Annotation of sys/arch/m68k/fpsp/slogn.sa, Revision 1.1.1.1
1.1 nbrk 1: * $OpenBSD: slogn.sa,v 1.3 2003/11/07 10:36:10 miod Exp $
2: * $NetBSD: slogn.sa,v 1.3 1994/10/26 07:49:54 cgd Exp $
3:
4: * MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
5: * M68000 Hi-Performance Microprocessor Division
6: * M68040 Software Package
7: *
8: * M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
9: * All rights reserved.
10: *
11: * THE SOFTWARE is provided on an "AS IS" basis and without warranty.
12: * To the maximum extent permitted by applicable law,
13: * MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
14: * INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
15: * PARTICULAR PURPOSE and any warranty against infringement with
16: * regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
17: * and any accompanying written materials.
18: *
19: * To the maximum extent permitted by applicable law,
20: * IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
21: * (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
22: * PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
23: * OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
24: * SOFTWARE. Motorola assumes no responsibility for the maintenance
25: * and support of the SOFTWARE.
26: *
27: * You are hereby granted a copyright license to use, modify, and
28: * distribute the SOFTWARE so long as this entire notice is retained
29: * without alteration in any modified and/or redistributed versions,
30: * and that such modified versions are clearly identified as such.
31: * No licenses are granted by implication, estoppel or otherwise
32: * under any patents or trademarks of Motorola, Inc.
33:
34: *
35: * slogn.sa 3.1 12/10/90
36: *
37: * slogn computes the natural logarithm of an
38: * input value. slognd does the same except the input value is a
39: * denormalized number. slognp1 computes log(1+X), and slognp1d
40: * computes log(1+X) for denormalized X.
41: *
42: * Input: Double-extended value in memory location pointed to by address
43: * register a0.
44: *
45: * Output: log(X) or log(1+X) returned in floating-point register Fp0.
46: *
47: * Accuracy and Monotonicity: The returned result is within 2 ulps in
48: * 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
49: * result is subsequently rounded to double precision. The
50: * result is provably monotonic in double precision.
51: *
52: * Speed: The program slogn takes approximately 190 cycles for input
53: * argument X such that |X-1| >= 1/16, which is the usual
54: * situation. For those arguments, slognp1 takes approximately
55: * 210 cycles. For the less common arguments, the program will
56: * run no worse than 10% slower.
57: *
58: * Algorithm:
59: * LOGN:
60: * Step 1. If |X-1| < 1/16, approximate log(X) by an odd polynomial in
61: * u, where u = 2(X-1)/(X+1). Otherwise, move on to Step 2.
62: *
63: * Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first seven
64: * significant bits of Y plus 2**(-7), i.e. F = 1.xxxxxx1 in base
65: * 2 where the six "x" match those of Y. Note that |Y-F| <= 2**(-7).
66: *
67: * Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a polynomial in u,
68: * log(1+u) = poly.
69: *
70: * Step 4. Reconstruct log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u)
71: * by k*log(2) + (log(F) + poly). The values of log(F) are calculated
72: * beforehand and stored in the program.
73: *
74: * lognp1:
75: * Step 1: If |X| < 1/16, approximate log(1+X) by an odd polynomial in
76: * u where u = 2X/(2+X). Otherwise, move on to Step 2.
77: *
78: * Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done in Step 2
79: * of the algorithm for LOGN and compute log(1+X) as
80: * k*log(2) + log(F) + poly where poly approximates log(1+u),
81: * u = (Y-F)/F.
82: *
83: * Implementation Notes:
84: * Note 1. There are 64 different possible values for F, thus 64 log(F)'s
85: * need to be tabulated. Moreover, the values of 1/F are also
86: * tabulated so that the division in (Y-F)/F can be performed by a
87: * multiplication.
88: *
89: * Note 2. In Step 2 of lognp1, in order to preserved accuracy, the value
90: * Y-F has to be calculated carefully when 1/2 <= X < 3/2.
91: *
92: * Note 3. To fully exploit the pipeline, polynomials are usually separated
93: * into two parts evaluated independently before being added up.
