arch/m68k/fpsp040/srem_mod.S

   1 |
   2 |       srem_mod.sa 3.1 12/10/90
   3 |
   4 |      The entry point sMOD computes the floating point MOD of the
   5 |      input values X and Y. The entry point sREM computes the floating
   6 |      point (IEEE) REM of the input values X and Y.
   7 |
   8 |      INPUT
   9 |      -----
  10 |      Double-extended value Y is pointed to by address in register
  11 |      A0. Double-extended value X is located in -12(A0). The values
  12 |      of X and Y are both nonzero and finite; although either or both
  13 |      of them can be denormalized. The special cases of zeros, NaNs,
  14 |      and infinities are handled elsewhere.
  15 |
  16 |      OUTPUT
  17 |      ------
  18 |      FREM(X,Y) or FMOD(X,Y), depending on entry point.
  19 |
  20 |       ALGORITHM
  21 |       ---------
  22 |
  23 |       Step 1.  Save and strip signs of X and Y: signX := sign(X),
  24 |                signY := sign(Y), X := |X|, Y := |Y|,
  25 |                signQ := signX EOR signY. Record whether MOD or REM
  26 |                is requested.
  27 |
  28 |       Step 2.  Set L := expo(X)-expo(Y), k := 0, Q := 0.
  29 |                If (L < 0) then
  30 |                   R := X, go to Step 4.
  31 |                else
  32 |                   R := 2^(-L)X, j := L.
  33 |                endif
  34 |
  35 |       Step 3.  Perform MOD(X,Y)
  36 |            3.1 If R = Y, go to Step 9.
  37 |            3.2 If R > Y, then { R := R - Y, Q := Q + 1}
  38 |            3.3 If j = 0, go to Step 4.
  39 |            3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to
  40 |                Step 3.1.
  41 |
  42 |       Step 4.  At this point, R = X - QY = MOD(X,Y). Set
  43 |                Last_Subtract := false (used in Step 7 below). If
  44 |                MOD is requested, go to Step 6.
  45 |
  46 |       Step 5.  R = MOD(X,Y), but REM(X,Y) is requested.
  47 |            5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to
  48 |                Step 6.
  49 |            5.2 If R > Y/2, then { set Last_Subtract := true,
  50 |                Q := Q + 1, Y := signY*Y }. Go to Step 6.
  51 |            5.3 This is the tricky case of R = Y/2. If Q is odd,
  52 |                then { Q := Q + 1, signX := -signX }.
  53 |
  54 |       Step 6.  R := signX*R.
  55 |
  56 |       Step 7.  If Last_Subtract = true, R := R - Y.
  57 |
  58 |       Step 8.  Return signQ, last 7 bits of Q, and R as required.
  59 |
  60 |       Step 9.  At this point, R = 2^(-j)*X - Q Y = Y. Thus,
  61 |                X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1),
  62 |                R := 0. Return signQ, last 7 bits of Q, and R.
  63 |
  64 |
  65
  66 |               Copyright (C) Motorola, Inc. 1990
  67 |                       All Rights Reserved
  68 |
  69 |       For details on the license for this file, please see the
  70 |       file, README, in this same directory.
