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1 *       $NetBSD: satan.sa,v 1.3 1994/10/26 07:49:31 cgd Exp $
3 *       MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
4 *       M68000 Hi-Performance Microprocessor Division
5 *       M68040 Software Package 
7 *       M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
8 *       All rights reserved.
10 *       THE SOFTWARE is provided on an "AS IS" basis and without warranty.
11 *       To the maximum extent permitted by applicable law,
12 *       MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
13 *       INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
14 *       PARTICULAR PURPOSE and any warranty against infringement with
15 *       regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
16 *       and any accompanying written materials. 
18 *       To the maximum extent permitted by applicable law,
19 *       IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
20 *       (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
21 *       PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
22 *       OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
23 *       SOFTWARE.  Motorola assumes no responsibility for the maintenance
24 *       and support of the SOFTWARE.  
26 *       You are hereby granted a copyright license to use, modify, and
27 *       distribute the SOFTWARE so long as this entire notice is retained
28 *       without alteration in any modified and/or redistributed versions,
29 *       and that such modified versions are clearly identified as such.
30 *       No licenses are granted by implication, estoppel or otherwise
31 *       under any patents or trademarks of Motorola, Inc.
34 *       satan.sa 3.3 12/19/90
36 *       The entry point satan computes the arctagent of an
37 *       input value. satand does the same except the input value is a
38 *       denormalized number.
40 *       Input: Double-extended value in memory location pointed to by address
41 *               register a0.
43 *       Output: Arctan(X) returned in floating-point register Fp0.
45 *       Accuracy and Monotonicity: The returned result is within 2 ulps in
46 *               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
47 *               result is subsequently rounded to double precision. The
48 *               result is provably monotonic in double precision.
50 *       Speed: The program satan takes approximately 160 cycles for input
51 *               argument X such that 1/16 < |X| < 16. For the other arguments,
52 *               the program will run no worse than 10% slower.
54 *       Algorithm:
55 *       Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
57 *       Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
58 *               Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
59 *               of X with a bit-1 attached at the 6-th bit position. Define u
60 *               to be u = (X-F) / (1 + X*F).
62 *       Step 3. Approximate arctan(u) by a polynomial poly.
64 *       Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
65 *               calculated beforehand. Exit.
67 *       Step 5. If |X| >= 16, go to Step 7.
69 *       Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
71 *       Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
72 *               Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
75 satan   IDNT    2,1 Motorola 040 Floating Point Software Package
