CoCalc -- satan.S

GitHub Repository: awilliam/linux-vfio
Path: blob/master/arch/m68k/fpsp040/satan.S
¹⁰⁸¹⁸ views
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|
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|	satan.sa 3.3 12/19/90
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|
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|	The entry point satan computes the arctangent of an
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|	input value. satand does the same except the input value is a
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|	denormalized number.
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|
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|	Input: Double-extended value in memory location pointed to by address
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|		register a0.
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|
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|	Output:	Arctan(X) returned in floating-point register Fp0.
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|
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|	Accuracy and Monotonicity: The returned result is within 2 ulps in
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|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
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|		result is subsequently rounded to double precision. The
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|		result is provably monotonic in double precision.
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|
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|	Speed: The program satan takes approximately 160 cycles for input
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|		argument X such that 1/16 < |X| < 16. For the other arguments,
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|		the program will run no worse than 10% slower.
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|
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|	Algorithm:
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|	Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
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|
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|	Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
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|		Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
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|		of X with a bit-1 attached at the 6-th bit position. Define u
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|		to be u = (X-F) / (1 + X*F).
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|
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|	Step 3. Approximate arctan(u) by a polynomial poly.
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|
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|	Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
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|		calculated beforehand. Exit.
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|
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|	Step 5. If |X| >= 16, go to Step 7.
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|
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|	Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
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|
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|	Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
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|		Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
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|
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|		Copyright (C) Motorola, Inc. 1990
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|			All Rights Reserved
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|
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|       For details on the license for this file, please see the
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|       file, README, in this same directory.
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|satan	idnt	2,1 | Motorola 040 Floating Point Software Package
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	|section	8
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#include "fpsp.h"
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BOUNDS1:	.long 0x3FFB8000,0x4002FFFF
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ONE:	.long 0x3F800000
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	.long 0x00000000
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ATANA3:	.long 0xBFF6687E,0x314987D8
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ATANA2:	.long 0x4002AC69,0x34A26DB3
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ATANA1:	.long 0xBFC2476F,0x4E1DA28E
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ATANB6:	.long 0x3FB34444,0x7F876989
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ATANB5:	.long 0xBFB744EE,0x7FAF45DB
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ATANB4:	.long 0x3FBC71C6,0x46940220
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ATANB3:	.long 0xBFC24924,0x921872F9
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ATANB2:	.long 0x3FC99999,0x99998FA9
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ATANB1:	.long 0xBFD55555,0x55555555
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ATANC5:	.long 0xBFB70BF3,0x98539E6A
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ATANC4:	.long 0x3FBC7187,0x962D1D7D
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ATANC3:	.long 0xBFC24924,0x827107B8
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ATANC2:	.long 0x3FC99999,0x9996263E
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ATANC1:	.long 0xBFD55555,0x55555536
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PPIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
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NPIBY2:	.long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
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PTINY:	.long 0x00010000,0x80000000,0x00000000,0x00000000
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NTINY:	.long 0x80010000,0x80000000,0x00000000,0x00000000
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ATANTBL:
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	.long	0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
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	.long	0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
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	.long	0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
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	.long	0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
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	.long	0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
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	.long	0x3FFB0000,0xAB98E943,0x62765619,0x00000000
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	.long	0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
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	.long	0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
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	.long	0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
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	.long	0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
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	.long	0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
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	.long	0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
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	.long	0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
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	.long	0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
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	.long	0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
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	.long	0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
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	.long	0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
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	.long	0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
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	.long	0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
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	.long	0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
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	.long	0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
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	.long	0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
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	.long	0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
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	.long	0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
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	.long	0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
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	.long	0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
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	.long	0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
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	.long	0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
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	.long	0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
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	.long	0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
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	.long	0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
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	.long	0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
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	.long	0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
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	.long	0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
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	.long	0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
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	.long	0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
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	.long	0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
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	.long	0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
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	.long	0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
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	.long	0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
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	.long	0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
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	.long	0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
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	.long	0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
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	.long	0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
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	.long	0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
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	.long	0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
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	.long	0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
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	.long	0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
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	.long	0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
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	.long	0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
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	.long	0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
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	.long	0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
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	.long	0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
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	.long	0x3FFE0000,0x97731420,0x365E538C,0x00000000
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	.long	0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
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	.long	0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
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	.long	0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
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	.long	0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
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	.long	0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
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	.long	0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
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	.long	0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
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	.long	0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
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	.long	0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
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	.long	0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
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	.long	0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
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	.long	0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
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	.long	0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
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	.long	0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
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	.long	0x3FFE0000,0xE8771129,0xC4353259,0x00000000
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	.long	0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
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	.long	0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
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	.long	0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
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	.long	0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
