Intel 80287, 80286 manual Coce

NUMERIC PROGRAMMING EXAMPLES

iAPX2B6 MACRO ASSEMBLER	80287 Trignometric Functions		10: 13: 51 09/25/83 PI\QE
LOC DB'"	LINE	SOURCE

301least three signUieant bits of an extended T'eal format number, The

302PLM/S6 c.alling fOTmat is:

303

tangent:

proceduT'1!

Cangle)

1'8al

external;

304

30S

declare

angle

reall

306

end

tangentl

307

TIIIO

stack

registers

are

used.

The

re5ult of

the

tangent

function is

308

30.

defined for the follollling cases:

310

angle

Tll'sult

311

31'

< 2**62

correct

value

313

vali.d 01'

unnormal

in

magnitude

314

o

o

31S

denol'mal

> 2**b2

correct

denormal

316

valid Dr

unnormal

in

magnitude

indefinite

317

NAN

NAN

318

infinity

indefinite

31'

empty

Itmptl,!

320

The tangent in.tt'uction uses the

fptan

instruction.

Four

possible

321

32.

relations

are used:

323

l..et

R a

langle

HOD PI/41

324

32.

B ...

- lor

1

depend ing

the

sign of the

angle

3.6

1 l teneR)

tan1PI/4-Rl

l/tanlR)

l/tanCPI/4-R)

327

2)

3)

4)

328

The fo1101111"g table is used to decide which relation to use depending

32.

330

on in IIIhich octant the angle fell.

331

octant

332

333

334

335

336

337

338

33.

340

,

341

34.

OOBD

343

tangent proc

344

fxam

OOBD

D9E5

34S

l.ook

at

tfie

parameter

DOOF

9BDFEO

346

fstslll

ax

get

ham

.tatus

OOC:;!:

2EDB2EOOOO

347

fld

pi_Cl.uilrte,.

I

get

PI/4

OOC7

9E

348

sahf

I

CF = co.

PF"'C2.

ZF"'C3

OOCS

72CO

34'

JC

funn\lJilrameter

350

351

or

denol'mal.

352

fxch

I

steO) ... angle. stll)

... PI/4

·OOCA D9CQ

353

coce

7i117

354

JPe

355

356Angle is either an normal 01' denormal.

357Reduce the angle to the range -PI/4 < result < PI/4.

358If fprem cannot perform this operation in one try. the magnitude of the

35. angle must be ) 2**b2. Such an angle is so large that an\! rounding

360errors could make a verI,! large difference in the reduced angle.

361It ls safest to call tllis verl,l rare case an et'ror.

36.

aOCE		363
		364	fprem		•	Quotient		in CO. C3. Cl
DOCE	D9FB	365
		366	xchg	ax. bx		Convert		denormals	into unnormals
0000	93	367				Quotient		identifies		octant
0001	9BDFEO	368	fstsbl		I
		36.	xchg	ax. bx		original		angle fell		into
OOD4	93	370				Test	for	complete	reduction
0005 F6C704		371	test	bh, highlmask	cond2)
OODS 7S0D		372	Jnz	angle_tao_big	I	Exit	if	angle bias	too big

373

374See if the angle must be reversed.

376Assert: -PI/4 < steO) < PI/4

OODA	D9El	378		fabs			I 0 <= stlO) < P1I4
		37.						C3 In bl has the sign flag
CODe	F6C702	380		test	bh. highlmask condl)		I	must be revet-sed
OODF	740E	381		J'	no_tan_reverse
		38.		Angle	fell	in octants 1.3.5.7.	Neverse	It, sUO'li'ratl; ii. i"um ~:;,;..;.
		383
OOEI	DEE9	380		fsub			I	Reverse	angle
		385
OOE3 EBIS		386		Jmp	short	do_tangent
		387	,	Angle is either zero or an unnormal.
		388
		38.
ODES		3.0	tan_zero_unnormal:
ODE' DDD9		3"			stll)		;	Remove	PI/4
		392
OOE7	7405	3.3
		3"		Angle	is an	unnormal.
		3.5

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

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