77         section 8
79         include fpsp.h
80         
81 BOUNDS1 DC.L $3FFB8000,$4002FFFF
83 ONE     DC.L $3F800000
85         DC.L $00000000
87 ATANA3  DC.L $BFF6687E,$314987D8
88 ATANA2  DC.L $4002AC69,$34A26DB3
90 ATANA1  DC.L $BFC2476F,$4E1DA28E
91 ATANB6  DC.L $3FB34444,$7F876989
93 ATANB5  DC.L $BFB744EE,$7FAF45DB
94 ATANB4  DC.L $3FBC71C6,$46940220
96 ATANB3  DC.L $BFC24924,$921872F9
97 ATANB2  DC.L $3FC99999,$99998FA9
99 ATANB1  DC.L $BFD55555,$55555555
100 ATANC5  DC.L $BFB70BF3,$98539E6A
102 ATANC4  DC.L $3FBC7187,$962D1D7D
103 ATANC3  DC.L $BFC24924,$827107B8
105 ATANC2  DC.L $3FC99999,$9996263E
106 ATANC1  DC.L $BFD55555,$55555536
108 PPIBY2  DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
109 NPIBY2  DC.L $BFFF0000,$C90FDAA2,$2168C235,$00000000
110 PTINY   DC.L $00010000,$80000000,$00000000,$00000000
111 NTINY   DC.L $80010000,$80000000,$00000000,$00000000
113 ATANTBL:
114         DC.L    $3FFB0000,$83D152C5,$060B7A51,$00000000
115         DC.L    $3FFB0000,$8BC85445,$65498B8B,$00000000
116         DC.L    $3FFB0000,$93BE4060,$17626B0D,$00000000
117         DC.L    $3FFB0000,$9BB3078D,$35AEC202,$00000000
118         DC.L    $3FFB0000,$A3A69A52,$5DDCE7DE,$00000000
119         DC.L    $3FFB0000,$AB98E943,$62765619,$00000000
120         DC.L    $3FFB0000,$B389E502,$F9C59862,$00000000
121         DC.L    $3FFB0000,$BB797E43,$6B09E6FB,$00000000
122         DC.L    $3FFB0000,$C367A5C7,$39E5F446,$00000000
123         DC.L    $3FFB0000,$CB544C61,$CFF7D5C6,$00000000
124         DC.L    $3FFB0000,$D33F62F8,$2488533E,$00000000
125         DC.L    $3FFB0000,$DB28DA81,$62404C77,$00000000
126         DC.L    $3FFB0000,$E310A407,$8AD34F18,$00000000
127         DC.L    $3FFB0000,$EAF6B0A8,$188EE1EB,$00000000
128         DC.L    $3FFB0000,$F2DAF194,$9DBE79D5,$00000000
129         DC.L    $3FFB0000,$FABD5813,$61D47E3E,$00000000
130         DC.L    $3FFC0000,$8346AC21,$0959ECC4,$00000000
131         DC.L    $3FFC0000,$8B232A08,$304282D8,$00000000
132         DC.L    $3FFC0000,$92FB70B8,$D29AE2F9,$00000000
133         DC.L    $3FFC0000,$9ACF476F,$5CCD1CB4,$00000000
134         DC.L    $3FFC0000,$A29E7630,$4954F23F,$00000000
135         DC.L    $3FFC0000,$AA68C5D0,$8AB85230,$00000000
136         DC.L    $3FFC0000,$B22DFFFD,$9D539F83,$00000000
137         DC.L    $3FFC0000,$B9EDEF45,$3E900EA5,$00000000
138         DC.L    $3FFC0000,$C1A85F1C,$C75E3EA5,$00000000
139         DC.L    $3FFC0000,$C95D1BE8,$28138DE6,$00000000
140         DC.L    $3FFC0000,$D10BF300,$840D2DE4,$00000000
141         DC.L    $3FFC0000,$D8B4B2BA,$6BC05E7A,$00000000
142         DC.L    $3FFC0000,$E0572A6B,$B42335F6,$00000000
143         DC.L    $3FFC0000,$E7F32A70,$EA9CAA8F,$00000000
144         DC.L    $3FFC0000,$EF888432,$64ECEFAA,$00000000
145         DC.L    $3FFC0000,$F7170A28,$ECC06666,$00000000
146         DC.L    $3FFD0000,$812FD288,$332DAD32,$00000000
147         DC.L    $3FFD0000,$88A8D1B1,$218E4D64,$00000000
148         DC.L    $3FFD0000,$9012AB3F,$23E4AEE8,$00000000
149         DC.L    $3FFD0000,$976CC3D4,$11E7F1B9,$00000000
150         DC.L    $3FFD0000,$9EB68949,$3889A227,$00000000
151         DC.L    $3FFD0000,$A5EF72C3,$4487361B,$00000000
152         DC.L    $3FFD0000,$AD1700BA,$F07A7227,$00000000
153         DC.L    $3FFD0000,$B42CBCFA,$FD37EFB7,$00000000
154         DC.L    $3FFD0000,$BB303A94,$0BA80F89,$00000000
155         DC.L    $3FFD0000,$C22115C6,$FCAEBBAF,$00000000