94: *
95:
96: slogn IDNT 2,1 Motorola 040 Floating Point Software Package
97:
98: section 8
99:
100: include fpsp.h
101:
102: BOUNDS1 DC.L $3FFEF07D,$3FFF8841
103: BOUNDS2 DC.L $3FFE8000,$3FFFC000
104:
105: LOGOF2 DC.L $3FFE0000,$B17217F7,$D1CF79AC,$00000000
106:
107: one DC.L $3F800000
108: zero DC.L $00000000
109: infty DC.L $7F800000
110: negone DC.L $BF800000
111:
112: LOGA6 DC.L $3FC2499A,$B5E4040B
113: LOGA5 DC.L $BFC555B5,$848CB7DB
114:
115: LOGA4 DC.L $3FC99999,$987D8730
116: LOGA3 DC.L $BFCFFFFF,$FF6F7E97
117:
118: LOGA2 DC.L $3FD55555,$555555A4
119: LOGA1 DC.L $BFE00000,$00000008
120:
121: LOGB5 DC.L $3F175496,$ADD7DAD6
122: LOGB4 DC.L $3F3C71C2,$FE80C7E0
123:
124: LOGB3 DC.L $3F624924,$928BCCFF
125: LOGB2 DC.L $3F899999,$999995EC
126:
127: LOGB1 DC.L $3FB55555,$55555555
128: TWO DC.L $40000000,$00000000
129:
130: LTHOLD DC.L $3f990000,$80000000,$00000000,$00000000
131:
132: LOGTBL:
133: DC.L $3FFE0000,$FE03F80F,$E03F80FE,$00000000
134: DC.L $3FF70000,$FF015358,$833C47E2,$00000000
135: DC.L $3FFE0000,$FA232CF2,$52138AC0,$00000000
136: DC.L $3FF90000,$BDC8D83E,$AD88D549,$00000000
137: DC.L $3FFE0000,$F6603D98,$0F6603DA,$00000000
138: DC.L $3FFA0000,$9CF43DCF,$F5EAFD48,$00000000
139: DC.L $3FFE0000,$F2B9D648,$0F2B9D65,$00000000
140: DC.L $3FFA0000,$DA16EB88,$CB8DF614,$00000000
141: DC.L $3FFE0000,$EF2EB71F,$C4345238,$00000000
142: DC.L $3FFB0000,$8B29B775,$1BD70743,$00000000
143: DC.L $3FFE0000,$EBBDB2A5,$C1619C8C,$00000000
144: DC.L $3FFB0000,$A8D839F8,$30C1FB49,$00000000
145: DC.L $3FFE0000,$E865AC7B,$7603A197,$00000000
146: DC.L $3FFB0000,$C61A2EB1,$8CD907AD,$00000000
147: DC.L $3FFE0000,$E525982A,$F70C880E,$00000000
148: DC.L $3FFB0000,$E2F2A47A,$DE3A18AF,$00000000
149: DC.L $3FFE0000,$E1FC780E,$1FC780E2,$00000000
150: DC.L $3FFB0000,$FF64898E,$DF55D551,$00000000
151: DC.L $3FFE0000,$DEE95C4C,$A037BA57,$00000000
152: DC.L $3FFC0000,$8DB956A9,$7B3D0148,$00000000
153: DC.L $3FFE0000,$DBEB61EE,$D19C5958,$00000000
154: DC.L $3FFC0000,$9B8FE100,$F47BA1DE,$00000000
155: DC.L $3FFE0000,$D901B203,$6406C80E,$00000000
156: DC.L $3FFC0000,$A9372F1D,$0DA1BD17,$00000000
157: DC.L $3FFE0000,$D62B80D6,$2B80D62C,$00000000
158: DC.L $3FFC0000,$B6B07F38,$CE90E46B,$00000000
159: DC.L $3FFE0000,$D3680D36,$80D3680D,$00000000
160: DC.L $3FFC0000,$C3FD0329,$06488481,$00000000
161: DC.L $3FFE0000,$D0B69FCB,$D2580D0B,$00000000
162: DC.L $3FFC0000,$D11DE0FF,$15AB18CA,$00000000
163: DC.L $3FFE0000,$CE168A77,$25080CE1,$00000000
164: DC.L $3FFC0000,$DE1433A1,$6C66B150,$00000000
