Annotation of sys/arch/m68k/fpsp/satan.sa, Revision 1.1.1.1
1.1 nbrk 1: * $OpenBSD: satan.sa,v 1.2 1996/05/29 21:05:35 niklas Exp $
2: * $NetBSD: satan.sa,v 1.3 1994/10/26 07:49:31 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: * satan.sa 3.3 12/19/90
36: *
37: * The entry point satan computes the arctagent of an
38: * input value. satand does the same except the input value is a
39: * denormalized number.
40: *
41: * Input: Double-extended value in memory location pointed to by address
42: * register a0.
43: *
44: * Output: Arctan(X) returned in floating-point register Fp0.
45: *
46: * Accuracy and Monotonicity: The returned result is within 2 ulps in
47: * 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
48: * result is subsequently rounded to double precision. The
49: * result is provably monotonic in double precision.
50: *
51: * Speed: The program satan takes approximately 160 cycles for input
52: * argument X such that 1/16 < |X| < 16. For the other arguments,
53: * the program will run no worse than 10% slower.
54: *
55: * Algorithm:
56: * Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5.
57: *
58: * Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. Note that k = -4, -3,..., or 3.
59: * Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 significant bits
60: * of X with a bit-1 attached at the 6-th bit position. Define u
61: * to be u = (X-F) / (1 + X*F).
62: *
63: * Step 3. Approximate arctan(u) by a polynomial poly.
64: *
65: * Step 4. Return arctan(F) + poly, arctan(F) is fetched from a table of values
66: * calculated beforehand. Exit.
67: *
68: * Step 5. If |X| >= 16, go to Step 7.
69: *
70: * Step 6. Approximate arctan(X) by an odd polynomial in X. Exit.
71: *
72: * Step 7. Define X' = -1/X. Approximate arctan(X') by an odd polynomial in X'.
73: * Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit.
74: *
75:
76: satan IDNT 2,1 Motorola 040 Floating Point Software Package
77:
78: section 8
79:
80: include fpsp.h
81:
82: BOUNDS1 DC.L $3FFB8000,$4002FFFF
83:
84: ONE DC.L $3F800000
85:
86: DC.L $00000000
87:
88: ATANA3 DC.L $BFF6687E,$314987D8
89: ATANA2 DC.L $4002AC69,$34A26DB3
90:
91: ATANA1 DC.L $BFC2476F,$4E1DA28E
92: ATANB6 DC.L $3FB34444,$7F876989
93:
94: ATANB5 DC.L $BFB744EE,$7FAF45DB
95: ATANB4 DC.L $3FBC71C6,$46940220
96:
97: ATANB3 DC.L $BFC24924,$921872F9
98: ATANB2 DC.L $3FC99999,$99998FA9
99:
100: ATANB1 DC.L $BFD55555,$55555555
101: ATANC5 DC.L $BFB70BF3,$98539E6A
102:
103: ATANC4 DC.L $3FBC7187,$962D1D7D
104: ATANC3 DC.L $BFC24924,$827107B8
105:
106: ATANC2 DC.L $3FC99999,$9996263E
107: ATANC1 DC.L $BFD55555,$55555536
108:
109: PPIBY2 DC.L $3FFF0000,$C90FDAA2,$2168C235,$00000000
110: NPIBY2 DC.L $BFFF0000,$C90FDAA2,$2168C235,$00000000
111: PTINY DC.L $00010000,$80000000,$00000000,$00000000
112: NTINY DC.L $80010000,$80000000,$00000000,$00000000
113:
114: ATANTBL:
115: DC.L $3FFB0000,$83D152C5,$060B7A51,$00000000