  71
  72 SREM_MOD:    |idnt    2,1 | Motorola 040 Floating Point Software Package
  73
  74         |section    8
  75
  76 #include "fpsp.h"
  77
  78         .set    Mod_Flag,L_SCR3
  79         .set    SignY,FP_SCR3+4
  80         .set    SignX,FP_SCR3+8
  81         .set    SignQ,FP_SCR3+12
  82         .set    Sc_Flag,FP_SCR4
  83
  84         .set    Y,FP_SCR1
  85         .set    Y_Hi,Y+4
  86         .set    Y_Lo,Y+8
  87
  88         .set    R,FP_SCR2
  89         .set    R_Hi,R+4
  90         .set    R_Lo,R+8
  91
  92
  93 Scale:     .long        0x00010000,0x80000000,0x00000000,0x00000000
  94
  95         |xref   t_avoid_unsupp
  96
  97         .global        smod
  98 smod:
  99
 100    movel               #0,Mod_Flag(%a6)
 101    bras                Mod_Rem
 102
 103         .global        srem
 104 srem:
 105
 106    movel               #1,Mod_Flag(%a6)
 107
 108 Mod_Rem:
 109 |..Save sign of X and Y
 110    moveml              %d2-%d7,-(%a7)     | ...save data registers
 111    movew               (%a0),%d3
 112    movew               %d3,SignY(%a6)
 113    andil               #0x00007FFF,%d3   | ...Y := |Y|
 114
 115 |
 116    movel               4(%a0),%d4
 117    movel               8(%a0),%d5        | ...(D3,D4,D5) is |Y|
 118
 119    tstl                %d3
 120    bnes                Y_Normal
 121
 122    movel               #0x00003FFE,%d3  | ...$3FFD + 1
 123    tstl                %d4
 124    bnes                HiY_not0
 125
 126 HiY_0:
 127    movel               %d5,%d4
 128    clrl                %d5
 129    subil               #32,%d3
 130    clrl                %d6
 131    bfffo                %d4{#0:#32},%d6
 132    lsll                %d6,%d4
 133    subl                %d6,%d3           | ...(D3,D4,D5) is normalized
 134 |                                       ...with bias $7FFD
 135    bras                Chk_X
 136
 137 HiY_not0:
 138    clrl                %d6
 139    bfffo                %d4{#0:#32},%d6
 140    subl                %d6,%d3
 141    lsll                %d6,%d4
 142    movel               %d5,%d7           | ...a copy of D5
 143    lsll                %d6,%d5
 144    negl                %d6
 145    addil               #32,%d6
 146    lsrl                %d6,%d7
 147    orl                 %d7,%d4           | ...(D3,D4,D5) normalized
 148 |                                       ...with bias $7FFD
 149    bras                Chk_X
 150
 151 Y_Normal:
 152    addil               #0x00003FFE,%d3   | ...(D3,D4,D5) normalized
 153 |                                       ...with bias $7FFD
 154
 155 Chk_X:
 156    movew               -12(%a0),%d0
 157    movew               %d0,SignX(%a6)
 158    movew               SignY(%a6),%d1
 159    eorl                %d0,%d1
 160    andil               #0x00008000,%d1
 161    movew               %d1,SignQ(%a6)   | ...sign(Q) obtained
 162    andil               #0x00007FFF,%d0
 163    movel               -8(%a0),%d1
 164    movel               -4(%a0),%d2       | ...(D0,D1,D2) is |X|
 165    tstl                %d0
 166    bnes                X_Normal
 167    movel               #0x00003FFE,%d0
 168    tstl                %d1
 169    bnes                HiX_not0
 170
 171 HiX_0:
 172    movel               %d2,%d1
 173    clrl                %d2
 174    subil               #32,%d0
 175    clrl                %d6
 176    bfffo                %d1{#0:#32},%d6
 177    lsll                %d6,%d1
 178    subl                %d6,%d0           | ...(D0,D1,D2) is normalized
 179 |                                       ...with bias $7FFD
 180    bras                Init
 181
 182 HiX_not0:
 183    clrl                %d6
 184    bfffo                %d1{#0:#32},%d6
 185    subl                %d6,%d0
 186    lsll                %d6,%d1
 187    movel               %d2,%d7           | ...a copy of D2
 188    lsll                %d6,%d2
 189    negl                %d6
 190    addil               #32,%d6
 191    lsrl                %d6,%d7
 192    orl                 %d7,%d1           | ...(D0,D1,D2) normalized
