* $OpenBSD: round.sa,v 1.3 2005/11/15 21:09:45 miod Exp $
* $NetBSD: round.sa,v 1.3 1994/10/26 07:49:24 cgd Exp $
* MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
* M68000 Hi-Performance Microprocessor Division
* M68040 Software Package
*
* M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
* All rights reserved.
*
* THE SOFTWARE is provided on an "AS IS" basis and without warranty.
* To the maximum extent permitted by applicable law,
* MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
* INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
* PARTICULAR PURPOSE and any warranty against infringement with
* regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
* and any accompanying written materials.
*
* To the maximum extent permitted by applicable law,
* IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
* (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
* PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
* OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
* SOFTWARE. Motorola assumes no responsibility for the maintenance
* and support of the SOFTWARE.
*
* You are hereby granted a copyright license to use, modify, and
* distribute the SOFTWARE so long as this entire notice is retained
* without alteration in any modified and/or redistributed versions,
* and that such modified versions are clearly identified as such.
* No licenses are granted by implication, estoppel or otherwise
* under any patents or trademarks of Motorola, Inc.
*
* round.sa 3.4 7/29/91
*
* handle rounding and normalization tasks
*
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 = $xxxx0011
* d0{31:29} contains the g,r,s bits (extended)
*
* On return the value pointed to by a0 is correctly rounded,
* a0 is preserved and the g-r-s bits in d0 are cleared.
* The result is not typed - the tag field is invalid. The
* result is still in the internal extended format.
*
* The INEX bit of USER_FPSR will be set if the rounded result was
* inexact (i.e. if any of the g-r-s bits were set).
*
xdef round
round:
* If g=r=s=0 then result is exact and round is done, else set
* the inex flag in status reg and continue.
*
bsr.b ext_grs ;this subroutine looks at the
* :rounding precision and sets
* ;the appropriate g-r-s bits.
tst.l d0 ;if grs are zero, go force
bne.w rnd_cont ;lower bits to zero for size
swap d1 ;set up d1.w for round prec.
bra.w truncate
rnd_cont:
*
* Use rounding mode as an index into a jump table for these modes.
*
or.l #inx2a_mask,USER_FPSR(a6) ;set inex2/ainex
lea mode_tab,a1
move.l (a1,d1.w*4),a1
jmp (a1)
*
* Jump table indexed by rounding mode in d1.w. All following assumes
* grs != 0.
*
mode_tab:
dc.l rnd_near
dc.l rnd_zero
dc.l rnd_mnus
dc.l rnd_plus
*
* ROUND PLUS INFINITY
*
* If sign of fp number = 0 (positive), then add 1 to l.
*
rnd_plus:
swap d1 ;set up d1 for round prec.
tst.b LOCAL_SGN(a0) ;check for sign
bmi.w truncate ;if positive then truncate
move.l #$ffffffff,d0 ;force g,r,s to be all f's
lea add_to_l,a1
move.l (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.
tst.b LOCAL_SGN(a0) ;check for sign
bpl.w truncate ;if negative then truncate
move.l #$ffffffff,d0 ;force g,r,s to be all f's
lea add_to_l,a1
move.l (a1,d1.w*4),a1
jmp (a1)
*
* ROUND ZERO
*
* Always truncate.
rnd_zero:
swap d1 ;set up d1 for round prec.
bra.w 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.
add.l d0,d0 ;shift g-bit to c-bit
bcc.w truncate ;if (g=1) then
lea add_to_l,a1
move.l (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
tst.w d1
bne.b sgl_or_dbl
bra.b end_ext_grs
sgl_or_dbl:
movem.l d2/d3,-(a7) ;make some temp registers
cmpi.w #1,d1
bne.b grs_dbl
grs_sgl:
bfextu LOCAL_HI(a0){24:2},d3 ;sgl prec. g-r are 2 bits right
move.l #30,d2 ;of the sgl prec. limits
lsl.l d2,d3 ;shift g-r bits to MSB of d3
move.l LOCAL_HI(a0),d2 ;get word 2 for s-bit test
andi.l #$0000003f,d2 ;s bit is the or of all other
bne.b st_stky ;bits to the right of g-r
tst.l LOCAL_LO(a0) ;test lower mantissa
bne.b st_stky ;if any are set, set sticky
tst.l d0 ;test original g,r,s
bne.b st_stky ;if any are set, set sticky
