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      1 *	$NetBSD: ssinh.sa,v 1.3 1994/10/26 07:50:05 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 *	ssinh.sa 3.1 12/10/90
     35 *
     36 *       The entry point sSinh computes the hyperbolic sine of
     37 *       an input argument; sSinhd does the same except for denormalized
     38 *       input.
     39 *
     40 *       Input: Double-extended number X in location pointed to 
     41 *		by address register a0.
     42 *
     43 *       Output: The value sinh(X) returned in floating-point register Fp0.
     44 *
     45 *       Accuracy and Monotonicity: The returned result is within 3 ulps in
     46 *               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
     47 *               result is subsequently rounded to double precision. The
     48 *               result is provably monotonic in double precision.
     49 *
     50 *       Speed: The program sSINH takes approximately 280 cycles.
     51 *
     52 *       Algorithm:
     53 *
     54 *       SINH
     55 *       1. If |X| > 16380 log2, go to 3.
     56 *
     57 *       2. (|X| <= 16380 log2) Sinh(X) is obtained by the formulae
     58 *               y = |X|, sgn = sign(X), and z = expm1(Y),
     59 *               sinh(X) = sgn*(1/2)*( z + z/(1+z) ).
     60 *          Exit.
     61 *
     62 *       3. If |X| > 16480 log2, go to 5.
     63 *
     64 *       4. (16380 log2 < |X| <= 16480 log2)
     65 *               sinh(X) = sign(X) * exp(|X|)/2.
     66 *          However, invoking exp(|X|) may cause premature overflow.
     67 *          Thus, we calculate sinh(X) as follows:
     68 *             Y       := |X|
     69 *             sgn     := sign(X)
     70 *             sgnFact := sgn * 2**(16380)
     71 *             Y'      := Y - 16381 log2
     72 *             sinh(X) := sgnFact * exp(Y').
     73 *          Exit.
     74 *
     75 *       5. (|X| > 16480 log2) sinh(X) must overflow. Return
     76 *          sign(X)*Huge*Huge to generate overflow and an infinity with
     77 *          the appropriate sign. Huge is the largest finite number in
     78 *          extended format. Exit.
     79 *
     80 
     81 SSINH	IDNT	2,1 Motorola 040 Floating Point Software Package
     82 
     83 	section	8
     84 
     85 T1	DC.L $40C62D38,$D3D64634 ... 16381 LOG2 LEAD
     86 T2	DC.L $3D6F90AE,$B1E75CC7 ... 16381 LOG2 TRAIL
     87 
     88 	xref	t_frcinx
     89 	xref	t_ovfl
     90 	xref	t_extdnrm
     91 	xref	setox
     92 	xref	setoxm1
     93 
     94 	xdef	ssinhd
     95 ssinhd:
     96 *--SINH(X) = X FOR DENORMALIZED X
     97 
     98 	bra	t_extdnrm
     99 
    100 	xdef	ssinh
    101 ssinh:
    102 	FMOVE.x	(a0),FP0	...LOAD INPUT
    103 
    104 	move.l	(a0),d0
    105 	move.w	4(a0),d0
    106 	move.l	d0,a1		save a copy of original (compacted) operand
    107 	AND.L	#$7FFFFFFF,D0
    108 	CMP.L	#$400CB167,D0
    109 	BGT.B	SINHBIG
    110 
    111 *--THIS IS THE USUAL CASE, |X| < 16380 LOG2
    112 *--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
    113 
    114 	FABS.X	FP0		...Y = |X|
    115 
    116 	movem.l	a1/d1,-(sp)
    117 	fmovem.x fp0,(a0)
    118 	clr.l	d1
    119 	bsr	setoxm1	 	...FP0 IS Z = EXPM1(Y)
    120 	fmove.l	#0,fpcr
    121 	movem.l	(sp)+,a1/d1
    122 
    123 	FMOVE.X	FP0,FP1
    124 	FADD.S	#:3F800000,FP1	...1+Z
    125 	FMOVE.X	FP0,-(sp)
    126 	FDIV.X	FP1,FP0		...Z/(1+Z)
    127 	MOVE.L	a1,d0
    128 	AND.L	#$80000000,D0
    129 	OR.L	#$3F000000,D0
    130 	FADD.X	(sp)+,FP0
    131 	MOVE.L	D0,-(sp)
    132 
    133 	fmove.l	d1,fpcr
    134 	fmul.s	(sp)+,fp0	;last fp inst - possible exceptions set
    135 
    136 	bra	t_frcinx
    137 
    138 SINHBIG:
    139 	cmp.l	#$400CB2B3,D0
    140 	bgt	t_ovfl
    141 	FABS.X	FP0
    142 	FSUB.D	T1(pc),FP0	...(|X|-16381LOG2_LEAD)
    143 	clr.l	-(sp)
    144 	move.l	#$80000000,-(sp)
    145 	move.l	a1,d0
    146 	AND.L	#$80000000,D0
    147 	OR.L	#$7FFB0000,D0
    148 	MOVE.L	D0,-(sp)	...EXTENDED FMT
    149 	FSUB.D	T2(pc),FP0	...|X| - 16381 LOG2, ACCURATE
    150 
    151 	move.l	d1,-(sp)
    152 	clr.l	d1
    153 	fmovem.x fp0,(a0)
    154 	bsr	setox
    155 	fmove.l	(sp)+,fpcr
    156 
    157 	fmul.x	(sp)+,fp0	;possible exception
    158 	bra	t_frcinx
    159 
    160 	end
    161