satanh.s

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

//
//      $Id: satanh.S,v 1.1 1998/12/14 23:15:25 joel Exp $
//
//	satanh.sa 3.3 12/19/90
//
//	The entry point satanh computes the inverse
//	hyperbolic tangent of
//	an input argument; satanhd does the same except for denormalized
//	input.
//
//	Input: Double-extended number X in location pointed to
//		by address register a0.
//
//	Output: The value arctanh(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 satanh takes approximately 270 cycles.
//
//	Algorithm:
//
//	ATANH
//	1. If |X| >= 1, go to 3.
//
//	2. (|X| < 1) Calculate atanh(X) by
//		sgn := sign(X)
//		y := |X|
//		z := 2y/(1-y)
//		atanh(X) := sgn * (1/2) * logp1(z)
//		Exit.
//
//	3. If |X| > 1, go to 5.
//
//	4. (|X| = 1) Generate infinity with an appropriate sign and
//		divide-by-zero by	
//		sgn := sign(X)
//		atan(X) := sgn / (+0).
//		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//	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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.

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

	|section	8

	|xref	t_dz
	|xref	t_operr
	|xref	t_frcinx
	|xref	t_extdnrm
	|xref	slognp1

	.global	satanhd
satanhd:
//--ATANH(X) = X FOR DENORMALIZED X

	bra		t_extdnrm

	.global	satanh
satanh:
	movel		(%a0),%d0
	movew		4(%a0),%d0
	andil		#0x7FFFFFFF,%d0
	cmpil		#0x3FFF8000,%d0
	bges		ATANHBIG

//--THIS IS THE USUAL CASE, |X| < 1
//--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).

	fabsx		(%a0),%fp0	// ...Y = |X|
	fmovex		%fp0,%fp1
	fnegx		%fp1		// ...-Y
	faddx		%fp0,%fp0		// ...2Y
	fadds		#0x3F800000,%fp1	// ...1-Y
	fdivx		%fp1,%fp0		// ...2Y/(1-Y)
	movel		(%a0),%d0
	andil		#0x80000000,%d0
	oril		#0x3F000000,%d0	// ...SIGN(X)*HALF
	movel		%d0,-(%sp)

	fmovemx	%fp0-%fp0,(%a0)	// ...overwrite input
	movel		%d1,-(%sp)
	clrl		%d1
	bsr		slognp1		// ...LOG1P(Z)
	fmovel		(%sp)+,%fpcr
	fmuls		(%sp)+,%fp0
	bra		t_frcinx

ATANHBIG:
	fabsx		(%a0),%fp0	// ...|X|
	fcmps		#0x3F800000,%fp0
	fbgt		t_operr
	bra		t_dz

	|end