165: DC.L $3FFE0000,$CB8727C0,$65C393E0,$00000000
166: DC.L $3FFC0000,$EAE10B5A,$7DDC8ADD,$00000000
167: DC.L $3FFE0000,$C907DA4E,$871146AD,$00000000
168: DC.L $3FFC0000,$F7856E5E,$E2C9B291,$00000000
169: DC.L $3FFE0000,$C6980C69,$80C6980C,$00000000
170: DC.L $3FFD0000,$82012CA5,$A68206D7,$00000000
171: DC.L $3FFE0000,$C4372F85,$5D824CA6,$00000000
172: DC.L $3FFD0000,$882C5FCD,$7256A8C5,$00000000
173: DC.L $3FFE0000,$C1E4BBD5,$95F6E947,$00000000
174: DC.L $3FFD0000,$8E44C60B,$4CCFD7DE,$00000000
175: DC.L $3FFE0000,$BFA02FE8,$0BFA02FF,$00000000
176: DC.L $3FFD0000,$944AD09E,$F4351AF6,$00000000
177: DC.L $3FFE0000,$BD691047,$07661AA3,$00000000
178: DC.L $3FFD0000,$9A3EECD4,$C3EAA6B2,$00000000
179: DC.L $3FFE0000,$BB3EE721,$A54D880C,$00000000
180: DC.L $3FFD0000,$A0218434,$353F1DE8,$00000000
181: DC.L $3FFE0000,$B92143FA,$36F5E02E,$00000000
182: DC.L $3FFD0000,$A5F2FCAB,$BBC506DA,$00000000
183: DC.L $3FFE0000,$B70FBB5A,$19BE3659,$00000000
184: DC.L $3FFD0000,$ABB3B8BA,$2AD362A5,$00000000
185: DC.L $3FFE0000,$B509E68A,$9B94821F,$00000000
186: DC.L $3FFD0000,$B1641795,$CE3CA97B,$00000000
187: DC.L $3FFE0000,$B30F6352,$8917C80B,$00000000
188: DC.L $3FFD0000,$B7047551,$5D0F1C61,$00000000
189: DC.L $3FFE0000,$B11FD3B8,$0B11FD3C,$00000000
190: DC.L $3FFD0000,$BC952AFE,$EA3D13E1,$00000000
191: DC.L $3FFE0000,$AF3ADDC6,$80AF3ADE,$00000000
192: DC.L $3FFD0000,$C2168ED0,$F458BA4A,$00000000
193: DC.L $3FFE0000,$AD602B58,$0AD602B6,$00000000
194: DC.L $3FFD0000,$C788F439,$B3163BF1,$00000000
195: DC.L $3FFE0000,$AB8F69E2,$8359CD11,$00000000
196: DC.L $3FFD0000,$CCECAC08,$BF04565D,$00000000
197: DC.L $3FFE0000,$A9C84A47,$A07F5638,$00000000
198: DC.L $3FFD0000,$D2420487,$2DD85160,$00000000
199: DC.L $3FFE0000,$A80A80A8,$0A80A80B,$00000000
200: DC.L $3FFD0000,$D7894992,$3BC3588A,$00000000
201: DC.L $3FFE0000,$A655C439,$2D7B73A8,$00000000
202: DC.L $3FFD0000,$DCC2C4B4,$9887DACC,$00000000
203: DC.L $3FFE0000,$A4A9CF1D,$96833751,$00000000
204: DC.L $3FFD0000,$E1EEBD3E,$6D6A6B9E,$00000000
205: DC.L $3FFE0000,$A3065E3F,$AE7CD0E0,$00000000
206: DC.L $3FFD0000,$E70D785C,$2F9F5BDC,$00000000
207: DC.L $3FFE0000,$A16B312E,$A8FC377D,$00000000
208: DC.L $3FFD0000,$EC1F392C,$5179F283,$00000000
209: DC.L $3FFE0000,$9FD809FD,$809FD80A,$00000000
210: DC.L $3FFD0000,$F12440D3,$E36130E6,$00000000
211: DC.L $3FFE0000,$9E4CAD23,$DD5F3A20,$00000000
212: DC.L $3FFD0000,$F61CCE92,$346600BB,$00000000
213: DC.L $3FFE0000,$9CC8E160,$C3FB19B9,$00000000
