GeneralsZeroHour/GeneralsMD/Code/GameEngine/Source/Common/System/Trig.cpp

/*
**	Command & Conquer Generals Zero Hour(tm)
**	Copyright 2025 Electronic Arts Inc.
**
**	This program is free software: you can redistribute it and/or modify
**	it under the terms of the GNU General Public License as published by
**	the Free Software Foundation, either version 3 of the License, or
**	(at your option) any later version.
**
**	This program is distributed in the hope that it will be useful,
**	but WITHOUT ANY WARRANTY; without even the implied warranty of
**	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
**	GNU General Public License for more details.
**
**	You should have received a copy of the GNU General Public License
**	along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

////////////////////////////////////////////////////////////////////////////////
//																																						//
//  (c) 2001-2003 Electronic Arts Inc.																				//
//																																						//
////////////////////////////////////////////////////////////////////////////////

// Trig.cpp
// fast trig functions
// Author: Michael S. Booth, March 1994
// Converted to Generals by Matthew D. Campbell, February 2002

#include "PreRTS.h"

#include <math.h>
#include <limits.h>

#include "Lib/BaseType.h"
#include "Lib/Trig.h"

#define TWOPI			6.28318530718f
#define DEG2RAD 	0.0174532925199f
#define TRIG_RES 4096

// the following are for fixed point ints with 12 fractional bits
#define INT_ONE								4096
#define INT_TWOPI							25736
#define INT_THREEPIOVERTWO 		19302
#define INT_PI								12868
#define INT_HALFPI 						6434
#define intCos(x) intSin( INT_HALFPI - (x) )

// sinLookup and arcCosLookup were statically initialized on a mcampbell2k, a 1GHz PIII running Win2K
// on Feb 12, 2002.  To regenerate, define REGENERATE_TRIG_TABLES, run the program, and copy the
// resulting trig.txt file here.

