Annotation of sys/arch/m68k/fpsp/stan.sa, Revision 1.1
1.1 ! nbrk 1: * $OpenBSD: stan.sa,v 1.3 2003/11/07 10:36:10 miod Exp $
! 2: * $NetBSD: stan.sa,v 1.3 1994/10/26 07:50:10 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: * stan.sa 3.3 7/29/91
! 36: *
! 37: * The entry point stan computes the tangent of
! 38: * an input argument;
! 39: * stand does the same except for denormalized input.
! 40: *
! 41: * Input: Double-extended number X in location pointed to
! 42: * by address register a0.
! 43: *
! 44: * Output: The value tan(X) returned in floating-point register Fp0.
! 45: *
! 46: * Accuracy and Monotonicity: The returned result is within 3 ulp 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 sTAN takes approximately 170 cycles for
! 52: * input argument X such that |X| < 15Pi, which is the usual
! 53: * situation.
! 54: *
! 55: * Algorithm:
! 56: *
! 57: * 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.
! 58: *
! 59: * 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
! 60: * k = N mod 2, so in particular, k = 0 or 1.
! 61: *
! 62: * 3. If k is odd, go to 5.
! 63: *
! 64: * 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a
! 65: * rational function U/V where
! 66: * U = r + r*s*(P1 + s*(P2 + s*P3)), and
! 67: * V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r.
! 68: * Exit.
! 69: *
! 70: * 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by a
! 71: * rational function U/V where
! 72: * U = r + r*s*(P1 + s*(P2 + s*P3)), and
! 73: * V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r,
! 74: * -Cot(r) = -V/U. Exit.
! 75: *
! 76: * 6. If |X| > 1, go to 8.
! 77: *
! 78: * 7. (|X|<2**(-40)) Tan(X) = X. Exit.
! 79: *
! 80: * 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.
! 81: *
! 82:
! 83: STAN IDNT 2,1 Motorola 040 Floating Point Software Package
! 84:
! 85: section 8
! 86:
! 87: include fpsp.h
! 88:
! 89: BOUNDS1 DC.L $3FD78000,$4004BC7E
! 90: TWOBYPI DC.L $3FE45F30,$6DC9C883
! 91:
! 92: TANQ4 DC.L $3EA0B759,$F50F8688
! 93: TANP3 DC.L $BEF2BAA5,$A8924F04
! 94:
! 95: TANQ3 DC.L $BF346F59,$B39BA65F,$00000000,$00000000
! 96:
! 97: TANP2 DC.L $3FF60000,$E073D3FC,$199C4A00,$00000000
! 98:
! 99: TANQ2 DC.L $3FF90000,$D23CD684,$15D95FA1,$00000000
! 100:
! 101: TANP1 DC.L $BFFC0000,$8895A6C5,$FB423BCA,$00000000
! 102:
! 103: TANQ1 DC.L $BFFD0000,$EEF57E0D,$A84BC8CE,$00000000
! 104:
! 105: INVTWOPI DC.L $3FFC0000,$A2F9836E,$4E44152A,$00000000
! 106:
! 107: TWOPI1 DC.L $40010000,$C90FDAA2,$00000000,$00000000
! 108: TWOPI2 DC.L $3FDF0000,$85A308D4,$00000000,$00000000
! 109:
! 110: *--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING
! 111: *--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT
! 112: *--MOST 69 BITS LONG.
