slogn.sa revision 1.2 
1*	MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
2*	M68000 Hi-Performance Microprocessor Division
3*	M68040 Software Package 
4*
5*	M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
6*	All rights reserved.
7*
8*	THE SOFTWARE is provided on an "AS IS" basis and without warranty.
9*	To the maximum extent permitted by applicable law,
10*	MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
11*	INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
12*	PARTICULAR PURPOSE and any warranty against infringement with
13*	regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
14*	and any accompanying written materials. 
15*
16*	To the maximum extent permitted by applicable law,
17*	IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
18*	(INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
19*	PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
20*	OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
21*	SOFTWARE.  Motorola assumes no responsibility for the maintenance
22*	and support of the SOFTWARE.  
23*
24*	You are hereby granted a copyright license to use, modify, and
25*	distribute the SOFTWARE so long as this entire notice is retained
26*	without alteration in any modified and/or redistributed versions,
27*	and that such modified versions are clearly identified as such.
28*	No licenses are granted by implication, estoppel or otherwise
29*	under any patents or trademarks of Motorola, Inc.
30
31*
32*	slogn.sa 3.1 12/10/90
33*
34*	slogn computes the natural logarithm of an
35*	input value. slognd does the same except the input value is a
36*	denormalized number. slognp1 computes log(1+X), and slognp1d
37*	computes log(1+X) for denormalized X.
38*
39*	Input: Double-extended value in memory location pointed to by address
40*		register a0.
41*
42*	Output:	log(X) or log(1+X) returned in floating-point register Fp0.
43*
44*	Accuracy and Monotonicity: The returned result is within 2 ulps in
45*		64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
46*		result is subsequently rounded to double precision. The 
47*		result is provably monotonic in double precision.
48*
49*	Speed: The program slogn takes approximately 190 cycles for input 
50*		argument X such that |X-1| >= 1/16, which is the the usual 
51*		situation. For those arguments, slognp1 takes approximately
52*		 210 cycles. For the less common arguments, the program will
53*		 run no worse than 10% slower.
54*
55*	Algorithm:
56*	LOGN:
57*	Step 1. If |X-1| < 1/16, approximate log(X) by an odd polynomial in
58*		u, where u = 2(X-1)/(X+1). Otherwise, move on to Step 2.
59*
60*	Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first seven
61*		significant bits of Y plus 2**(-7), i.e. F = 1.xxxxxx1 in base
62*		2 where the six "x" match those of Y. Note that |Y-F| <= 2**(-7).
63*
64*	Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a polynomial in u,
65*		log(1+u) = poly.
66*
67*	Step 4. Reconstruct log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u)
68*		by k*log(2) + (log(F) + poly). The values of log(F) are calculated
69*		beforehand and stored in the program.
70*
71*	lognp1:
72*	Step 1: If |X| < 1/16, approximate log(1+X) by an odd polynomial in
73*		u where u = 2X/(2+X). Otherwise, move on to Step 2.
74*
75*	Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done in Step 2
76*		of the algorithm for LOGN and compute log(1+X) as
77*		k*log(2) + log(F) + poly where poly approximates log(1+u),
78*		u = (Y-F)/F. 
79*
80*	Implementation Notes:
81*	Note 1. There are 64 different possible values for F, thus 64 log(F)'s
82*		need to be tabulated. Moreover, the values of 1/F are also 
83*		tabulated so that the division in (Y-F)/F can be performed by a
84*		multiplication.
85*
86*	Note 2. In Step 2 of lognp1, in order to preserved accuracy, the value
87*		Y-F has to be calculated carefully when 1/2 <= X < 3/2. 
88*
89*	Note 3. To fully exploit the pipeline, polynomials are usually separated
90*		into two parts evaluated independently before being added up.
