movel	d5,a6@(XFRAC+4)     negl	d2     movel	d2,a6@(ADJK)     fmovex	a6@(X),fp0     moveml	A7@+,d2-d7		|...restore registers     lea	a6@(X),a0     jra 	LOGBGN			|...begin regular log(X)HiX_not0:     clrl	d6     bfffo	d4{#0:#32},d6		|...find first 1     movel	d6,d2			|...get k     lsll	d6,d4     movel	d5,d7			|...a copy of d5     lsll	d6,d5     negl	d6     addil	#32,d6     lsrl	d6,d7     orl	d7,d4			|...(D3,d4,d5) normalized     movel	d3,a6@(X)     movel	d4,a6@(XFRAC)     movel	d5,a6@(XFRAC+4)     negl	d2     movel	d2,a6@(ADJK)     fmovex	a6@(X),fp0     moveml	A7@+,d2-d7		|...restore registers     lea	a6@(X),a0     jra 	LOGBGN			|...begin regular log(X)	.globl	__x_slogn__x_slogn:/* |--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S */	fmovex		A0@,fp0	|...lOAD INPUT	movel		#0x00000000,a6@(ADJK)LOGBGN:|--fpcr SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS|--A FINITE, NON-ZERO, NORMALIZED NUMBER.	movel	a0@,d0	movew	a0@(4),d0	movel	a0@,a6@(X)	movel	a0@(4),a6@(X+4)	movel	a0@(8),a6@(X+8)	cmpil	#0,d0		|...CHECK IF X IS NEGATIVE	jlt 	LOGNEG		|...lOG OF NEGATIVE ARGUMENT IS INVALID	cmp2l	BOUNDS1,d0	|...X IS POSITIVE, CHECK IF X IS NEAR 1	jcc 	LOGNEAR1	|...BOUNDS IS ROUGHLY [15/16, 17/16]LOGMAIN:|--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1|--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.|--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.|--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)|--			 = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).|--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING|--LOG(1+U) CAN BE VERY EFFICIENT.|--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO|--DIVISION IS NEEDED TO CALCULATE (Y-F)/F.|--GET K, Y, F, AND ADDRESS OF 1/F.	asrl	#8,d0	asrl	#8,d0		|...SHIFTED 16 BITS, BIASED EXPO. OF X	subil	#0x3FFF,d0 	|...THIS IS K	addl	a6@(ADJK),d0	|...ADJUST K, ORIGINAL INPUT MAY BE  DENORM.	lea	LOGTBL,a0 	|...BASE ADDRESS OF 1/F AND LOG(F)	fmovel	d0,fp1		|...CONVERT K TO FLOATING-POINT FORMAT|--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F	movel	#0x3FFF0000,a6@(X)	|...X IS NOW Y, I.E. 2^(-K)*X	movel	a6@(XFRAC),a6@(FFRAC)	andil	#0xFE000000,a6@(FFRAC) |...FIRST 7 BITS OF Y	oril	#0x01000000,a6@(FFRAC) |...GET F: ATTACH A 1 AT THE EIGHTH BIT	movel	a6@(FFRAC),d0	|...READY TO GET ADDRESS OF 1/F	andil	#0x7E000000,d0	asrl	#8,d0	asrl	#8,d0	asrl	#4,d0		|...SHIFTED 20, d0 IS THE DISPLACEMENT	addal	d0,a0		|...A0 IS THE ADDRESS FOR 1/F	fmovex	a6@(X),fp0	movel	#0x3fff0000,a6@(F)	clrl	a6@(F+8)	fsubx	a6@(F),fp0		|...Y-F	fmovemx fp2/fp3,a7@-	|...SAVE fp2 WHILE fp0 IS NOT