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//

//      $Id: round.S,v 1.2 2001-09-27 12:01:22 chris Exp $

//

//      round.sa 3.4 7/29/91

//

//      handle rounding and normalization tasks

//

//

//

//              Copyright (C) Motorola, Inc. 1990

//                      All Rights Reserved

//

//      THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA

//      The copyright notice above does not evidence any

//      actual or intended publication of such source code.

//ROUND idnt    2,1 | Motorola 040 Floating Point Software Package

        |section        8

#include "fpsp.defs"

//

//      round --- round result according to precision/mode

//

//      a0 points to the input operand in the internal extended format

//      d1(high word) contains rounding precision:

//              ext = $0000xxxx

//              sgl = $0001xxxx

//              dbl = $0002xxxx

//      d1(low word) contains rounding mode:

//              RN  = $xxxx0000

//              RZ  = $xxxx0001

//              RM  = $xxxx0010

//              RP  = $xxxx0011

//      d0{31:29} contains the g,r,s bits (extended)

//

//      On return the value pointed to by a0 is correctly rounded,

//      a0 is preserved and the g-r-s bits in d0 are cleared.

//      The result is not typed - the tag field is invalid.  The

//      result is still in the internal extended format.

//

//      The INEX bit of USER_FPSR will be set if the rounded result was

//      inexact (i.e. if any of the g-r-s bits were set).

//

        .global round

round:

// If g=r=s=0 then result is exact and round is done, else set

// the inex flag in status reg and continue.

//

        bsrs    ext_grs                 //this subroutine looks at the

//                                      :rounding precision and sets

//                                      ;the appropriate g-r-s bits.

        tstl    %d0                     //if grs are zero, go force

        bne     rnd_cont                //lower bits to zero for size

        swap    %d1                     //set up d1.w for round prec.

        bra     truncate

rnd_cont:

//

// Use rounding mode as an index into a jump table for these modes.

//

        orl     #inx2a_mask,USER_FPSR(%a6) //set inex2/ainex

        lea     mode_tab,%a1

        movel   (%a1,%d1.w*4),%a1

        jmp     (%a1)

//

// Jump table indexed by rounding mode in d1.w.  All following assumes

// grs != 0.

//

mode_tab:

        .long   rnd_near

        .long   rnd_zero

        .long   rnd_mnus

        .long   rnd_plus

//

//      ROUND PLUS INFINITY

//

//      If sign of fp number = 0 (positive), then add 1 to l.

//

rnd_plus:

        swap    %d1                     //set up d1 for round prec.

        tstb    LOCAL_SGN(%a0)          //check for sign

        bmi     truncate                //if positive then truncate

        movel   #0xffffffff,%d0         //force g,r,s to be all f's

        lea     add_to_l,%a1

        movel   (%a1,%d1.w*4),%a1

        jmp     (%a1)

//

//      ROUND MINUS INFINITY

//

//      If sign of fp number = 1 (negative), then add 1 to l.

//

rnd_mnus:

        swap    %d1                     //set up d1 for round prec.

        tstb    LOCAL_SGN(%a0)          //check for sign

        bpl     truncate                //if negative then truncate

        movel   #0xffffffff,%d0         //force g,r,s to be all f's

        lea     add_to_l,%a1

        movel   (%a1,%d1.w*4),%a1

        jmp     (%a1)

//

//      ROUND ZERO

//

//      Always truncate.

rnd_zero:

        swap    %d1                     //set up d1 for round prec.

        bra     truncate

//

//

//      ROUND NEAREST

//

//      If (g=1), then add 1 to l and if (r=s=0), then clear l

//      Note that this will round to even in case of a tie.

//

rnd_near:

        swap    %d1                     //set up d1 for round prec.

        asll    #1,%d0                  //shift g-bit to c-bit

        bcc     truncate                //if (g=1) then

        lea     add_to_l,%a1

        movel   (%a1,%d1.w*4),%a1

        jmp     (%a1)

//

//      ext_grs --- extract guard, round and sticky bits

//

// Input:       d1 =            PREC:ROUND

// Output:      d0{31:29}=      guard, round, sticky

//

// The ext_grs extract the guard/round/sticky bits according to the

// selected rounding precision. It is called by the round subroutine

// only.  All registers except d0 are kept intact. d0 becomes an

// updated guard,round,sticky in d0{31:29}

//

// Notes: the ext_grs uses the round PREC, and therefore has to swap d1

//       prior to usage, and needs to restore d1 to original.