91*	
92
93slogn	IDNT	2,1 Motorola 040 Floating Point Software Package
94
95	section	8
96
97	include fpsp.h
98
99BOUNDS1  DC.L $3FFEF07D,$3FFF8841
100BOUNDS2  DC.L $3FFE8000,$3FFFC000
101
102LOGOF2	DC.L $3FFE0000,$B17217F7,$D1CF79AC,$00000000
103
104one	DC.L $3F800000
105zero	DC.L $00000000
106infty	DC.L $7F800000
107negone	DC.L $BF800000
108
109LOGA6	DC.L $3FC2499A,$B5E4040B
110LOGA5	DC.L $BFC555B5,$848CB7DB
111
112LOGA4	DC.L $3FC99999,$987D8730
113LOGA3	DC.L $BFCFFFFF,$FF6F7E97
114
115LOGA2	DC.L $3FD55555,$555555A4
116LOGA1	DC.L $BFE00000,$00000008
117
118LOGB5	DC.L $3F175496,$ADD7DAD6
119LOGB4	DC.L $3F3C71C2,$FE80C7E0
120
121LOGB3	DC.L $3F624924,$928BCCFF
122LOGB2	DC.L $3F899999,$999995EC
123
124LOGB1	DC.L $3FB55555,$55555555
125TWO	DC.L $40000000,$00000000
126
127LTHOLD	DC.L $3f990000,$80000000,$00000000,$00000000
128
129LOGTBL:
130	DC.L  $3FFE0000,$FE03F80F,$E03F80FE,$00000000
131	DC.L  $3FF70000,$FF015358,$833C47E2,$00000000
132	DC.L  $3FFE0000,$FA232CF2,$52138AC0,$00000000
133	DC.L  $3FF90000,$BDC8D83E,$AD88D549,$00000000
134	DC.L  $3FFE0000,$F6603D98,$0F6603DA,$00000000
135	DC.L  $3FFA0000,$9CF43DCF,$F5EAFD48,$00000000
136	DC.L  $3FFE0000,$F2B9D648,$0F2B9D65,$00000000
137	DC.L  $3FFA0000,$DA16EB88,$CB8DF614,$00000000
138	DC.L  $3FFE0000,$EF2EB71F,$C4345238,$00000000
139	DC.L  $3FFB0000,$8B29B775,$1BD70743,$00000000
140	DC.L  $3FFE0000,$EBBDB2A5,$C1619C8C,$00000000
141	DC.L  $3FFB0000,$A8D839F8,$30C1FB49,$00000000
142	DC.L  $3FFE0000,$E865AC7B,$7603A197,$00000000
143	DC.L  $3FFB0000,$C61A2EB1,$8CD907AD,$00000000
144	DC.L  $3FFE0000,$E525982A,$F70C880E,$00000000
145	DC.L  $3FFB0000,$E2F2A47A,$DE3A18AF,$00000000
146	DC.L  $3FFE0000,$E1FC780E,$1FC780E2,$00000000
147	DC.L  $3FFB0000,$FF64898E,$DF55D551,$00000000
148	DC.L  $3FFE0000,$DEE95C4C,$A037BA57,$00000000
149	DC.L  $3FFC0000,$8DB956A9,$7B3D0148,$00000000
150	DC.L  $3FFE0000,$DBEB61EE,$D19C5958,$00000000
151	DC.L  $3FFC0000,$9B8FE100,$F47BA1DE,$00000000
152	DC.L  $3FFE0000,$D901B203,$6406C80E,$00000000
153	DC.L  $3FFC0000,$A9372F1D,$0DA1BD17,$00000000
154	DC.L  $3FFE0000,$D62B80D6,$2B80D62C,$00000000
155	DC.L  $3FFC0000,$B6B07F38,$CE90E46B,$00000000
156	DC.L  $3FFE0000,$D3680D36,$80D3680D,$00000000
157	DC.L  $3FFC0000,$C3FD0329,$06488481,$00000000
158	DC.L  $3FFE0000,$D0B69FCB,$D2580D0B,$00000000
159	DC.L  $3FFC0000,$D11DE0FF,$15AB18CA,$00000000
160	DC.L  $3FFE0000,$CE168A77,$25080CE1,$00000000
161	DC.L  $3FFC0000,$DE1433A1,$6C66B150,$00000000
162	DC.L  $3FFE0000,$CB8727C0,$65C393E0,$00000000