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	.long	0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
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	.long	0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
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	.long	0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
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	.long	0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
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	.long	0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
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	.long	0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
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	.long	0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
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	.long	0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
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	.long	0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
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	.long	0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
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	.long	0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
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	.long	0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
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	.long	0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
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	.long	0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
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	.long	0x3FFF0000,0x9F100575,0x006CC571,0x00000000
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	.long	0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
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	.long	0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
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	.long	0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
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	.long	0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
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	.long	0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
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	.long	0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
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	.long	0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
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	.long	0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
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	.long	0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
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	.long	0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
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	.long	0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
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	.long	0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
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	.long	0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
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	.long	0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
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	.long	0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
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	.long	0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
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	.long	0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
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	.long	0x3FFF0000,0xB525529D,0x562246BD,0x00000000
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	.long	0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
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	.long	0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
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	.long	0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
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	.long	0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
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	.long	0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
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	.long	0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
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	.long	0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
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	.long	0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
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	.long	0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
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	.long	0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
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	.long	0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
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	.long	0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
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	.long	0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
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	.long	0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
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	.long	0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
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	.long	0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
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	.long	0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
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	.long	0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
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	.long	0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
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	.long	0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
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	.long	0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
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	.long	0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
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	.set	X,FP_SCR1
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	.set	XDCARE,X+2
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	.set	XFRAC,X+4
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	.set	XFRACLO,X+8
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	.set	ATANF,FP_SCR2
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	.set	ATANFHI,ATANF+4
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	.set	ATANFLO,ATANF+8
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	| xref	t_frcinx
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	|xref	t_extdnrm
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	.global	satand
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satand:
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|--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
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	bra		t_extdnrm
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	.global	satan
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satan:
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|--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
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	fmovex		(%a0),%fp0	| ...LOAD INPUT
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	movel		(%a0),%d0
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	movew		4(%a0),%d0
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	fmovex		%fp0,X(%a6)
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	andil		#0x7FFFFFFF,%d0
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	cmpil		#0x3FFB8000,%d0		| ...|X| >= 1/16?
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	bges		ATANOK1
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	bra		ATANSM
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ATANOK1:
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	cmpil		#0x4002FFFF,%d0		| ...|X| < 16 ?
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	bles		ATANMAIN
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	bra		ATANBIG
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|--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
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|--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
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|--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
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|--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
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|--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
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|--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
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|--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
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|--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
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|--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
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|--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
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|--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
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|--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
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|--WILL INVOLVE A VERY LONG POLYNOMIAL.
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|--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
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|--WE CHOSE F TO BE +-2^K * 1.BBBB1
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|--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
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|--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
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|--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
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|-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
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ATANMAIN:
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	movew		#0x0000,XDCARE(%a6)	| ...CLEAN UP X JUST IN CASE
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	andil		#0xF8000000,XFRAC(%a6)	| ...FIRST 5 BITS
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	oril		#0x04000000,XFRAC(%a6)	| ...SET 6-TH BIT TO 1
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	movel		#0x00000000,XFRACLO(%a6)	| ...LOCATION OF X IS NOW F
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	fmovex		%fp0,%fp1			| ...FP1 IS X
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	fmulx		X(%a6),%fp1		| ...FP1 IS X*F, NOTE THAT X*F > 0
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	fsubx		X(%a6),%fp0		| ...FP0 IS X-F
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	fadds		#0x3F800000,%fp1		| ...FP1 IS 1 + X*F
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	fdivx		%fp1,%fp0			| ...FP0 IS U = (X-F)/(1+X*F)
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|--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
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|--CREATE ATAN(F) AND STORE IT IN ATANF, AND
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|--SAVE REGISTERS FP2.
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	movel		%d2,-(%a7)	| ...SAVE d2 TEMPORARILY
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	movel		%d0,%d2		| ...THE EXPO AND 16 BITS OF X
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	andil		#0x00007800,%d0	| ...4 VARYING BITS OF F'S FRACTION
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	andil		#0x7FFF0000,%d2	| ...EXPONENT OF F
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	subil		#0x3FFB0000,%d2	| ...K+4
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	asrl		#1,%d2
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	addl		%d2,%d0		| ...THE 7 BITS IDENTIFYING F
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	asrl		#7,%d0		| ...INDEX INTO TBL OF ATAN(|F|)
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	lea		ATANTBL,%a1
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	addal		%d0,%a1		| ...ADDRESS OF ATAN(|F|)
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	movel		(%a1)+,ATANF(%a6)
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	movel		(%a1)+,ATANFHI(%a6)
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	movel		(%a1)+,ATANFLO(%a6)	| ...ATANF IS NOW ATAN(|F|)
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	movel		X(%a6),%d0		| ...LOAD SIGN AND EXPO. AGAIN
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	andil		#0x80000000,%d0	| ...SIGN(F)
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	orl		%d0,ATANF(%a6)	| ...ATANF IS NOW SIGN(F)*ATAN(|F|)
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	movel		(%a7)+,%d2	| ...RESTORE d2
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|--THAT'S ALL I HAVE TO DO FOR NOW,
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|--BUT ALAS, THE DIVIDE IS STILL CRANKING!
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|--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
317
|--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
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|--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
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|--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
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|--WHAT WE HAVE HERE IS MERELY	A1 = A3, A2 = A1/A3, A3 = A2/A3.
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|--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
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|--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
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325
	fmovex		%fp0,%fp1
326
	fmulx		%fp1,%fp1
327
	fmoved		ATANA3,%fp2
328
	faddx		%fp1,%fp2		| ...A3+V
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	fmulx		%fp1,%fp2		| ...V*(A3+V)
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	fmulx		%fp0,%fp1		| ...U*V
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	faddd		ATANA2,%fp2	| ...A2+V*(A3+V)
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	fmuld		ATANA1,%fp1	| ...A1*U*V
333
	fmulx		%fp2,%fp1		| ...A1*U*V*(A2+V*(A3+V))
334

