Intel 80287, 80286 manual Arg

NUMERIC PROGRAMMING EXAMPLES

iAPX286 MACRO ASSEMBLER		80287
LaC	OBJ	LINE
002F	ODDS	113
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0031	09E8	115
0033	C3	116
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		".
0034		121
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0034	09E5	123
		12.
0036 'rOOFED		125
0039 2E082EOOOO		126
003E	9E	127
003F	7249	128
		12.
		130
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0041	D9C9	132
0043	13100	133
0045	7Ee7	13.
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		"3

T'I'ignometric Functions			10: 13: 51 09/25/83 PAGE
SOURCE
fstp	stCO)	Remove	a
fld 1		Return	1
rot

All ",ork is done as a sine function. By adding PI/2 to the angle

a cosine is converted to a sine. Of c:ourse the angle addition is not done to the argument but rather to the program logic control ",alues.

sine:		I	Entry		point		for sine		function
fXam			Look		at	the	parameter
fstsw	ax		Look		at	f!~am	status
f!ld	pi_quarter		Get	PI/4		",alue
sahf			CF	==	CO.	PF	::	C2. ZF	==	C3
J'	funnlJ-parameter		,Jump		if	emptlJ'		NAN.	or	infinity
Angle is unnormal. normal.		denormal.
fxch	cl,O	I	ST(1)		II:	PI/4,		steO)	angle
mov		;	Signal sine
Jpo	5 i ne_z ero_unnorma 1	; ,Jump if %ero or unnormal

ST(O) is either a normal or denormal ",alue. Both will work.

Use the fprem instruction to accuratellJ reduce the range of the gi",en

angle to within 0 and PI/4 in magnitude. If fprem cannot reduce the angle in one shot, the angle is too big to be meaningful, > 2*".62

radians. Any roundoff error in the calculation of the angle given

could completellJ change the result of this function. It is safE'st to call this verlJ rare c:ase an E'rror.

0047		144
0047	D9FB	145
		146
		147
		148
		14.
0049	93	150
		151
004A	9BDFEO	152
0040	93	153
		154
004E	F6C704	155
0051	7544	156
		157

enter _sine:

fprem
xchg	ax. b x
fstsw	ax
xchg	ax. b x
test	bh, high(mask cond2l
Jnz	angle_too_big

IReduce angle

Note that fprem will force a

Idenormal to a verlJ small unnormal Fptan of a very small unnormal will be the same very small unnormal. which is correct.

Save old status in EX

Check if reduction was complete

IQuotient in CO. C3. Cl Put new status in bx

=sin(x)sin(2*N*PI+~)

		158
		15.
		160
		161
0053	09El	162
		163
0055	OAe9	164
		165
0057	740F	166
		167
		168
		16.
		170
0059 eOE4FD		171
		172
Dose	BOeFBQ	173
		174
005F	80C74Q	175
		176
0062	BODO	177
0064	Dono	178
0066	32F8	179
		180
		181
		182
		183
		184
0068		185
0068	F6C102	186
		187
006B	7404	188
		18.
		,.0
0060	DEE9	",.2
OOoF EBCE		,.3
		,I..5'
		,.6
		,.7
0071		,.8
0071	09E4	200
0073	91	'"
		201
0074	9BDFEO	202
0077	91	203
0078	0009	204
007A	F6C540	205
0070	7514	206

Set sign flags and test for whic:h eighth of the revolution the angle fell into

Assert· -PI/4 < st(O) < PI/4

fabs		Force the al'gument positive
		cond1 bit in bx holds the sign
Dr	cLcl	Test for sine Ol' cosine function
J'	sine_select	,Jump if sine function
	This is a cosine function.	Ignol'e the origlnal sign of the angle

and add a G.uarter revolution to the octant id from the fpl'em instruction. cos (A) :::: sin(A+PI/2) and c:os( :A:) :::: cosCA)

and	ah,not high(mask condll	Turn Off sign of argument
	bh, SOH	Prepare	to add	010 to CO, C3, Cl
		status	value in	ax
	bh, high (mask con(3)	Set busy bit so carry out from
add		C3 will go into the carry flag
mov	a}, 0	Extract	carrlJ flag
rol	al,l	Put carrlJ flag in low bit
	bh, al	Add carry to CO not changing
		Cl flag

See if the argument should be revel'sed, depending on the octant in which the argument fell during fprem.

test	bh, high(mask condU		J Reverse angle if' Cl
Angle was in oct nt~ 1.3....		5,7.
fsub			Invert	sense of rotation
Jmp			o < arg	<= PI/4

Angle was in octants 0,2,4,6.

Test for a zero aT'gument since fptan will not WOT'k if st(O) :::: 0

ftst		Test for		zero	angle
xchg	ax, cx	c,c'ind3	= 1	if'	st(Q) = 0
fstsw	ax
xchg	ax, c x
fstp	st( 1)	Remove	PI/4
te~t	ch,high(mask cond3)	I If C3==1. argument is zero
Jnz	sine_argument_zero

Figure 4-7. Calculating Trigonometric Functions (Cont'd.)

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