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1.1 ! nbrk 1: * $OpenBSD: srem_mod.sa,v 1.2 1996/05/29 21:05:41 niklas Exp $
! 2: * $NetBSD: srem_mod.sa,v 1.3 1994/10/26 07:49:58 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: * srem_mod.sa 3.1 12/10/90
! 36: *
! 37: * The entry point sMOD computes the floating point MOD of the
! 38: * input values X and Y. The entry point sREM computes the floating
! 39: * point (IEEE) REM of the input values X and Y.
! 40: *
! 41: * INPUT
! 42: * -----
! 43: * Double-extended value Y is pointed to by address in register
! 44: * A0. Double-extended value X is located in -12(A0). The values
! 45: * of X and Y are both nonzero and finite; although either or both
! 46: * of them can be denormalized. The special cases of zeros, NaNs,
! 47: * and infinities are handled elsewhere.
! 48: *
! 49: * OUTPUT
! 50: * ------
! 51: * FREM(X,Y) or FMOD(X,Y), depending on entry point.
! 52: *
! 53: * ALGORITHM
! 54: * ---------
! 55: *
! 56: * Step 1. Save and strip signs of X and Y: signX := sign(X),
! 57: * signY := sign(Y), X := |X|, Y := |Y|,
! 58: * signQ := signX EOR signY. Record whether MOD or REM
! 59: * is requested.
! 60: *
! 61: * Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0.
! 62: * If (L < 0) then
! 63: * R := X, go to Step 4.
! 64: * else
! 65: * R := 2^(-L)X, j := L.
! 66: * endif
! 67: *
! 68: * Step 3. Perform MOD(X,Y)
! 69: * 3.1 If R = Y, go to Step 9.
! 70: * 3.2 If R > Y, then { R := R - Y, Q := Q + 1}
! 71: * 3.3 If j = 0, go to Step 4.
! 72: * 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to
! 73: * Step 3.1.
! 74: *
! 75: * Step 4. At this point, R = X - QY = MOD(X,Y). Set
! 76: * Last_Subtract := false (used in Step 7 below). If
! 77: * MOD is requested, go to Step 6.
! 78: *
! 79: * Step 5. R = MOD(X,Y), but REM(X,Y) is requested.
! 80: * 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to
! 81: * Step 6.
! 82: * 5.2 If R > Y/2, then { set Last_Subtract := true,
! 83: * Q := Q + 1, Y := signY*Y }. Go to Step 6.
! 84: * 5.3 This is the tricky case of R = Y/2. If Q is odd,
! 85: * then { Q := Q + 1, signX := -signX }.
! 86: *
! 87: * Step 6. R := signX*R.
! 88: *
! 89: * Step 7. If Last_Subtract = true, R := R - Y.
! 90: *
! 91: * Step 8. Return signQ, last 7 bits of Q, and R as required.
! 92: *
! 93: * Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus,
! 94: * X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1),
! 95: * R := 0. Return signQ, last 7 bits of Q, and R.