//

ext_grs:

        swap    %d1                     //have d1.w point to round precision

        cmpiw   #0,%d1

        bnes    sgl_or_dbl

        bras    end_ext_grs

sgl_or_dbl:

        moveml  %d2/%d3,-(%a7)          //make some temp registers

        cmpiw   #1,%d1

        bnes    grs_dbl

grs_sgl:

        bfextu  LOCAL_HI(%a0){#24:#2},%d3       //sgl prec. g-r are 2 bits right

        movel   #30,%d2                 //of the sgl prec. limits

        lsll    %d2,%d3                 //shift g-r bits to MSB of d3

        movel   LOCAL_HI(%a0),%d2               //get word 2 for s-bit test

        andil   #0x0000003f,%d2         //s bit is the or of all other

        bnes    st_stky                 //bits to the right of g-r

        tstl    LOCAL_LO(%a0)           //test lower mantissa

        bnes    st_stky                 //if any are set, set sticky

        tstl    %d0                     //test original g,r,s

        bnes    st_stky                 //if any are set, set sticky

        bras    end_sd                  //if words 3 and 4 are clr, exit

grs_dbl:

        bfextu  LOCAL_LO(%a0){#21:#2},%d3       //dbl-prec. g-r are 2 bits right

        movel   #30,%d2                 //of the dbl prec. limits

        lsll    %d2,%d3                 //shift g-r bits to the MSB of d3

        movel   LOCAL_LO(%a0),%d2               //get lower mantissa  for s-bit test

        andil   #0x000001ff,%d2         //s bit is the or-ing of all

        bnes    st_stky                 //other bits to the right of g-r

        tstl    %d0                     //test word original g,r,s

        bnes    st_stky                 //if any are set, set sticky

        bras    end_sd                  //if clear, exit

st_stky:

        bset    #rnd_stky_bit,%d3

end_sd:

        movel   %d3,%d0                 //return grs to d0

        moveml  (%a7)+,%d2/%d3          //restore scratch registers

end_ext_grs:

        swap    %d1                     //restore d1 to original

        rts

//*******************  Local Equates

        .set    ad_1_sgl,0x00000100     //  constant to add 1 to l-bit in sgl prec

        .set    ad_1_dbl,0x00000800     //  constant to add 1 to l-bit in dbl prec

//Jump table for adding 1 to the l-bit indexed by rnd prec

add_to_l:

        .long   add_ext

        .long   add_sgl

        .long   add_dbl

        .long   add_dbl

//

//      ADD SINGLE

//

add_sgl:

        addl    #ad_1_sgl,LOCAL_HI(%a0)

        bccs    scc_clr                 //no mantissa overflow

        roxrw  LOCAL_HI(%a0)            //shift v-bit back in

        roxrw  LOCAL_HI+2(%a0)          //shift v-bit back in

        addw    #0x1,LOCAL_EX(%a0)      //and incr exponent

scc_clr:

        tstl    %d0                     //test for rs = 0

        bnes    sgl_done

        andiw  #0xfe00,LOCAL_HI+2(%a0)  //clear the l-bit

sgl_done:

        andil   #0xffffff00,LOCAL_HI(%a0) //truncate bits beyond sgl limit

        clrl    LOCAL_LO(%a0)           //clear d2

        rts

//

//      ADD EXTENDED

//

add_ext:

        addql  #1,LOCAL_LO(%a0)         //add 1 to l-bit

        bccs    xcc_clr                 //test for carry out

        addql  #1,LOCAL_HI(%a0)         //propagate carry

        bccs    xcc_clr

        roxrw  LOCAL_HI(%a0)            //mant is 0 so restore v-bit

        roxrw  LOCAL_HI+2(%a0)          //mant is 0 so restore v-bit

        roxrw   LOCAL_LO(%a0)

        roxrw   LOCAL_LO+2(%a0)

        addw    #0x1,LOCAL_EX(%a0)      //and inc exp

xcc_clr:

        tstl    %d0                     //test rs = 0

        bnes    add_ext_done

        andib   #0xfe,LOCAL_LO+3(%a0)   //clear the l bit

add_ext_done:

        rts

//

//      ADD DOUBLE

//

add_dbl:

        addl    #ad_1_dbl,LOCAL_LO(%a0)

        bccs    dcc_clr

        addql   #1,LOCAL_HI(%a0)                //propagate carry

        bccs    dcc_clr

        roxrw   LOCAL_HI(%a0)           //mant is 0 so restore v-bit

        roxrw   LOCAL_HI+2(%a0)         //mant is 0 so restore v-bit

        roxrw   LOCAL_LO(%a0)

        roxrw   LOCAL_LO+2(%a0)

        addw    #0x1,LOCAL_EX(%a0)      //incr exponent

dcc_clr:

        tstl    %d0                     //test for rs = 0

        bnes    dbl_done

        andiw   #0xf000,LOCAL_LO+2(%a0) //clear the l-bit

dbl_done:

        andil   #0xfffff800,LOCAL_LO(%a0) //truncate bits beyond dbl limit

        rts

error:

        rts

//

// Truncate all other bits

//

trunct:

        .long   end_rnd

        .long   sgl_done

        .long   dbl_done

        .long   dbl_done

truncate:

        lea     trunct,%a1

        movel   (%a1,%d1.w*4),%a1

        jmp     (%a1)

end_rnd:

        rts

//

//      NORMALIZE

//

// These routines (nrm_zero & nrm_set) normalize the unnorm.  This

// is done by shifting the mantissa left while decrementing the

// exponent.

//

// NRM_SET shifts and decrements until there is a 1 set in the integer

// bit of the mantissa (msb in d1).

//

// NRM_ZERO shifts and decrements until there is a 1 set in the integer

// bit of the mantissa (msb in d1) unless this would mean the exponent

// would go less than 0.  In that case the number becomes a denorm - the

// exponent (d0) is set to 0 and the mantissa (d1 & d2) is not

// normalized.

//

// Note that both routines have been optimized (for the worst case) and

// therefore do not have the easy to follow decrement/shift loop.

//

//      NRM_ZERO

//

//      Distance to first 1 bit in mantissa = X

//      Distance to 0 from exponent = Y

//      If X < Y

//      Then

//        nrm_set

//      Else

//        shift mantissa by Y

//        set exponent = 0

//

//input:

//      FP_SCR1 = exponent, ms mantissa part, ls mantissa part

//output:

//      L_SCR1{4} = fpte15 or ete15 bit

//

        .global nrm_zero

nrm_zero:

        movew   LOCAL_EX(%a0),%d0

        cmpw   #64,%d0          //see if exp > 64

        bmis    d0_less

        bsr     nrm_set         //exp > 64 so exp won't exceed 0

        rts

d0_less:

        moveml  %d2/%d3/%d5/%d6,-(%a7)

        movel   LOCAL_HI(%a0),%d1

        movel   LOCAL_LO(%a0),%d2

        bfffo   %d1{#0:#32},%d3 //get the distance to the first 1

//                              ;in ms mant

        beqs    ms_clr          //branch if no bits were set

        cmpw    %d3,%d0         //of X>Y

        bmis    greater         //then exp will go past 0 (neg) if

//                              ;it is just shifted

        bsr     nrm_set         //else exp won't go past 0

        moveml  (%a7)+,%d2/%d3/%d5/%d6

        rts

greater:

        movel   %d2,%d6         //save ls mant in d6

        lsll    %d0,%d2         //shift ls mant by count

        lsll    %d0,%d1         //shift ms mant by count

        movel   #32,%d5

        subl    %d0,%d5         //make op a denorm by shifting bits

        lsrl    %d5,%d6         //by the number in the exp, then

//                              ;set exp = 0.

        orl     %d6,%d1         //shift the ls mant bits into the ms mant

        movel   #0,%d0          //same as if decremented exp to 0

//                              ;while shifting

        movew   %d0,LOCAL_EX(%a0)

        movel   %d1,LOCAL_HI(%a0)

        movel   %d2,LOCAL_LO(%a0)

        moveml  (%a7)+,%d2/%d3/%d5/%d6

        rts

ms_clr:

        bfffo   %d2{#0:#32},%d3 //check if any bits set in ls mant

        beqs    all_clr         //branch if none set

        addw    #32,%d3

        cmpw    %d3,%d0         //if X>Y

        bmis    greater         //then branch

        bsr     nrm_set         //else exp won't go past 0

        moveml  (%a7)+,%d2/%d3/%d5/%d6

        rts

all_clr:

        movew   #0,LOCAL_EX(%a0)        //no mantissa bits set. Set exp = 0.

