sasin.s

RTEMS (Real-Time Executive for Multiprocessor Systems) is a free open source real-time operating sys

//
//      $Id: sasin.S,v 1.1 1998/12/14 23:15:25 joel Exp $
//
//	sasin.sa 3.3 12/19/90
//
//	Description: The entry point sAsin computes the inverse sine of
//		an input argument; sAsind does the same except for denormalized
//		input.
//
//	Input: Double-extended number X in location pointed to
//		by address register a0.
//
//	Output: The value arcsin(X) returned in floating-point register Fp0.
//
//	Accuracy and Monotonicity: The returned result is within 3 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 sASIN takes approximately 310 cycles.
//
//	Algorithm:
//
//	ASIN
//	1. If |X| >= 1, go to 3.
//
//	2. (|X| < 1) Calculate asin(X) by
//		z := sqrt( [1-X][1+X] )
//		asin(X) = atan( x / z ).
//		Exit.
//
//	3. If |X| > 1, go to 5.
//
//	4. (|X| = 1) sgn := sign(X), return asin(X) := sgn * Pi/2. Exit.
//
//	5. (|X| > 1) Generate an invalid operation by 0 * infinity.
//		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//	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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.

//SASIN	idnt	2,1 | Motorola 040 Floating Point Software Package

	|section	8

PIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000

	|xref	t_operr
	|xref	t_frcinx
	|xref	t_extdnrm
	|xref	satan

	.global	sasind
sasind:
//--ASIN(X) = X FOR DENORMALIZED X

	bra		t_extdnrm

	.global	sasin
sasin:
	fmovex		(%a0),%fp0	// ...LOAD INPUT

	movel		(%a0),%d0
	movew		4(%a0),%d0
	andil		#0x7FFFFFFF,%d0
	cmpil		#0x3FFF8000,%d0
	bges		asinbig

//--THIS IS THE USUAL CASE, |X| < 1
//--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )

	fmoves		#0x3F800000,%fp1
	fsubx		%fp0,%fp1		// ...1-X
	fmovemx	%fp2-%fp2,-(%a7)
	fmoves		#0x3F800000,%fp2
	faddx		%fp0,%fp2		// ...1+X
	fmulx		%fp2,%fp1		// ...(1+X)(1-X)
	fmovemx	(%a7)+,%fp2-%fp2
	fsqrtx		%fp1		// ...SQRT([1-X][1+X])
	fdivx		%fp1,%fp0	 	// ...X/SQRT([1-X][1+X])
	fmovemx	%fp0-%fp0,(%a0)
	bsr		satan
	bra		t_frcinx

asinbig:
	fabsx		%fp0	 // ...|X|
	fcmps		#0x3F800000,%fp0
	fbgt		t_operr		//cause an operr exception

//--|X| = 1, ASIN(X) = +- PI/2.

	fmovex		PIBY2,%fp0
	movel		(%a0),%d0
	andil		#0x80000000,%d0	// ...SIGN BIT OF X
	oril		#0x3F800000,%d0	// ...+-1 IN SGL FORMAT
	movel		%d0,-(%sp)	// ...push SIGN(X) IN SGL-FMT
	fmovel		%d1,%FPCR		
	fmuls		(%sp)+,%fp0
	bra		t_frcinx

	|end