163	DC.L  $3FFC0000,$EAE10B5A,$7DDC8ADD,$00000000
164	DC.L  $3FFE0000,$C907DA4E,$871146AD,$00000000
165	DC.L  $3FFC0000,$F7856E5E,$E2C9B291,$00000000
166	DC.L  $3FFE0000,$C6980C69,$80C6980C,$00000000
167	DC.L  $3FFD0000,$82012CA5,$A68206D7,$00000000
168	DC.L  $3FFE0000,$C4372F85,$5D824CA6,$00000000
169	DC.L  $3FFD0000,$882C5FCD,$7256A8C5,$00000000
170	DC.L  $3FFE0000,$C1E4BBD5,$95F6E947,$00000000
171	DC.L  $3FFD0000,$8E44C60B,$4CCFD7DE,$00000000
172	DC.L  $3FFE0000,$BFA02FE8,$0BFA02FF,$00000000
173	DC.L  $3FFD0000,$944AD09E,$F4351AF6,$00000000
174	DC.L  $3FFE0000,$BD691047,$07661AA3,$00000000
175	DC.L  $3FFD0000,$9A3EECD4,$C3EAA6B2,$00000000
176	DC.L  $3FFE0000,$BB3EE721,$A54D880C,$00000000
177	DC.L  $3FFD0000,$A0218434,$353F1DE8,$00000000
178	DC.L  $3FFE0000,$B92143FA,$36F5E02E,$00000000
179	DC.L  $3FFD0000,$A5F2FCAB,$BBC506DA,$00000000
180	DC.L  $3FFE0000,$B70FBB5A,$19BE3659,$00000000
181	DC.L  $3FFD0000,$ABB3B8BA,$2AD362A5,$00000000
182	DC.L  $3FFE0000,$B509E68A,$9B94821F,$00000000
183	DC.L  $3FFD0000,$B1641795,$CE3CA97B,$00000000
184	DC.L  $3FFE0000,$B30F6352,$8917C80B,$00000000
185	DC.L  $3FFD0000,$B7047551,$5D0F1C61,$00000000
186	DC.L  $3FFE0000,$B11FD3B8,$0B11FD3C,$00000000
187	DC.L  $3FFD0000,$BC952AFE,$EA3D13E1,$00000000
188	DC.L  $3FFE0000,$AF3ADDC6,$80AF3ADE,$00000000
189	DC.L  $3FFD0000,$C2168ED0,$F458BA4A,$00000000
190	DC.L  $3FFE0000,$AD602B58,$0AD602B6,$00000000
191	DC.L  $3FFD0000,$C788F439,$B3163BF1,$00000000
192	DC.L  $3FFE0000,$AB8F69E2,$8359CD11,$00000000
193	DC.L  $3FFD0000,$CCECAC08,$BF04565D,$00000000
194	DC.L  $3FFE0000,$A9C84A47,$A07F5638,$00000000
195	DC.L  $3FFD0000,$D2420487,$2DD85160,$00000000
196	DC.L  $3FFE0000,$A80A80A8,$0A80A80B,$00000000
197	DC.L  $3FFD0000,$D7894992,$3BC3588A,$00000000
198	DC.L  $3FFE0000,$A655C439,$2D7B73A8,$00000000
199	DC.L  $3FFD0000,$DCC2C4B4,$9887DACC,$00000000
200	DC.L  $3FFE0000,$A4A9CF1D,$96833751,$00000000
201	DC.L  $3FFD0000,$E1EEBD3E,$6D6A6B9E,$00000000
202	DC.L  $3FFE0000,$A3065E3F,$AE7CD0E0,$00000000
203	DC.L  $3FFD0000,$E70D785C,$2F9F5BDC,$00000000
204	DC.L  $3FFE0000,$A16B312E,$A8FC377D,$00000000
205	DC.L  $3FFD0000,$EC1F392C,$5179F283,$00000000
206	DC.L  $3FFE0000,$9FD809FD,$809FD80A,$00000000
207	DC.L  $3FFD0000,$F12440D3,$E36130E6,$00000000
208	DC.L  $3FFE0000,$9E4CAD23,$DD5F3A20,$00000000
209	DC.L  $3FFD0000,$F61CCE92,$346600BB,$00000000
210	DC.L  $3FFE0000,$9CC8E160,$C3FB19B9,$00000000
211	DC.L  $3FFD0000,$FB091FD3,$8145630A,$00000000
212	DC.L  $3FFE0000,$9B4C6F9E,$F03A3CAA,$00000000