116: DC.L $3FFB0000,$8BC85445,$65498B8B,$00000000
117: DC.L $3FFB0000,$93BE4060,$17626B0D,$00000000
118: DC.L $3FFB0000,$9BB3078D,$35AEC202,$00000000
119: DC.L $3FFB0000,$A3A69A52,$5DDCE7DE,$00000000
120: DC.L $3FFB0000,$AB98E943,$62765619,$00000000
121: DC.L $3FFB0000,$B389E502,$F9C59862,$00000000
122: DC.L $3FFB0000,$BB797E43,$6B09E6FB,$00000000
123: DC.L $3FFB0000,$C367A5C7,$39E5F446,$00000000
124: DC.L $3FFB0000,$CB544C61,$CFF7D5C6,$00000000
125: DC.L $3FFB0000,$D33F62F8,$2488533E,$00000000
126: DC.L $3FFB0000,$DB28DA81,$62404C77,$00000000
127: DC.L $3FFB0000,$E310A407,$8AD34F18,$00000000
128: DC.L $3FFB0000,$EAF6B0A8,$188EE1EB,$00000000
129: DC.L $3FFB0000,$F2DAF194,$9DBE79D5,$00000000
130: DC.L $3FFB0000,$FABD5813,$61D47E3E,$00000000
131: DC.L $3FFC0000,$8346AC21,$0959ECC4,$00000000
132: DC.L $3FFC0000,$8B232A08,$304282D8,$00000000
133: DC.L $3FFC0000,$92FB70B8,$D29AE2F9,$00000000
134: DC.L $3FFC0000,$9ACF476F,$5CCD1CB4,$00000000
135: DC.L $3FFC0000,$A29E7630,$4954F23F,$00000000
136: DC.L $3FFC0000,$AA68C5D0,$8AB85230,$00000000
137: DC.L $3FFC0000,$B22DFFFD,$9D539F83,$00000000
138: DC.L $3FFC0000,$B9EDEF45,$3E900EA5,$00000000
139: DC.L $3FFC0000,$C1A85F1C,$C75E3EA5,$00000000
140: DC.L $3FFC0000,$C95D1BE8,$28138DE6,$00000000
141: DC.L $3FFC0000,$D10BF300,$840D2DE4,$00000000
142: DC.L $3FFC0000,$D8B4B2BA,$6BC05E7A,$00000000
143: DC.L $3FFC0000,$E0572A6B,$B42335F6,$00000000
144: DC.L $3FFC0000,$E7F32A70,$EA9CAA8F,$00000000
145: DC.L $3FFC0000,$EF888432,$64ECEFAA,$00000000
146: DC.L $3FFC0000,$F7170A28,$ECC06666,$00000000
147: DC.L $3FFD0000,$812FD288,$332DAD32,$00000000
148: DC.L $3FFD0000,$88A8D1B1,$218E4D64,$00000000
149: DC.L $3FFD0000,$9012AB3F,$23E4AEE8,$00000000
150: DC.L $3FFD0000,$976CC3D4,$11E7F1B9,$00000000
151: DC.L $3FFD0000,$9EB68949,$3889A227,$00000000
152: DC.L $3FFD0000,$A5EF72C3,$4487361B,$00000000
153: DC.L $3FFD0000,$AD1700BA,$F07A7227,$00000000
154: DC.L $3FFD0000,$B42CBCFA,$FD37EFB7,$00000000
155: DC.L $3FFD0000,$BB303A94,$0BA80F89,$00000000
156: DC.L $3FFD0000,$C22115C6,$FCAEBBAF,$00000000
157: DC.L $3FFD0000,$C8FEF3E6,$86331221,$00000000
158: DC.L $3FFD0000,$CFC98330,$B4000C70,$00000000
159: DC.L $3FFD0000,$D6807AA1,$102C5BF9,$00000000
160: DC.L $3FFD0000,$DD2399BC,$31252AA3,$00000000
161: DC.L $3FFD0000,$E3B2A855,$6B8FC517,$00000000
162: DC.L $3FFD0000,$EA2D764F,$64315989,$00000000
163: DC.L $3FFD0000,$F3BF5BF8,$BAD1A21D,$00000000
164: DC.L $3FFE0000,$801CE39E,$0D205C9A,$00000000
165: DC.L $3FFE0000,$8630A2DA,$DA1ED066,$00000000
166: DC.L $3FFE0000,$8C1AD445,$F3E09B8C,$00000000
167: DC.L $3FFE0000,$91DB8F16,$64F350E2,$00000000
168: DC.L $3FFE0000,$97731420,$365E538C,$00000000
169: DC.L $3FFE0000,$9CE1C8E6,$A0B8CDBA,$00000000
170: DC.L $3FFE0000,$A22832DB,$CADAAE09,$00000000
171: DC.L $3FFE0000,$A746F2DD,$B7602294,$00000000
172: DC.L $3FFE0000,$AC3EC0FB,$997DD6A2,$00000000
173: DC.L $3FFE0000,$B110688A,$EBDC6F6A,$00000000
174: DC.L $3FFE0000,$B5BCC490,$59ECC4B0,$00000000