static Int sinLookup[TRIG_RES] = {
	0x00000000, 0x00000006, 0x0000000C, 0x00000012, 0x00000019, 0x0000001F, 0x00000025, 0x0000002B,
	0x00000032, 0x00000038, 0x0000003E, 0x00000045, 0x0000004B, 0x00000051, 0x00000057, 0x0000005E,
	0x00000064, 0x0000006A, 0x00000071, 0x00000077, 0x0000007D, 0x00000083, 0x0000008A, 0x00000090,
	0x00000096, 0x0000009D, 0x000000A3, 0x000000A9, 0x000000AF, 0x000000B6, 0x000000BC, 0x000000C2,
	0x000000C8, 0x000000CF, 0x000000D5, 0x000000DB, 0x000000E2, 0x000000E8, 0x000000EE, 0x000000F4,
	0x000000FB, 0x00000101, 0x00000107, 0x0000010D, 0x00000114, 0x0000011A, 0x00000120, 0x00000127,
	0x0000012D, 0x00000133, 0x00000139, 0x00000140, 0x00000146, 0x0000014C, 0x00000152, 0x00000159,
	0x0000015F, 0x00000165, 0x0000016B, 0x00000172, 0x00000178, 0x0000017E, 0x00000184, 0x0000018B,
	0x00000191, 0x00000197, 0x0000019D, 0x000001A4, 0x000001AA, 0x000001B0, 0x000001B6, 0x000001BD,
	0x000001C3, 0x000001C9, 0x000001CF, 0x000001D6, 0x000001DC, 0x000001E2, 0x000001E8, 0x000001EF,
	0x000001F5, 0x000001FB, 0x00000201, 0x00000208, 0x0000020E, 0x00000214, 0x0000021A, 0x00000221,
	0x00000227, 0x0000022D, 0x00000233, 0x00000239, 0x00000240, 0x00000246, 0x0000024C, 0x00000252,
	0x00000259, 0x0000025F, 0x00000265, 0x0000026B, 0x00000271, 0x00000278, 0x0000027E, 0x00000284,
	0x0000028A, 0x00000290, 0x00000297, 0x0000029D, 0x000002A3, 0x000002A9, 0x000002AF, 0x000002B6,
	0x000002BC, 0x000002C2, 0x000002C8, 0x000002CE, 0x000002D5, 0x000002DB, 0x000002E1, 0x000002E7,
	0x000002ED, 0x000002F3, 0x000002FA, 0x00000300, 0x00000306, 0x0000030C, 0x00000312, 0x00000318,
	0x0000031F, 0x00000325, 0x0000032B, 0x00000331, 0x00000337, 0x0000033D, 0x00000344, 0x0000034A,
	0x00000350, 0x00000356, 0x0000035C, 0x00000362, 0x00000368, 0x0000036F, 0x00000375, 0x0000037B,
	0x00000381, 0x00000387, 0x0000038D, 0x00000393, 0x00000399, 0x000003A0, 0x000003A6, 0x000003AC,
	0x000003B2, 0x000003B8, 0x000003BE, 0x000003C4, 0x000003CA, 0x000003D0, 0x000003D7, 0x000003DD,
	0x000003E3, 0x000003E9, 0x000003EF, 0x000003F5, 0x000003FB, 0x00000401, 0x00000407, 0x0000040D,
	0x00000413, 0x0000041A, 0x00000420, 0x00000426, 0x0000042C, 0x00000432, 0x00000438, 0x0000043E,
	0x00000444, 0x0000044A, 0x00000450, 0x00000456, 0x0000045C, 0x00000462, 0x00000468, 0x0000046E,
	0x00000474, 0x0000047A, 0x00000480, 0x00000486, 0x0000048C, 0x00000492, 0x00000498, 0x0000049E,
	0x000004A5, 0x000004AB, 0x000004B1, 0x000004B7, 0x000004BD, 0x000004C3, 0x000004C9, 0x000004CF,
	0x000004D5, 0x000004DB, 0x000004E0, 0x000004E6, 0x000004EC, 0x000004F2, 0x000004F8, 0x000004FE,
	0x00000504, 0x0000050A, 0x00000510, 0x00000516, 0x0000051C, 0x00000522, 0x00000528, 0x0000052E,
	0x00000534, 0x0000053A, 0x00000540, 0x00000546, 0x0000054C, 0x00000552, 0x00000558, 0x0000055D,
	0x00000563, 0x00000569, 0x0000056F, 0x00000575, 0x0000057B, 0x00000581, 0x00000587, 0x0000058D,
	0x00000593, 0x00000599, 0x0000059E, 0x000005A4, 0x000005AA, 0x000005B0, 0x000005B6, 0x000005BC,
	0x000005C2, 0x000005C7, 0x000005CD, 0x000005D3, 0x000005D9, 0x000005DF, 0x000005E5, 0x000005EB,
	0x000005F0, 0x000005F6, 0x000005FC, 0x00000602, 0x00000608, 0x0000060E, 0x00000613, 0x00000619,
	0x0000061F, 0x00000625, 0x0000062B, 0x00000630, 0x00000636, 0x0000063C, 0x00000642, 0x00000648,
	0x0000064D, 0x00000653, 0x00000659, 0x0000065F, 0x00000664, 0x0000066A, 0x00000670, 0x00000676,
	0x0000067B, 0x00000681, 0x00000687, 0x0000068D, 0x00000692, 0x00000698, 0x0000069E, 0x000006A3,
	0x000006A9, 0x000006AF, 0x000006B5, 0x000006BA, 0x000006C0, 0x000006C6, 0x000006CB, 0x000006D1,
	0x000006D7, 0x000006DC, 0x000006E2, 0x000006E8, 0x000006ED, 0x000006F3, 0x000006F9, 0x000006FE,
	0x00000704, 0x0000070A, 0x0000070F, 0x00000715, 0x0000071B, 0x00000720, 0x00000726, 0x0000072B,
	0x00000731, 0x00000737, 0x0000073C, 0x00000742, 0x00000748, 0x0000074D, 0x00000753, 0x00000758,
	0x0000075E, 0x00000763, 0x00000769, 0x0000076F, 0x00000774, 0x0000077A, 0x0000077F, 0x00000785,
	0x0000078A, 0x00000790, 0x00000795, 0x0000079B, 0x000007A0, 0x000007A6, 0x000007AC, 0x000007B1,
	0x000007B7, 0x000007BC, 0x000007C2, 0x000007C7, 0x000007CD, 0x000007D2, 0x000007D7, 0x000007DD,
	0x000007E2, 0x000007E8, 0x000007ED, 0x000007F3, 0x000007F8, 0x000007FE, 0x00000803, 0x00000809,
	0x0000080E, 0x00000813, 0x00000819, 0x0000081E, 0x00000824, 0x00000829, 0x0000082E, 0x00000834,
	0x00000839, 0x0000083F, 0x00000844, 0x00000849, 0x0000084F, 0x00000854, 0x0000085A, 0x0000085F,
	0x00000864, 0x0000086A, 0x0000086F, 0x00000874, 0x0000087A, 0x0000087F, 0x00000884, 0x0000088A,
	0x0000088F, 0x00000894, 0x00000899, 0x0000089F, 0x000008A4, 0x000008A9, 0x000008AF, 0x000008B4,
	0x000008B9, 0x000008BE, 0x000008C4, 0x000008C9, 0x000008CE, 0x000008D3, 0x000008D9, 0x000008DE,
	0x000008E3, 0x000008E8, 0x000008EE, 0x000008F3, 0x000008F8, 0x000008FD, 0x00000902, 0x00000908,
	0x0000090D, 0x00000912, 0x00000917, 0x0000091C, 0x00000921, 0x00000927, 0x0000092C, 0x00000931,
	0x00000936, 0x0000093B, 0x00000940, 0x00000945, 0x0000094B, 0x00000950, 0x00000955, 0x0000095A,
	0x0000095F, 0x00000964, 0x00000969, 0x0000096E, 0x00000973, 0x00000978, 0x0000097D, 0x00000982,
	0x00000987, 0x0000098D, 0x00000992, 0x00000997, 0x0000099C, 0x000009A1, 0x000009A6, 0x000009AB,
	0x000009B0, 0x000009B5, 0x000009BA, 0x000009BF, 0x000009C4, 0x000009C9, 0x000009CE, 0x000009D3,