READY|--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K|--REGISTERS SAVED: fpcr, FP1, FP2LP1CONT1:|--AN RE-ENTRY POINT FOR LOGNP1	fmulx	A0@,fp0	|...FP0 IS U = (Y-F)/F	fmulx	LOGOF2,fp1	|...GET K*LOG2 WHILE fp0 IS NOT READY	fmovex	fp0,fp2	fmulx	fp2,fp2		|...FP2 IS V=U*U	fmovex	fp1,a6@(KLOG2)	|...PUT K*LOG2 IN MEMEORY, FREE fp1|--LOG(1+U) IS APPROXIMATED BY|--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS|--[U + V*(A1+V*(A3+V*A5))]  +  [U*V*(A2+V*(A4+V*A6))]	fmovex	fp2,fp3	fmovex	fp2,fp1	fmuld	LOGA6,fp1	|...V*A6	fmuld	LOGA5,fp2	|...V*A5	faddd	LOGA4,fp1	|...A4+V*A6	faddd	LOGA3,fp2	|...A3+V*A5	fmulx	fp3,fp1		|...V*(A4+V*A6)	fmulx	fp3,fp2		|...V*(A3+V*A5)	faddd	LOGA2,fp1	|...A2+V*(A4+V*A6)	faddd	LOGA1,fp2	|...A1+V*(A3+V*A5)	fmulx	fp3,fp1		|...V*(A2+V*(A4+V*A6))	addal	#16,a0		|...ADDRESS OF LOG(F)	fmulx	fp3,fp2		|...V*(A1+V*(A3+V*A5)), fp3 RELEASED	fmulx	fp0,fp1		|...U*V*(A2+V*(A4+V*A6))	faddx	fp2,fp0		|...U+V*(A1+V*(A3+V*A5)), fp2 RELEASED	faddx	A0@,fp1	|...lOG(F)+U*V*(A2+V*(A4+V*A6))	fmovemx 	a7@+,fp2/fp3	|...RESTORE fp2	faddx	fp1,fp0		|...FP0 IS LOG(F) + LOG(1+U)	fmovel	d1,fpcr	faddx	a6@(KLOG2),fp0	|...FINAL ADD	jra 	__x_t_frcinxLOGNEAR1:|--REGISTERS SAVED: fpcr, FP1. FP0 CONTAINS THE INPUT.	fmovex	fp0,fp1	fsubs	one,fp1		|...FP1 IS X-1	fadds	one,fp0		|...FP0 IS X+1	faddx	fp1,fp1		|...FP1 IS 2(X-1)|--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL|--IN U, U = 2(X-1)/(X+1) = FP1/FP0LP1CONT2:|--THIS IS AN RE-ENTRY POINT FOR LOGNP1	fdivx	fp0,fp1		|...FP1 IS U	fmovemx fp2/fp3,a7@-	 |...SAVE fp2|--REGISTERS SAVED ARE NOW fpcr,FP1,FP2,FP3|--LET V=U*U, W=V*V, CALCULATE|--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY|--U + U*V*(  [B1 + W*(B3 + W*B5)]  +  [V*(B2 + W*B4)]  )	fmovex	fp1,fp0	fmulx	fp0,fp0		|...FP0 IS V	fmovex	fp1,a6@(SAVEU) 	|...STORE U IN MEMORY, FREE fp1	fmovex	fp0,fp1	fmulx	fp1,fp1		|...FP1 IS W	fmoved	LOGB5,fp3	fmoved	LOGB4,fp2	fmulx	fp1,fp3		|...w*B5	fmulx	fp1,fp2		|...w*B4	faddd	LOGB3,fp3 	|...B3+W*B5	faddd	LOGB2,fp2 	|...B2+W*B4	fmulx	fp3,fp1		|...w*(B3+W*B5), fp3 RELEASED	fmulx	fp0,fp2		|...V*(B2+W*B4)	faddd	LOGB1,fp1 	|...B1+W*(B3+W*B5)	fmulx	a6@(SAVEU),fp0 	|...FP0 IS U*V	faddx	fp2,fp1		|...B1+W*(B3+W*B5) + V*(B2+W*B4), fp2 RELEASED	fmovemx	a7@+,fp2/fp3 	|...FP2 RESTORED	fmulx	fp1,fp0		|...U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )	fmovel	d1,fpcr	faddx	a6@(SAVEU),fp0	jra 	__x_t_frcinx	rtsLOGNEG:|--REGISTERS SAVED fpcr. LOG(-VE) IS INVALID	jra 	__x_t_operr	.globl	__x_slognp1d__x_slognp1d:|--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED INPUT| Simply return the __x_denorm	jra 	__x_t_extdnrm	.globl	