156         DC.L    $3FFD0000,$C8FEF3E6,$86331221,$00000000
157         DC.L    $3FFD0000,$CFC98330,$B4000C70,$00000000
158         DC.L    $3FFD0000,$D6807AA1,$102C5BF9,$00000000
159         DC.L    $3FFD0000,$DD2399BC,$31252AA3,$00000000
160         DC.L    $3FFD0000,$E3B2A855,$6B8FC517,$00000000
161         DC.L    $3FFD0000,$EA2D764F,$64315989,$00000000
162         DC.L    $3FFD0000,$F3BF5BF8,$BAD1A21D,$00000000
163         DC.L    $3FFE0000,$801CE39E,$0D205C9A,$00000000
164         DC.L    $3FFE0000,$8630A2DA,$DA1ED066,$00000000
165         DC.L    $3FFE0000,$8C1AD445,$F3E09B8C,$00000000
166         DC.L    $3FFE0000,$91DB8F16,$64F350E2,$00000000
167         DC.L    $3FFE0000,$97731420,$365E538C,$00000000
168         DC.L    $3FFE0000,$9CE1C8E6,$A0B8CDBA,$00000000
169         DC.L    $3FFE0000,$A22832DB,$CADAAE09,$00000000
170         DC.L    $3FFE0000,$A746F2DD,$B7602294,$00000000
171         DC.L    $3FFE0000,$AC3EC0FB,$997DD6A2,$00000000
172         DC.L    $3FFE0000,$B110688A,$EBDC6F6A,$00000000
173         DC.L    $3FFE0000,$B5BCC490,$59ECC4B0,$00000000
174         DC.L    $3FFE0000,$BA44BC7D,$D470782F,$00000000
175         DC.L    $3FFE0000,$BEA94144,$FD049AAC,$00000000
176         DC.L    $3FFE0000,$C2EB4ABB,$661628B6,$00000000
177         DC.L    $3FFE0000,$C70BD54C,$E602EE14,$00000000
178         DC.L    $3FFE0000,$CD000549,$ADEC7159,$00000000
179         DC.L    $3FFE0000,$D48457D2,$D8EA4EA3,$00000000
180         DC.L    $3FFE0000,$DB948DA7,$12DECE3B,$00000000
181         DC.L    $3FFE0000,$E23855F9,$69E8096A,$00000000
182         DC.L    $3FFE0000,$E8771129,$C4353259,$00000000
183         DC.L    $3FFE0000,$EE57C16E,$0D379C0D,$00000000
184         DC.L    $3FFE0000,$F3E10211,$A87C3779,$00000000
185         DC.L    $3FFE0000,$F919039D,$758B8D41,$00000000
186         DC.L    $3FFE0000,$FE058B8F,$64935FB3,$00000000
187         DC.L    $3FFF0000,$8155FB49,$7B685D04,$00000000
188         DC.L    $3FFF0000,$83889E35,$49D108E1,$00000000
189         DC.L    $3FFF0000,$859CFA76,$511D724B,$00000000
190         DC.L    $3FFF0000,$87952ECF,$FF8131E7,$00000000
191         DC.L    $3FFF0000,$89732FD1,$9557641B,$00000000
192         DC.L    $3FFF0000,$8B38CAD1,$01932A35,$00000000
193         DC.L    $3FFF0000,$8CE7A8D8,$301EE6B5,$00000000
194         DC.L    $3FFF0000,$8F46A39E,$2EAE5281,$00000000
195         DC.L    $3FFF0000,$922DA7D7,$91888487,$00000000
196         DC.L    $3FFF0000,$94D19FCB,$DEDF5241,$00000000
197         DC.L    $3FFF0000,$973AB944,$19D2A08B,$00000000
198         DC.L    $3FFF0000,$996FF00E,$08E10B96,$00000000
199         DC.L    $3FFF0000,$9B773F95,$12321DA7,$00000000
200         DC.L    $3FFF0000,$9D55CC32,$0F935624,$00000000
201         DC.L    $3FFF0000,$9F100575,$006CC571,$00000000
202         DC.L    $3FFF0000,$A0A9C290,$D97CC06C,$00000000
203         DC.L    $3FFF0000,$A22659EB,$EBC0630A,$00000000
204         DC.L    $3FFF0000,$A388B4AF,$F6EF0EC9,$00000000
205         DC.L    $3FFF0000,$A4D35F10,$61D292C4,$00000000
206         DC.L    $3FFF0000,$A60895DC,$FBE3187E,$00000000
207         DC.L    $3FFF0000,$A72A51DC,$7367BEAC,$00000000
208         DC.L    $3FFF0000,$A83A5153,$0956168F,$00000000
209         DC.L    $3FFF0000,$A93A2007,$7539546E,$00000000
210         DC.L    $3FFF0000,$AA9E7245,$023B2605,$00000000
211         DC.L    $3FFF0000,$AC4C84BA,$6FE4D58F,$00000000
212         DC.L    $3FFF0000,$ADCE4A4A,$606B9712,$00000000
213         DC.L    $3FFF0000,$AF2A2DCD,$8D263C9C,$00000000