214: DC.L $3FFD0000,$FB091FD3,$8145630A,$00000000
215: DC.L $3FFE0000,$9B4C6F9E,$F03A3CAA,$00000000
216: DC.L $3FFD0000,$FFE97042,$BFA4C2AD,$00000000
217: DC.L $3FFE0000,$99D722DA,$BDE58F06,$00000000
218: DC.L $3FFE0000,$825EFCED,$49369330,$00000000
219: DC.L $3FFE0000,$9868C809,$868C8098,$00000000
220: DC.L $3FFE0000,$84C37A7A,$B9A905C9,$00000000
221: DC.L $3FFE0000,$97012E02,$5C04B809,$00000000
222: DC.L $3FFE0000,$87224C2E,$8E645FB7,$00000000
223: DC.L $3FFE0000,$95A02568,$095A0257,$00000000
224: DC.L $3FFE0000,$897B8CAC,$9F7DE298,$00000000
225: DC.L $3FFE0000,$94458094,$45809446,$00000000
226: DC.L $3FFE0000,$8BCF55DE,$C4CD05FE,$00000000
227: DC.L $3FFE0000,$92F11384,$0497889C,$00000000
228: DC.L $3FFE0000,$8E1DC0FB,$89E125E5,$00000000
229: DC.L $3FFE0000,$91A2B3C4,$D5E6F809,$00000000
230: DC.L $3FFE0000,$9066E68C,$955B6C9B,$00000000
231: DC.L $3FFE0000,$905A3863,$3E06C43B,$00000000
232: DC.L $3FFE0000,$92AADE74,$C7BE59E0,$00000000
233: DC.L $3FFE0000,$8F1779D9,$FDC3A219,$00000000
234: DC.L $3FFE0000,$94E9BFF6,$15845643,$00000000
235: DC.L $3FFE0000,$8DDA5202,$37694809,$00000000
236: DC.L $3FFE0000,$9723A1B7,$20134203,$00000000
237: DC.L $3FFE0000,$8CA29C04,$6514E023,$00000000
238: DC.L $3FFE0000,$995899C8,$90EB8990,$00000000
239: DC.L $3FFE0000,$8B70344A,$139BC75A,$00000000
240: DC.L $3FFE0000,$9B88BDAA,$3A3DAE2F,$00000000
241: DC.L $3FFE0000,$8A42F870,$5669DB46,$00000000
242: DC.L $3FFE0000,$9DB4224F,$FFE1157C,$00000000
243: DC.L $3FFE0000,$891AC73A,$E9819B50,$00000000
244: DC.L $3FFE0000,$9FDADC26,$8B7A12DA,$00000000
245: DC.L $3FFE0000,$87F78087,$F78087F8,$00000000
246: DC.L $3FFE0000,$A1FCFF17,$CE733BD4,$00000000
247: DC.L $3FFE0000,$86D90544,$7A34ACC6,$00000000
248: DC.L $3FFE0000,$A41A9E8F,$5446FB9F,$00000000
249: DC.L $3FFE0000,$85BF3761,$2CEE3C9B,$00000000
250: DC.L $3FFE0000,$A633CD7E,$6771CD8B,$00000000
251: DC.L $3FFE0000,$84A9F9C8,$084A9F9D,$00000000
252: DC.L $3FFE0000,$A8489E60,$0B435A5E,$00000000
253: DC.L $3FFE0000,$83993052,$3FBE3368,$00000000
254: DC.L $3FFE0000,$AA59233C,$CCA4BD49,$00000000
255: DC.L $3FFE0000,$828CBFBE,$B9A020A3,$00000000
256: DC.L $3FFE0000,$AC656DAE,$6BCC4985,$00000000
257: DC.L $3FFE0000,$81848DA8,$FAF0D277,$00000000
258: DC.L $3FFE0000,$AE6D8EE3,$60BB2468,$00000000
259: DC.L $3FFE0000,$80808080,$80808081,$00000000
260: DC.L $3FFE0000,$B07197A2,$3C46C654,$00000000
261:
262: ADJK equ L_SCR1
263:
264: X equ FP_SCR1
265: XDCARE equ X+2
266: XFRAC equ X+4
267:
268: F equ FP_SCR2
269: FFRAC equ F+4
270:
271: KLOG2 equ FP_SCR3