! 113: xdef PITBL
! 114: PITBL:
! 115: DC.L $C0040000,$C90FDAA2,$2168C235,$21800000
! 116: DC.L $C0040000,$C2C75BCD,$105D7C23,$A0D00000
! 117: DC.L $C0040000,$BC7EDCF7,$FF523611,$A1E80000
! 118: DC.L $C0040000,$B6365E22,$EE46F000,$21480000
! 119: DC.L $C0040000,$AFEDDF4D,$DD3BA9EE,$A1200000
! 120: DC.L $C0040000,$A9A56078,$CC3063DD,$21FC0000
! 121: DC.L $C0040000,$A35CE1A3,$BB251DCB,$21100000
! 122: DC.L $C0040000,$9D1462CE,$AA19D7B9,$A1580000
! 123: DC.L $C0040000,$96CBE3F9,$990E91A8,$21E00000
! 124: DC.L $C0040000,$90836524,$88034B96,$20B00000
! 125: DC.L $C0040000,$8A3AE64F,$76F80584,$A1880000
! 126: DC.L $C0040000,$83F2677A,$65ECBF73,$21C40000
! 127: DC.L $C0030000,$FB53D14A,$A9C2F2C2,$20000000
! 128: DC.L $C0030000,$EEC2D3A0,$87AC669F,$21380000
! 129: DC.L $C0030000,$E231D5F6,$6595DA7B,$A1300000
! 130: DC.L $C0030000,$D5A0D84C,$437F4E58,$9FC00000
! 131: DC.L $C0030000,$C90FDAA2,$2168C235,$21000000
! 132: DC.L $C0030000,$BC7EDCF7,$FF523611,$A1680000
! 133: DC.L $C0030000,$AFEDDF4D,$DD3BA9EE,$A0A00000
! 134: DC.L $C0030000,$A35CE1A3,$BB251DCB,$20900000
! 135: DC.L $C0030000,$96CBE3F9,$990E91A8,$21600000
! 136: DC.L $C0030000,$8A3AE64F,$76F80584,$A1080000
! 137: DC.L $C0020000,$FB53D14A,$A9C2F2C2,$1F800000
! 138: DC.L $C0020000,$E231D5F6,$6595DA7B,$A0B00000
! 139: DC.L $C0020000,$C90FDAA2,$2168C235,$20800000
! 140: DC.L $C0020000,$AFEDDF4D,$DD3BA9EE,$A0200000
! 141: DC.L $C0020000,$96CBE3F9,$990E91A8,$20E00000
! 142: DC.L $C0010000,$FB53D14A,$A9C2F2C2,$1F000000
! 143: DC.L $C0010000,$C90FDAA2,$2168C235,$20000000
! 144: DC.L $C0010000,$96CBE3F9,$990E91A8,$20600000
! 145: DC.L $C0000000,$C90FDAA2,$2168C235,$1F800000
! 146: DC.L $BFFF0000,$C90FDAA2,$2168C235,$1F000000
! 147: DC.L $00000000,$00000000,$00000000,$00000000
! 148: DC.L $3FFF0000,$C90FDAA2,$2168C235,$9F000000
! 149: DC.L $40000000,$C90FDAA2,$2168C235,$9F800000
! 150: DC.L $40010000,$96CBE3F9,$990E91A8,$A0600000
! 151: DC.L $40010000,$C90FDAA2,$2168C235,$A0000000
! 152: DC.L $40010000,$FB53D14A,$A9C2F2C2,$9F000000
! 153: DC.L $40020000,$96CBE3F9,$990E91A8,$A0E00000
! 154: DC.L $40020000,$AFEDDF4D,$DD3BA9EE,$20200000
! 155: DC.L $40020000,$C90FDAA2,$2168C235,$A0800000
! 156: DC.L $40020000,$E231D5F6,$6595DA7B,$20B00000
! 157: DC.L $40020000,$FB53D14A,$A9C2F2C2,$9F800000