175: DC.L $3FFE0000,$BA44BC7D,$D470782F,$00000000
176: DC.L $3FFE0000,$BEA94144,$FD049AAC,$00000000
177: DC.L $3FFE0000,$C2EB4ABB,$661628B6,$00000000
178: DC.L $3FFE0000,$C70BD54C,$E602EE14,$00000000
179: DC.L $3FFE0000,$CD000549,$ADEC7159,$00000000
180: DC.L $3FFE0000,$D48457D2,$D8EA4EA3,$00000000
181: DC.L $3FFE0000,$DB948DA7,$12DECE3B,$00000000
182: DC.L $3FFE0000,$E23855F9,$69E8096A,$00000000
183: DC.L $3FFE0000,$E8771129,$C4353259,$00000000
184: DC.L $3FFE0000,$EE57C16E,$0D379C0D,$00000000
185: DC.L $3FFE0000,$F3E10211,$A87C3779,$00000000
186: DC.L $3FFE0000,$F919039D,$758B8D41,$00000000
187: DC.L $3FFE0000,$FE058B8F,$64935FB3,$00000000
188: DC.L $3FFF0000,$8155FB49,$7B685D04,$00000000
189: DC.L $3FFF0000,$83889E35,$49D108E1,$00000000
190: DC.L $3FFF0000,$859CFA76,$511D724B,$00000000
191: DC.L $3FFF0000,$87952ECF,$FF8131E7,$00000000
192: DC.L $3FFF0000,$89732FD1,$9557641B,$00000000
193: DC.L $3FFF0000,$8B38CAD1,$01932A35,$00000000
194: DC.L $3FFF0000,$8CE7A8D8,$301EE6B5,$00000000
195: DC.L $3FFF0000,$8F46A39E,$2EAE5281,$00000000
196: DC.L $3FFF0000,$922DA7D7,$91888487,$00000000
197: DC.L $3FFF0000,$94D19FCB,$DEDF5241,$00000000
198: DC.L $3FFF0000,$973AB944,$19D2A08B,$00000000
199: DC.L $3FFF0000,$996FF00E,$08E10B96,$00000000
200: DC.L $3FFF0000,$9B773F95,$12321DA7,$00000000
201: DC.L $3FFF0000,$9D55CC32,$0F935624,$00000000
202: DC.L $3FFF0000,$9F100575,$006CC571,$00000000
203: DC.L $3FFF0000,$A0A9C290,$D97CC06C,$00000000
204: DC.L $3FFF0000,$A22659EB,$EBC0630A,$00000000
205: DC.L $3FFF0000,$A388B4AF,$F6EF0EC9,$00000000
206: DC.L $3FFF0000,$A4D35F10,$61D292C4,$00000000
207: DC.L $3FFF0000,$A60895DC,$FBE3187E,$00000000
208: DC.L $3FFF0000,$A72A51DC,$7367BEAC,$00000000
209: DC.L $3FFF0000,$A83A5153,$0956168F,$00000000
210: DC.L $3FFF0000,$A93A2007,$7539546E,$00000000
211: DC.L $3FFF0000,$AA9E7245,$023B2605,$00000000
212: DC.L $3FFF0000,$AC4C84BA,$6FE4D58F,$00000000
213: DC.L $3FFF0000,$ADCE4A4A,$606B9712,$00000000
214: DC.L $3FFF0000,$AF2A2DCD,$8D263C9C,$00000000
215: DC.L $3FFF0000,$B0656F81,$F22265C7,$00000000
216: DC.L $3FFF0000,$B1846515,$0F71496A,$00000000
217: DC.L $3FFF0000,$B28AAA15,$6F9ADA35,$00000000
218: DC.L $3FFF0000,$B37B44FF,$3766B895,$00000000
219: DC.L $3FFF0000,$B458C3DC,$E9630433,$00000000
220: DC.L $3FFF0000,$B525529D,$562246BD,$00000000
221: DC.L $3FFF0000,$B5E2CCA9,$5F9D88CC,$00000000
222: DC.L $3FFF0000,$B692CADA,$7ACA1ADA,$00000000
223: DC.L $3FFF0000,$B736AEA7,$A6925838,$00000000
224: DC.L $3FFF0000,$B7CFAB28,$7E9F7B36,$00000000
225: DC.L $3FFF0000,$B85ECC66,$CB219835,$00000000
226: DC.L $3FFF0000,$B8E4FD5A,$20A593DA,$00000000
227: DC.L $3FFF0000,$B99F41F6,$4AFF9BB5,$00000000
228: DC.L $3FFF0000,$BA7F1E17,$842BBE7B,$00000000
229: DC.L $3FFF0000,$BB471285,$7637E17D,$00000000
230: DC.L $3FFF0000,$BBFABE8A,$4788DF6F,$00000000
231: DC.L $3FFF0000,$BC9D0FAD,$2B689D79,$00000000
232: DC.L $3FFF0000,$BD306A39,$471ECD86,$00000000
233: DC.L $3FFF0000,$BDB6C731,$856AF18A,$00000000