        moveml  (%a7)+,%d2/%d3/%d5/%d6

        rts

//

//      NRM_SET

//

        .global nrm_set

nrm_set:

        movel   %d7,-(%a7)

        bfffo   LOCAL_HI(%a0){#0:#32},%d7 //find first 1 in ms mant to d7)

        beqs    lower           //branch if ms mant is all 0's

        movel   %d6,-(%a7)

        subw    %d7,LOCAL_EX(%a0)       //sub exponent by count

        movel   LOCAL_HI(%a0),%d0       //d0 has ms mant

        movel   LOCAL_LO(%a0),%d1 //d1 has ls mant

        lsll    %d7,%d0         //shift first 1 to j bit position

        movel   %d1,%d6         //copy ls mant into d6

        lsll    %d7,%d6         //shift ls mant by count

        movel   %d6,LOCAL_LO(%a0)       //store ls mant into memory

        moveql  #32,%d6

        subl    %d7,%d6         //continue shift

        lsrl    %d6,%d1         //shift off all bits but those that will

//                              ;be shifted into ms mant

        orl     %d1,%d0         //shift the ls mant bits into the ms mant

        movel   %d0,LOCAL_HI(%a0)       //store ms mant into memory

        moveml  (%a7)+,%d7/%d6  //restore registers

        rts

//

// We get here if ms mant was = 0, and we assume ls mant has bits

// set (otherwise this would have been tagged a zero not a denorm).

//

lower:

        movew   LOCAL_EX(%a0),%d0       //d0 has exponent

        movel   LOCAL_LO(%a0),%d1       //d1 has ls mant

        subw    #32,%d0         //account for ms mant being all zeros

        bfffo   %d1{#0:#32},%d7 //find first 1 in ls mant to d7)

        subw    %d7,%d0         //subtract shift count from exp

        lsll    %d7,%d1         //shift first 1 to integer bit in ms mant

        movew   %d0,LOCAL_EX(%a0)       //store ms mant

        movel   %d1,LOCAL_HI(%a0)       //store exp

        clrl    LOCAL_LO(%a0)   //clear ls mant

        movel   (%a7)+,%d7

        rts

//

//      denorm --- denormalize an intermediate result

//

//      Used by underflow.

//

// Input:

//      a0       points to the operand to be denormalized

//               (in the internal extended format)

//

//      d0:      rounding precision

// Output:

//      a0       points to the denormalized result

//               (in the internal extended format)

//

//      d0      is guard,round,sticky

//

// d0 comes into this routine with the rounding precision. It

// is then loaded with the denormalized exponent threshold for the

// rounding precision.

//

        .global denorm

denorm:

        btstb   #6,LOCAL_EX(%a0)        //check for exponents between $7fff-$4000

        beqs    no_sgn_ext

        bsetb   #7,LOCAL_EX(%a0)        //sign extend if it is so

no_sgn_ext:

        cmpib   #0,%d0          //if 0 then extended precision

        bnes    not_ext         //else branch

        clrl    %d1             //load d1 with ext threshold

        clrl    %d0             //clear the sticky flag

        bsr     dnrm_lp         //denormalize the number

        tstb    %d1             //check for inex

        beq     no_inex         //if clr, no inex

        bras    dnrm_inex       //if set, set inex

not_ext:

        cmpil   #1,%d0          //if 1 then single precision

        beqs    load_sgl        //else must be 2, double prec

load_dbl:

        movew   #dbl_thresh,%d1 //put copy of threshold in d1

        movel   %d1,%d0         //copy d1 into d0

        subw    LOCAL_EX(%a0),%d0       //diff = threshold - exp

        cmpw    #67,%d0         //if diff > 67 (mant + grs bits)

        bpls    chk_stky        //then branch (all bits would be

//                              ; shifted off in denorm routine)