	0x000009D7, 0x000009DC, 0x000009E1, 0x000009E6, 0x000009EB, 0x000009F0, 0x000009F5, 0x000009FA,
	0x000009FF, 0x00000A04, 0x00000A09, 0x00000A0E, 0x00000A12, 0x00000A17, 0x00000A1C, 0x00000A21,
	0x00000A26, 0x00000A2B, 0x00000A30, 0x00000A35, 0x00000A39, 0x00000A3E, 0x00000A43, 0x00000A48,
	0x00000A4D, 0x00000A51, 0x00000A56, 0x00000A5B, 0x00000A60, 0x00000A65, 0x00000A69, 0x00000A6E,
	0x00000A73, 0x00000A78, 0x00000A7C, 0x00000A81, 0x00000A86, 0x00000A8B, 0x00000A8F, 0x00000A94,
	0x00000A99, 0x00000A9D, 0x00000AA2, 0x00000AA7, 0x00000AAC, 0x00000AB0, 0x00000AB5, 0x00000ABA,
	0x00000ABE, 0x00000AC3, 0x00000AC8, 0x00000ACC, 0x00000AD1, 0x00000AD5, 0x00000ADA, 0x00000ADF,
	0x00000AE3, 0x00000AE8, 0x00000AEC, 0x00000AF1, 0x00000AF6, 0x00000AFA, 0x00000AFF, 0x00000B03,
	0x00000B08, 0x00000B0C, 0x00000B11, 0x00000B15, 0x00000B1A, 0x00000B1F, 0x00000B23, 0x00000B28,
	0x00000B2C, 0x00000B31, 0x00000B35, 0x00000B3A, 0x00000B3E, 0x00000B42, 0x00000B47, 0x00000B4B,
	0x00000B50, 0x00000B54, 0x00000B59, 0x00000B5D, 0x00000B62, 0x00000B66, 0x00000B6A, 0x00000B6F,
	0x00000B73, 0x00000B78, 0x00000B7C, 0x00000B80, 0x00000B85, 0x00000B89, 0x00000B8D, 0x00000B92,
	0x00000B96, 0x00000B9A, 0x00000B9F, 0x00000BA3, 0x00000BA7, 0x00000BAC, 0x00000BB0, 0x00000BB4,
	0x00000BB8, 0x00000BBD, 0x00000BC1, 0x00000BC5, 0x00000BCA, 0x00000BCE, 0x00000BD2, 0x00000BD6,
	0x00000BDA, 0x00000BDF, 0x00000BE3, 0x00000BE7, 0x00000BEB, 0x00000BEF, 0x00000BF4, 0x00000BF8,
	0x00000BFC, 0x00000C00, 0x00000C04, 0x00000C08, 0x00000C0D, 0x00000C11, 0x00000C15, 0x00000C19,
	0x00000C1D, 0x00000C21, 0x00000C25, 0x00000C29, 0x00000C2D, 0x00000C31, 0x00000C36, 0x00000C3A,
	0x00000C3E, 0x00000C42, 0x00000C46, 0x00000C4A, 0x00000C4E, 0x00000C52, 0x00000C56, 0x00000C5A,
	0x00000C5E, 0x00000C62, 0x00000C66, 0x00000C6A, 0x00000C6E, 0x00000C72, 0x00000C76, 0x00000C79,
	0x00000C7D, 0x00000C81, 0x00000C85, 0x00000C89, 0x00000C8D, 0x00000C91, 0x00000C95, 0x00000C99,
	0x00000C9D, 0x00000CA0, 0x00000CA4, 0x00000CA8, 0x00000CAC, 0x00000CB0, 0x00000CB4, 0x00000CB7,
	0x00000CBB, 0x00000CBF, 0x00000CC3, 0x00000CC7, 0x00000CCA, 0x00000CCE, 0x00000CD2, 0x00000CD6,
	0x00000CD9, 0x00000CDD, 0x00000CE1, 0x00000CE5, 0x00000CE8, 0x00000CEC, 0x00000CF0, 0x00000CF3,
	0x00000CF7, 0x00000CFB, 0x00000CFE, 0x00000D02, 0x00000D06, 0x00000D09, 0x00000D0D, 0x00000D11,
	0x00000D14, 0x00000D18, 0x00000D1C, 0x00000D1F, 0x00000D23, 0x00000D26, 0x00000D2A, 0x00000D2D,
	0x00000D31, 0x00000D35, 0x00000D38, 0x00000D3C, 0x00000D3F, 0x00000D43, 0x00000D46, 0x00000D4A,
	0x00000D4D, 0x00000D51, 0x00000D54, 0x00000D58, 0x00000D5B, 0x00000D5F, 0x00000D62, 0x00000D65,
	0x00000D69, 0x00000D6C, 0x00000D70, 0x00000D73, 0x00000D77, 0x00000D7A, 0x00000D7D, 0x00000D81,
	0x00000D84, 0x00000D87, 0x00000D8B, 0x00000D8E, 0x00000D91, 0x00000D95, 0x00000D98, 0x00000D9B,
	0x00000D9F, 0x00000DA2, 0x00000DA5, 0x00000DA9, 0x00000DAC, 0x00000DAF, 0x00000DB2, 0x00000DB6,
	0x00000DB9, 0x00000DBC, 0x00000DBF, 0x00000DC2, 0x00000DC6, 0x00000DC9, 0x00000DCC, 0x00000DCF,
	0x00000DD2, 0x00000DD5, 0x00000DD9, 0x00000DDC, 0x00000DDF, 0x00000DE2, 0x00000DE5, 0x00000DE8,
	0x00000DEB, 0x00000DEE, 0x00000DF2, 0x00000DF5, 0x00000DF8, 0x00000DFB, 0x00000DFE, 0x00000E01,
	0x00000E04, 0x00000E07, 0x00000E0A, 0x00000E0D, 0x00000E10, 0x00000E13, 0x00000E16, 0x00000E19,
	0x00000E1C, 0x00000E1F, 0x00000E22, 0x00000E25, 0x00000E28, 0x00000E2B, 0x00000E2D, 0x00000E30,
	0x00000E33, 0x00000E36, 0x00000E39, 0x00000E3C, 0x00000E3F, 0x00000E42, 0x00000E44, 0x00000E47,
	0x00000E4A, 0x00000E4D, 0x00000E50, 0x00000E53, 0x00000E55, 0x00000E58, 0x00000E5B, 0x00000E5E,
	0x00000E60, 0x00000E63, 0x00000E66, 0x00000E69, 0x00000E6B, 0x00000E6E, 0x00000E71, 0x00000E74,
	0x00000E76, 0x00000E79, 0x00000E7C, 0x00000E7E, 0x00000E81, 0x00000E84, 0x00000E86, 0x00000E89,
	0x00000E8B, 0x00000E8E, 0x00000E91, 0x00000E93, 0x00000E96, 0x00000E98, 0x00000E9B, 0x00000E9E,
	0x00000EA0, 0x00000EA3, 0x00000EA5, 0x00000EA8, 0x00000EAA, 0x00000EAD, 0x00000EAF, 0x00000EB2,
	0x00000EB4, 0x00000EB7, 0x00000EB9, 0x00000EBC, 0x00000EBE, 0x00000EC0, 0x00000EC3, 0x00000EC5,
	0x00000EC8, 0x00000ECA, 0x00000ECD, 0x00000ECF, 0x00000ED1, 0x00000ED4, 0x00000ED6, 0x00000ED8,
	0x00000EDB, 0x00000EDD, 0x00000EDF, 0x00000EE2, 0x00000EE4, 0x00000EE6, 0x00000EE8, 0x00000EEB,
	0x00000EED, 0x00000EEF, 0x00000EF2, 0x00000EF4, 0x00000EF6, 0x00000EF8, 0x00000EFA, 0x00000EFD,
	0x00000EFF, 0x00000F01, 0x00000F03, 0x00000F05, 0x00000F08, 0x00000F0A, 0x00000F0C, 0x00000F0E,
	0x00000F10, 0x00000F12, 0x00000F14, 0x00000F16, 0x00000F18, 0x00000F1B, 0x00000F1D, 0x00000F1F,
	0x00000F21, 0x00000F23, 0x00000F25, 0x00000F27, 0x00000F29, 0x00000F2B, 0x00000F2D, 0x00000F2F,
	0x00000F31, 0x00000F33, 0x00000F35, 0x00000F37, 0x00000F39, 0x00000F3B, 0x00000F3C, 0x00000F3E,
	0x00000F40, 0x00000F42, 0x00000F44, 0x00000F46, 0x00000F48, 0x00000F4A, 0x00000F4B, 0x00000F4D,
	0x00000F4F, 0x00000F51, 0x00000F53, 0x00000F55, 0x00000F56, 0x00000F58, 0x00000F5A, 0x00000F5C,
	0x00000F5D, 0x00000F5F, 0x00000F61, 0x00000F63, 0x00000F64, 0x00000F66, 0x00000F68, 0x00000F69,
	0x00000F6B, 0x00000F6D, 0x00000F6E, 0x00000F70, 0x00000F72, 0x00000F73, 0x00000F75, 0x00000F77,
	0x00000F78, 0x00000F7A, 0x00000F7B, 0x00000F7D, 0x00000F7F, 0x00000F80, 0x00000F82, 0x00000F83,
	0x00000F85, 0x00000F86, 0x00000F88, 0x00000F89, 0x00000F8B, 0x00000F8C, 0x00000F8E, 0x00000F8F,
