Annotation of sys/arch/m68k/fpsp/satan.sa, Revision 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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