214         DC.L    $3FFF0000,$B0656F81,$F22265C7,$00000000
215         DC.L    $3FFF0000,$B1846515,$0F71496A,$00000000
216         DC.L    $3FFF0000,$B28AAA15,$6F9ADA35,$00000000
217         DC.L    $3FFF0000,$B37B44FF,$3766B895,$00000000
218         DC.L    $3FFF0000,$B458C3DC,$E9630433,$00000000
219         DC.L    $3FFF0000,$B525529D,$562246BD,$00000000
220         DC.L    $3FFF0000,$B5E2CCA9,$5F9D88CC,$00000000
221         DC.L    $3FFF0000,$B692CADA,$7ACA1ADA,$00000000
222         DC.L    $3FFF0000,$B736AEA7,$A6925838,$00000000
223         DC.L    $3FFF0000,$B7CFAB28,$7E9F7B36,$00000000
224         DC.L    $3FFF0000,$B85ECC66,$CB219835,$00000000
225         DC.L    $3FFF0000,$B8E4FD5A,$20A593DA,$00000000
226         DC.L    $3FFF0000,$B99F41F6,$4AFF9BB5,$00000000
227         DC.L    $3FFF0000,$BA7F1E17,$842BBE7B,$00000000
228         DC.L    $3FFF0000,$BB471285,$7637E17D,$00000000
229         DC.L    $3FFF0000,$BBFABE8A,$4788DF6F,$00000000
230         DC.L    $3FFF0000,$BC9D0FAD,$2B689D79,$00000000
231         DC.L    $3FFF0000,$BD306A39,$471ECD86,$00000000
232         DC.L    $3FFF0000,$BDB6C731,$856AF18A,$00000000
233         DC.L    $3FFF0000,$BE31CAC5,$02E80D70,$00000000
234         DC.L    $3FFF0000,$BEA2D55C,$E33194E2,$00000000
235         DC.L    $3FFF0000,$BF0B10B7,$C03128F0,$00000000
236         DC.L    $3FFF0000,$BF6B7A18,$DACB778D,$00000000
237         DC.L    $3FFF0000,$BFC4EA46,$63FA18F6,$00000000
238         DC.L    $3FFF0000,$C0181BDE,$8B89A454,$00000000
239         DC.L    $3FFF0000,$C065B066,$CFBF6439,$00000000
240         DC.L    $3FFF0000,$C0AE345F,$56340AE6,$00000000
241         DC.L    $3FFF0000,$C0F22291,$9CB9E6A7,$00000000
243 X       equ     FP_SCR1
244 XDCARE  equ     X+2
245 XFRAC   equ     X+4
246 XFRACLO equ     X+8
248 ATANF   equ     FP_SCR2
249 ATANFHI equ     ATANF+4
250 ATANFLO equ     ATANF+8
253         xref    t_frcinx
254         xref    t_extdnrm
256         xdef    satand
257 satand:
258 *--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
260         bra             t_extdnrm
262         xdef    satan
263 satan:
264 *--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
266         FMOVE.X         (A0),FP0        ...LOAD INPUT
268         MOVE.L          (A0),D0
269         MOVE.W          4(A0),D0
270         FMOVE.X         FP0,X(a6)
271         ANDI.L          #$7FFFFFFF,D0
273         CMPI.L          #$3FFB8000,D0           ...|X| >= 1/16?
274         BGE.B           ATANOK1
275         BRA.W           ATANSM
277 ATANOK1:
278         CMPI.L          #$4002FFFF,D0           ...|X| < 16 ?
279         BLE.B           ATANMAIN
280         BRA.W           ATANBIG
283 *--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
284 *--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
285 *--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
286 *--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
287 *--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
288 *--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
289 *--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
290 *--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
291 *--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
292 *--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
293 *--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
294 *--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
295 *--WILL INVOLVE A VERY LONG POLYNOMIAL.