213	DC.L  $3FFD0000,$FFE97042,$BFA4C2AD,$00000000
214	DC.L  $3FFE0000,$99D722DA,$BDE58F06,$00000000
215	DC.L  $3FFE0000,$825EFCED,$49369330,$00000000
216	DC.L  $3FFE0000,$9868C809,$868C8098,$00000000
217	DC.L  $3FFE0000,$84C37A7A,$B9A905C9,$00000000
218	DC.L  $3FFE0000,$97012E02,$5C04B809,$00000000
219	DC.L  $3FFE0000,$87224C2E,$8E645FB7,$00000000
220	DC.L  $3FFE0000,$95A02568,$095A0257,$00000000
221	DC.L  $3FFE0000,$897B8CAC,$9F7DE298,$00000000
222	DC.L  $3FFE0000,$94458094,$45809446,$00000000
223	DC.L  $3FFE0000,$8BCF55DE,$C4CD05FE,$00000000
224	DC.L  $3FFE0000,$92F11384,$0497889C,$00000000
225	DC.L  $3FFE0000,$8E1DC0FB,$89E125E5,$00000000
226	DC.L  $3FFE0000,$91A2B3C4,$D5E6F809,$00000000
227	DC.L  $3FFE0000,$9066E68C,$955B6C9B,$00000000
228	DC.L  $3FFE0000,$905A3863,$3E06C43B,$00000000
229	DC.L  $3FFE0000,$92AADE74,$C7BE59E0,$00000000
230	DC.L  $3FFE0000,$8F1779D9,$FDC3A219,$00000000
231	DC.L  $3FFE0000,$94E9BFF6,$15845643,$00000000
232	DC.L  $3FFE0000,$8DDA5202,$37694809,$00000000
233	DC.L  $3FFE0000,$9723A1B7,$20134203,$00000000
234	DC.L  $3FFE0000,$8CA29C04,$6514E023,$00000000
235	DC.L  $3FFE0000,$995899C8,$90EB8990,$00000000
236	DC.L  $3FFE0000,$8B70344A,$139BC75A,$00000000
237	DC.L  $3FFE0000,$9B88BDAA,$3A3DAE2F,$00000000
238	DC.L  $3FFE0000,$8A42F870,$5669DB46,$00000000
239	DC.L  $3FFE0000,$9DB4224F,$FFE1157C,$00000000
240	DC.L  $3FFE0000,$891AC73A,$E9819B50,$00000000
241	DC.L  $3FFE0000,$9FDADC26,$8B7A12DA,$00000000
242	DC.L  $3FFE0000,$87F78087,$F78087F8,$00000000
243	DC.L  $3FFE0000,$A1FCFF17,$CE733BD4,$00000000
244	DC.L  $3FFE0000,$86D90544,$7A34ACC6,$00000000
245	DC.L  $3FFE0000,$A41A9E8F,$5446FB9F,$00000000
246	DC.L  $3FFE0000,$85BF3761,$2CEE3C9B,$00000000
247	DC.L  $3FFE0000,$A633CD7E,$6771CD8B,$00000000
248	DC.L  $3FFE0000,$84A9F9C8,$084A9F9D,$00000000
249	DC.L  $3FFE0000,$A8489E60,$0B435A5E,$00000000
250	DC.L  $3FFE0000,$83993052,$3FBE3368,$00000000
251	DC.L  $3FFE0000,$AA59233C,$CCA4BD49,$00000000
252	DC.L  $3FFE0000,$828CBFBE,$B9A020A3,$00000000
253	DC.L  $3FFE0000,$AC656DAE,$6BCC4985,$00000000
254	DC.L  $3FFE0000,$81848DA8,$FAF0D277,$00000000
255	DC.L  $3FFE0000,$AE6D8EE3,$60BB2468,$00000000
256	DC.L  $3FFE0000,$80808080,$80808081,$00000000
257	DC.L  $3FFE0000,$B07197A2,$3C46C654,$00000000
258
259ADJK	equ	L_SCR1
260
261X	equ	FP_SCR1
262XDCARE	equ	X+2
263XFRAC	equ	X+4
264
265F	equ	FP_SCR2
266FFRAC	equ	F+4
267
268KLOG2	equ	FP_SCR3
269
270SAVEU	equ	FP_SCR4
271
272	xref	t_frcinx
273	xref	t_extdnrm
274	xref	t_operr
275	xref	t_dz
