[GitHub/mt8127/android_kernel_alcatel_ttab.git] / arch / m68k / fpsp040 / sacos.S

|
|	sacos.sa 3.3 12/19/90
|
|	Description: The entry point sAcos computes the inverse cosine of
|		an input argument; sAcosd does the same except for denormalized
|		input.
|
|	Input: Double-extended number X in location pointed to
|		by address register a0.
|
|	Output: The value arccos(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 sCOS takes approximately 310 cycles.
|
|	Algorithm:
|
|	ACOS
|	1. If |X| >= 1, go to 3.
|
|	2. (|X| < 1) Calculate acos(X) by
|		z := (1-X) / (1+X)
|		acos(X) = 2 * atan( sqrt(z) ).
|		Exit.
|
|	3. If |X| > 1, go to 5.
|
|	4. (|X| = 1) If X > 0, return 0. Otherwise, return Pi. 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|	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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.

|SACOS	idnt	2,1 | Motorola 040 Floating Point Software Package

	|section	8

PI:	.long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
PIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000

	|xref	t_operr
	|xref	t_frcinx
	|xref	satan

	.global	sacosd
sacosd:
|--ACOS(X) = PI/2 FOR DENORMALIZED X
	fmovel		%d1,%fpcr		| ...load user's rounding mode/precision
	fmovex		PIBY2,%fp0
	bra		t_frcinx

	.global	sacos
sacos:
	fmovex		(%a0),%fp0	| ...LOAD INPUT

	movel		(%a0),%d0		| ...pack exponent with upper 16 fraction
	movew		4(%a0),%d0
	andil		#0x7FFFFFFF,%d0
	cmpil		#0x3FFF8000,%d0
	bges		ACOSBIG

|--THIS IS THE USUAL CASE, |X| < 1
|--ACOS(X) = 2 * ATAN(	SQRT( (1-X)/(1+X) )	)

	fmoves		#0x3F800000,%fp1
	faddx		%fp0,%fp1		| ...1+X
	fnegx		%fp0		| ... -X
	fadds		#0x3F800000,%fp0	| ...1-X
	fdivx		%fp1,%fp0		| ...(1-X)/(1+X)
	fsqrtx		%fp0		| ...SQRT((1-X)/(1+X))
	fmovemx	%fp0-%fp0,(%a0)	| ...overwrite input
	movel		%d1,-(%sp)	|save original users fpcr
	clrl		%d1
	bsr		satan		| ...ATAN(SQRT([1-X]/[1+X]))
	fmovel		(%sp)+,%fpcr	|restore users exceptions
	faddx		%fp0,%fp0		| ...2 * ATAN( STUFF )
	bra		t_frcinx

ACOSBIG:
	fabsx		%fp0
	fcmps		#0x3F800000,%fp0
	fbgt		t_operr		|cause an operr exception

|--|X| = 1, ACOS(X) = 0 OR PI
	movel		(%a0),%d0		| ...pack exponent with upper 16 fraction
	movew		4(%a0),%d0
	cmpl		#0,%d0		|D0 has original exponent+fraction
	bgts		ACOSP1

|--X = -1
|Returns PI and inexact exception
	fmovex		PI,%fp0
	fmovel		%d1,%FPCR
	fadds		#0x00800000,%fp0	|cause an inexact exception to be put
|					;into the 040 - will not trap until next
|					;fp inst.
	bra		t_frcinx

ACOSP1:
	fmovel		%d1,%FPCR
	fmoves		#0x00000000,%fp0
	rts				|Facos ; of +1 is exact