297 *--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
298 *--WE CHOSE F TO BE +-2^K * 1.BBBB1
299 *--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
300 *--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
301 *--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
302 *-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
304 ATANMAIN:
306         CLR.W           XDCARE(a6)              ...CLEAN UP X JUST IN CASE
307         ANDI.L          #$F8000000,XFRAC(a6)    ...FIRST 5 BITS
308         ORI.L           #$04000000,XFRAC(a6)    ...SET 6-TH BIT TO 1
309         CLR.L           XFRACLO(a6)             ...LOCATION OF X IS NOW F
311         FMOVE.X         FP0,FP1                 ...FP1 IS X
312         FMUL.X          X(a6),FP1               ...FP1 IS X*F, NOTE THAT X*F > 0
313         FSUB.X          X(a6),FP0               ...FP0 IS X-F
314         FADD.S          #:3F800000,FP1          ...FP1 IS 1 + X*F
315         FDIV.X          FP1,FP0                 ...FP0 IS U = (X-F)/(1+X*F)
317 *--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
318 *--CREATE ATAN(F) AND STORE IT IN ATANF, AND
319 *--SAVE REGISTERS FP2.
321         MOVE.L          d2,-(a7)        ...SAVE d2 TEMPORARILY
322         MOVE.L          d0,d2           ...THE EXPO AND 16 BITS OF X
323         ANDI.L          #$00007800,d0   ...4 VARYING BITS OF F'S FRACTION
324         ANDI.L          #$7FFF0000,d2   ...EXPONENT OF F
325         SUBI.L          #$3FFB0000,d2   ...K+4
326         ASR.L           #1,d2
327         ADD.L           d2,d0           ...THE 7 BITS IDENTIFYING F
328         ASR.L           #7,d0           ...INDEX INTO TBL OF ATAN(|F|)
329         LEA             ATANTBL,a1
330         ADDA.L          d0,a1           ...ADDRESS OF ATAN(|F|)
331         MOVE.L          (a1)+,ATANF(a6)
332         MOVE.L          (a1)+,ATANFHI(a6)
333         MOVE.L          (a1)+,ATANFLO(a6)       ...ATANF IS NOW ATAN(|F|)
334         MOVE.L          X(a6),d0                ...LOAD SIGN AND EXPO. AGAIN
335         ANDI.L          #$80000000,d0   ...SIGN(F)
336         OR.L            d0,ATANF(a6)    ...ATANF IS NOW SIGN(F)*ATAN(|F|)
337         MOVE.L          (a7)+,d2        ...RESTORE d2
339 *--THAT'S ALL I HAVE TO DO FOR NOW,
340 *--BUT ALAS, THE DIVIDE IS STILL CRANKING!
342 *--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
343 *--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
344 *--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
345 *--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
346 *--WHAT WE HAVE HERE IS MERELY  A1 = A3, A2 = A1/A3, A3 = A2/A3.
347 *--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
348 *--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
350         
351         FMOVE.X         FP0,FP1
352         FMUL.X          FP1,FP1
353         FMOVE.D         ATANA3,FP2
354         FADD.X          FP1,FP2         ...A3+V
355         FMUL.X          FP1,FP2         ...V*(A3+V)
356         FMUL.X          FP0,FP1         ...U*V
357         FADD.D          ATANA2,FP2      ...A2+V*(A3+V)
358         FMUL.D          ATANA1,FP1      ...A1*U*V
359         FMUL.X          FP2,FP1         ...A1*U*V*(A2+V*(A3+V))
360         
361         FADD.X          FP1,FP0         ...ATAN(U), FP1 RELEASED
362         FMOVE.L         d1,FPCR         ;restore users exceptions
363         FADD.X          ATANF(a6),FP0   ...ATAN(X)
364         bra             t_frcinx
366 ATANBORS:
367 *--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
368 *--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
369         CMPI.L          #$3FFF8000,d0
370         BGT.W           ATANBIG ...I.E. |X| >= 16
372 ATANSM:
373 *--|X| <= 1/16
374 *--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
375 *--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
376 *--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
377 *--WHERE Y = X*X, AND Z = Y*Y.