234: DC.L $3FFF0000,$BE31CAC5,$02E80D70,$00000000
235: DC.L $3FFF0000,$BEA2D55C,$E33194E2,$00000000
236: DC.L $3FFF0000,$BF0B10B7,$C03128F0,$00000000
237: DC.L $3FFF0000,$BF6B7A18,$DACB778D,$00000000
238: DC.L $3FFF0000,$BFC4EA46,$63FA18F6,$00000000
239: DC.L $3FFF0000,$C0181BDE,$8B89A454,$00000000
240: DC.L $3FFF0000,$C065B066,$CFBF6439,$00000000
241: DC.L $3FFF0000,$C0AE345F,$56340AE6,$00000000
242: DC.L $3FFF0000,$C0F22291,$9CB9E6A7,$00000000
243:
244: X equ FP_SCR1
245: XDCARE equ X+2
246: XFRAC equ X+4
247: XFRACLO equ X+8
248:
249: ATANF equ FP_SCR2
250: ATANFHI equ ATANF+4
251: ATANFLO equ ATANF+8
252:
253:
254: xref t_frcinx
255: xref t_extdnrm
256:
257: xdef satand
258: satand:
259: *--ENTRY POINT FOR ATAN(X) FOR DENORMALIZED ARGUMENT
260:
261: bra t_extdnrm
262:
263: xdef satan
264: satan:
265: *--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
266:
267: FMOVE.X (A0),FP0 ...LOAD INPUT
268:
269: MOVE.L (A0),D0
270: MOVE.W 4(A0),D0
271: FMOVE.X FP0,X(a6)
272: ANDI.L #$7FFFFFFF,D0
273:
274: CMPI.L #$3FFB8000,D0 ...|X| >= 1/16?
275: BGE.B ATANOK1
276: BRA.W ATANSM
277:
278: ATANOK1:
279: CMPI.L #$4002FFFF,D0 ...|X| < 16 ?
280: BLE.B ATANMAIN
281: BRA.W ATANBIG
282:
283:
284: *--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
285: *--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
286: *--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
287: *--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
288: *--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
289: *--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
290: *--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
291: *--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
292: *--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
293: *--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
294: *--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
295: *--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
296: *--WILL INVOLVE A VERY LONG POLYNOMIAL.
297:
298: *--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
299: *--WE CHOSE F TO BE +-2^K * 1.BBBB1
300: *--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
301: *--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
302: *--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
303: *-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
304:
305: ATANMAIN:
306:
307: CLR.W XDCARE(a6) ...CLEAN UP X JUST IN CASE
308: ANDI.L #$F8000000,XFRAC(a6) ...FIRST 5 BITS
309: ORI.L #$04000000,XFRAC(a6) ...SET 6-TH BIT TO 1
310: CLR.L XFRACLO(a6) ...LOCATION OF X IS NOW F
311:
312: FMOVE.X FP0,FP1 ...FP1 IS X
313: FMUL.X X(a6),FP1 ...FP1 IS X*F, NOTE THAT X*F > 0
314: FSUB.X X(a6),FP0 ...FP0 IS X-F
315: FADD.S #:3F800000,FP1 ...FP1 IS 1 + X*F
316: FDIV.X FP1,FP0 ...FP0 IS U = (X-F)/(1+X*F)
317:
318: *--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
319: *--CREATE ATAN(F) AND STORE IT IN ATANF, AND
320: *--SAVE REGISTERS FP2.
