Method Arctan

TSMath.cpp:398–448

}

float Terathon::Arctan(float x)
{
	// Values of arctan(n / 64) for integers n in the range [0, 64].

	alignas(64) static const uint32 table[65] =
	{
		0x00000000, 0x3C7FFAAB, 0x3CFFEAAE, 0x3D3FDC0C, 0x3D7FAADE, 0x3D9FACF8, 0x3DBF70C1, 0x3DDF1CF6,
		0x3DFEADD5, 0x3E0F0FD8, 0x3E1EB777, 0x3E2E4C09, 0x3E3DCBDA, 0x3E4D3547, 0x3E5C86BB, 0x3E6BBEAF,
		0x3E7ADBB0, 0x3E84EE2D, 0x3E8C5FAD, 0x3E93C1B9, 0x3E9B13BA, 0x3EA25522, 0x3EA9856D, 0x3EB0A420,
		0x3EB7B0CA, 0x3EBEAB02, 0x3EC5926A, 0x3ECC66AA, 0x3ED32776, 0x3ED9D489, 0x3EE06DA6, 0x3EE6F29A,
		0x3EED6338, 0x3EF3BF5C, 0x3EFA06E8, 0x3F001CE4, 0x3F032BF5, 0x3F0630A3, 0x3F092AED, 0x3F0C1AD4,
		0x3F0F005D, 0x3F11DB8F, 0x3F14AC73, 0x3F177314, 0x3F1A2F81, 0x3F1CE1C9, 0x3F1F89FE, 0x3F222833,
		0x3F24BC7D, 0x3F2746F3, 0x3F29C7AC, 0x3F2C3EC1, 0x3F2EAC4C, 0x3F311069, 0x3F336B32, 0x3F35BCC5,
		0x3F38053E, 0x3F3A44BC, 0x3F3C7B5E, 0x3F3EA941, 0x3F40CE86, 0x3F42EB4B, 0x3F44FFB0, 0x3F470BD5, 0x3F490FDB
	};

	// arctan(a) = arctan(b) + arctan((a - b) / (ab + 1))

	float a = Fabs(x);
	if (a <= 1.0F)
	{
		float b = a * 64.0F;
		float i = PositiveFloor(b);
		b = i * 0.015625F;

		float arctan_b = reinterpret_cast<const float *>(table)[int32(i)];
		float c = (a - b) / (a * b + 1.0F);
		float c2 = c * c;

		float arctan_c = c * (1.0F - c2 * (0.3333333333F + c2 * (0.2F - c2 * 0.1428571429F)));
		a = arctan_b + arctan_c;
	}
	else
	{
		// arctan(a) = tau / 4 - arctan(1 / a)

		a = 1.0F / a;
		float b = a * 64.0F;
		float i = PositiveFloor(b);
		b = i * 0.015625F;

		float arctan_b = reinterpret_cast<const float *>(table)[int32(i)];
		float c = (a - b) / (a * b + 1.0F);
		float c2 = c * c;

		float arctan_c = c * (1.0F - c2 * (0.3333333333F + c2 * (0.2F - c2 * 0.1428571429F)));
		a = Math::tau_over_4 - (arctan_b + arctan_c);
	}

	return ((x < 0.0F) ? -a : a);
}

float Terathon::Arctan(float y, float x)
{