379         CMPI.L          #$3FD78000,d0
380         BLT.W           ATANTINY
381 *--COMPUTE POLYNOMIAL
382         FMUL.X          FP0,FP0 ...FP0 IS Y = X*X
384         
385         CLR.W           XDCARE(a6)
387         FMOVE.X         FP0,FP1
388         FMUL.X          FP1,FP1         ...FP1 IS Z = Y*Y
390         FMOVE.D         ATANB6,FP2
391         FMOVE.D         ATANB5,FP3
393         FMUL.X          FP1,FP2         ...Z*B6
394         FMUL.X          FP1,FP3         ...Z*B5
396         FADD.D          ATANB4,FP2      ...B4+Z*B6
397         FADD.D          ATANB3,FP3      ...B3+Z*B5
399         FMUL.X          FP1,FP2         ...Z*(B4+Z*B6)
400         FMUL.X          FP3,FP1         ...Z*(B3+Z*B5)
402         FADD.D          ATANB2,FP2      ...B2+Z*(B4+Z*B6)
403         FADD.D          ATANB1,FP1      ...B1+Z*(B3+Z*B5)
405         FMUL.X          FP0,FP2         ...Y*(B2+Z*(B4+Z*B6))
406         FMUL.X          X(a6),FP0               ...X*Y
408         FADD.X          FP2,FP1         ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
409         
411         FMUL.X          FP1,FP0 ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
413         FMOVE.L         d1,FPCR         ;restore users exceptions
414         FADD.X          X(a6),FP0
416         bra             t_frcinx
418 ATANTINY:
419 *--|X| < 2^(-40), ATAN(X) = X
420         CLR.W           XDCARE(a6)
422         FMOVE.L         d1,FPCR         ;restore users exceptions
423         FMOVE.X         X(a6),FP0       ;last inst - possible exception set
425         bra             t_frcinx
427 ATANBIG:
428 *--IF |X| > 2^(100), RETURN     SIGN(X)*(PI/2 - TINY). OTHERWISE,
429 *--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
430         CMPI.L          #$40638000,d0
431         BGT.W           ATANHUGE
433 *--APPROXIMATE ATAN(-1/X) BY
434 *--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
435 *--THIS CAN BE RE-WRITTEN AS
436 *--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
438         FMOVE.S         #:BF800000,FP1  ...LOAD -1
439         FDIV.X          FP0,FP1         ...FP1 IS -1/X
441         
442 *--DIVIDE IS STILL CRANKING
444         FMOVE.X         FP1,FP0         ...FP0 IS X'
445         FMUL.X          FP0,FP0         ...FP0 IS Y = X'*X'
446         FMOVE.X         FP1,X(a6)               ...X IS REALLY X'
448         FMOVE.X         FP0,FP1
449         FMUL.X          FP1,FP1         ...FP1 IS Z = Y*Y
451         FMOVE.D         ATANC5,FP3
452         FMOVE.D         ATANC4,FP2
454         FMUL.X          FP1,FP3         ...Z*C5
455         FMUL.X          FP1,FP2         ...Z*B4
457         FADD.D          ATANC3,FP3      ...C3+Z*C5
458         FADD.D          ATANC2,FP2      ...C2+Z*C4
460         FMUL.X          FP3,FP1         ...Z*(C3+Z*C5), FP3 RELEASED
461         FMUL.X          FP0,FP2         ...Y*(C2+Z*C4)
463         FADD.D          ATANC1,FP1      ...C1+Z*(C3+Z*C5)
464         FMUL.X          X(a6),FP0               ...X'*Y
466         FADD.X          FP2,FP1         ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
467         
469         FMUL.X          FP1,FP0         ...X'*Y*([B1+Z*(B3+Z*B5)]
470 *                                       ...     +[Y*(B2+Z*(B4+Z*B6))])
471         FADD.X          X(a6),FP0
473         FMOVE.L         d1,FPCR         ;restore users exceptions
474         
475         btst.b          #7,(a0)
476         beq.b           pos_big
478 neg_big:
479         FADD.X          NPIBY2,FP0
480         bra             t_frcinx
482 pos_big:
483         FADD.X          PPIBY2,FP0
484         bra             t_frcinx
486 ATANHUGE:
487 *--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
488         btst.b          #7,(a0)
489         beq.b           pos_huge
491 neg_huge:
492         FMOVE.X         NPIBY2,fp0
493         fmove.l         d1,fpcr
494         fsub.x          NTINY,fp0
495         bra             t_frcinx
497 pos_huge:
498         FMOVE.X         PPIBY2,fp0
499         fmove.l         d1,fpcr
500         fsub.x          PTINY,fp0
501         bra             t_frcinx
502         
503         end