m68k/fpsp040/satan.S

11 |	Output:	Arctan(X) returned in floating-point register Fp0.
19 |		argument X such that 1/16 < |X| < 16. For the other arguments,
23 |	Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
25 |	Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
27 |		of X with a bit-1 attached at the 6-th bit position. Define u
28 |		to be u = (X-F) / (1 + X*F).
35 |	Step 5. If |X| >= 16, go to Step 7.
37 |	Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
39 |	Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
217 	.set	X,FP_SCR1  define
218 	.set	XDCARE,X+2
219 	.set	XFRAC,X+4
220 	.set	XFRACLO,X+8
232 |--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
238 |--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
280 	movew		#0x0000,XDCARE(%a6)	| ...CLEAN UP X JUST IN CASE
283 	movel		#0x00000000,XFRACLO(%a6)	| ...LOCATION OF X IS NOW F
285 	fmovex		%fp0,%fp1			| ...FP1 IS X
286 	fmulx		X(%a6),%fp1		| ...FP1 IS X*F, NOTE THAT X*F > 0
287 	fsubx		X(%a6),%fp0		| ...FP0 IS X-F
288 	fadds		#0x3F800000,%fp1		| ...FP1 IS 1 + X*F
289 	fdivx		%fp1,%fp0			| ...FP0 IS U = (X-F)/(1+X*F)
296 	movel		%d0,%d2		| ...THE EXPO AND 16 BITS OF X
337 	faddx		ATANF(%a6),%fp0	| ...ATAN(X)
341 |--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
342 |--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
344 	bgt		ATANBIG	| ...I.E. |X| >= 16
347 |--|X| <= 1/16
348 |--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
349 |--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
350 |--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
351 |--WHERE Y = X*X, AND Z = Y*Y.
356 	fmulx		%fp0,%fp0	| ...FP0 IS Y = X*X
380 	fmulx		X(%a6),%fp0		| ...X*Y
385 	fmulx		%fp1,%fp0	| ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
388 	faddx		X(%a6),%fp0
393 |--|X| < 2^(-40), ATAN(X) = X
397 	fmovex		X(%a6),%fp0	|last inst - possible exception set
402 |--IF |X| > 2^(100), RETURN	SIGN(X)*(PI/2 - TINY). OTHERWISE,
403 |--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
407 |--APPROXIMATE ATAN(-1/X) BY
408 |--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
410 |--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
419 	fmulx		%fp0,%fp0		| ...FP0 IS Y = X'*X'
420 	fmovex		%fp1,X(%a6)		| ...X IS REALLY X'
443 	fmulx		%fp1,%fp0		| ...X'*Y*([B1+Z*(B3+Z*B5)]