	0x00000F91, 0x00000F92, 0x00000F94, 0x00000F95, 0x00000F96, 0x00000F98, 0x00000F99, 0x00000F9B,
	0x00000F9C, 0x00000F9D, 0x00000F9F, 0x00000FA0, 0x00000FA1, 0x00000FA3, 0x00000FA4, 0x00000FA5,
	0x00000FA7, 0x00000FA8, 0x00000FA9, 0x00000FAB, 0x00000FAC, 0x00000FAD, 0x00000FAE, 0x00000FB0,
	0x00000FB1, 0x00000FB2, 0x00000FB3, 0x00000FB4, 0x00000FB6, 0x00000FB7, 0x00000FB8, 0x00000FB9,
	0x00000FBA, 0x00000FBB, 0x00000FBD, 0x00000FBE, 0x00000FBF, 0x00000FC0, 0x00000FC1, 0x00000FC2,
	0x00000FC3, 0x00000FC4, 0x00000FC5, 0x00000FC6, 0x00000FC7, 0x00000FC8, 0x00000FC9, 0x00000FCA,
	0x00000FCB, 0x00000FCC, 0x00000FCD, 0x00000FCE, 0x00000FCF, 0x00000FD0, 0x00000FD1, 0x00000FD2,
	0x00000FD3, 0x00000FD4, 0x00000FD5, 0x00000FD6, 0x00000FD7, 0x00000FD8, 0x00000FD9, 0x00000FD9,
	0x00000FDA, 0x00000FDB, 0x00000FDC, 0x00000FDD, 0x00000FDE, 0x00000FDE, 0x00000FDF, 0x00000FE0,
	0x00000FE1, 0x00000FE1, 0x00000FE2, 0x00000FE3, 0x00000FE4, 0x00000FE4, 0x00000FE5, 0x00000FE6,
	0x00000FE7, 0x00000FE7, 0x00000FE8, 0x00000FE9, 0x00000FE9, 0x00000FEA, 0x00000FEB, 0x00000FEB,
	0x00000FEC, 0x00000FEC, 0x00000FED, 0x00000FEE, 0x00000FEE, 0x00000FEF, 0x00000FEF, 0x00000FF0,
	0x00000FF0, 0x00000FF1, 0x00000FF1, 0x00000FF2, 0x00000FF2, 0x00000FF3, 0x00000FF3, 0x00000FF4,
	0x00000FF4, 0x00000FF5, 0x00000FF5, 0x00000FF6, 0x00000FF6, 0x00000FF7, 0x00000FF7, 0x00000FF7,
	0x00000FF8, 0x00000FF8, 0x00000FF9, 0x00000FF9, 0x00000FF9, 0x00000FFA, 0x00000FFA, 0x00000FFA,
	0x00000FFB, 0x00000FFB, 0x00000FFB, 0x00000FFB, 0x00000FFC, 0x00000FFC, 0x00000FFC, 0x00000FFC,
	0x00000FFD, 0x00000FFD, 0x00000FFD, 0x00000FFD, 0x00000FFE, 0x00000FFE, 0x00000FFE, 0x00000FFE,
	0x00000FFE, 0x00000FFE, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF,
	0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF,
	0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF,
	0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFF, 0x00000FFE,
	0x00000FFE, 0x00000FFE, 0x00000FFE, 0x00000FFE, 0x00000FFE, 0x00000FFD, 0x00000FFD, 0x00000FFD,
	0x00000FFD, 0x00000FFC, 0x00000FFC, 0x00000FFC, 0x00000FFC, 0x00000FFB, 0x00000FFB, 0x00000FFB,
	0x00000FFB, 0x00000FFA, 0x00000FFA, 0x00000FFA, 0x00000FF9, 0x00000FF9, 0x00000FF9, 0x00000FF8,
	0x00000FF8, 0x00000FF7, 0x00000FF7, 0x00000FF7, 0x00000FF6, 0x00000FF6, 0x00000FF5, 0x00000FF5,
	0x00000FF4, 0x00000FF4, 0x00000FF3, 0x00000FF3, 0x00000FF2, 0x00000FF2, 0x00000FF1, 0x00000FF1,
	0x00000FF0, 0x00000FF0, 0x00000FEF, 0x00000FEF, 0x00000FEE, 0x00000FEE, 0x00000FED, 0x00000FEC,
	0x00000FEC, 0x00000FEB, 0x00000FEB, 0x00000FEA, 0x00000FE9, 0x00000FE9, 0x00000FE8, 0x00000FE7,
	0x00000FE7, 0x00000FE6, 0x00000FE5, 0x00000FE4, 0x00000FE4, 0x00000FE3, 0x00000FE2, 0x00000FE1,
	0x00000FE1, 0x00000FE0, 0x00000FDF, 0x00000FDE, 0x00000FDE, 0x00000FDD, 0x00000FDC, 0x00000FDB,
	0x00000FDA, 0x00000FD9, 0x00000FD9, 0x00000FD8, 0x00000FD7, 0x00000FD6, 0x00000FD5, 0x00000FD4,
	0x00000FD3, 0x00000FD2, 0x00000FD1, 0x00000FD0, 0x00000FCF, 0x00000FCE, 0x00000FCD, 0x00000FCC,
	0x00000FCB, 0x00000FCA, 0x00000FC9, 0x00000FC8, 0x00000FC7, 0x00000FC6, 0x00000FC5, 0x00000FC4,
	0x00000FC3, 0x00000FC2, 0x00000FC1, 0x00000FC0, 0x00000FBF, 0x00000FBE, 0x00000FBD, 0x00000FBB,
	0x00000FBA, 0x00000FB9, 0x00000FB8, 0x00000FB7, 0x00000FB6, 0x00000FB4, 0x00000FB3, 0x00000FB2,
	0x00000FB1, 0x00000FB0, 0x00000FAE, 0x00000FAD, 0x00000FAC, 0x00000FAB, 0x00000FA9, 0x00000FA8,
	0x00000FA7, 0x00000FA5, 0x00000FA4, 0x00000FA3, 0x00000FA1, 0x00000FA0, 0x00000F9F, 0x00000F9D,
	0x00000F9C, 0x00000F9B, 0x00000F99, 0x00000F98, 0x00000F96, 0x00000F95, 0x00000F94, 0x00000F92,
	0x00000F91, 0x00000F8F, 0x00000F8E, 0x00000F8C, 0x00000F8B, 0x00000F89, 0x00000F88, 0x00000F86,
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	0xFFFFF3C2, 0xFFFFF3C6, 0xFFFFF3CA, 0xFFFFF3CF, 0xFFFFF3D3, 0xFFFFF3D7, 0xFFFFF3DB, 0xFFFFF3DF,
	0xFFFFF3E3, 0xFFFFF3E7, 0xFFFFF3EB, 0xFFFFF3EF, 0xFFFFF3F3, 0xFFFFF3F8, 0xFFFFF3FC, 0xFFFFF400,
	0xFFFFF404, 0xFFFFF408, 0xFFFFF40C, 0xFFFFF411, 0xFFFFF415, 0xFFFFF419, 0xFFFFF41D, 0xFFFFF421,
	0xFFFFF426, 0xFFFFF42A, 0xFFFFF42E, 0xFFFFF432, 0xFFFFF436, 0xFFFFF43B, 0xFFFFF43F, 0xFFFFF443,
	0xFFFFF448, 0xFFFFF44C, 0xFFFFF450, 0xFFFFF454, 0xFFFFF459, 0xFFFFF45D, 0xFFFFF461, 0xFFFFF466,
	0xFFFFF46A, 0xFFFFF46E, 0xFFFFF473, 0xFFFFF477, 0xFFFFF47B, 0xFFFFF480, 0xFFFFF484, 0xFFFFF488,
	0xFFFFF48D, 0xFFFFF491, 0xFFFFF496, 0xFFFFF49A, 0xFFFFF49E, 0xFFFFF4A3, 0xFFFFF4A7, 0xFFFFF4AC,
	0xFFFFF4B0, 0xFFFFF4B5, 0xFFFFF4B9, 0xFFFFF4BE, 0xFFFFF4C2, 0xFFFFF4C6, 0xFFFFF4CB, 0xFFFFF4CF,
	0xFFFFF4D4, 0xFFFFF4D8, 0xFFFFF4DD, 0xFFFFF4E1, 0xFFFFF4E6, 0xFFFFF4EB, 0xFFFFF4EF, 0xFFFFF4F4,
	0xFFFFF4F8, 0xFFFFF4FD, 0xFFFFF501, 0xFFFFF506, 0xFFFFF50A, 0xFFFFF50F, 0xFFFFF514, 0xFFFFF518,
	0xFFFFF51D, 0xFFFFF521, 0xFFFFF526, 0xFFFFF52B, 0xFFFFF52F, 0xFFFFF534, 0xFFFFF538, 0xFFFFF53D,
	0xFFFFF542, 0xFFFFF546, 0xFFFFF54B, 0xFFFFF550, 0xFFFFF554, 0xFFFFF559, 0xFFFFF55E, 0xFFFFF563,
	0xFFFFF567, 0xFFFFF56C, 0xFFFFF571, 0xFFFFF575, 0xFFFFF57A, 0xFFFFF57F, 0xFFFFF584, 0xFFFFF588,
	0xFFFFF58D, 0xFFFFF592, 0xFFFFF597, 0xFFFFF59B, 0xFFFFF5A0, 0xFFFFF5A5, 0xFFFFF5AA, 0xFFFFF5AF,
	0xFFFFF5B3, 0xFFFFF5B8, 0xFFFFF5BD, 0xFFFFF5C2, 0xFFFFF5C7, 0xFFFFF5CB, 0xFFFFF5D0, 0xFFFFF5D5,
	0xFFFFF5DA, 0xFFFFF5DF, 0xFFFFF5E4, 0xFFFFF5E9, 0xFFFFF5EE, 0xFFFFF5F2, 0xFFFFF5F7, 0xFFFFF5FC,