321:
322: MOVE.L d2,-(a7) ...SAVE d2 TEMPORARILY
323: MOVE.L d0,d2 ...THE EXPO AND 16 BITS OF X
324: ANDI.L #$00007800,d0 ...4 VARYING BITS OF F'S FRACTION
325: ANDI.L #$7FFF0000,d2 ...EXPONENT OF F
326: SUBI.L #$3FFB0000,d2 ...K+4
327: ASR.L #1,d2
328: ADD.L d2,d0 ...THE 7 BITS IDENTIFYING F
329: ASR.L #7,d0 ...INDEX INTO TBL OF ATAN(|F|)
330: LEA ATANTBL,a1
331: ADDA.L d0,a1 ...ADDRESS OF ATAN(|F|)
332: MOVE.L (a1)+,ATANF(a6)
333: MOVE.L (a1)+,ATANFHI(a6)
334: MOVE.L (a1)+,ATANFLO(a6) ...ATANF IS NOW ATAN(|F|)
335: MOVE.L X(a6),d0 ...LOAD SIGN AND EXPO. AGAIN
336: ANDI.L #$80000000,d0 ...SIGN(F)
337: OR.L d0,ATANF(a6) ...ATANF IS NOW SIGN(F)*ATAN(|F|)
338: MOVE.L (a7)+,d2 ...RESTORE d2
339:
340: *--THAT'S ALL I HAVE TO DO FOR NOW,
341: *--BUT ALAS, THE DIVIDE IS STILL CRANKING!
342:
343: *--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
344: *--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
345: *--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
346: *--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
347: *--WHAT WE HAVE HERE IS MERELY A1 = A3, A2 = A1/A3, A3 = A2/A3.
348: *--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
349: *--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
350:
351:
352: FMOVE.X FP0,FP1
353: FMUL.X FP1,FP1
354: FMOVE.D ATANA3,FP2
355: FADD.X FP1,FP2 ...A3+V
356: FMUL.X FP1,FP2 ...V*(A3+V)
357: FMUL.X FP0,FP1 ...U*V
358: FADD.D ATANA2,FP2 ...A2+V*(A3+V)
359: FMUL.D ATANA1,FP1 ...A1*U*V
360: FMUL.X FP2,FP1 ...A1*U*V*(A2+V*(A3+V))
361:
362: FADD.X FP1,FP0 ...ATAN(U), FP1 RELEASED
363: FMOVE.L d1,FPCR ;restore users exceptions
364: FADD.X ATANF(a6),FP0 ...ATAN(X)
365: bra t_frcinx
366:
367: ATANBORS:
368: *--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
369: *--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
370: CMPI.L #$3FFF8000,d0
371: BGT.W ATANBIG ...I.E. |X| >= 16
372:
373: ATANSM:
374: *--|X| <= 1/16
375: *--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
376: *--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
377: *--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
378: *--WHERE Y = X*X, AND Z = Y*Y.