272:
273: SAVEU equ FP_SCR4
274:
275: xref t_frcinx
276: xref t_extdnrm
277: xref t_operr
278: xref t_dz
279:
280: xdef slognd
281: slognd:
282: *--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INPUT
283:
284: MOVE.L #-100,ADJK(a6) ...INPUT = 2^(ADJK) * FP0
285:
286: *----normalize the input value by left shifting k bits (k to be determined
287: *----below), adjusting exponent and storing -k to ADJK
288: *----the value TWOTO100 is no longer needed.
289: *----Note that this code assumes the denormalized input is NON-ZERO.
290:
291: MoveM.L D2-D7,-(A7) ...save some registers
292: Clr.L D3 ...D3 is exponent of smallest norm. #
293: Move.L 4(A0),D4
294: Move.L 8(A0),D5 ...(D4,D5) is (Hi_X,Lo_X)
295: Clr.L D2 ...D2 used for holding K
296:
297: Tst.L D4
298: BNE.B HiX_not0
299:
300: HiX_0:
301: Move.L D5,D4
302: Clr.L D5
303: Move.L #32,D2
304: Clr.L D6
305: BFFFO D4{0:32},D6
306: LSL.L D6,D4
307: Add.L D6,D2 ...(D3,D4,D5) is normalized
308:
309: Move.L D3,X(a6)
310: Move.L D4,XFRAC(a6)
311: Move.L D5,XFRAC+4(a6)
312: Neg.L D2
313: Move.L D2,ADJK(a6)
314: FMove.X X(a6),FP0
315: MoveM.L (A7)+,D2-D7 ...restore registers
316: LEA X(a6),A0
317: Bra.B LOGBGN ...begin regular log(X)
318:
319:
320: HiX_not0:
321: Clr.L D6
322: BFFFO D4{0:32},D6 ...find first 1
323: Move.L D6,D2 ...get k
324: LSL.L D6,D4
325: Move.L D5,D7 ...a copy of D5
326: LSL.L D6,D5
327: Neg.L D6
328: AddI.L #32,D6
329: LSR.L D6,D7
330: Or.L D7,D4 ...(D3,D4,D5) normalized
331:
332: Move.L D3,X(a6)
333: Move.L D4,XFRAC(a6)
334: Move.L D5,XFRAC+4(a6)
335: Neg.L D2
336: Move.L D2,ADJK(a6)
337: FMove.X X(a6),FP0
338: MoveM.L (A7)+,D2-D7 ...restore registers
339: LEA X(a6),A0
340: Bra.B LOGBGN ...begin regular log(X)
341:
342:
343: xdef slogn
344: slogn:
345: *--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S
346:
347: FMOVE.X (A0),FP0 ...LOAD INPUT
348: CLR.L ADJK(a6)
349:
350: LOGBGN:
351: *--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS
352: *--A FINITE, NON-ZERO, NORMALIZED NUMBER.
353:
354: move.l (a0),d0
355: move.w 4(a0),d0
356:
357: move.l (a0),X(a6)
358: move.l 4(a0),X+4(a6)
359: move.l 8(a0),X+8(a6)
360:
361: TST.L D0 ...CHECK IF X IS NEGATIVE
362: BLT.W LOGNEG ...LOG OF NEGATIVE ARGUMENT IS INVALID
363: CMP2.L BOUNDS1,D0 ...X IS POSITIVE, CHECK IF X IS NEAR 1
364: BCC.W LOGNEAR1 ...BOUNDS IS ROUGHLY [15/16, 17/16]
365:
366: LOGMAIN:
367: *--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1
368:
369: *--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.
