Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
awilliam
GitHub Repository: awilliam/linux-vfio
 Path: blob/master/arch/m68k/fpsp040/sacos.S
10817 views
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
|       For details on the license for this file, please see the

42
|       file, README, in this same directory.

43


44
|SACOS	idnt	2,1 | Motorola 040 Floating Point Software Package

45


46
	|section	8

47


48
PI:	.long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000

49
PIBY2:	.long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000

50


51
	|xref	t_operr

52
	|xref	t_frcinx

53
	|xref	satan

54


55
	.global	sacosd

56
sacosd:

57
|--ACOS(X) = PI/2 FOR DENORMALIZED X

58
	fmovel		%d1,%fpcr		| ...load user's rounding mode/precision

59
	fmovex		PIBY2,%fp0

60
	bra		t_frcinx

61


62
	.global	sacos

63
sacos:

64
	fmovex		(%a0),%fp0	| ...LOAD INPUT

65


66
	movel		(%a0),%d0		| ...pack exponent with upper 16 fraction

67
	movew		4(%a0),%d0

68
	andil		#0x7FFFFFFF,%d0

69
	cmpil		#0x3FFF8000,%d0

70
	bges		ACOSBIG

71


72
|--THIS IS THE USUAL CASE, |X| < 1

73
|--ACOS(X) = 2 * ATAN(	SQRT( (1-X)/(1+X) )	)

74


75
	fmoves		#0x3F800000,%fp1

76
	faddx		%fp0,%fp1		| ...1+X

77
	fnegx		%fp0		| ... -X

78
	fadds		#0x3F800000,%fp0	| ...1-X

79
	fdivx		%fp1,%fp0		| ...(1-X)/(1+X)

80
	fsqrtx		%fp0		| ...SQRT((1-X)/(1+X))

81
	fmovemx	%fp0-%fp0,(%a0)	| ...overwrite input

82
	movel		%d1,-(%sp)	|save original users fpcr

83
	clrl		%d1

84
	bsr		satan		| ...ATAN(SQRT([1-X]/[1+X]))

85
	fmovel		(%sp)+,%fpcr	|restore users exceptions

86
	faddx		%fp0,%fp0		| ...2 * ATAN( STUFF )

87
	bra		t_frcinx

88


89
ACOSBIG:

90
	fabsx		%fp0

91
	fcmps		#0x3F800000,%fp0

92
	fbgt		t_operr		|cause an operr exception

93


94
|--|X| = 1, ACOS(X) = 0 OR PI

95
	movel		(%a0),%d0		| ...pack exponent with upper 16 fraction

96
	movew		4(%a0),%d0

97
	cmpl		#0,%d0		|D0 has original exponent+fraction

98
	bgts		ACOSP1

99


100
|--X = -1

101
|Returns PI and inexact exception

102
	fmovex		PI,%fp0

103
	fmovel		%d1,%FPCR

104
	fadds		#0x00800000,%fp0	|cause an inexact exception to be put

105
|					;into the 040 - will not trap until next

106
|					;fp inst.

107
	bra		t_frcinx

108


109
ACOSP1:

110
	fmovel		%d1,%FPCR

111
	fmoves		#0x00000000,%fp0

112
	rts				|Facos ; of +1 is exact

113


114
	|end

115


116