	0xFFFFF601, 0xFFFFF606, 0xFFFFF60B, 0xFFFFF610, 0xFFFFF615, 0xFFFFF61A, 0xFFFFF61F, 0xFFFFF624,
	0xFFFFF629, 0xFFFFF62D, 0xFFFFF632, 0xFFFFF637, 0xFFFFF63C, 0xFFFFF641, 0xFFFFF646, 0xFFFFF64B,
	0xFFFFF650, 0xFFFFF655, 0xFFFFF65A, 0xFFFFF65F, 0xFFFFF664, 0xFFFFF669, 0xFFFFF66E, 0xFFFFF673,
	0xFFFFF679, 0xFFFFF67E, 0xFFFFF683, 0xFFFFF688, 0xFFFFF68D, 0xFFFFF692, 0xFFFFF697, 0xFFFFF69C,
	0xFFFFF6A1, 0xFFFFF6A6, 0xFFFFF6AB, 0xFFFFF6B0, 0xFFFFF6B5, 0xFFFFF6BB, 0xFFFFF6C0, 0xFFFFF6C5,
	0xFFFFF6CA, 0xFFFFF6CF, 0xFFFFF6D4, 0xFFFFF6D9, 0xFFFFF6DF, 0xFFFFF6E4, 0xFFFFF6E9, 0xFFFFF6EE,
	0xFFFFF6F3, 0xFFFFF6F8, 0xFFFFF6FE, 0xFFFFF703, 0xFFFFF708, 0xFFFFF70D, 0xFFFFF712, 0xFFFFF718,
	0xFFFFF71D, 0xFFFFF722, 0xFFFFF727, 0xFFFFF72D, 0xFFFFF732, 0xFFFFF737, 0xFFFFF73C, 0xFFFFF742,
	0xFFFFF747, 0xFFFFF74C, 0xFFFFF751, 0xFFFFF757, 0xFFFFF75C, 0xFFFFF761, 0xFFFFF767, 0xFFFFF76C,
	0xFFFFF771, 0xFFFFF776, 0xFFFFF77C, 0xFFFFF781, 0xFFFFF786, 0xFFFFF78C, 0xFFFFF791, 0xFFFFF796,
	0xFFFFF79C, 0xFFFFF7A1, 0xFFFFF7A6, 0xFFFFF7AC, 0xFFFFF7B1, 0xFFFFF7B7, 0xFFFFF7BC, 0xFFFFF7C1,
	0xFFFFF7C7, 0xFFFFF7CC, 0xFFFFF7D2, 0xFFFFF7D7, 0xFFFFF7DC, 0xFFFFF7E2, 0xFFFFF7E7, 0xFFFFF7ED,
	0xFFFFF7F2, 0xFFFFF7F7, 0xFFFFF7FD, 0xFFFFF802, 0xFFFFF808, 0xFFFFF80D, 0xFFFFF813, 0xFFFFF818,
	0xFFFFF81E, 0xFFFFF823, 0xFFFFF829, 0xFFFFF82E, 0xFFFFF833, 0xFFFFF839, 0xFFFFF83E, 0xFFFFF844,
	0xFFFFF849, 0xFFFFF84F, 0xFFFFF854, 0xFFFFF85A, 0xFFFFF860, 0xFFFFF865, 0xFFFFF86B, 0xFFFFF870,
	0xFFFFF876, 0xFFFFF87B, 0xFFFFF881, 0xFFFFF886, 0xFFFFF88C, 0xFFFFF891, 0xFFFFF897, 0xFFFFF89D,
	0xFFFFF8A2, 0xFFFFF8A8, 0xFFFFF8AD, 0xFFFFF8B3, 0xFFFFF8B8, 0xFFFFF8BE, 0xFFFFF8C4, 0xFFFFF8C9,
	0xFFFFF8CF, 0xFFFFF8D5, 0xFFFFF8DA, 0xFFFFF8E0, 0xFFFFF8E5, 0xFFFFF8EB, 0xFFFFF8F1, 0xFFFFF8F6,
	0xFFFFF8FC, 0xFFFFF902, 0xFFFFF907, 0xFFFFF90D, 0xFFFFF913, 0xFFFFF918, 0xFFFFF91E, 0xFFFFF924,
	0xFFFFF929, 0xFFFFF92F, 0xFFFFF935, 0xFFFFF93A, 0xFFFFF940, 0xFFFFF946, 0xFFFFF94B, 0xFFFFF951,
	0xFFFFF957, 0xFFFFF95D, 0xFFFFF962, 0xFFFFF968, 0xFFFFF96E, 0xFFFFF973, 0xFFFFF979, 0xFFFFF97F,
	0xFFFFF985, 0xFFFFF98A, 0xFFFFF990, 0xFFFFF996, 0xFFFFF99C, 0xFFFFF9A1, 0xFFFFF9A7, 0xFFFFF9AD,
	0xFFFFF9B3, 0xFFFFF9B8, 0xFFFFF9BE, 0xFFFFF9C4, 0xFFFFF9CA, 0xFFFFF9D0, 0xFFFFF9D5, 0xFFFFF9DB,
	0xFFFFF9E1, 0xFFFFF9E7, 0xFFFFF9ED, 0xFFFFF9F2, 0xFFFFF9F8, 0xFFFFF9FE, 0xFFFFFA04, 0xFFFFFA0A,
	0xFFFFFA10, 0xFFFFFA15, 0xFFFFFA1B, 0xFFFFFA21, 0xFFFFFA27, 0xFFFFFA2D, 0xFFFFFA33, 0xFFFFFA39,
	0xFFFFFA3E, 0xFFFFFA44, 0xFFFFFA4A, 0xFFFFFA50, 0xFFFFFA56, 0xFFFFFA5C, 0xFFFFFA62, 0xFFFFFA67,
	0xFFFFFA6D, 0xFFFFFA73, 0xFFFFFA79, 0xFFFFFA7F, 0xFFFFFA85, 0xFFFFFA8B, 0xFFFFFA91, 0xFFFFFA97,
	0xFFFFFA9D, 0xFFFFFAA3, 0xFFFFFAA8, 0xFFFFFAAE, 0xFFFFFAB4, 0xFFFFFABA, 0xFFFFFAC0, 0xFFFFFAC6,
	0xFFFFFACC, 0xFFFFFAD2, 0xFFFFFAD8, 0xFFFFFADE, 0xFFFFFAE4, 0xFFFFFAEA, 0xFFFFFAF0, 0xFFFFFAF6,
	0xFFFFFAFC, 0xFFFFFB02, 0xFFFFFB08, 0xFFFFFB0E, 0xFFFFFB14, 0xFFFFFB1A, 0xFFFFFB20, 0xFFFFFB25,
	0xFFFFFB2B, 0xFFFFFB31, 0xFFFFFB37, 0xFFFFFB3D, 0xFFFFFB43, 0xFFFFFB49, 0xFFFFFB4F, 0xFFFFFB55,
	0xFFFFFB5B, 0xFFFFFB62, 0xFFFFFB68, 0xFFFFFB6E, 0xFFFFFB74, 0xFFFFFB7A, 0xFFFFFB80, 0xFFFFFB86,
	0xFFFFFB8C, 0xFFFFFB92, 0xFFFFFB98, 0xFFFFFB9E, 0xFFFFFBA4, 0xFFFFFBAA, 0xFFFFFBB0, 0xFFFFFBB6,
	0xFFFFFBBC, 0xFFFFFBC2, 0xFFFFFBC8, 0xFFFFFBCE, 0xFFFFFBD4, 0xFFFFFBDA, 0xFFFFFBE0, 0xFFFFFBE6,
	0xFFFFFBED, 0xFFFFFBF3, 0xFFFFFBF9, 0xFFFFFBFF, 0xFFFFFC05, 0xFFFFFC0B, 0xFFFFFC11, 0xFFFFFC17,
	0xFFFFFC1D, 0xFFFFFC23, 0xFFFFFC29, 0xFFFFFC30, 0xFFFFFC36, 0xFFFFFC3C, 0xFFFFFC42, 0xFFFFFC48,
	0xFFFFFC4E, 0xFFFFFC54, 0xFFFFFC5A, 0xFFFFFC60, 0xFFFFFC67, 0xFFFFFC6D, 0xFFFFFC73, 0xFFFFFC79,
	0xFFFFFC7F, 0xFFFFFC85, 0xFFFFFC8B, 0xFFFFFC91, 0xFFFFFC98, 0xFFFFFC9E, 0xFFFFFCA4, 0xFFFFFCAA,
	0xFFFFFCB0, 0xFFFFFCB6, 0xFFFFFCBC, 0xFFFFFCC3, 0xFFFFFCC9, 0xFFFFFCCF, 0xFFFFFCD5, 0xFFFFFCDB,
	0xFFFFFCE1, 0xFFFFFCE8, 0xFFFFFCEE, 0xFFFFFCF4, 0xFFFFFCFA, 0xFFFFFD00, 0xFFFFFD06, 0xFFFFFD0D,
	0xFFFFFD13, 0xFFFFFD19, 0xFFFFFD1F, 0xFFFFFD25, 0xFFFFFD2B, 0xFFFFFD32, 0xFFFFFD38, 0xFFFFFD3E,
	0xFFFFFD44, 0xFFFFFD4A, 0xFFFFFD51, 0xFFFFFD57, 0xFFFFFD5D, 0xFFFFFD63, 0xFFFFFD69, 0xFFFFFD70,
	0xFFFFFD76, 0xFFFFFD7C, 0xFFFFFD82, 0xFFFFFD88, 0xFFFFFD8F, 0xFFFFFD95, 0xFFFFFD9B, 0xFFFFFDA1,
	0xFFFFFDA7, 0xFFFFFDAE, 0xFFFFFDB4, 0xFFFFFDBA, 0xFFFFFDC0, 0xFFFFFDC7, 0xFFFFFDCD, 0xFFFFFDD3,
	0xFFFFFDD9, 0xFFFFFDDF, 0xFFFFFDE6, 0xFFFFFDEC, 0xFFFFFDF2, 0xFFFFFDF8, 0xFFFFFDFF, 0xFFFFFE05,
	0xFFFFFE0B, 0xFFFFFE11, 0xFFFFFE18, 0xFFFFFE1E, 0xFFFFFE24, 0xFFFFFE2A, 0xFFFFFE31, 0xFFFFFE37,
	0xFFFFFE3D, 0xFFFFFE43, 0xFFFFFE4A, 0xFFFFFE50, 0xFFFFFE56, 0xFFFFFE5C, 0xFFFFFE63, 0xFFFFFE69,
	0xFFFFFE6F, 0xFFFFFE75, 0xFFFFFE7C, 0xFFFFFE82, 0xFFFFFE88, 0xFFFFFE8E, 0xFFFFFE95, 0xFFFFFE9B,
	0xFFFFFEA1, 0xFFFFFEA7, 0xFFFFFEAE, 0xFFFFFEB4, 0xFFFFFEBA, 0xFFFFFEC0, 0xFFFFFEC7, 0xFFFFFECD,
	0xFFFFFED3, 0xFFFFFED9, 0xFFFFFEE0, 0xFFFFFEE6, 0xFFFFFEEC, 0xFFFFFEF3, 0xFFFFFEF9, 0xFFFFFEFF,
	0xFFFFFF05, 0xFFFFFF0C, 0xFFFFFF12, 0xFFFFFF18, 0xFFFFFF1E, 0xFFFFFF25, 0xFFFFFF2B, 0xFFFFFF31,
	0xFFFFFF38, 0xFFFFFF3E, 0xFFFFFF44, 0xFFFFFF4A, 0xFFFFFF51, 0xFFFFFF57, 0xFFFFFF5D, 0xFFFFFF63,
	0xFFFFFF6A, 0xFFFFFF70, 0xFFFFFF76, 0xFFFFFF7D, 0xFFFFFF83, 0xFFFFFF89, 0xFFFFFF8F, 0xFFFFFF96,
	0xFFFFFF9C, 0xFFFFFFA2, 0xFFFFFFA9, 0xFFFFFFAF, 0xFFFFFFB5, 0xFFFFFFBB, 0xFFFFFFC2, 0xFFFFFFC8,
	0xFFFFFFCE, 0xFFFFFFD5, 0xFFFFFFDB, 0xFFFFFFE1, 0xFFFFFFE7, 0xFFFFFFEE, 0xFFFFFFF4, 0xFFFFFFFA
};