276
277	xdef	slognd
278slognd:
279*--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INPUT
280
281	MOVE.L		#-100,ADJK(a6)	...INPUT = 2^(ADJK) * FP0
282
283*----normalize the input value by left shifting k bits (k to be determined
284*----below), adjusting exponent and storing -k to  ADJK
285*----the value TWOTO100 is no longer needed.
286*----Note that this code assumes the denormalized input is NON-ZERO.
287
288     MoveM.L	D2-D7,-(A7)		...save some registers 
289     Clr.L	D3			...D3 is exponent of smallest norm. #
290     Move.L	4(A0),D4
291     Move.L	8(A0),D5		...(D4,D5) is (Hi_X,Lo_X)
292     Clr.L	D2			...D2 used for holding K
293
294     Tst.L	D4
295     BNE.B	HiX_not0
296
297HiX_0:
298     Move.L	D5,D4
299     Clr.L	D5
300     Move.L	#32,D2
301     Clr.L	D6
302     BFFFO      D4{0:32},D6
303     LSL.L      D6,D4
304     Add.L	D6,D2			...(D3,D4,D5) is normalized
305
306     Move.L	D3,X(a6)
307     Move.L	D4,XFRAC(a6)
308     Move.L	D5,XFRAC+4(a6)
309     Neg.L	D2
310     Move.L	D2,ADJK(a6)
311     FMove.X	X(a6),FP0
312     MoveM.L	(A7)+,D2-D7		...restore registers
313     LEA	X(a6),A0
314     Bra.B	LOGBGN			...begin regular log(X)
315
316
317HiX_not0:
318     Clr.L	D6
319     BFFFO	D4{0:32},D6		...find first 1
320     Move.L	D6,D2			...get k
321     LSL.L	D6,D4
322     Move.L	D5,D7			...a copy of D5
323     LSL.L	D6,D5
324     Neg.L	D6
325     AddI.L	#32,D6
326     LSR.L	D6,D7
327     Or.L	D7,D4			...(D3,D4,D5) normalized
328
329     Move.L	D3,X(a6)
330     Move.L	D4,XFRAC(a6)
331     Move.L	D5,XFRAC+4(a6)
332     Neg.L	D2
333     Move.L	D2,ADJK(a6)
334     FMove.X	X(a6),FP0
335     MoveM.L	(A7)+,D2-D7		...restore registers
336     LEA	X(a6),A0
337     Bra.B	LOGBGN			...begin regular log(X)
338
339
340	xdef	slogn
341slogn:
342*--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S
343
344	FMOVE.X		(A0),FP0	...LOAD INPUT
345	CLR.L		ADJK(a6)
346
347LOGBGN:
348*--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS
349*--A FINITE, NON-ZERO, NORMALIZED NUMBER.
350
351	move.l	(a0),d0
352	move.w	4(a0),d0
353
354	move.l	(a0),X(a6)
355	move.l	4(a0),X+4(a6)
356	move.l	8(a0),X+8(a6)
357
358	TST.L	D0		...CHECK IF X IS NEGATIVE
359	BLT.W	LOGNEG		...LOG OF NEGATIVE ARGUMENT IS INVALID
360	CMP2.L	BOUNDS1,D0	...X IS POSITIVE, CHECK IF X IS NEAR 1
361	BCC.W	LOGNEAR1	...BOUNDS IS ROUGHLY [15/16, 17/16]
362
363LOGMAIN:
364*--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1
365
366*--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.