 193 |                                       ...with bias $7FFD
 194    bras                Init
 195
 196 X_Normal:
 197    addil               #0x00003FFE,%d0   | ...(D0,D1,D2) normalized
 198 |                                       ...with bias $7FFD
 199
 200 Init:
 201 |
 202    movel               %d3,L_SCR1(%a6)   | ...save biased expo(Y)
 203    movel                %d0,L_SCR2(%a6) |save d0
 204    subl                %d3,%d0           | ...L := expo(X)-expo(Y)
 205 |   Move.L               D0,L            ...D0 is j
 206    clrl                %d6              | ...D6 := carry <- 0
 207    clrl                %d3              | ...D3 is Q
 208    moveal              #0,%a1           | ...A1 is k; j+k=L, Q=0
 209
 210 |..(Carry,D1,D2) is R
 211    tstl                %d0
 212    bges                Mod_Loop
 213
 214 |..expo(X) < expo(Y). Thus X = mod(X,Y)
 215 |
 216    movel                L_SCR2(%a6),%d0 |restore d0
 217    bra                Get_Mod
 218
 219 |..At this point  R = 2^(-L)X; Q = 0; k = 0; and  k+j = L
 220
 221
 222 Mod_Loop:
 223    tstl                %d6              | ...test carry bit
 224    bgts                R_GT_Y
 225
 226 |..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
 227    cmpl                %d4,%d1           | ...compare hi(R) and hi(Y)
 228    bnes                R_NE_Y
 229    cmpl                %d5,%d2           | ...compare lo(R) and lo(Y)
 230    bnes                R_NE_Y
 231
 232 |..At this point, R = Y
 233    bra                Rem_is_0
 234
 235 R_NE_Y:
 236 |..use the borrow of the previous compare
 237    bcss                R_LT_Y          | ...borrow is set iff R < Y
 238
 239 R_GT_Y:
 240 |..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
 241 |..and Y < (D1,D2) < 2Y. Either way, perform R - Y
 242    subl                %d5,%d2           | ...lo(R) - lo(Y)
 243    subxl               %d4,%d1           | ...hi(R) - hi(Y)
 244    clrl                %d6              | ...clear carry
 245    addql               #1,%d3           | ...Q := Q + 1
 246
 247 R_LT_Y:
 248 |..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
 249    tstl                %d0              | ...see if j = 0.
 250    beqs                PostLoop
 251
 252    addl                %d3,%d3           | ...Q := 2Q
 253    addl                %d2,%d2           | ...lo(R) = 2lo(R)
 254    roxll               #1,%d1           | ...hi(R) = 2hi(R) + carry
 255    scs                  %d6              | ...set Carry if 2(R) overflows
 256    addql               #1,%a1           | ...k := k+1
 257    subql               #1,%d0           | ...j := j - 1
 258 |..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
 259
 260    bras                Mod_Loop
 261
 262 PostLoop:
 263 |..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
 264
 265 |..normalize R.
 266    movel               L_SCR1(%a6),%d0           | ...new biased expo of R
 267    tstl                %d1
 268    bnes                HiR_not0
 269
 270 HiR_0:
 271    movel               %d2,%d1
 272    clrl                %d2
 273    subil               #32,%d0
 274    clrl                %d6
 275    bfffo                %d1{#0:#32},%d6
 276    lsll                %d6,%d1
 277    subl                %d6,%d0           | ...(D0,D1,D2) is normalized
 278 |                                       ...with bias $7FFD
 279    bras                Get_Mod
 280
 281 HiR_not0:
 282    clrl                %d6
 283    bfffo                %d1{#0:#32},%d6
 284    bmis                Get_Mod         | ...already normalized
 285    subl                %d6,%d0
 286    lsll                %d6,%d1
 287    movel               %d2,%d7           | ...a copy of D2
 288    lsll                %d6,%d2
 289    negl                %d6
 290    addil               #32,%d6
 291    lsrl                %d6,%d7
 292    orl                 %d7,%d1           | ...(D0,D1,D2) normalized
 293
 294 |
 295 Get_Mod:
 296    cmpil                #0x000041FE,%d0
 297    bges         No_Scale