static Int arcCosLookup[2 * INT_ONE] = {
	0x00003243, 0x000031E9, 0x000031C3, 0x000031A7, 0x0000318E, 0x00003179, 0x00003166, 0x00003154,
	0x00003143, 0x00003134, 0x00003125, 0x00003117, 0x0000310A, 0x000030FD, 0x000030F1, 0x000030E5,
	0x000030D9, 0x000030CE, 0x000030C3, 0x000030B9, 0x000030AF, 0x000030A5, 0x0000309B, 0x00003091,
	0x00003088, 0x0000307F, 0x00003076, 0x0000306D, 0x00003064, 0x0000305C, 0x00003053, 0x0000304B,
	0x00003043, 0x0000303B, 0x00003033, 0x0000302C, 0x00003024, 0x0000301D, 0x00003015, 0x0000300E,
	0x00003007, 0x00002FFF, 0x00002FF8, 0x00002FF1, 0x00002FEB, 0x00002FE4, 0x00002FDD, 0x00002FD6,
	0x00002FD0, 0x00002FC9, 0x00002FC3, 0x00002FBC, 0x00002FB6, 0x00002FB0, 0x00002FAA, 0x00002FA4,
	0x00002F9D, 0x00002F97, 0x00002F91, 0x00002F8B, 0x00002F86, 0x00002F80, 0x00002F7A, 0x00002F74,
	0x00002F6E, 0x00002F69, 0x00002F63, 0x00002F5E, 0x00002F58, 0x00002F53, 0x00002F4D, 0x00002F48,
	0x00002F42, 0x00002F3D, 0x00002F38, 0x00002F32, 0x00002F2D, 0x00002F28, 0x00002F23, 0x00002F1E,
	0x00002F19, 0x00002F14, 0x00002F0F, 0x00002F0A, 0x00002F05, 0x00002F00, 0x00002EFB, 0x00002EF6,
	0x00002EF1, 0x00002EEC, 0x00002EE7, 0x00002EE2, 0x00002EDE, 0x00002ED9, 0x00002ED4, 0x00002ED0,
	0x00002ECB, 0x00002EC6, 0x00002EC2, 0x00002EBD, 0x00002EB9, 0x00002EB4, 0x00002EAF, 0x00002EAB,
	0x00002EA7, 0x00002EA2, 0x00002E9E, 0x00002E99, 0x00002E95, 0x00002E90, 0x00002E8C, 0x00002E88,
	0x00002E83, 0x00002E7F, 0x00002E7B, 0x00002E77, 0x00002E72, 0x00002E6E, 0x00002E6A, 0x00002E66,
	0x00002E62, 0x00002E5D, 0x00002E59, 0x00002E55, 0x00002E51, 0x00002E4D, 0x00002E49, 0x00002E45,
	0x00002E41, 0x00002E3D, 0x00002E39, 0x00002E35, 0x00002E31, 0x00002E2D, 0x00002E29, 0x00002E25,
	0x00002E21, 0x00002E1D, 0x00002E19, 0x00002E15, 0x00002E11, 0x00002E0E, 0x00002E0A, 0x00002E06,
	0x00002E02, 0x00002DFE, 0x00002DFB, 0x00002DF7, 0x00002DF3, 0x00002DEF, 0x00002DEC, 0x00002DE8,
	0x00002DE4, 0x00002DE0, 0x00002DDD, 0x00002DD9, 0x00002DD5, 0x00002DD2, 0x00002DCE, 0x00002DCA,
	0x00002DC7, 0x00002DC3, 0x00002DC0, 0x00002DBC, 0x00002DB9, 0x00002DB5, 0x00002DB1, 0x00002DAE,
	0x00002DAA, 0x00002DA7, 0x00002DA3, 0x00002DA0, 0x00002D9C, 0x00002D99, 0x00002D95, 0x00002D92,
	0x00002D8E, 0x00002D8B, 0x00002D88, 0x00002D84, 0x00002D81, 0x00002D7D, 0x00002D7A, 0x00002D76,
	0x00002D73, 0x00002D70, 0x00002D6C, 0x00002D69, 0x00002D66, 0x00002D62, 0x00002D5F, 0x00002D5C,
	0x00002D58, 0x00002D55, 0x00002D52, 0x00002D4F, 0x00002D4B, 0x00002D48, 0x00002D45, 0x00002D41,
	0x00002D3E, 0x00002D3B, 0x00002D38, 0x00002D35, 0x00002D31, 0x00002D2E, 0x00002D2B, 0x00002D28,
	0x00002D25, 0x00002D21, 0x00002D1E, 0x00002D1B, 0x00002D18, 0x00002D15, 0x00002D12, 0x00002D0E,
	0x00002D0B, 0x00002D08, 0x00002D05, 0x00002D02, 0x00002CFF, 0x00002CFC, 0x00002CF9, 0x00002CF6,
	0x00002CF3, 0x00002CF0, 0x00002CED, 0x00002CE9, 0x00002CE6, 0x00002CE3, 0x00002CE0, 0x00002CDD,
	0x00002CDA, 0x00002CD7, 0x00002CD4, 0x00002CD1, 0x00002CCE, 0x00002CCB, 0x00002CC8, 0x00002CC5,
	0x00002CC2, 0x00002CBF, 0x00002CBC, 0x00002CBA, 0x00002CB7, 0x00002CB4, 0x00002CB1, 0x00002CAE,
	0x00002CAB, 0x00002CA8, 0x00002CA5, 0x00002CA2, 0x00002C9F, 0x00002C9C, 0x00002C99, 0x00002C97,
	0x00002C94, 0x00002C91, 0x00002C8E, 0x00002C8B, 0x00002C88, 0x00002C85, 0x00002C83, 0x00002C80,
	0x00002C7D, 0x00002C7A, 0x00002C77, 0x00002C74, 0x00002C72, 0x00002C6F, 0x00002C6C, 0x00002C69,
	0x00002C66, 0x00002C64, 0x00002C61, 0x00002C5E, 0x00002C5B, 0x00002C58, 0x00002C56, 0x00002C53,
	0x00002C50, 0x00002C4D, 0x00002C4B, 0x00002C48, 0x00002C45, 0x00002C43, 0x00002C40, 0x00002C3D,
	0x00002C3A, 0x00002C38, 0x00002C35, 0x00002C32, 0x00002C30, 0x00002C2D, 0x00002C2A, 0x00002C27,
	0x00002C25, 0x00002C22, 0x00002C1F, 0x00002C1D, 0x00002C1A, 0x00002C17, 0x00002C15, 0x00002C12,
	0x00002C0F, 0x00002C0D, 0x00002C0A, 0x00002C08, 0x00002C05, 0x00002C02, 0x00002C00, 0x00002BFD,
	0x00002BFA, 0x00002BF8, 0x00002BF5, 0x00002BF3, 0x00002BF0, 0x00002BED, 0x00002BEB, 0x00002BE8,
	0x00002BE6, 0x00002BE3, 0x00002BE1, 0x00002BDE, 0x00002BDB, 0x00002BD9, 0x00002BD6, 0x00002BD4,
	0x00002BD1, 0x00002BCF, 0x00002BCC, 0x00002BCA, 0x00002BC7, 0x00002BC4, 0x00002BC2, 0x00002BBF,
	0x00002BBD, 0x00002BBA, 0x00002BB8, 0x00002BB5, 0x00002BB3, 0x00002BB0, 0x00002BAE, 0x00002BAB,
	0x00002BA9, 0x00002BA6, 0x00002BA4, 0x00002BA1, 0x00002B9F, 0x00002B9C, 0x00002B9A, 0x00002B97,
	0x00002B95, 0x00002B93, 0x00002B90, 0x00002B8E, 0x00002B8B, 0x00002B89, 0x00002B86, 0x00002B84,
	0x00002B81, 0x00002B7F, 0x00002B7C, 0x00002B7A, 0x00002B78, 0x00002B75, 0x00002B73, 0x00002B70,
	0x00002B6E, 0x00002B6C, 0x00002B69, 0x00002B67, 0x00002B64, 0x00002B62, 0x00002B60, 0x00002B5D,
	0x00002B5B, 0x00002B58, 0x00002B56, 0x00002B54, 0x00002B51, 0x00002B4F, 0x00002B4C, 0x00002B4A,
	0x00002B48, 0x00002B45, 0x00002B43, 0x00002B41, 0x00002B3E, 0x00002B3C, 0x00002B3A, 0x00002B37,
	0x00002B35, 0x00002B33, 0x00002B30, 0x00002B2E, 0x00002B2C, 0x00002B29, 0x00002B27, 0x00002B25,
	0x00002B22, 0x00002B20, 0x00002B1E, 0x00002B1B, 0x00002B19, 0x00002B17, 0x00002B14, 0x00002B12,
	0x00002B10, 0x00002B0D, 0x00002B0B, 0x00002B09, 0x00002B07, 0x00002B04, 0x00002B02, 0x00002B00,
	0x00002AFD, 0x00002AFB, 0x00002AF9, 0x00002AF7, 0x00002AF4, 0x00002AF2, 0x00002AF0, 0x00002AEE,
	0x00002AEB, 0x00002AE9, 0x00002AE7, 0x00002AE5, 0x00002AE2, 0x00002AE0, 0x00002ADE, 0x00002ADC,
	0x00002AD9, 0x00002AD7, 0x00002AD5, 0x00002AD3, 0x00002AD0, 0x00002ACE, 0x00002ACC, 0x00002ACA,
	0x00002AC8, 0x00002AC5, 0x00002AC3, 0x00002AC1, 0x00002ABF, 0x00002ABC, 0x00002ABA, 0x00002AB8,
	0x00002AB6, 0x00002AB4, 0x00002AB1, 0x00002AAF, 0x00002AAD, 0x00002AAB, 0x00002AA9, 0x00002AA7,
	0x00002AA4, 0x00002AA2, 0x00002AA0, 0x00002A9E, 0x00002A9C, 0x00002A99, 0x00002A97, 0x00002A95,
	0x00002A93, 0x00002A91, 0x00002A8F, 0x00002A8C, 0x00002A8A, 0x00002A88, 0x00002A86, 0x00002A84,
	0x00002A82, 0x00002A80, 0x00002A7D, 0x00002A7B, 0x00002A79, 0x00002A77, 0x00002A75, 0x00002A73,
	0x00002A71, 0x00002A6F, 0x00002A6C, 0x00002A6A, 0x00002A68, 0x00002A66, 0x00002A64, 0x00002A62,
	0x00002A60, 0x00002A5E, 0x00002A5B, 0x00002A59, 0x00002A57, 0x00002A55, 0x00002A53, 0x00002A51,
	0x00002A4F, 0x00002A4D, 0x00002A4B, 0x00002A49, 0x00002A46, 0x00002A44, 0x00002A42, 0x00002A40,
	0x00002A3E, 0x00002A3C, 0x00002A3A, 0x00002A38, 0x00002A36, 0x00002A34, 0x00002A32, 0x00002A30,
	0x00002A2E, 0x00002A2B, 0x00002A29, 0x00002A27, 0x00002A25, 0x00002A23, 0x00002A21, 0x00002A1F,
	0x00002A1D, 0x00002A1B, 0x00002A19, 0x00002A17, 0x00002A15, 0x00002A13, 0x00002A11, 0x00002A0F,
	0x00002A0D, 0x00002A0B, 0x00002A09, 0x00002A07, 0x00002A05, 0x00002A03, 0x00002A01, 0x000029FF,
	0x000029FC, 0x000029FA, 0x000029F8, 0x000029F6, 0x000029F4, 0x000029F2, 0x000029F0, 0x000029EE,
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	0x000018A1, 0x000018A0, 0x0000189F, 0x0000189E, 0x0000189D, 0x0000189C, 0x0000189B, 0x0000189A,