379:
380: CMPI.L #$3FD78000,d0
381: BLT.W ATANTINY
382: *--COMPUTE POLYNOMIAL
383: FMUL.X FP0,FP0 ...FP0 IS Y = X*X
384:
385:
386: CLR.W XDCARE(a6)
387:
388: FMOVE.X FP0,FP1
389: FMUL.X FP1,FP1 ...FP1 IS Z = Y*Y
390:
391: FMOVE.D ATANB6,FP2
392: FMOVE.D ATANB5,FP3
393:
394: FMUL.X FP1,FP2 ...Z*B6
395: FMUL.X FP1,FP3 ...Z*B5
396:
397: FADD.D ATANB4,FP2 ...B4+Z*B6
398: FADD.D ATANB3,FP3 ...B3+Z*B5
399:
400: FMUL.X FP1,FP2 ...Z*(B4+Z*B6)
401: FMUL.X FP3,FP1 ...Z*(B3+Z*B5)
402:
403: FADD.D ATANB2,FP2 ...B2+Z*(B4+Z*B6)
404: FADD.D ATANB1,FP1 ...B1+Z*(B3+Z*B5)
405:
406: FMUL.X FP0,FP2 ...Y*(B2+Z*(B4+Z*B6))
407: FMUL.X X(a6),FP0 ...X*Y
408:
409: FADD.X FP2,FP1 ...[B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))]
410:
411:
412: FMUL.X FP1,FP0 ...X*Y*([B1+Z*(B3+Z*B5)]+[Y*(B2+Z*(B4+Z*B6))])
413:
414: FMOVE.L d1,FPCR ;restore users exceptions
415: FADD.X X(a6),FP0
416:
417: bra t_frcinx
418:
419: ATANTINY:
420: *--|X| < 2^(-40), ATAN(X) = X
421: CLR.W XDCARE(a6)
422:
423: FMOVE.L d1,FPCR ;restore users exceptions
424: FMOVE.X X(a6),FP0 ;last inst - possible exception set
425:
426: bra t_frcinx
427:
428: ATANBIG:
429: *--IF |X| > 2^(100), RETURN SIGN(X)*(PI/2 - TINY). OTHERWISE,
430: *--RETURN SIGN(X)*PI/2 + ATAN(-1/X).
431: CMPI.L #$40638000,d0
432: BGT.W ATANHUGE
433:
434: *--APPROXIMATE ATAN(-1/X) BY
435: *--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
436: *--THIS CAN BE RE-WRITTEN AS
437: *--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
438:
439: FMOVE.S #:BF800000,FP1 ...LOAD -1
440: FDIV.X FP0,FP1 ...FP1 IS -1/X
441:
442:
443: *--DIVIDE IS STILL CRANKING
444:
445: FMOVE.X FP1,FP0 ...FP0 IS X'
446: FMUL.X FP0,FP0 ...FP0 IS Y = X'*X'
447: FMOVE.X FP1,X(a6) ...X IS REALLY X'
448:
449: FMOVE.X FP0,FP1
450: FMUL.X FP1,FP1 ...FP1 IS Z = Y*Y
451:
452: FMOVE.D ATANC5,FP3
453: FMOVE.D ATANC4,FP2
454:
455: FMUL.X FP1,FP3 ...Z*C5
456: FMUL.X FP1,FP2 ...Z*B4
457:
458: FADD.D ATANC3,FP3 ...C3+Z*C5
459: FADD.D ATANC2,FP2 ...C2+Z*C4
460:
461: FMUL.X FP3,FP1 ...Z*(C3+Z*C5), FP3 RELEASED
462: FMUL.X FP0,FP2 ...Y*(C2+Z*C4)
463:
464: FADD.D ATANC1,FP1 ...C1+Z*(C3+Z*C5)
465: FMUL.X X(a6),FP0 ...X'*Y
466:
467: FADD.X FP2,FP1 ...[Y*(C2+Z*C4)]+[C1+Z*(C3+Z*C5)]
468:
469:
470: FMUL.X FP1,FP0 ...X'*Y*([B1+Z*(B3+Z*B5)]
471: * ... +[Y*(B2+Z*(B4+Z*B6))])
472: FADD.X X(a6),FP0
473:
474: FMOVE.L d1,FPCR ;restore users exceptions
475:
476: btst.b #7,(a0)
477: beq.b pos_big
478:
479: neg_big:
480: FADD.X NPIBY2,FP0
481: bra t_frcinx
482:
483: pos_big:
484: FADD.X PPIBY2,FP0
485: bra t_frcinx
486:
487: ATANHUGE:
488: *--RETURN SIGN(X)*(PIBY2 - TINY) = SIGN(X)*PIBY2 - SIGN(X)*TINY
489: btst.b #7,(a0)
490: beq.b pos_huge
491:
492: neg_huge:
493: FMOVE.X NPIBY2,fp0
494: fmove.l d1,fpcr
495: fsub.x NTINY,fp0
496: bra t_frcinx
497:
498: pos_huge:
499: FMOVE.X PPIBY2,fp0
500: fmove.l d1,fpcr
501: fsub.x PTINY,fp0
502: bra t_frcinx
503:
504: end
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