335
	faddx		%fp1,%fp0		| ...ATAN(U), FP1 RELEASED
336
	fmovel		%d1,%FPCR		|restore users exceptions
337
	faddx		ATANF(%a6),%fp0	| ...ATAN(X)
338
	bra		t_frcinx
339

340
ATANBORS:
341
|--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
342
|--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
343
	cmpil		#0x3FFF8000,%d0
344
	bgt		ATANBIG	| ...I.E. |X| >= 16
345

346
ATANSM:
347
|--|X| <= 1/16
348
|--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
349
|--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
350
|--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
351
|--WHERE Y = X*X, AND Z = Y*Y.
352

353
	cmpil		#0x3FD78000,%d0
354
	blt		ATANTINY
355
|--COMPUTE POLYNOMIAL
356
	fmulx		%fp0,%fp0	| ...FP0 IS Y = X*X
357

358

359
	movew		#0x0000,XDCARE(%a6)
360

361
	fmovex		%fp0,%fp1
362
	fmulx		%fp1,%fp1		| ...FP1 IS Z = Y*Y
363

364
	fmoved		ATANB6,%fp2
365
	fmoved		ATANB5,%fp3
366

367
	fmulx		%fp1,%fp2		| ...Z*B6
368
	fmulx		%fp1,%fp3		| ...Z*B5
369

370
	faddd		ATANB4,%fp2	| ...B4+Z*B6
371
	faddd		ATANB3,%fp3	| ...B3+Z*B5
372

373
	fmulx		%fp1,%fp2		| ...Z*(B4+Z*B6)
374
	fmulx		%fp3,%fp1		| ...Z*(B3+Z*B5)
375