367*--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.
368*--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)
369*--			 = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).
370*--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
371*--LOG(1+U) CAN BE VERY EFFICIENT.
372*--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO
373*--DIVISION IS NEEDED TO CALCULATE (Y-F)/F. 
374
375*--GET K, Y, F, AND ADDRESS OF 1/F.
376	ASR.L	#8,D0
377	ASR.L	#8,D0		...SHIFTED 16 BITS, BIASED EXPO. OF X
378	SUBI.L	#$3FFF,D0 	...THIS IS K
379	ADD.L	ADJK(a6),D0	...ADJUST K, ORIGINAL INPUT MAY BE  DENORM.
380	LEA	LOGTBL,A0 	...BASE ADDRESS OF 1/F AND LOG(F)
381	FMOVE.L	D0,FP1		...CONVERT K TO FLOATING-POINT FORMAT
382
383*--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F
384	MOVE.L	#$3FFF0000,X(a6)	...X IS NOW Y, I.E. 2^(-K)*X
385	MOVE.L	XFRAC(a6),FFRAC(a6)
386	ANDI.L	#$FE000000,FFRAC(a6) ...FIRST 7 BITS OF Y
387	ORI.L	#$01000000,FFRAC(a6) ...GET F: ATTACH A 1 AT THE EIGHTH BIT
388	MOVE.L	FFRAC(a6),D0	...READY TO GET ADDRESS OF 1/F
389	ANDI.L	#$7E000000,D0	
390	ASR.L	#8,D0
391	ASR.L	#8,D0
392	ASR.L	#4,D0		...SHIFTED 20, D0 IS THE DISPLACEMENT
393	ADDA.L	D0,A0		...A0 IS THE ADDRESS FOR 1/F
394
395	FMOVE.X	X(a6),FP0
396	move.l	#$3fff0000,F(a6)
397	clr.l	F+8(a6)
398	FSUB.X	F(a6),FP0		...Y-F
399	FMOVEm.X FP2/fp3,-(sp)	...SAVE FP2 WHILE FP0 IS NOT READY
400*--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K
401*--REGISTERS SAVED: FPCR, FP1, FP2
402
403LP1CONT1:
404*--AN RE-ENTRY POINT FOR LOGNP1
405	FMUL.X	(A0),FP0	...FP0 IS U = (Y-F)/F
406	FMUL.X	LOGOF2,FP1	...GET K*LOG2 WHILE FP0 IS NOT READY
407	FMOVE.X	FP0,FP2
408	FMUL.X	FP2,FP2		...FP2 IS V=U*U
409	FMOVE.X	FP1,KLOG2(a6)	...PUT K*LOG2 IN MEMEORY, FREE FP1
410
411*--LOG(1+U) IS APPROXIMATED BY
412*--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS
413*--[U + V*(A1+V*(A3+V*A5))]  +  [U*V*(A2+V*(A4+V*A6))]
414
415	FMOVE.X	FP2,FP3
416	FMOVE.X	FP2,FP1	
417
418	FMUL.D	LOGA6,FP1	...V*A6
419	FMUL.D	LOGA5,FP2	...V*A5
420
421	FADD.D	LOGA4,FP1	...A4+V*A6
422	FADD.D	LOGA3,FP2	...A3+V*A5
423
424	FMUL.X	FP3,FP1		...V*(A4+V*A6)
425	FMUL.X	FP3,FP2		...V*(A3+V*A5)
426
427	FADD.D	LOGA2,FP1	...A2+V*(A4+V*A6)
428	FADD.D	LOGA1,FP2	...A1+V*(A3+V*A5)
429
430	FMUL.X	FP3,FP1		...V*(A2+V*(A4+V*A6))
431	ADDA.L	#16,A0		...ADDRESS OF LOG(F)
432	FMUL.X	FP3,FP2		...V*(A1+V*(A3+V*A5)), FP3 RELEASED
433
434	FMUL.X	FP0,FP1		...U*V*(A2+V*(A4+V*A6))
435	FADD.X	FP2,FP0		...U+V*(A1+V*(A3+V*A5)), FP2 RELEASED
436
437	FADD.X	(A0),FP1	...LOG(F)+U*V*(A2+V*(A4+V*A6))
438	FMOVEm.X  (sp)+,FP2/fp3	...RESTORE FP2
439	FADD.X	FP1,FP0		...FP0 IS LOG(F) + LOG(1+U)
440
441	fmove.l	d1,fpcr
442	FADD.X	KLOG2(a6),FP0	...FINAL ADD
443	bra	t_frcinx
444
445
446LOGNEAR1:
447*--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS THE INPUT.