! 158: DC.L $40030000,$8A3AE64F,$76F80584,$21080000
! 159: DC.L $40030000,$96CBE3F9,$990E91A8,$A1600000
! 160: DC.L $40030000,$A35CE1A3,$BB251DCB,$A0900000
! 161: DC.L $40030000,$AFEDDF4D,$DD3BA9EE,$20A00000
! 162: DC.L $40030000,$BC7EDCF7,$FF523611,$21680000
! 163: DC.L $40030000,$C90FDAA2,$2168C235,$A1000000
! 164: DC.L $40030000,$D5A0D84C,$437F4E58,$1FC00000
! 165: DC.L $40030000,$E231D5F6,$6595DA7B,$21300000
! 166: DC.L $40030000,$EEC2D3A0,$87AC669F,$A1380000
! 167: DC.L $40030000,$FB53D14A,$A9C2F2C2,$A0000000
! 168: DC.L $40040000,$83F2677A,$65ECBF73,$A1C40000
! 169: DC.L $40040000,$8A3AE64F,$76F80584,$21880000
! 170: DC.L $40040000,$90836524,$88034B96,$A0B00000
! 171: DC.L $40040000,$96CBE3F9,$990E91A8,$A1E00000
! 172: DC.L $40040000,$9D1462CE,$AA19D7B9,$21580000
! 173: DC.L $40040000,$A35CE1A3,$BB251DCB,$A1100000
! 174: DC.L $40040000,$A9A56078,$CC3063DD,$A1FC0000
! 175: DC.L $40040000,$AFEDDF4D,$DD3BA9EE,$21200000
! 176: DC.L $40040000,$B6365E22,$EE46F000,$A1480000
! 177: DC.L $40040000,$BC7EDCF7,$FF523611,$21E80000
! 178: DC.L $40040000,$C2C75BCD,$105D7C23,$20D00000
! 179: DC.L $40040000,$C90FDAA2,$2168C235,$A1800000
! 180:
! 181: INARG equ FP_SCR4
! 182:
! 183: TWOTO63 equ L_SCR1
! 184: ENDFLAG equ L_SCR2
! 185: N equ L_SCR3
! 186:
! 187: xref t_frcinx
! 188: xref t_extdnrm
! 189:
! 190: xdef stand
! 191: stand:
! 192: *--TAN(X) = X FOR DENORMALIZED X
! 193:
! 194: bra t_extdnrm
! 195:
! 196: xdef stan
! 197: stan:
! 198: FMOVE.X (a0),FP0 ...LOAD INPUT
! 199:
! 200: MOVE.L (A0),D0
! 201: MOVE.W 4(A0),D0
! 202: ANDI.L #$7FFFFFFF,D0
! 203:
! 204: CMPI.L #$3FD78000,D0 ...|X| >= 2**(-40)?
! 205: BGE.B TANOK1
! 206: BRA.W TANSM
! 207: TANOK1:
! 208: CMPI.L #$4004BC7E,D0 ...|X| < 15 PI?
! 209: BLT.B TANMAIN
! 210: BRA.W REDUCEX
! 211:
! 212:
! 213: TANMAIN:
! 214: *--THIS IS THE USUAL CASE, |X| <= 15 PI.
! 215: *--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
! 216: FMOVE.X FP0,FP1
! 217: FMUL.D TWOBYPI,FP1 ...X*2/PI
! 218:
! 219: *--HIDE THE NEXT TWO INSTRUCTIONS
! 220: lea.l PITBL+$200,a1 ...TABLE OF N*PI/2, N = -32,...,32
! 221:
! 222: *--FP1 IS NOW READY
! 223: FMOVE.L FP1,D0 ...CONVERT TO INTEGER
! 224:
! 225: ASL.L #4,D0
! 226: ADDA.L D0,a1 ...ADDRESS N*PIBY2 IN Y1, Y2
! 227:
! 228: FSUB.X (a1)+,FP0 ...X-Y1