 298 Do_Scale:
 299    movew                %d0,R(%a6)
 300    clrw         R+2(%a6)
 301    movel                %d1,R_Hi(%a6)
 302    movel                %d2,R_Lo(%a6)
 303    movel                L_SCR1(%a6),%d6
 304    movew                %d6,Y(%a6)
 305    clrw         Y+2(%a6)
 306    movel                %d4,Y_Hi(%a6)
 307    movel                %d5,Y_Lo(%a6)
 308    fmovex               R(%a6),%fp0             | ...no exception
 309    movel                #1,Sc_Flag(%a6)
 310    bras         ModOrRem
 311 No_Scale:
 312    movel                %d1,R_Hi(%a6)
 313    movel                %d2,R_Lo(%a6)
 314    subil                #0x3FFE,%d0
 315    movew                %d0,R(%a6)
 316    clrw         R+2(%a6)
 317    movel                L_SCR1(%a6),%d6
 318    subil                #0x3FFE,%d6
 319    movel                %d6,L_SCR1(%a6)
 320    fmovex               R(%a6),%fp0
 321    movew                %d6,Y(%a6)
 322    movel                %d4,Y_Hi(%a6)
 323    movel                %d5,Y_Lo(%a6)
 324    movel                #0,Sc_Flag(%a6)
 325
 326 |
 327
 328
 329 ModOrRem:
 330    movel               Mod_Flag(%a6),%d6
 331    beqs                Fix_Sign
 332
 333    movel               L_SCR1(%a6),%d6           | ...new biased expo(Y)
 334    subql               #1,%d6           | ...biased expo(Y/2)
 335    cmpl                %d6,%d0
 336    blts                Fix_Sign
 337    bgts                Last_Sub
 338
 339    cmpl                %d4,%d1
 340    bnes                Not_EQ
 341    cmpl                %d5,%d2
 342    bnes                Not_EQ
 343    bra                Tie_Case
 344
 345 Not_EQ:
 346    bcss                Fix_Sign
 347
 348 Last_Sub:
 349 |
 350    fsubx                Y(%a6),%fp0             | ...no exceptions
 351    addql               #1,%d3           | ...Q := Q + 1
 352
 353 |
 354
 355 Fix_Sign:
 356 |..Get sign of X
 357    movew               SignX(%a6),%d6
 358    bges         Get_Q
 359    fnegx                %fp0
 360
 361 |..Get Q
 362 |
 363 Get_Q:
 364    clrl         %d6
 365    movew               SignQ(%a6),%d6        | ...D6 is sign(Q)
 366    movel               #8,%d7
 367    lsrl                %d7,%d6
 368    andil               #0x0000007F,%d3   | ...7 bits of Q
 369    orl                 %d6,%d3           | ...sign and bits of Q
 370    swap                 %d3
 371    fmovel              %fpsr,%d6
 372    andil               #0xFF00FFFF,%d6
 373    orl                 %d3,%d6
 374    fmovel              %d6,%fpsr         | ...put Q in fpsr
 375
 376 |
 377 Restore:
 378    moveml              (%a7)+,%d2-%d7
 379    fmovel              USER_FPCR(%a6),%fpcr
 380    movel               Sc_Flag(%a6),%d0
 381    beqs                Finish
 382    fmulx                Scale(%pc),%fp0 | ...may cause underflow
 383    bra                  t_avoid_unsupp  |check for denorm as a
 384 |                                       ;result of the scaling
 385
 386 Finish:
 387         fmovex          %fp0,%fp0               |capture exceptions & round
 388         rts
 389
 390 Rem_is_0:
 391 |..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
 392    addql               #1,%d3
 393    cmpil               #8,%d0           | ...D0 is j
 394    bges                Q_Big
 395
 396    lsll                %d0,%d3
 397    bras                Set_R_0
 398
 399 Q_Big:
 400    clrl                %d3
 401
 402 Set_R_0:
 403    fmoves               #0x00000000,%fp0
 404    movel                #0,Sc_Flag(%a6)
 405    bra                Fix_Sign
 406
 407 Tie_Case:
 408 |..Check parity of Q
 409    movel               %d3,%d6
 410    andil               #0x00000001,%d6
 411    tstl                %d6
 412    beq                Fix_Sign  | ...Q is even
 413
 414 |..Q is odd, Q := Q + 1, signX := -signX
 415    addql               #1,%d3
 416    movew               SignX(%a6),%d6
 417    eoril               #0x00008000,%d6
 418    movew               %d6,SignX(%a6)
 419    bra                Fix_Sign
 420
 421    |end