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	0x00001869, 0x00001868, 0x00001867, 0x00001866, 0x00001865, 0x00001864, 0x00001863, 0x00001862,
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	0x00001821, 0x00001820, 0x0000181F, 0x0000181E, 0x0000181D, 0x0000181C, 0x0000181B, 0x0000181A,
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	0x00001809, 0x00001808, 0x00001807, 0x00001806, 0x00001805, 0x00001804, 0x00001803, 0x00001802,
	0x00001801, 0x00001800, 0x000017FF, 0x000017FE, 0x000017FD, 0x000017FC, 0x000017FB, 0x000017FA,
	0x000017F9, 0x000017F8, 0x000017F7, 0x000017F6, 0x000017F5, 0x000017F4, 0x000017F3, 0x000017F2,
	0x000017F1, 0x000017F0, 0x000017EF, 0x000017EE, 0x000017ED, 0x000017EC, 0x000017EB, 0x000017EA,
	0x000017E9, 0x000017E8, 0x000017E7, 0x000017E6, 0x000017E5, 0x000017E4, 0x000017E3, 0x000017E2,
	0x000017E1, 0x000017E0, 0x000017DF, 0x000017DE, 0x000017DD, 0x000017DC, 0x000017DB, 0x000017DA,
	0x000017D9, 0x000017D8, 0x000017D7, 0x000017D6, 0x000017D5, 0x000017D4, 0x000017D3, 0x000017D2,
	0x000017D1, 0x000017D0, 0x000017CF, 0x000017CE, 0x000017CD, 0x000017CC, 0x000017CB, 0x000017CA,
	0x000017C9, 0x000017C8, 0x000017C7, 0x000017C6, 0x000017C5, 0x000017C4, 0x000017C3, 0x000017C2,
	0x000017C1, 0x000017C0, 0x000017BF, 0x000017BE, 0x000017BD, 0x000017BC, 0x000017BB, 0x000017BA,
	0x000017B9, 0x000017B8, 0x000017B7, 0x000017B6, 0x000017B5, 0x000017B4, 0x000017B3, 0x000017B2,
	0x000017B1, 0x000017B0, 0x000017AF, 0x000017AE, 0x000017AD, 0x000017AC, 0x000017AB, 0x000017AA,
	0x000017A9, 0x000017A8, 0x000017A7, 0x000017A6, 0x000017A5, 0x000017A4, 0x000017A3, 0x000017A2,
	0x000017A1, 0x000017A0, 0x0000179F, 0x0000179E, 0x0000179D, 0x0000179C, 0x0000179B, 0x0000179A,
	0x00001799, 0x00001798, 0x00001797, 0x00001796, 0x00001795, 0x00001794, 0x00001793, 0x00001792,
	0x00001791, 0x00001790, 0x0000178F, 0x0000178E, 0x0000178D, 0x0000178C, 0x0000178B, 0x0000178A,
	0x00001789, 0x00001788, 0x00001787, 0x00001786, 0x00001785, 0x00001784, 0x00001783, 0x00001782,
	0x00001781, 0x00001780, 0x0000177F, 0x0000177E, 0x0000177D, 0x0000177C, 0x0000177B, 0x0000177A,
	0x00001779, 0x00001778, 0x00001777, 0x00001776, 0x00001775, 0x00001774, 0x00001773, 0x00001772,
	0x00001771, 0x00001770, 0x0000176F, 0x0000176E, 0x0000176D, 0x0000176C, 0x0000176B, 0x0000176A,
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	0x00001761, 0x00001760, 0x0000175F, 0x0000175E, 0x0000175D, 0x0000175C, 0x0000175B, 0x0000175A,
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	0x000016F8, 0x000016F7, 0x000016F6, 0x000016F5, 0x000016F4, 0x000016F3, 0x000016F2, 0x000016F1,
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	0x0000169F, 0x0000169E, 0x0000169D, 0x0000169C, 0x0000169B, 0x0000169A, 0x00001699, 0x00001698,
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	0x0000168F, 0x0000168E, 0x0000168D, 0x0000168C, 0x0000168B, 0x0000168A, 0x00001689, 0x00001688,
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	0x000013FB, 0x000013FA, 0x000013F9, 0x000013F8, 0x000013F7, 0x000013F6, 0x000013F5, 0x000013F3,
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	0x0000061E, 0x0000061C, 0x00000619, 0x00000616, 0x00000613, 0x00000611, 0x0000060E, 0x0000060B,
	0x00000609, 0x00000606, 0x00000603, 0x00000600, 0x000005FE, 0x000005FB, 0x000005F8, 0x000005F6,
	0x000005F3, 0x000005F0, 0x000005ED, 0x000005EB, 0x000005E8, 0x000005E5, 0x000005E2, 0x000005DF,
	0x000005DD, 0x000005DA, 0x000005D7, 0x000005D4, 0x000005D1, 0x000005CF, 0x000005CC, 0x000005C9,
	0x000005C6, 0x000005C3, 0x000005C0, 0x000005BE, 0x000005BB, 0x000005B8, 0x000005B5, 0x000005B2,
	0x000005AF, 0x000005AC, 0x000005AA, 0x000005A7, 0x000005A4, 0x000005A1, 0x0000059E, 0x0000059B,
	0x00000598, 0x00000595, 0x00000592, 0x0000058F, 0x0000058C, 0x00000589, 0x00000587, 0x00000584,
	0x00000581, 0x0000057E, 0x0000057B, 0x00000578, 0x00000575, 0x00000572, 0x0000056F, 0x0000056C,
	0x00000569, 0x00000566, 0x00000563, 0x00000560, 0x0000055D, 0x0000055A, 0x00000556, 0x00000553,
	0x00000550, 0x0000054D, 0x0000054A, 0x00000547, 0x00000544, 0x00000541, 0x0000053E, 0x0000053B,
	0x00000538, 0x00000535, 0x00000531, 0x0000052E, 0x0000052B, 0x00000528, 0x00000525, 0x00000522,
	0x0000051E, 0x0000051B, 0x00000518, 0x00000515, 0x00000512, 0x0000050E, 0x0000050B, 0x00000508,
	0x00000505, 0x00000502, 0x000004FE, 0x000004FB, 0x000004F8, 0x000004F4, 0x000004F1, 0x000004EE,
	0x000004EB, 0x000004E7, 0x000004E4, 0x000004E1, 0x000004DD, 0x000004DA, 0x000004D7, 0x000004D3,
	0x000004D0, 0x000004CD, 0x000004C9, 0x000004C6, 0x000004C2, 0x000004BF, 0x000004BB, 0x000004B8,
	0x000004B5, 0x000004B1, 0x000004AE, 0x000004AA, 0x000004A7, 0x000004A3, 0x000004A0, 0x0000049C,
	0x00000499, 0x00000495, 0x00000492, 0x0000048E, 0x0000048A, 0x00000487, 0x00000483, 0x00000480,
	0x0000047C, 0x00000479, 0x00000475, 0x00000471, 0x0000046E, 0x0000046A, 0x00000466, 0x00000463,
	0x0000045F, 0x0000045B, 0x00000457, 0x00000454, 0x00000450, 0x0000044C, 0x00000448, 0x00000445,
	0x00000441, 0x0000043D, 0x00000439, 0x00000435, 0x00000432, 0x0000042E, 0x0000042A, 0x00000426,
	0x00000422, 0x0000041E, 0x0000041A, 0x00000416, 0x00000412, 0x0000040E, 0x0000040A, 0x00000406,
	0x00000402, 0x000003FE, 0x000003FA, 0x000003F6, 0x000003F2, 0x000003EE, 0x000003EA, 0x000003E6,
	0x000003E1, 0x000003DD, 0x000003D9, 0x000003D5, 0x000003D1, 0x000003CC, 0x000003C8, 0x000003C4,
	0x000003C0, 0x000003BB, 0x000003B7, 0x000003B3, 0x000003AE, 0x000003AA, 0x000003A5, 0x000003A1,
	0x0000039C, 0x00000398, 0x00000394, 0x0000038F, 0x0000038A, 0x00000386, 0x00000381, 0x0000037D,
	0x00000378, 0x00000373, 0x0000036F, 0x0000036A, 0x00000365, 0x00000361, 0x0000035C, 0x00000357,
	0x00000352, 0x0000034D, 0x00000348, 0x00000343, 0x0000033E, 0x00000339, 0x00000334, 0x0000032F,
	0x0000032A, 0x00000325, 0x00000320, 0x0000031B, 0x00000316, 0x00000311, 0x0000030B, 0x00000306,
	0x00000301, 0x000002FB, 0x000002F6, 0x000002F0, 0x000002EB, 0x000002E5, 0x000002E0, 0x000002DA,
	0x000002D5, 0x000002CF, 0x000002C9, 0x000002C3, 0x000002BD, 0x000002B8, 0x000002B2, 0x000002AC,
	0x000002A6, 0x0000029F, 0x00000299, 0x00000293, 0x0000028D, 0x00000287, 0x00000280, 0x0000027A,
	0x00000273, 0x0000026D, 0x00000266, 0x0000025F, 0x00000258, 0x00000252, 0x0000024B, 0x00000244,
	0x0000023C, 0x00000235, 0x0000022E, 0x00000226, 0x0000021F, 0x00000217, 0x00000210, 0x00000208,
	0x00000200, 0x000001F8, 0x000001F0, 0x000001E7, 0x000001DF, 0x000001D6, 0x000001CD, 0x000001C4,
	0x000001BB, 0x000001B2, 0x000001A8, 0x0000019E, 0x00000194, 0x0000018A, 0x00000180, 0x00000175,
	0x0000016A, 0x0000015E, 0x00000152, 0x00000146, 0x00000139, 0x0000012C, 0x0000011E, 0x0000010F,
	0x00000100, 0x000000EF, 0x000000DD, 0x000000CA, 0x000000B5, 0x0000009C, 0x00000080, 0x0000005A
};


