE_CXX)
#define OMNI_USE_CXX_MATH
#endif
#if defined(OMNI_NO_USE_CXX_MATH) && defined(OMNI_USE_CXX_MATH)
// if C++11 is enabled, but you don't want to use the C++11 math functions
#undef OMNI_USE_CXX_MATH
#endif
#endif // OMNI_MATH_DEF_HPP