370: *--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.
371: *--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)
372: *-- = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).
373: *--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
374: *--LOG(1+U) CAN BE VERY EFFICIENT.
375: *--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO
376: *--DIVISION IS NEEDED TO CALCULATE (Y-F)/F.
377:
378: *--GET K, Y, F, AND ADDRESS OF 1/F.
379: ASR.L #8,D0
380: ASR.L #8,D0 ...SHIFTED 16 BITS, BIASED EXPO. OF X
381: SUBI.L #$3FFF,D0 ...THIS IS K
382: ADD.L ADJK(a6),D0 ...ADJUST K, ORIGINAL INPUT MAY BE DENORM.
383: LEA LOGTBL,A0 ...BASE ADDRESS OF 1/F AND LOG(F)
384: FMOVE.L D0,FP1 ...CONVERT K TO FLOATING-POINT FORMAT
385:
386: *--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F
387: MOVE.L #$3FFF0000,X(a6) ...X IS NOW Y, I.E. 2^(-K)*X
388: MOVE.L XFRAC(a6),FFRAC(a6)
389: ANDI.L #$FE000000,FFRAC(a6) ...FIRST 7 BITS OF Y
390: ORI.L #$01000000,FFRAC(a6) ...GET F: ATTACH A 1 AT THE EIGHTH BIT
391: MOVE.L FFRAC(a6),D0 ...READY TO GET ADDRESS OF 1/F
392: ANDI.L #$7E000000,D0
393: ASR.L #8,D0
394: ASR.L #8,D0
395: ASR.L #4,D0 ...SHIFTED 20, D0 IS THE DISPLACEMENT
396: ADDA.L D0,A0 ...A0 IS THE ADDRESS FOR 1/F
397:
398: FMOVE.X X(a6),FP0
399: move.l #$3fff0000,F(a6)
400: clr.l F+8(a6)
401: FSUB.X F(a6),FP0 ...Y-F
402: FMOVEm.X FP2/fp3,-(sp) ...SAVE FP2 WHILE FP0 IS NOT READY
403: *--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K
404: *--REGISTERS SAVED: FPCR, FP1, FP2
405:
406: LP1CONT1:
407: *--AN RE-ENTRY POINT FOR LOGNP1
408: FMUL.X (A0),FP0 ...FP0 IS U = (Y-F)/F
409: FMUL.X LOGOF2,FP1 ...GET K*LOG2 WHILE FP0 IS NOT READY
410: FMOVE.X FP0,FP2
411: FMUL.X FP2,FP2 ...FP2 IS V=U*U
412: FMOVE.X FP1,KLOG2(a6) ...PUT K*LOG2 IN MEMEORY, FREE FP1
413:
414: *--LOG(1+U) IS APPROXIMATED BY
415: *--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS
416: *--[U + V*(A1+V*(A3+V*A5))] + [U*V*(A2+V*(A4+V*A6))]
417:
418: FMOVE.X FP2,FP3
419: FMOVE.X FP2,FP1
420:
421: FMUL.D LOGA6,FP1 ...V*A6
422: FMUL.D LOGA5,FP2 ...V*A5
423:
424: FADD.D LOGA4,FP1 ...A4+V*A6
425: FADD.D LOGA3,FP2 ...A3+V*A5
426:
427: FMUL.X FP3,FP1 ...V*(A4+V*A6)
428: FMUL.X FP3,FP2 ...V*(A3+V*A5)
429:
430: FADD.D LOGA2,FP1 ...A2+V*(A4+V*A6)
431: FADD.D LOGA1,FP2 ...A1+V*(A3+V*A5)
432:
433: FMUL.X FP3,FP1 ...V*(A2+V*(A4+V*A6))
434: ADDA.L #16,A0 ...ADDRESS OF LOG(F)
435: FMUL.X FP3,FP2 ...V*(A1+V*(A3+V*A5)), FP3 RELEASED
436:
437: FMUL.X FP0,FP1 ...U*V*(A2+V*(A4+V*A6))
438: FADD.X FP2,FP0 ...U+V*(A1+V*(A3+V*A5)), FP2 RELEASED
439:
440: FADD.X (A0),FP1 ...LOG(F)+U*V*(A2+V*(A4+V*A6))
441: FMOVEm.X (sp)+,FP2/fp3 ...RESTORE FP2
442: FADD.X FP1,FP0 ...FP0 IS LOG(F) + LOG(1+U)
443:
444: fmove.l d1,fpcr
445: FADD.X KLOG2(a6),FP0 ...FINAL ADD
446: bra t_frcinx
447:
448:
449: LOGNEAR1:
450: *--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS THE INPUT.
