m68k/fpsp040/slogn.S

30 |	Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first seven
31 |		significant bits of Y plus 2**(-7), i.e. F = 1.xxxxxx1 in base
32 |		2 where the six "x" match those of Y. Note that |Y-F| <= 2**(-7).
34 |	Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a polynomial in u,
37 |	Step 4. Reconstruct log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u)
38 |		by k*log(2) + (log(F) + poly). The values of log(F) are calculated
45 |	Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done in Step 2
47 |		k*log(2) + log(F) + poly where poly approximates log(1+u),
48 |		u = (Y-F)/F.
51 |	Note 1. There are 64 different possible values for F, thus 64 log(F)'s
52 |		need to be tabulated. Moreover, the values of 1/F are also
53 |		tabulated so that the division in (Y-F)/F can be performed by a
57 |		Y-F has to be calculated carefully when 1/2 <= X < 3/2.
241 	.set	F,FP_SCR2
242 	.set	FFRAC,F+4
343 |--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.
345 |--			 = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).
346 |--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
348 |--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO
349 |--DIVISION IS NEEDED TO CALCULATE (Y-F)/F.
351 |--GET K, Y, F, AND ADDRESS OF 1/F.
356 	lea	LOGTBL,%a0	| ...BASE ADDRESS OF 1/F AND LOG(F)
359 |--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F
363 	oril	#0x01000000,FFRAC(%a6) | ...GET F: ATTACH A 1 AT THE EIGHTH BIT
364 	movel	FFRAC(%a6),%d0	| ...READY TO GET ADDRESS OF 1/F
369 	addal	%d0,%a0		| ...A0 IS THE ADDRESS FOR 1/F
372 	movel	#0x3fff0000,F(%a6)
373 	clrl	F+8(%a6)
374 	fsubx	F(%a6),%fp0		| ...Y-F
376 |--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K
381 	fmulx	(%a0),%fp0	| ...FP0 IS U = (Y-F)/F
407 	addal	#16,%a0		| ...ADDRESS OF LOG(F)
413 	faddx	(%a0),%fp1	| ...LOG(F)+U*V*(A2+V*(A4+V*A6))
415 	faddx	%fp1,%fp0		| ...FP0 IS LOG(F) + LOG(1+U)
529 |--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z
530 |--CASE 2: 1+Z > 1, THEN K = 0  AND Y-F = (1-F) + Z
532 |--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
536 	oril	#0x01000000,FFRAC(%a6)	| ...F OBTAINED
542 	movel	#0x3fff0000,F(%a6)
543 	clrl	F+8(%a6)
544 	fsubx	F(%a6),%fp0	| ...2-F
549 	asrl	#4,%d0		| ...D0 CONTAINS DISPLACEMENT FOR 1/F
552 	faddx	%fp1,%fp0		| ...FP0 IS Y-F = (2-F)+2Z
553 	lea	LOGTBL,%a0	| ...A0 IS ADDRESS OF 1/F
560 	movel	#0x3fff0000,F(%a6)
561 	clrl	F+8(%a6)
562 	fsubx	F(%a6),%fp0		| ...1-F
568 	faddx	%fp1,%fp0		| ...FP0 IS Y-F
571 	addal	%d0,%a0		| ...A0 IS ADDRESS OF 1/F