376
	faddd		ATANB2,%fp2	| ...B2+Z*(B4+Z*B6)
377
	faddd		ATANB1,%fp1	| ...B1+Z*(B3+Z*B5)
378

379
	fmulx		%fp0,%fp2		| ...Y*(B2+Z*(B4+Z*B6))
380
	fmulx		X(%a6),%fp0		| ...X*Y
381

382
	faddx		%fp2,%fp1		| ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
383

384

385
	fmulx		%fp1,%fp0	| ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
386

387
	fmovel		%d1,%FPCR		|restore users exceptions
388
	faddx		X(%a6),%fp0
389

390
	bra		t_frcinx
391

392
ATANTINY:
393
|--|X| < 2^(-40), ATAN(X) = X
394
	movew		#0x0000,XDCARE(%a6)
395

396
	fmovel		%d1,%FPCR		|restore users exceptions
397
	fmovex		X(%a6),%fp0	|last inst - possible exception set
398

399
	bra		t_frcinx
400

401
ATANBIG:
402
|--IF |X| > 2^(100), RETURN	SIGN(X)*(PI/2 - TINY). OTHERWISE,
403
|--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
404
	cmpil		#0x40638000,%d0
405
	bgt		ATANHUGE
406

407
|--APPROXIMATE ATAN(-1/X) BY
408
|--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
409
|--THIS CAN BE RE-WRITTEN AS
410
|--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
411

412
	fmoves		#0xBF800000,%fp1	| ...LOAD -1
413
	fdivx		%fp0,%fp1		| ...FP1 IS -1/X
414

415

416
|--DIVIDE IS STILL CRANKING
417

418
	fmovex		%fp1,%fp0		| ...FP0 IS X'
419
	fmulx		%fp0,%fp0		| ...FP0 IS Y = X'*X'
420
	fmovex		%fp1,X(%a6)		| ...X IS REALLY X'
421

422
	fmovex		%fp0,%fp1
423
	fmulx		%fp1,%fp1		| ...FP1 IS Z = Y*Y
424

425
	fmoved		ATANC5,%fp3
426
	fmoved		ATANC4,%fp2
427

428
	fmulx		%fp1,%fp3		| ...Z*C5
429
	fmulx		%fp1,%fp2		| ...Z*B4
430

431
	faddd		ATANC3,%fp3	| ...C3+Z*C5
432
	faddd		ATANC2,%fp2	| ...C2+Z*C4
433

434
	fmulx		%fp3,%fp1		| ...Z*(C3+Z*C5), FP3 RELEASED
435
	fmulx		%fp0,%fp2		| ...Y*(C2+Z*C4)
436

437
	faddd		ATANC1,%fp1	| ...C1+Z*(C3+Z*C5)
438
	fmulx		X(%a6),%fp0		| ...X'*Y
439

440
	faddx		%fp2,%fp1		| ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
441

442

443
	fmulx		%fp1,%fp0		| ...X'*Y*([B1+Z*(B3+Z*B5)]
444
|					...	+[Y*(B2+Z*(B4+Z*B6))])
445
	faddx		X(%a6),%fp0
446

447
	fmovel		%d1,%FPCR		|restore users exceptions
448

449
	btstb		#7,(%a0)
450
	beqs		pos_big
451

452
neg_big:
453
	faddx		NPIBY2,%fp0
454
	bra		t_frcinx
455

456
pos_big:
457
	faddx		PPIBY2,%fp0
458
	bra		t_frcinx
459

460
ATANHUGE:
461
|--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
462
	btstb		#7,(%a0)
463
	beqs		pos_huge
464

465
neg_huge:
466
	fmovex		NPIBY2,%fp0
467
	fmovel		%d1,%fpcr
468
	fsubx		NTINY,%fp0
469
	bra		t_frcinx
470

471
pos_huge:
472
	fmovex		PPIBY2,%fp0
473
	fmovel		%d1,%fpcr
474
	fsubx		PTINY,%fp0
475
	bra		t_frcinx
476

477
	|end
478

479
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