451: FMOVE.X FP0,FP1
452: FSUB.S one,FP1 ...FP1 IS X-1
453: FADD.S one,FP0 ...FP0 IS X+1
454: FADD.X FP1,FP1 ...FP1 IS 2(X-1)
455: *--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL
456: *--IN U, U = 2(X-1)/(X+1) = FP1/FP0
457:
458: LP1CONT2:
459: *--THIS IS AN RE-ENTRY POINT FOR LOGNP1
460: FDIV.X FP0,FP1 ...FP1 IS U
461: FMOVEm.X FP2/fp3,-(sp) ...SAVE FP2
462: *--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3
463: *--LET V=U*U, W=V*V, CALCULATE
464: *--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY
465: *--U + U*V*( [B1 + W*(B3 + W*B5)] + [V*(B2 + W*B4)] )
466: FMOVE.X FP1,FP0
467: FMUL.X FP0,FP0 ...FP0 IS V
468: FMOVE.X FP1,SAVEU(a6) ...STORE U IN MEMORY, FREE FP1
469: FMOVE.X FP0,FP1
470: FMUL.X FP1,FP1 ...FP1 IS W
471:
472: FMOVE.D LOGB5,FP3
473: FMOVE.D LOGB4,FP2
474:
475: FMUL.X FP1,FP3 ...W*B5
476: FMUL.X FP1,FP2 ...W*B4
477:
478: FADD.D LOGB3,FP3 ...B3+W*B5
479: FADD.D LOGB2,FP2 ...B2+W*B4
480:
481: FMUL.X FP3,FP1 ...W*(B3+W*B5), FP3 RELEASED
482:
483: FMUL.X FP0,FP2 ...V*(B2+W*B4)
484:
485: FADD.D LOGB1,FP1 ...B1+W*(B3+W*B5)
486: FMUL.X SAVEU(a6),FP0 ...FP0 IS U*V
487:
488: FADD.X FP2,FP1 ...B1+W*(B3+W*B5) + V*(B2+W*B4), FP2 RELEASED
489: FMOVEm.X (sp)+,FP2/fp3 ...FP2 RESTORED
490:
491: FMUL.X FP1,FP0 ...U*V*( [B1+W*(B3+W*B5)] + [V*(B2+W*B4)] )
492:
493: fmove.l d1,fpcr
494: FADD.X SAVEU(a6),FP0
495: bra t_frcinx
496: rts
497:
498: LOGNEG:
499: *--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID
500: bra t_operr
501:
502: xdef slognp1d
503: slognp1d:
504: *--ENTRY POINT FOR LOG(1+Z) FOR DENORMALIZED INPUT
505: * Simply return the denorm
506:
507: bra t_extdnrm
508:
509: xdef slognp1
510: slognp1:
511: *--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S
512:
513: FMOVE.X (A0),FP0 ...LOAD INPUT
514: fabs.x fp0 ;test magnitude
515: fcmp.x LTHOLD,fp0 ;compare with min threshold
516: fbgt.w LP1REAL ;if greater, continue
517: fmove.l #0,fpsr ;clr N flag from compare
518: fmove.l d1,fpcr
519: fmove.x (a0),fp0 ;return signed argument
520: bra t_frcinx
521:
522: LP1REAL:
523: FMOVE.X (A0),FP0 ...LOAD INPUT
524: CLR.L ADJK(a6)
525: FMOVE.X FP0,FP1 ...FP1 IS INPUT Z
526: FADD.S one,FP0 ...X := ROUND(1+Z)
527: FMOVE.X FP0,X(a6)
528: MOVE.W XFRAC(a6),XDCARE(a6)
529: MOVE.L X(a6),D0
530: TST.L D0
531: BLE.W LP1NEG0 ...LOG OF ZERO OR -VE
532: CMP2.L BOUNDS2,D0
533: BCS.W LOGMAIN ...BOUNDS2 IS [1/2,3/2]
534: *--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z,
535: *--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE,
536: *--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).