        clrl    %d0             //else clear the sticky flag

        bsr     dnrm_lp         //denormalize the number

        tstb    %d1             //check flag

        beqs    no_inex         //if clr, no inex

        bras    dnrm_inex       //if set, set inex

load_sgl:

        movew   #sgl_thresh,%d1 //put copy of threshold in d1

        movel   %d1,%d0         //copy d1 into d0

        subw    LOCAL_EX(%a0),%d0       //diff = threshold - exp

        cmpw    #67,%d0         //if diff > 67 (mant + grs bits)

        bpls    chk_stky        //then branch (all bits would be

//                              ; shifted off in denorm routine)

        clrl    %d0             //else clear the sticky flag

        bsr     dnrm_lp         //denormalize the number

        tstb    %d1             //check flag

        beqs    no_inex         //if clr, no inex

        bras    dnrm_inex       //if set, set inex

chk_stky:

        tstl    LOCAL_HI(%a0)   //check for any bits set

        bnes    set_stky

        tstl    LOCAL_LO(%a0)   //check for any bits set

        bnes    set_stky

        bras    clr_mant

set_stky:

        orl     #inx2a_mask,USER_FPSR(%a6) //set inex2/ainex

        movel   #0x20000000,%d0 //set sticky bit in return value

clr_mant:

        movew   %d1,LOCAL_EX(%a0)               //load exp with threshold

        movel   #0,LOCAL_HI(%a0)        //set d1 = 0 (ms mantissa)

        movel   #0,LOCAL_LO(%a0)                //set d2 = 0 (ms mantissa)

        rts

dnrm_inex:

        orl     #inx2a_mask,USER_FPSR(%a6) //set inex2/ainex

no_inex:

        rts

//

//      dnrm_lp --- normalize exponent/mantissa to specified threshold

//

// Input:

//      a0              points to the operand to be denormalized

//      d0{31:29}       initial guard,round,sticky

//      d1{15:0}        denormalization threshold

// Output:

//      a0              points to the denormalized operand

//      d0{31:29}       final guard,round,sticky

//      d1.b            inexact flag:  all ones means inexact result

//

// The LOCAL_LO and LOCAL_GRS parts of the value are copied to FP_SCR2

// so that bfext can be used to extract the new low part of the mantissa.

// Dnrm_lp can be called with a0 pointing to ETEMP or WBTEMP and there

// is no LOCAL_GRS scratch word following it on the fsave frame.

//

        .global dnrm_lp

dnrm_lp:

        movel   %d2,-(%sp)              //save d2 for temp use

        btstb   #E3,E_BYTE(%a6)         //test for type E3 exception

        beqs    not_E3                  //not type E3 exception

        bfextu  WBTEMP_GRS(%a6){#6:#3},%d2      //extract guard,round, sticky  bit

        movel   #29,%d0

        lsll    %d0,%d2                 //shift g,r,s to their positions

        movel   %d2,%d0

not_E3:

        movel   (%sp)+,%d2              //restore d2

        movel   LOCAL_LO(%a0),FP_SCR2+LOCAL_LO(%a6)

        movel   %d0,FP_SCR2+LOCAL_GRS(%a6)

        movel   %d1,%d0                 //copy the denorm threshold

        subw    LOCAL_EX(%a0),%d1               //d1 = threshold - uns exponent

        bles    no_lp                   //d1 <= 0

        cmpw    #32,%d1

        blts    case_1                  //0 = d1 < 32

        cmpw    #64,%d1

        blts    case_2                  //32 <= d1 < 64

        bra     case_3                  //d1 >= 64

//

// No normalization necessary

//

no_lp:

        clrb    %d1                     //set no inex2 reported

        movel   FP_SCR2+LOCAL_GRS(%a6),%d0      //restore original g,r,s

        rts

//

// case (0

//

case_1:

        movel   %d2,-(%sp)