448	FMOVE.X	FP0,FP1
449	FSUB.S	one,FP1		...FP1 IS X-1
450	FADD.S	one,FP0		...FP0 IS X+1
451	FADD.X	FP1,FP1		...FP1 IS 2(X-1)
452*--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL
453*--IN U, U = 2(X-1)/(X+1) = FP1/FP0
454
455LP1CONT2:
456*--THIS IS AN RE-ENTRY POINT FOR LOGNP1
457	FDIV.X	FP0,FP1		...FP1 IS U
458	FMOVEm.X FP2/fp3,-(sp)	 ...SAVE FP2
459*--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3
460*--LET V=U*U, W=V*V, CALCULATE
461*--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY
462*--U + U*V*(  [B1 + W*(B3 + W*B5)]  +  [V*(B2 + W*B4)]  )
463	FMOVE.X	FP1,FP0
464	FMUL.X	FP0,FP0	...FP0 IS V
465	FMOVE.X	FP1,SAVEU(a6) ...STORE U IN MEMORY, FREE FP1
466	FMOVE.X	FP0,FP1	
467	FMUL.X	FP1,FP1	...FP1 IS W
468
469	FMOVE.D	LOGB5,FP3
470	FMOVE.D	LOGB4,FP2
471
472	FMUL.X	FP1,FP3	...W*B5
473	FMUL.X	FP1,FP2	...W*B4
474
475	FADD.D	LOGB3,FP3 ...B3+W*B5
476	FADD.D	LOGB2,FP2 ...B2+W*B4
477
478	FMUL.X	FP3,FP1	...W*(B3+W*B5), FP3 RELEASED
479
480	FMUL.X	FP0,FP2	...V*(B2+W*B4)
481
482	FADD.D	LOGB1,FP1 ...B1+W*(B3+W*B5)
483	FMUL.X	SAVEU(a6),FP0 ...FP0 IS U*V
484
485	FADD.X	FP2,FP1	...B1+W*(B3+W*B5) + V*(B2+W*B4), FP2 RELEASED
486	FMOVEm.X (sp)+,FP2/fp3 ...FP2 RESTORED
487
488	FMUL.X	FP1,FP0	...U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )
489
490	fmove.l	d1,fpcr
491	FADD.X	SAVEU(a6),FP0		
492	bra	t_frcinx
493	rts
494
495LOGNEG:
496*--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID
497	bra	t_operr
498
499	xdef	slognp1d
500slognp1d:
501*--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED INPUT
502* Simply return the denorm
503
504	bra	t_extdnrm
505
506	xdef	slognp1
507slognp1:
508*--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S
509
510	FMOVE.X	(A0),FP0	...LOAD INPUT
511	fabs.x	fp0		;test magnitude
512	fcmp.x	LTHOLD,fp0	;compare with min threshold
513	fbgt.w	LP1REAL		;if greater, continue
514	fmove.l	#0,fpsr		;clr N flag from compare
515	fmove.l	d1,fpcr
516	fmove.x	(a0),fp0	;return signed argument
517	bra	t_frcinx
518
519LP1REAL:
520	FMOVE.X	(A0),FP0	...LOAD INPUT
521	CLR.L	ADJK(a6)
522	FMOVE.X	FP0,FP1	...FP1 IS INPUT Z
523	FADD.S	one,FP0	...X := ROUND(1+Z)
524	FMOVE.X	FP0,X(a6)
525	MOVE.W	XFRAC(a6),XDCARE(a6)
526	MOVE.L	X(a6),D0
527	TST.L	D0
528	BLE.W	LP1NEG0	...LOG OF ZERO OR -VE
529	CMP2.L	BOUNDS2,D0
530	BCS.W	LOGMAIN	...BOUNDS2 IS [1/2,3/2]
531*--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z,
532*--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE,
533*--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).
