satan.s

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|
|	satan.sa 3.3 12/19/90
|
|	The entry point satan computes the arctangent of an
|	input value. satand does the same except the input value is a
|	denormalized number.
|
|	Input: Double-extended value in memory location pointed to by address
|		register a0.
|
|	Output:	Arctan(X) returned in floating-point register Fp0.
|
|	Accuracy and Monotonicity: The returned result is within 2 ulps in
|		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
|		result is subsequently rounded to double precision. The
|		result is provably monotonic in double precision.
|
|	Speed: The program satan takes approximately 160 cycles for input
|		argument X such that 1/16 < |X| < 16. For the other arguments,
|		the program will run no worse than 10% slower.
|
|	Algorithm:
|	Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
|
|	Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
|		Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
|		of X with a bit-1 attached at the 6-th bit position. Define u
|		to be u = (X-F) / (1 + X*F).
|
|	Step 3. Approximate arctan(u) by a polynomial poly.
|
|	Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
|		calculated beforehand. Exit.
|
|	Step 5. If |X| >= 16, go to Step 7.
|
|	Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
|
|	Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
|		Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
|

|		Copyright (C) Motorola, Inc. 1990
|			All Rights Reserved
|
|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 
|	The copyright notice above does not evidence any  
|	actual or intended publication of such source code.

|satan	idnt	2,1 | Motorola 040 Floating Point Software Package

	|section	8

	.include "fpsp.h"
	
BOUNDS1:	.long 0x3FFB8000,0x4002FFFF

ONE:	.long 0x3F800000

	.long 0x00000000

ATANA3:	.long 0xBFF6687E,0x314987D8
ATANA2:	.long 0x4002AC69,0x34A26DB3

ATANA1:	.long 0xBFC2476F,0x4E1DA28E
ATANB6:	.long 0x3FB34444,0x7F876989

ATANB5:	.long 0xBFB744EE,0x7FAF45DB
ATANB4:	.long 0x3FBC71C6,0x46940220

ATANB3:	.long 0xBFC24924,0x921872F9
ATANB2:	.long 0x3FC99999,0x99998FA9

ATANB1:	.long 0xBFD55555,0x55555555
ATANC5:	.long 0xBFB70BF3,0x98539E6A

ATANC4:	.long 0x3FBC7187,0x962D1D7D
ATANC3:	.long 0xBFC24924,0x827107B8

ATANC2:	.long 0x3FC99999,0x9996263E
ATANC1:	.long 0xBFD55555,0x55555536

PPIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
NPIBY2:	.long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
PTINY:	.long 0x00010000,0x80000000,0x00000000,0x00000000
NTINY:	.long 0x80010000,0x80000000,0x00000000,0x00000000

ATANTBL:
	.long	0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
	.long	0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
	.long	0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
	.long	0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
	.long	0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
	.long	0x3FFB0000,0xAB98E943,0x62765619,0x00000000
	.long	0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
	.long	0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
	.long	0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
	.long	0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
	.long	0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
	.long	0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
	.long	0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
	.long	0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
	.long	0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
	.long	0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
	.long	0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
	.long	0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
	.long	0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
	.long	0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
	.long	0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
	.long	0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
	.long	0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
	.long	0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
	.long	0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
	.long	0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
	.long	0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
	.long	0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
	.long	0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
	.long	0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
	.long	0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
	.long	0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
	.long	0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
	.long	0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
	.long	0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
	.long	0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
	.long	0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
	.long	0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
	.long	0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
	.long	0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
	.long	0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
	.long	0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
	.long	0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
	.long	0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
	.long	0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
	.long	0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
	.long	0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
	.long	0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
	.long	0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
	.long	0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
	.long	0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
	.long	0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
	.long	0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
	.long	0x3FFE0000,0x97731420,0x365E538C,0x00000000
	.long	0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
	.long	0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
	.long	0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
	.long	0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
	.long	0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
	.long	0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
	.long	0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
	.long	0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
	.long	0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
	.long	0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
	.long	0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
	.long	0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
	.long	0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
	.long	0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
	.long	0x3FFE0000,0xE8771129,0xC4353259,0x00000000
	.long	0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
	.long	0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
	.long	0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
	.long	0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
	.long	0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
	.long	0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
	.long	0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
	.long	0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
	.long	0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
	.long	0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
	.long	0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
	.long	0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
	.long	0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
	.long	0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
	.long	0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
	.long	0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
	.long	0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
	.long	0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
	.long	0x3FFF0000,0x9F100575,0x006CC571,0x00000000
	.long	0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
	.long	0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
	.long	0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
	.long	0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
	.long	0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
	.long	0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
	.long	0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
	.long	0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
	.long	0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
	.long	0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
	.long	0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
	.long	0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
	.long	0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
	.long	0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
	.long	0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
	.long	0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
	.long	0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
	.long	0x3FFF0000,0xB525529D,0x562246BD,0x00000000
	.long	0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
	.long	0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
	.long	0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
	.long	0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
	.long	0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
	.long	0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
	.long	0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
	.long	0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
	.long	0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
	.long	0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
	.long	0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
	.long	0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
	.long	0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
	.long	0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
	.long	0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
	.long	0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
	.long	0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
	.long	0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
	.long	0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
	.long	0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
	.long	0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
	.long	0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000

	.set	X,FP_SCR1
	.set	XDCARE,X+2
	.set	XFRAC,X+4
	.set	XFRACLO,X+8

	.set	ATANF,FP_SCR2
	.set	ATANFHI,ATANF+4
	.set	ATANFLO,ATANF+8


	| xref	t_frcinx
	|xref	t_extdnrm

	.global	satand
satand:
|--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT

	bra		t_extdnrm

	.global	satan
satan:
|--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S