l_satan.s

VXWORKS源代码

/* l_satan.s - Motorola 68040 FP arc-tangent routines (LIB) */

/* Copyright 1991-1993 Wind River Systems, Inc. */
	.data
	.globl	_copyright_wind_river
	.long	_copyright_wind_river

/*
modification history
--------------------
01e,21jul93,kdl  added .text (SPR #2372).
01d,23aug92,jcf  changed bxxx to jxx.
01c,26may92,rrr  the tree shuffle
01b,09jan92,kdl  added modification history; general cleanup.
01a,15aug91,kdl  original version, from Motorola FPSP v2.0.
*/

/*
DESCRIPTION


	satansa 3.3 12/19/90

	The entry point __l_satan computes the arctagent of an
	input value. __l_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 __l_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 * 1xxxxxxxx...x. Note that k = -4, -3,...,
		or 3.
		Define F = sgn * 2**k * 1xxxx1, 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	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.

__l_satan	IDNT	2,1 Motorola 040 Floating Point Software Package

	section	8

NOMANUAL
*/

#include "fpsp040L.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

#define	X		FP_SCR1
#define	XDCARE		X+2
#define	XFRAC		X+4
#define	XFRACLO		X+8

#define	ATANF		FP_SCR2
#define	ATANFHI		ATANF+4
#define	ATANFLO		ATANF+8


|	xref	__l_t_frcinx