! 229: *--HIDE THE NEXT ONE
! 230:
! 231: FSUB.S (a1),FP0 ...FP0 IS R = (X-Y1)-Y2
! 232:
! 233: ROR.L #5,D0
! 234: ANDI.L #$80000000,D0 ...D0 WAS ODD IFF D0 < 0
! 235:
! 236: TANCONT:
! 237:
! 238: TST.L D0
! 239: BLT.W NODD
! 240:
! 241: FMOVE.X FP0,FP1
! 242: FMUL.X FP1,FP1 ...S = R*R
! 243:
! 244: FMOVE.D TANQ4,FP3
! 245: FMOVE.D TANP3,FP2
! 246:
! 247: FMUL.X FP1,FP3 ...SQ4
! 248: FMUL.X FP1,FP2 ...SP3
! 249:
! 250: FADD.D TANQ3,FP3 ...Q3+SQ4
! 251: FADD.X TANP2,FP2 ...P2+SP3
! 252:
! 253: FMUL.X FP1,FP3 ...S(Q3+SQ4)
! 254: FMUL.X FP1,FP2 ...S(P2+SP3)
! 255:
! 256: FADD.X TANQ2,FP3 ...Q2+S(Q3+SQ4)
! 257: FADD.X TANP1,FP2 ...P1+S(P2+SP3)
! 258:
! 259: FMUL.X FP1,FP3 ...S(Q2+S(Q3+SQ4))
! 260: FMUL.X FP1,FP2 ...S(P1+S(P2+SP3))
! 261:
! 262: FADD.X TANQ1,FP3 ...Q1+S(Q2+S(Q3+SQ4))
! 263: FMUL.X FP0,FP2 ...RS(P1+S(P2+SP3))
! 264:
! 265: FMUL.X FP3,FP1 ...S(Q1+S(Q2+S(Q3+SQ4)))
! 266:
! 267:
! 268: FADD.X FP2,FP0 ...R+RS(P1+S(P2+SP3))
! 269:
! 270:
! 271: FADD.S #:3F800000,FP1 ...1+S(Q1+...)
! 272:
! 273: FMOVE.L d1,fpcr ;restore users exceptions
! 274: FDIV.X FP1,FP0 ;last inst - possible exception set
! 275:
! 276: bra t_frcinx
! 277:
! 278: NODD:
! 279: FMOVE.X FP0,FP1
! 280: FMUL.X FP0,FP0 ...S = R*R
! 281:
! 282: FMOVE.D TANQ4,FP3
! 283: FMOVE.D TANP3,FP2
! 284:
! 285: FMUL.X FP0,FP3 ...SQ4
! 286: FMUL.X FP0,FP2 ...SP3
! 287:
! 288: FADD.D TANQ3,FP3 ...Q3+SQ4
! 289: FADD.X TANP2,FP2 ...P2+SP3
! 290:
! 291: FMUL.X FP0,FP3 ...S(Q3+SQ4)
! 292: FMUL.X FP0,FP2 ...S(P2+SP3)
! 293:
! 294: FADD.X TANQ2,FP3 ...Q2+S(Q3+SQ4)
! 295: FADD.X TANP1,FP2 ...P1+S(P2+SP3)
! 296:
! 297: FMUL.X FP0,FP3 ...S(Q2+S(Q3+SQ4))
! 298: FMUL.X FP0,FP2 ...S(P1+S(P2+SP3))
! 299:
! 300: FADD.X TANQ1,FP3 ...Q1+S(Q2+S(Q3+SQ4))
! 301: FMUL.X FP1,FP2 ...RS(P1+S(P2+SP3))
! 302:
! 303: FMUL.X FP3,FP0 ...S(Q1+S(Q2+S(Q3+SQ4)))
! 304:
! 305:
! 306: FADD.X FP2,FP1 ...R+RS(P1+S(P2+SP3))
! 307: FADD.S #:3F800000,FP0 ...1+S(Q1+...)
! 308:
! 309:
! 310: FMOVE.X FP1,-(sp)
! 311: EORI.L #$80000000,(sp)
! 312:
! 313: FMOVE.L d1,fpcr ;restore users exceptions
! 314: FDIV.X (sp)+,FP0 ;last inst - possible exception set
! 315:
! 316: bra t_frcinx
! 317:
! 318: TANBORS:
! 319: *--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
! 320: *--IF |X| < 2**(-40), RETURN X OR 1.