537:
538: LP1NEAR1:
539: *--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)
540: CMP2.L BOUNDS1,D0
541: BCS.B LP1CARE
542:
543: LP1ONE16:
544: *--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2)
545: *--WHERE U = 2Z/(2+Z) = 2Z/(1+X).
546: FADD.X FP1,FP1 ...FP1 IS 2Z
547: FADD.S one,FP0 ...FP0 IS 1+X
548: *--U = FP1/FP0
549: BRA.W LP1CONT2
550:
551: LP1CARE:
552: *--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE
553: *--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST
554: *--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2],
555: *--THERE ARE ONLY TWO CASES.
556: *--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z
557: *--CASE 2: 1+Z > 1, THEN K = 0 AND Y-F = (1-F) + Z
558: *--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF
559: *--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
560:
561: MOVE.L XFRAC(a6),FFRAC(a6)
562: ANDI.L #$FE000000,FFRAC(a6)
563: ORI.L #$01000000,FFRAC(a6) ...F OBTAINED
564: CMPI.L #$3FFF8000,D0 ...SEE IF 1+Z > 1
565: BGE.B KISZERO
566:
567: KISNEG1:
568: FMOVE.S TWO,FP0
569: move.l #$3fff0000,F(a6)
570: clr.l F+8(a6)
571: FSUB.X F(a6),FP0 ...2-F
572: MOVE.L FFRAC(a6),D0
573: ANDI.L #$7E000000,D0
574: ASR.L #8,D0
575: ASR.L #8,D0
576: ASR.L #4,D0 ...D0 CONTAINS DISPLACEMENT FOR 1/F
577: FADD.X FP1,FP1 ...GET 2Z
578: FMOVEm.X FP2/fp3,-(sp) ...SAVE FP2
579: FADD.X FP1,FP0 ...FP0 IS Y-F = (2-F)+2Z
580: LEA LOGTBL,A0 ...A0 IS ADDRESS OF 1/F
581: ADDA.L D0,A0
582: FMOVE.S negone,FP1 ...FP1 IS K = -1
583: BRA.W LP1CONT1
584:
585: KISZERO:
586: FMOVE.S one,FP0
587: move.l #$3fff0000,F(a6)
588: clr.l F+8(a6)
589: FSUB.X F(a6),FP0 ...1-F
590: MOVE.L FFRAC(a6),D0
591: ANDI.L #$7E000000,D0
592: ASR.L #8,D0
593: ASR.L #8,D0
594: ASR.L #4,D0
595: FADD.X FP1,FP0 ...FP0 IS Y-F
596: FMOVEm.X FP2/fp3,-(sp) ...FP2 SAVED
597: LEA LOGTBL,A0
598: ADDA.L D0,A0 ...A0 IS ADDRESS OF 1/F
599: FMOVE.S zero,FP1 ...FP1 IS K = 0
600: BRA.W LP1CONT1
601:
602: LP1NEG0:
603: *--FPCR SAVED. D0 IS X IN COMPACT FORM.
604: TST.L D0
605: BLT.B LP1NEG
606: LP1ZERO:
607: FMOVE.S negone,FP0
608:
609: fmove.l d1,fpcr
610: bra t_dz
611:
612: LP1NEG:
613: FMOVE.S zero,FP0
614:
615: fmove.l d1,fpcr
616: bra t_operr
617:
618: end
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