__x_slognp1__x_slognp1:/* |--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S */	fmovex	A0@,fp0	|...lOAD INPUT	fabsx	fp0		| test magnitude	fcmpx	LTHOLD,fp0	| compare with min threshold	fbgt	LP1REAL		| if greater, continue	fmovel	#0,fpsr		| clr N flag from compare	fmovel	d1,fpcr	fmovex	a0@,fp0	| return signed argument	jra 	__x_t_frcinxLP1REAL:	fmovex	A0@,fp0	|...lOAD INPUT	movel	#0x00000000,a6@(ADJK)	fmovex	fp0,fp1	|...FP1 IS INPUT Z	fadds	one,fp0	|...X := ROUND(1+Z)	fmovex	fp0,a6@(X)	movew	a6@(XFRAC),a6@(XDCARE)	movel	a6@(X),d0	cmpil	#0,d0	jle 	LP1NEG0	|...lOG OF ZERO OR -VE	cmp2l	BOUNDS2,d0	jcs 	LOGMAIN	|...BOUNDS2 IS [1/2,3/2]|--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z,|--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE,|--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).LP1NEAR1:|--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)	cmp2l	BOUNDS1,d0	jcs 	LP1CARELP1ONE16:|--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2)|--WHERE U = 2Z/(2+Z) = 2Z/(1+X).	faddx	fp1,fp1		|...FP1 IS 2Z	fadds	one,fp0		|...FP0 IS 1+X|--U = FP1/FP0	jra 	LP1CONT2LP1CARE:|--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE|--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST|--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2],|--THERE ARE ONLY TWO CASES.|--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z|--CASE 2: 1+Z > 1, THEN K = 0  AND Y-F = (1-F) + Z|--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF|--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.	movel	a6@(XFRAC),a6@(FFRAC)	andil	#0xFE000000,a6@(FFRAC)	oril	#0x01000000,a6@(FFRAC)	|...F OBTAINED	cmpil	#0x3FFF8000,d0	|...SEE IF 1+Z > 1	jge 	KISZEROKISNEG1:	fmoves	TWO,fp0	movel	#0x3fff0000,a6@(F)	clrl	a6@(F+8)	fsubx	a6@(F),fp0	|...2-F	movel	a6@(FFRAC),d0	andil	#0x7E000000,d0	asrl	#8,d0	asrl	#8,d0	asrl	#4,d0		|...D0 CONTAINS DISPLACEMENT FOR 1/F	faddx	fp1,fp1		|...GET 2Z	fmovemx fp2/fp3,a7@-	|...SAVE fp2	faddx	fp1,fp0		|...FP0 IS Y-F = (2-F)+2Z	lea	LOGTBL,a0	|...A0 IS ADDRESS OF 1/F	addal	d0,a0	fmoves	negone,fp1	|...FP1 IS K = -1	jra 	LP1CONT1KISZERO:	fmoves	one,fp0	movel	#0x3fff0000,a6@(F)	clrl	a6@(F+8)	fsubx	a6@(F),fp0		|...1-F	movel	a6@(FFRAC),d0	andil	#0x7E000000,d0	asrl	#8,d0	asrl	#8,d0	asrl	#4,d0	faddx	fp1,fp0		|...FP0 IS Y-F	fmovemx fp2/fp3,a7@-	|...FP2 SAVED	lea	LOGTBL,a0	addal	d0,a0	 	|...A0 IS ADDRESS OF 1/F	fmoves	zero,fp1	|...FP1 IS K = 0	jra 	LP1CONT1LP1NEG0:|--fpcr SAVED. D0 IS X IN COMPACT FORM.	cmpil	#0,d0	jlt 	LP1NEGLP1ZERO:	fmoves	negone,fp0	fmovel	d1,fpcr	jra  __x_t_dzLP1NEG:	fmoves	zero,fp0	fmovel	d1,fpcr	jra 	__x_t_operr|	end