static Int intArcCos( Int c )
{
	c += INT_ONE;
	if (c < 0)
		c = 0;

	if (c >= 2 * INT_ONE)
		c = (2 * INT_ONE)-1;

	return arcCosLookup[c];
}

static Int intSin( Int angle )
{
	while (angle < 0)
		angle += INT_TWOPI;

	while (angle >= INT_TWOPI)
		angle -= INT_TWOPI;

	return sinLookup[(angle * TRIG_RES)/INT_TWOPI];
}

static Int intTan( Int angle )
{
	Int s, c;

	s = intSin(angle);
	c = intCos(angle);

	if (c == 0) {
		if (s > 0)
			return INT_MAX;
		else
			return INT_MIN;
	}

	return INT_ONE * s / c;
}

// These calls are somewhat less accurate than the standard library calls, but use a
// precalculated lookup table for speed and repeatability across different machines
#define DEFAULT_TRIG
Real Sin(Real x)
{
#ifdef DEFAULT_TRIG
	return sinf(x);
#else
	return (Real)intSin((Int)((x) * INT_ONE)) / (Real)INT_ONE;
#endif
}

Real Cos(Real x)
{
#ifdef DEFAULT_TRIG
	return cosf(x);
#else
	return (Real)intCos((Int)((x) * INT_ONE)) / (Real)INT_ONE;
#endif
}

Real Tan(Real x)
{
#ifdef DEFAULT_TRIG
	return tanf(x);
#else
	return (Real)intTan((Int)((x) * INT_ONE)) / (Real)INT_ONE;
#endif
}

Real ACos(Real x)
{
#ifdef DEFAULT_TRIG
	return acosf(x);
#else
	return (Real)(intArcCos((Int)((x) * INT_ONE))) * TWOPI / (Real)INT_TWOPI;
#endif
}

Real ASin(Real x)
{
	return asinf(x);
}

#ifdef REGENERATE_TRIG_TABLES
#include <stdio.h>
void initTrig( void )
{
	static Byte inited = FALSE;
	Real angle, r;
	int i;

	if (inited)
		return;

	inited = TRUE;

	static int columns = 8;
	int column = 0;
	FILE *fp = fopen("trig.txt", "w");
	fprintf(fp, "static Int sinLookup[TRIG_RES] = {\n");
	for( i=0; i<TRIG_RES; i++ ) {
		angle = TWOPI * i / (Real)TRIG_RES;
		sinLookup[i] = (Int)(sin(angle) * INT_ONE);

		if (i == 0)
		{
			fprintf(fp, "\t0x%8.8X", sinLookup[i]);
		}
		else if (column == 0)
		{
		fprintf(fp, ",\n\t0x%8.8X", sinLookup[i]);
		}
		else
		{
		fprintf(fp, ", 0x%8.8X", sinLookup[i]);
		}
		column = (column + 1) % columns;
	}
	fprintf(fp, "\n};\n\n");

	column = 0;
	fprintf(fp, "static Int arcCosLookup[2 * INT_ONE] = {\n");
	for( i=0; i<2*INT_ONE; i++ ) {
		r = (Real)i / (Real)INT_ONE - 1.0f;

		arcCosLookup[i] = (Int)(acos( (double)r ) * INT_TWOPI / TWOPI );

		if (i == 0)
		{
			fprintf(fp, "\t0x%8.8X", arcCosLookup[i]);
		}
		else if (column == 0)
		{
		fprintf(fp, ",\n\t0x%8.8X", arcCosLookup[i]);
		}
		else
		{
		fprintf(fp, ", 0x%8.8X", arcCosLookup[i]);
		}
		column = (column + 1) % columns;
	}
	fprintf(fp, "\n};\n\n");

	fclose(fp);
}

class TrigInit
{
public:
	TrigInit() { initTrig(); }
};
TrigInit trigInitializer;

#endif // REGENERATE_TRIG_TABLES