! 96: *
! 97:
! 98: SREM_MOD IDNT 2,1 Motorola 040 Floating Point Software Package
! 99:
! 100: section 8
! 101:
! 102: include fpsp.h
! 103:
! 104: Mod_Flag equ L_SCR3
! 105: SignY equ FP_SCR3+4
! 106: SignX equ FP_SCR3+8
! 107: SignQ equ FP_SCR3+12
! 108: Sc_Flag equ FP_SCR4
! 109:
! 110: Y equ FP_SCR1
! 111: Y_Hi equ Y+4
! 112: Y_Lo equ Y+8
! 113:
! 114: R equ FP_SCR2
! 115: R_Hi equ R+4
! 116: R_Lo equ R+8
! 117:
! 118:
! 119: Scale DC.L $00010000,$80000000,$00000000,$00000000
! 120:
! 121: xref t_avoid_unsupp
! 122:
! 123: xdef smod
! 124: smod:
! 125:
! 126: Clr.L Mod_Flag(a6)
! 127: BRA.B Mod_Rem
! 128:
! 129: xdef srem
! 130: srem:
! 131:
! 132: Move.L #1,Mod_Flag(a6)
! 133:
! 134: Mod_Rem:
! 135: *..Save sign of X and Y
! 136: MoveM.L D2-D7,-(A7) ...save data registers
! 137: Move.W (A0),D3
! 138: Move.W D3,SignY(a6)
! 139: AndI.L #$00007FFF,D3 ...Y := |Y|
! 140:
! 141: *
! 142: Move.L 4(A0),D4
! 143: Move.L 8(A0),D5 ...(D3,D4,D5) is |Y|
! 144:
! 145: Tst.L D3
! 146: BNE.B Y_Normal
! 147:
! 148: Move.L #$00003FFE,D3 ...$3FFD + 1
! 149: Tst.L D4
! 150: BNE.B HiY_not0
! 151:
! 152: HiY_0:
! 153: Move.L D5,D4
! 154: CLR.L D5
! 155: SubI.L #32,D3
! 156: CLR.L D6
! 157: BFFFO D4{0:32},D6
! 158: LSL.L D6,D4
! 159: Sub.L D6,D3 ...(D3,D4,D5) is normalized
! 160: * ...with bias $7FFD
! 161: BRA.B Chk_X
! 162:
! 163: HiY_not0:
! 164: CLR.L D6
! 165: BFFFO D4{0:32},D6
! 166: Sub.L D6,D3
! 167: LSL.L D6,D4
! 168: Move.L D5,D7 ...a copy of D5
! 169: LSL.L D6,D5
! 170: Neg.L D6
! 171: AddI.L #32,D6
! 172: LSR.L D6,D7
! 173: Or.L D7,D4 ...(D3,D4,D5) normalized
! 174: * ...with bias $7FFD
! 175: BRA.B Chk_X
! 176:
! 177: Y_Normal:
! 178: AddI.L #$00003FFE,D3 ...(D3,D4,D5) normalized
! 179: * ...with bias $7FFD
! 180:
! 181: Chk_X:
! 182: Move.W -12(A0),D0
! 183: Move.W D0,SignX(a6)
! 184: Move.W SignY(a6),D1
! 185: EOr.L D0,D1
! 186: AndI.L #$00008000,D1
! 187: Move.W D1,SignQ(a6) ...sign(Q) obtained
! 188: AndI.L #$00007FFF,D0
! 189: Move.L -8(A0),D1
! 190: Move.L -4(A0),D2 ...(D0,D1,D2) is |X|
! 191: Tst.L D0
! 192: BNE.B X_Normal
! 193: Move.L #$00003FFE,D0
! 194: Tst.L D1
! 195: BNE.B HiX_not0
! 196:
! 197: HiX_0:
! 198: Move.L D2,D1
! 199: CLR.L D2
! 200: SubI.L #32,D0
! 201: CLR.L D6
! 202: BFFFO D1{0:32},D6
! 203: LSL.L D6,D1
! 204: Sub.L D6,D0 ...(D0,D1,D2) is normalized
! 205: * ...with bias $7FFD
! 206: BRA.B Init
! 207:
! 208: HiX_not0:
! 209: CLR.L D6
! 210: BFFFO D1{0:32},D6
! 211: Sub.L D6,D0
! 212: LSL.L D6,D1
! 213: Move.L D2,D7 ...a copy of D2
! 214: LSL.L D6,D2
! 215: Neg.L D6
! 216: AddI.L #32,D6
! 217: LSR.L D6,D7
! 218: Or.L D7,D1 ...(D0,D1,D2) normalized
! 219: * ...with bias $7FFD
! 220: BRA.B Init
! 221:
! 222: X_Normal:
! 223: AddI.L #$00003FFE,D0 ...(D0,D1,D2) normalized
! 224: * ...with bias $7FFD
! 225:
! 226: Init:
! 227: *
! 228: Move.L D3,L_SCR1(a6) ...save biased expo(Y)
! 229: move.l d0,L_SCR2(a6) ;save d0
! 230: Sub.L D3,D0 ...L := expo(X)-expo(Y)
! 231: * Move.L D0,L ...D0 is j
! 232: CLR.L D6 ...D6 := carry <- 0
! 233: CLR.L D3 ...D3 is Q
! 234: MoveA.L #0,A1 ...A1 is k; j+k=L, Q=0
! 235:
! 236: *..(Carry,D1,D2) is R
! 237: Tst.L D0
! 238: BGE.B Mod_Loop
! 239:
! 240: *..expo(X) < expo(Y). Thus X = mod(X,Y)
! 241: *
! 242: move.l L_SCR2(a6),d0 ;restore d0
! 243: BRA.W Get_Mod
! 244:
! 245: *..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L
! 246:
! 247:
! 248: Mod_Loop:
! 249: Tst.L D6 ...test carry bit
! 250: BGT.B R_GT_Y
! 251:
! 252: *..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
! 253: Cmp.L D4,D1 ...compare hi(R) and hi(Y)
! 254: BNE.B R_NE_Y
! 255: Cmp.L D5,D2 ...compare lo(R) and lo(Y)
! 256: BNE.B R_NE_Y
! 257:
! 258: *..At this point, R = Y
! 259: BRA.W Rem_is_0
! 260:
! 261: R_NE_Y:
! 262: *..use the borrow of the previous compare
! 263: BCS.B R_LT_Y ...borrow is set iff R < Y
! 264:
! 265: R_GT_Y:
! 266: *..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
! 267: *..and Y < (D1,D2) < 2Y. Either way, perform R - Y
! 268: Sub.L D5,D2 ...lo(R) - lo(Y)
! 269: SubX.L D4,D1 ...hi(R) - hi(Y)
! 270: CLR.L D6 ...clear carry
! 271: AddQ.L #1,D3 ...Q := Q + 1
! 272:
! 273: R_LT_Y:
! 274: *..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
! 275: Tst.L D0 ...see if j = 0.
! 276: BEQ.B PostLoop
! 277:
! 278: Add.L D3,D3 ...Q := 2Q
! 279: Add.L D2,D2 ...lo(R) = 2lo(R)
! 280: AddX.L D1,D1 ...hi(R) = 2hi(R) + carry
! 281: SCS D6 ...set Carry if 2(R) overflows
! 282: AddQ.L #1,A1 ...k := k+1
! 283: SubQ.L #1,D0 ...j := j - 1
! 284: *..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
! 285:
! 286: BRA.B Mod_Loop
! 287:
! 288: PostLoop:
! 289: *..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
! 290:
! 291: *..normalize R.
! 292: Move.L L_SCR1(a6),D0 ...new biased expo of R
! 293: Tst.L D1
! 294: BNE.B HiR_not0
! 295:
! 296: HiR_0:
! 297: Move.L D2,D1
! 298: CLR.L D2
! 299: SubI.L #32,D0
! 300: CLR.L D6
! 301: BFFFO D1{0:32},D6
! 302: LSL.L D6,D1
! 303: Sub.L D6,D0 ...(D0,D1,D2) is normalized
! 304: * ...with bias $7FFD
! 305: BRA.B Get_Mod
! 306:
! 307: HiR_not0:
! 308: CLR.L D6
! 309: BFFFO D1{0:32},D6
! 310: BMI.B Get_Mod ...already normalized
! 311: Sub.L D6,D0
! 312: LSL.L D6,D1
! 313: Move.L D2,D7 ...a copy of D2
! 314: LSL.L D6,D2
! 315: Neg.L D6
! 316: AddI.L #32,D6
! 317: LSR.L D6,D7
! 318: Or.L D7,D1 ...(D0,D1,D2) normalized
! 319:
! 320: *
! 321: Get_Mod:
! 322: CmpI.L #$000041FE,D0
! 323: BGE.B No_Scale
! 324: Do_Scale:
! 325: Move.W D0,R(a6)
! 326: clr.w R+2(a6)
! 327: Move.L D1,R_Hi(a6)
! 328: Move.L D2,R_Lo(a6)
! 329: Move.L L_SCR1(a6),D6
! 330: Move.W D6,Y(a6)
! 331: clr.w Y+2(a6)
! 332: Move.L D4,Y_Hi(a6)
! 333: Move.L D5,Y_Lo(a6)
! 334: FMove.X R(a6),fp0 ...no exception
! 335: Move.L #1,Sc_Flag(a6)
! 336: BRA.B ModOrRem
! 337: No_Scale:
! 338: Move.L D1,R_Hi(a6)
! 339: Move.L D2,R_Lo(a6)
! 340: SubI.L #$3FFE,D0
! 341: Move.W D0,R(a6)
! 342: clr.w R+2(a6)
! 343: Move.L L_SCR1(a6),D6
! 344: SubI.L #$3FFE,D6
! 345: Move.L D6,L_SCR1(a6)
! 346: FMove.X R(a6),fp0
! 347: Move.W D6,Y(a6)
! 348: Move.L D4,Y_Hi(a6)
! 349: Move.L D5,Y_Lo(a6)
! 350: Clr.L Sc_Flag(a6)
! 351:
! 352: *
! 353:
! 354:
! 355: ModOrRem:
! 356: Move.L Mod_Flag(a6),D6
! 357: BEQ.B Fix_Sign
! 358:
! 359: Move.L L_SCR1(a6),D6 ...new biased expo(Y)
! 360: SubQ.L #1,D6 ...biased expo(Y/2)
! 361: Cmp.L D6,D0
! 362: BLT.B Fix_Sign
! 363: BGT.B Last_Sub
! 364:
! 365: Cmp.L D4,D1
! 366: BNE.B Not_EQ
! 367: Cmp.L D5,D2
! 368: BNE.B Not_EQ
! 369: BRA.W Tie_Case
! 370:
! 371: Not_EQ:
! 372: BCS.B Fix_Sign
! 373:
! 374: Last_Sub:
! 375: *
! 376: FSub.X Y(a6),fp0 ...no exceptions
! 377: AddQ.L #1,D3 ...Q := Q + 1
! 378:
! 379: *
! 380:
! 381: Fix_Sign:
! 382: *..Get sign of X
! 383: Move.W SignX(a6),D6
! 384: BGE.B Get_Q
! 385: FNeg.X fp0
! 386:
! 387: *..Get Q
! 388: *
! 389: Get_Q:
! 390: clr.l d6
! 391: Move.W SignQ(a6),D6 ...D6 is sign(Q)
! 392: Move.L #8,D7
! 393: LSR.L D7,D6
! 394: AndI.L #$0000007F,D3 ...7 bits of Q
! 395: Or.L D6,D3 ...sign and bits of Q
! 396: Swap D3
! 397: FMove.L fpsr,D6
! 398: AndI.L #$FF00FFFF,D6
! 399: Or.L D3,D6
! 400: FMove.L D6,fpsr ...put Q in fpsr
! 401:
! 402: *
! 403: Restore:
! 404: MoveM.L (A7)+,D2-D7
! 405: FMove.L USER_FPCR(a6),fpcr
! 406: Move.L Sc_Flag(a6),D0
! 407: BEQ.B Finish
! 408: FMul.X Scale(pc),fp0 ...may cause underflow
! 409: bra t_avoid_unsupp ;check for denorm as a
! 410: * ;result of the scaling
! 411:
! 412: Finish:
! 413: fmove.x fp0,fp0 ;capture exceptions & round
! 414: rts
! 415:
! 416: Rem_is_0:
! 417: *..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
! 418: AddQ.L #1,D3
! 419: CmpI.L #8,D0 ...D0 is j
! 420: BGE.B Q_Big
! 421:
! 422: LSL.L D0,D3
! 423: BRA.B Set_R_0
! 424:
! 425: Q_Big:
! 426: CLR.L D3
! 427:
! 428: Set_R_0:
! 429: FMove.S #:00000000,fp0
! 430: Clr.L Sc_Flag(a6)
! 431: BRA.W Fix_Sign
! 432:
! 433: Tie_Case:
! 434: *..Check parity of Q
! 435: Move.L D3,D6
! 436: AndI.L #$00000001,D6
! 437: Tst.L D6
! 438: BEq.W Fix_Sign ...Q is even
! 439:
! 440: *..Q is odd, Q := Q + 1, signX := -signX
! 441: AddQ.L #1,D3
! 442: Move.W SignX(a6),D6
! 443: EOrI.L #$00008000,D6
! 444: Move.W D6,SignX(a6)
! 445: BRA.W Fix_Sign
! 446:
! 447: End