! 321: CMPI.L #$3FFF8000,D0
! 322: BGT.B REDUCEX
! 323:
! 324: TANSM:
! 325:
! 326: FMOVE.X FP0,-(sp)
! 327: FMOVE.L d1,fpcr ;restore users exceptions
! 328: FMOVE.X (sp)+,FP0 ;last inst - posibble exception set
! 329:
! 330: bra t_frcinx
! 331:
! 332:
! 333: REDUCEX:
! 334: *--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
! 335: *--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
! 336: *--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
! 337:
! 338: FMOVEM.X FP2-FP5,-(A7) ...save FP2 through FP5
! 339: MOVE.L D2,-(A7)
! 340: FMOVE.S #:00000000,FP1
! 341:
! 342: *--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
! 343: *--there is a danger of unwanted overflow in first LOOP iteration. In this
! 344: *--case, reduce argument by one remainder step to make subsequent reduction
! 345: *--safe.
! 346: cmpi.l #$7ffeffff,d0 ;is argument dangerously large?
! 347: bne.b LOOP
! 348: move.l #$7ffe0000,FP_SCR2(a6) ;yes
! 349: * ;create 2**16383*PI/2
! 350: move.l #$c90fdaa2,FP_SCR2+4(a6)
! 351: clr.l FP_SCR2+8(a6)
! 352: ftst.x fp0 ;test sign of argument
! 353: move.l #$7fdc0000,FP_SCR3(a6) ;create low half of 2**16383*
! 354: * ;PI/2 at FP_SCR3
! 355: move.l #$85a308d3,FP_SCR3+4(a6)
! 356: clr.l FP_SCR3+8(a6)
! 357: fblt.w red_neg
! 358: or.w #$8000,FP_SCR2(a6) ;positive arg
! 359: or.w #$8000,FP_SCR3(a6)
! 360: red_neg:
! 361: fadd.x FP_SCR2(a6),fp0 ;high part of reduction is exact
! 362: fmove.x fp0,fp1 ;save high result in fp1
! 363: fadd.x FP_SCR3(a6),fp0 ;low part of reduction
! 364: fsub.x fp0,fp1 ;determine low component of result
! 365: fadd.x FP_SCR3(a6),fp1 ;fp0/fp1 are reduced argument.
! 366:
! 367: *--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
! 368: *--integer quotient will be stored in N
! 369: *--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1)
! 370:
! 371: LOOP:
! 372: FMOVE.X FP0,INARG(a6) ...+-2**K * F, 1 <= F < 2
! 373: MOVE.W INARG(a6),D0
! 374: MOVE.L D0,A1 ...save a copy of D0
! 375: ANDI.L #$00007FFF,D0
! 376: SUBI.L #$00003FFF,D0 ...D0 IS K
! 377: CMPI.L #28,D0
! 378: BLE.B LASTLOOP
! 379: CONTLOOP:
! 380: SUBI.L #27,D0 ...D0 IS L := K-27
! 381: CLR.L ENDFLAG(a6)
! 382: BRA.B WORK
! 383: LASTLOOP:
! 384: CLR.L D0 ...D0 IS L := 0
! 385: MOVE.L #1,ENDFLAG(a6)
! 386:
! 387: WORK:
! 388: *--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
! 389: *--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
! 390:
! 391: *--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
! 392: *--2**L * (PIby2_1), 2**L * (PIby2_2)
! 393:
! 394: MOVE.L #$00003FFE,D2 ...BIASED EXPO OF 2/PI
! 395: SUB.L D0,D2 ...BIASED EXPO OF 2**(-L)*(2/PI)
! 396:
! 397: MOVE.L #$A2F9836E,FP_SCR1+4(a6)
! 398: MOVE.L #$4E44152A,FP_SCR1+8(a6)
! 399: MOVE.W D2,FP_SCR1(a6) ...FP_SCR1 is 2**(-L)*(2/PI)
! 400:
! 401: FMOVE.X FP0,FP2
! 402: FMUL.X FP_SCR1(a6),FP2
! 403: *--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
! 404: *--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
! 405: *--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
! 406: *--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
! 407: *--US THE DESIRED VALUE IN FLOATING POINT.
