|
|       round.sa 3.4 7/29/91
|
|       handle rounding and normalization tasks
|
|
|
|               Copyright (C) Motorola, Inc. 1990
|                       All Rights Reserved
|
|       For details on the license for this file, please see the
|       file, README, in this same directory.

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

        |section        8

#include "fpsp.h"

|
|       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<d1<32)
|
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