        movew   %d0,LOCAL_EX(%a0)               //exponent = denorm threshold

        movel   #32,%d0

        subw    %d1,%d0                 //d0 = 32 - d1

        bfextu  LOCAL_EX(%a0){%d0:#32},%d2

        bfextu  %d2{%d1:%d0},%d2                //d2 = new LOCAL_HI

        bfextu  LOCAL_HI(%a0){%d0:#32},%d1      //d1 = new LOCAL_LO

        bfextu  FP_SCR2+LOCAL_LO(%a6){%d0:#32},%d0      //d0 = new G,R,S

        movel   %d2,LOCAL_HI(%a0)               //store new LOCAL_HI

        movel   %d1,LOCAL_LO(%a0)               //store new LOCAL_LO

        clrb    %d1

        bftst   %d0{#2:#30}

        beqs    c1nstky

        bsetl   #rnd_stky_bit,%d0

        st      %d1

c1nstky:

        movel   FP_SCR2+LOCAL_GRS(%a6),%d2      //restore original g,r,s

        andil   #0xe0000000,%d2         //clear all but G,R,S

        tstl    %d2                     //test if original G,R,S are clear

        beqs    grs_clear

        orl     #0x20000000,%d0         //set sticky bit in d0

grs_clear:

        andil   #0xe0000000,%d0         //clear all but G,R,S

        movel   (%sp)+,%d2

        rts

//

// case (32<=d1<64)

//

case_2:

        movel   %d2,-(%sp)

        movew   %d0,LOCAL_EX(%a0)               //unsigned exponent = threshold

        subw    #32,%d1                 //d1 now between 0 and 32

        movel   #32,%d0

        subw    %d1,%d0                 //d0 = 32 - d1

        bfextu  LOCAL_EX(%a0){%d0:#32},%d2

        bfextu  %d2{%d1:%d0},%d2                //d2 = new LOCAL_LO

        bfextu  LOCAL_HI(%a0){%d0:#32},%d1      //d1 = new G,R,S

        bftst   %d1{#2:#30}

        bnes    c2_sstky                //bra if sticky bit to be set

        bftst   FP_SCR2+LOCAL_LO(%a6){%d0:#32}

        bnes    c2_sstky                //bra if sticky bit to be set

        movel   %d1,%d0

        clrb    %d1

        bras    end_c2

c2_sstky:

        movel   %d1,%d0

        bsetl   #rnd_stky_bit,%d0

        st      %d1

end_c2:

        clrl    LOCAL_HI(%a0)           //store LOCAL_HI = 0

        movel   %d2,LOCAL_LO(%a0)               //store LOCAL_LO

        movel   FP_SCR2+LOCAL_GRS(%a6),%d2      //restore original g,r,s

        andil   #0xe0000000,%d2         //clear all but G,R,S

        tstl    %d2                     //test if original G,R,S are clear

        beqs    clear_grs

        orl     #0x20000000,%d0         //set sticky bit in d0

clear_grs:

        andil   #0xe0000000,%d0         //get rid of all but G,R,S

        movel   (%sp)+,%d2

        rts

//

// d1 >= 64 Force the exponent to be the denorm threshold with the

// correct sign.

//

case_3:

        movew   %d0,LOCAL_EX(%a0)

        tstw    LOCAL_SGN(%a0)

        bges    c3con

c3neg:

        orl     #0x80000000,LOCAL_EX(%a0)

c3con:

        cmpw    #64,%d1

        beqs    sixty_four

        cmpw    #65,%d1

        beqs    sixty_five

//

// Shift value is out of range.  Set d1 for inex2 flag and

// return a zero with the given threshold.

//

        clrl    LOCAL_HI(%a0)

        clrl    LOCAL_LO(%a0)

        movel   #0x20000000,%d0

        st      %d1

        rts

sixty_four:

        movel   LOCAL_HI(%a0),%d0

        bfextu  %d0{#2:#30},%d1

        andil   #0xc0000000,%d0

        bras    c3com

sixty_five:

        movel   LOCAL_HI(%a0),%d0

        bfextu  %d0{#1:#31},%d1

        andil   #0x80000000,%d0

        lsrl    #1,%d0                  //shift high bit into R bit

c3com:

        tstl    %d1

        bnes    c3ssticky

        tstl    LOCAL_LO(%a0)

        bnes    c3ssticky

        tstb    FP_SCR2+LOCAL_GRS(%a6)

        bnes    c3ssticky

        clrb    %d1

        bras    c3end

c3ssticky:

        bsetl   #rnd_stky_bit,%d0

        st      %d1

c3end:

        clrl    LOCAL_HI(%a0)

        clrl    LOCAL_LO(%a0)

        rts

        |end