	|end
Commit	Line	Data
1da177e4 LT	1	\|
	2	\| sacos.sa 3.3 12/19/90
	3	\|
	4	\| Description: The entry point sAcos computes the inverse cosine of
	5	\| an input argument; sAcosd does the same except for denormalized
	6	\| input.
	7	\|
	8	\| Input: Double-extended number X in location pointed to
	9	\| by address register a0.
	10	\|
	11	\| Output: The value arccos(X) returned in floating-point register Fp0.
	12	\|
	13	\| Accuracy and Monotonicity: The returned result is within 3 ulps in
	14	\| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
	15	\| result is subsequently rounded to double precision. The
	16	\| result is provably monotonic in double precision.
	17	\|
	18	\| Speed: The program sCOS takes approximately 310 cycles.
	19	\|
	20	\| Algorithm:
	21	\|
	22	\| ACOS
	23	\| 1. If \|X\| >= 1, go to 3.
	24	\|
	25	\| 2. (\|X\| < 1) Calculate acos(X) by
	26	\| z := (1-X) / (1+X)
	27	\| acos(X) = 2 * atan( sqrt(z) ).
	28	\| Exit.
	29	\|
	30	\| 3. If \|X\| > 1, go to 5.
	31	\|
	32	\| 4. (\|X\| = 1) If X > 0, return 0. Otherwise, return Pi. Exit.
	33	\|
	34	\| 5. (\|X\| > 1) Generate an invalid operation by 0 * infinity.
	35	\| Exit.
	36	\|
	37
	38	\| Copyright (C) Motorola, Inc. 1990
	39	\| All Rights Reserved
	40	\|
	41	\| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
	42	\| The copyright notice above does not evidence any
	43	\| actual or intended publication of such source code.
	44
	45	\|SACOS idnt 2,1 \| Motorola 040 Floating Point Software Package
	46
	47	\|section 8
	48
	49	PI: .long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
	50	PIBY2: .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
	51
	52	\|xref t_operr
	53	\|xref t_frcinx
	54	\|xref satan
	55
	56	.global sacosd
	57	sacosd:
	58	\|--ACOS(X) = PI/2 FOR DENORMALIZED X
	59	fmovel %d1,%fpcr \| ...load user's rounding mode/precision
	60	fmovex PIBY2,%fp0
	61	bra t_frcinx
	62
	63	.global sacos
	64	sacos:
65	fmovex (%a0),%fp0 \| ...LOAD INPUT
66
67	movel (%a0),%d0 \| ...pack exponent with upper 16 fraction
68	movew 4(%a0),%d0
69	andil #0x7FFFFFFF,%d0
70	cmpil #0x3FFF8000,%d0
71	bges ACOSBIG
72
73	\|--THIS IS THE USUAL CASE, \|X\| < 1
74	\|--ACOS(X) = 2 * ATAN( SQRT( (1-X)/(1+X) ) )
75
76	fmoves #0x3F800000,%fp1
77	faddx %fp0,%fp1 \| ...1+X
78	fnegx %fp0 \| ... -X
79	fadds #0x3F800000,%fp0 \| ...1-X
80	fdivx %fp1,%fp0 \| ...(1-X)/(1+X)
81	fsqrtx %fp0 \| ...SQRT((1-X)/(1+X))
82	fmovemx %fp0-%fp0,(%a0) \| ...overwrite input
83	movel %d1,-(%sp) \|save original users fpcr
84	clrl %d1
85	bsr satan \| ...ATAN(SQRT([1-X]/[1+X]))
86	fmovel (%sp)+,%fpcr \|restore users exceptions
87	faddx %fp0,%fp0 \| ...2 * ATAN( STUFF )
88	bra t_frcinx
89
90	ACOSBIG:
91	fabsx %fp0
92	fcmps #0x3F800000,%fp0
93	fbgt t_operr \|cause an operr exception
94
95	\|--\|X\| = 1, ACOS(X) = 0 OR PI
96	movel (%a0),%d0 \| ...pack exponent with upper 16 fraction
97	movew 4(%a0),%d0
98	cmpl #0,%d0 \|D0 has original exponent+fraction
99	bgts ACOSP1
100
101	\|--X = -1
102	\|Returns PI and inexact exception
103	fmovex PI,%fp0
104	fmovel %d1,%FPCR
105	fadds #0x00800000,%fp0 \|cause an inexact exception to be put
106	\| ;into the 040 - will not trap until next
107	\| ;fp inst.
108	bra t_frcinx
109
110	ACOSP1:
111	fmovel %d1,%FPCR
112	fmoves #0x00000000,%fp0
113	rts \|Facos ; of +1 is exact
114
115	\|end