534
535LP1NEAR1:
536*--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)
537	CMP2.L	BOUNDS1,D0
538	BCS.B	LP1CARE
539
540LP1ONE16:
541*--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2)
542*--WHERE U = 2Z/(2+Z) = 2Z/(1+X).
543	FADD.X	FP1,FP1	...FP1 IS 2Z
544	FADD.S	one,FP0	...FP0 IS 1+X
545*--U = FP1/FP0
546	BRA.W	LP1CONT2
547
548LP1CARE:
549*--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE
550*--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST
551*--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2],
552*--THERE ARE ONLY TWO CASES.
553*--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z
554*--CASE 2: 1+Z > 1, THEN K = 0  AND Y-F = (1-F) + Z
555*--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF
556*--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
557
558	MOVE.L	XFRAC(a6),FFRAC(a6)
559	ANDI.L	#$FE000000,FFRAC(a6)
560	ORI.L	#$01000000,FFRAC(a6)	...F OBTAINED
561	CMPI.L	#$3FFF8000,D0	...SEE IF 1+Z > 1
562	BGE.B	KISZERO
563
564KISNEG1:
565	FMOVE.S	TWO,FP0
566	move.l	#$3fff0000,F(a6)
567	clr.l	F+8(a6)
568	FSUB.X	F(a6),FP0	...2-F
569	MOVE.L	FFRAC(a6),D0
570	ANDI.L	#$7E000000,D0
571	ASR.L	#8,D0
572	ASR.L	#8,D0
573	ASR.L	#4,D0		...D0 CONTAINS DISPLACEMENT FOR 1/F
574	FADD.X	FP1,FP1		...GET 2Z
575	FMOVEm.X FP2/fp3,-(sp)	...SAVE FP2 
576	FADD.X	FP1,FP0		...FP0 IS Y-F = (2-F)+2Z
577	LEA	LOGTBL,A0	...A0 IS ADDRESS OF 1/F
578	ADDA.L	D0,A0
579	FMOVE.S	negone,FP1	...FP1 IS K = -1
580	BRA.W	LP1CONT1
581
582KISZERO:
583	FMOVE.S	one,FP0
584	move.l	#$3fff0000,F(a6)
585	clr.l	F+8(a6)
586	FSUB.X	F(a6),FP0		...1-F
587	MOVE.L	FFRAC(a6),D0
588	ANDI.L	#$7E000000,D0
589	ASR.L	#8,D0
590	ASR.L	#8,D0
591	ASR.L	#4,D0
592	FADD.X	FP1,FP0		...FP0 IS Y-F
593	FMOVEm.X FP2/fp3,-(sp)	...FP2 SAVED
594	LEA	LOGTBL,A0
595	ADDA.L	D0,A0	 	...A0 IS ADDRESS OF 1/F
596	FMOVE.S	zero,FP1	...FP1 IS K = 0
597	BRA.W	LP1CONT1
598
599LP1NEG0:
600*--FPCR SAVED. D0 IS X IN COMPACT FORM.
601	TST.L	D0
602	BLT.B	LP1NEG
603LP1ZERO:
604	FMOVE.S	negone,FP0
605
606	fmove.l	d1,fpcr
607	bra t_dz
608
609LP1NEG:
610	FMOVE.S	zero,FP0
611
612	fmove.l	d1,fpcr
613	bra	t_operr
614
615	end
616