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      1 *	$NetBSD: satanh.sa,v 1.2 1994/10/26 07:49:33 cgd Exp $
      2 
      3 *	MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
      4 *	M68000 Hi-Performance Microprocessor Division
      5 *	M68040 Software Package 
      6 *
      7 *	M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
      8 *	All rights reserved.
      9 *
     10 *	THE SOFTWARE is provided on an "AS IS" basis and without warranty.
     11 *	To the maximum extent permitted by applicable law,
     12 *	MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
     13 *	INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
     14 *	PARTICULAR PURPOSE and any warranty against infringement with
     15 *	regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
     16 *	and any accompanying written materials. 
     17 *
     18 *	To the maximum extent permitted by applicable law,
     19 *	IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
     20 *	(INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
     21 *	PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
     22 *	OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
     23 *	SOFTWARE.  Motorola assumes no responsibility for the maintenance
     24 *	and support of the SOFTWARE.  
     25 *
     26 *	You are hereby granted a copyright license to use, modify, and
     27 *	distribute the SOFTWARE so long as this entire notice is retained
     28 *	without alteration in any modified and/or redistributed versions,
     29 *	and that such modified versions are clearly identified as such.
     30 *	No licenses are granted by implication, estoppel or otherwise
     31 *	under any patents or trademarks of Motorola, Inc.
     32 
     33 *
     34 *	satanh.sa 3.3 12/19/90
     35 *
     36 *	The entry point satanh computes the inverse
     37 *	hyperbolic tangent of
     38 *	an input argument; satanhd does the same except for denormalized
     39 *	input.
     40 *
     41 *	Input: Double-extended number X in location pointed to
     42 *		by address register a0.
     43 *
     44 *	Output: The value arctanh(X) returned in floating-point register Fp0.
     45 *
     46 *	Accuracy and Monotonicity: The returned result is within 3 ulps in
     47 *		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
     48 *		result is subsequently rounded to double precision. The 
     49 *		result is provably monotonic in double precision.
     50 *
     51 *	Speed: The program satanh takes approximately 270 cycles.
     52 *
     53 *	Algorithm:
     54 *
     55 *	ATANH
     56 *	1. If |X| >= 1, go to 3.
     57 *
     58 *	2. (|X| < 1) Calculate atanh(X) by
     59 *		sgn := sign(X)
     60 *		y := |X|
     61 *		z := 2y/(1-y)
     62 *		atanh(X) := sgn * (1/2) * logp1(z)
     63 *		Exit.
     64 *
     65 *	3. If |X| > 1, go to 5.
     66 *
     67 *	4. (|X| = 1) Generate infinity with an appropriate sign and
     68 *		divide-by-zero by	
     69 *		sgn := sign(X)
     70 *		atan(X) := sgn / (+0).
     71 *		Exit.
     72 *
     73 *	5. (|X| > 1) Generate an invalid operation by 0 * infinity.
     74 *		Exit.
     75 *
     76 
     77 satanh	IDNT	2,1 Motorola 040 Floating Point Software Package
     78 
     79 	section	8
     80 
     81 	xref	t_dz
     82 	xref	t_operr
     83 	xref	t_frcinx
     84 	xref	t_extdnrm
     85 	xref	slognp1
     86 
     87 	xdef	satanhd
     88 satanhd:
     89 *--ATANH(X) = X FOR DENORMALIZED X
     90 
     91 	bra		t_extdnrm
     92 
     93 	xdef	satanh
     94 satanh:
     95 	move.l		(a0),d0
     96 	move.w		4(a0),d0
     97 	ANDI.L		#$7FFFFFFF,D0
     98 	CMPI.L		#$3FFF8000,D0
     99 	BGE.B		ATANHBIG
    100 
    101 *--THIS IS THE USUAL CASE, |X| < 1
    102 *--Y = |X|, Z = 2Y/(1-Y), ATANH(X) = SIGN(X) * (1/2) * LOG1P(Z).
    103 
    104 	FABS.X		(a0),FP0	...Y = |X|
    105 	FMOVE.X		FP0,FP1
    106 	FNEG.X		FP1		...-Y
    107 	FADD.X		FP0,FP0		...2Y
    108 	FADD.S		#:3F800000,FP1	...1-Y
    109 	FDIV.X		FP1,FP0		...2Y/(1-Y)
    110 	move.l		(a0),d0
    111 	ANDI.L		#$80000000,D0
    112 	ORI.L		#$3F000000,D0	...SIGN(X)*HALF
    113 	move.l		d0,-(sp)
    114 
    115 	fmovem.x	fp0,(a0)	...overwrite input
    116 	move.l		d1,-(sp)
    117 	clr.l		d1
    118 	bsr		slognp1		...LOG1P(Z)
    119 	fmove.l		(sp)+,fpcr
    120 	FMUL.S		(sp)+,FP0
    121 	bra		t_frcinx
    122 
    123 ATANHBIG:
    124 	FABS.X		(a0),FP0	...|X|
    125 	FCMP.S		#:3F800000,FP0
    126 	fbgt		t_operr
    127 	bra		t_dz
    128 
    129 	end
    130