! 408:
! 409: *--HIDE SIX CYCLES OF INSTRUCTION
! 410: MOVE.L A1,D2
! 411: SWAP D2
! 412: ANDI.L #$80000000,D2
! 413: ORI.L #$5F000000,D2 ...D2 IS SIGN(INARG)*2**63 IN SGL
! 414: MOVE.L D2,TWOTO63(a6)
! 415:
! 416: MOVE.L D0,D2
! 417: ADDI.L #$00003FFF,D2 ...BIASED EXPO OF 2**L * (PI/2)
! 418:
! 419: *--FP2 IS READY
! 420: FADD.S TWOTO63(a6),FP2 ...THE FRACTIONAL PART OF FP1 IS ROUNDED
! 421:
! 422: *--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1 and 2**(L)*Piby2_2
! 423: MOVE.W D2,FP_SCR2(a6)
! 424: CLR.W FP_SCR2+2(a6)
! 425: MOVE.L #$C90FDAA2,FP_SCR2+4(a6)
! 426: CLR.L FP_SCR2+8(a6) ...FP_SCR2 is 2**(L) * Piby2_1
! 427:
! 428: *--FP2 IS READY
! 429: FSUB.S TWOTO63(a6),FP2 ...FP2 is N
! 430:
! 431: ADDI.L #$00003FDD,D0
! 432: MOVE.W D0,FP_SCR3(a6)
! 433: CLR.W FP_SCR3+2(a6)
! 434: MOVE.L #$85A308D3,FP_SCR3+4(a6)
! 435: CLR.L FP_SCR3+8(a6) ...FP_SCR3 is 2**(L) * Piby2_2
! 436:
! 437: MOVE.L ENDFLAG(a6),D0
! 438:
! 439: *--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
! 440: *--P2 = 2**(L) * Piby2_2
! 441: FMOVE.X FP2,FP4
! 442: FMul.X FP_SCR2(a6),FP4 ...W = N*P1
! 443: FMove.X FP2,FP5
! 444: FMul.X FP_SCR3(a6),FP5 ...w = N*P2
! 445: FMove.X FP4,FP3
! 446: *--we want P+p = W+w but |p| <= half ulp of P
! 447: *--Then, we need to compute A := R-P and a := r-p
! 448: FAdd.X FP5,FP3 ...FP3 is P
! 449: FSub.X FP3,FP4 ...W-P
! 450:
! 451: FSub.X FP3,FP0 ...FP0 is A := R - P
! 452: FAdd.X FP5,FP4 ...FP4 is p = (W-P)+w
! 453:
! 454: FMove.X FP0,FP3 ...FP3 A
! 455: FSub.X FP4,FP1 ...FP1 is a := r - p
! 456:
! 457: *--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
! 458: *--|r| <= half ulp of R.
! 459: FAdd.X FP1,FP0 ...FP0 is R := A+a
! 460: *--No need to calculate r if this is the last loop
! 461: TST.L D0
! 462: BGT.W RESTORE
! 463:
! 464: *--Need to calculate r
! 465: FSub.X FP0,FP3 ...A-R
! 466: FAdd.X FP3,FP1 ...FP1 is r := (A-R)+a
! 467: BRA.W LOOP
! 468:
! 469: RESTORE:
! 470: FMOVE.L FP2,N(a6)
! 471: MOVE.L (A7)+,D2
! 472: FMOVEM.X (A7)+,FP2-FP5
! 473:
! 474:
! 475: MOVE.L N(a6),D0
! 476: ROR.L #1,D0
! 477:
! 478:
! 479: BRA.W TANCONT
! 480:
! 481: end
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