bra.b 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
move.l #30,d2 ;of the dbl prec. limits
lsl.l d2,d3 ;shift g-r bits to the MSB of d3
move.l LOCAL_LO(a0),d2 ;get lower mantissa for s-bit test
andi.l #$000001ff,d2 ;s bit is the or-ing of all
bne.b st_stky ;other bits to the right of g-r
tst.l d0 ;test word original g,r,s
bne.b st_stky ;if any are set, set sticky
bra.b end_sd ;if clear, exit
st_stky:
bset #rnd_stky_bit,d3
end_sd:
move.l d3,d0 ;return grs to d0
movem.l (a7)+,d2/d3 ;restore scratch registers
end_ext_grs:
swap d1 ;restore d1 to original
rts
******************** Local Equates
ad_1_sgl equ $00000100 constant to add 1 to l-bit in sgl prec
ad_1_dbl equ $00000800 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:
dc.l add_ext
dc.l add_sgl
dc.l add_dbl
dc.l add_dbl
*
* ADD SINGLE
*
add_sgl:
add.l #ad_1_sgl,LOCAL_HI(a0)
bcc.b scc_clr ;no mantissa overflow
roxr.w LOCAL_HI(a0) ;shift v-bit back in
roxr.w LOCAL_HI+2(a0) ;shift v-bit back in
add.w #$1,LOCAL_EX(a0) ;and incr exponent
scc_clr:
tst.l d0 ;test for rs = 0
bne.b sgl_done
andi.w #$fe00,LOCAL_HI+2(a0) ;clear the l-bit
sgl_done:
andi.l #$ffffff00,LOCAL_HI(a0) ;truncate bits beyond sgl limit
clr.l LOCAL_LO(a0) ;clear d2
rts
*
* ADD EXTENDED
*
add_ext:
addq.l #1,LOCAL_LO(a0) ;add 1 to l-bit
bcc.b xcc_clr ;test for carry out
addq.l #1,LOCAL_HI(a0) ;propogate carry
bcc.b xcc_clr
roxr.w LOCAL_HI(a0) ;mant is 0 so restore v-bit
roxr.w LOCAL_HI+2(a0) ;mant is 0 so restore v-bit
roxr.w LOCAL_LO(a0)
roxr.w LOCAL_LO+2(a0)
add.w #$1,LOCAL_EX(a0) ;and inc exp
xcc_clr:
tst.l d0 ;test rs = 0
bne.b add_ext_done
andi.b #$fe,LOCAL_LO+3(a0) ;clear the l bit
add_ext_done:
rts
*
* ADD DOUBLE
*
add_dbl:
add.l #ad_1_dbl,LOCAL_LO(a0)
bcc.b dcc_clr
addq.l #1,LOCAL_HI(a0) ;propogate carry
bcc.b dcc_clr
roxr.w LOCAL_HI(a0) ;mant is 0 so restore v-bit
roxr.w LOCAL_HI+2(a0) ;mant is 0 so restore v-bit
roxr.w LOCAL_LO(a0)
roxr.w LOCAL_LO+2(a0)
add.w #$1,LOCAL_EX(a0) ;incr exponent
dcc_clr:
tst.l d0 ;test for rs = 0
bne.b dbl_done
andi.w #$f000,LOCAL_LO+2(a0) ;clear the l-bit
dbl_done:
andi.l #$fffff800,LOCAL_LO(a0) ;truncate bits beyond dbl limit
rts
error:
rts
*
* Truncate all other bits
*
trunct:
dc.l end_rnd
dc.l sgl_done
dc.l dbl_done
dc.l dbl_done
truncate:
lea trunct,a1
move.l (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
*
xdef nrm_zero
nrm_zero:
move.w LOCAL_EX(a0),d0
cmp.w #64,d0 ;see if exp > 64
bmi.b d0_less
bsr nrm_set ;exp > 64 so exp won't exceed 0
rts
d0_less:
movem.l d2/d3/d5/d6,-(a7)
move.l LOCAL_HI(a0),d1
move.l LOCAL_LO(a0),d2
bfffo d1{0:32},d3 ;get the distance to the first 1
* ;in ms mant
beq.b ms_clr ;branch if no bits were set
cmp.w d3,d0 ;of X>Y
bmi.b greater ;then exp will go past 0 (neg) if
* ;it is just shifted
bsr nrm_set ;else exp won't go past 0
movem.l (a7)+,d2/d3/d5/d6
rts
greater:
move.l d2,d6 ;save ls mant in d6
lsl.l d0,d2 ;shift ls mant by count
lsl.l d0,d1 ;shift ms mant by count
move.l #32,d5
sub.l d0,d5 ;make op a denorm by shifting bits
lsr.l d5,d6 ;by the number in the exp, then
* ;set exp = 0.
or.l d6,d1 ;shift the ls mant bits into the ms mant
clr.l d0 ;same as if decremented exp to 0
* ;while shifting
move.w d0,LOCAL_EX(a0)
move.l d1,LOCAL_HI(a0)
move.l d2,LOCAL_LO(a0)
movem.l (a7)+,d2/d3/d5/d6
rts
ms_clr:
bfffo d2{0:32},d3 ;check if any bits set in ls mant
beq.b all_clr ;branch if none set
add.w #32,d3
cmp.w d3,d0 ;if X>Y
bmi.b greater ;then branch
bsr nrm_set ;else exp won't go past 0
movem.l (a7)+,d2/d3/d5/d6
rts
all_clr:
clr.w LOCAL_EX(a0) ;no mantissa bits set. Set exp = 0.
movem.l (a7)+,d2/d3/d5/d6
rts
*
* NRM_SET
*
xdef nrm_set
nrm_set:
move.l d7,-(a7)
bfffo LOCAL_HI(a0){0:32},d7 ;find first 1 in ms mant to d7)
beq.b lower ;branch if ms mant is all 0's
move.l d6,-(a7)
sub.w d7,LOCAL_EX(a0) ;sub exponent by count
move.l LOCAL_HI(a0),d0 ;d0 has ms mant
move.l LOCAL_LO(a0),d1 ;d1 has ls mant
lsl.l d7,d0 ;shift first 1 to j bit position
move.l d1,d6 ;copy ls mant into d6
lsl.l d7,d6 ;shift ls mant by count
move.l d6,LOCAL_LO(a0) ;store ls mant into memory
moveq.l #32,d6
sub.l d7,d6 ;continue shift
lsr.l d6,d1 ;shift off all bits but those that will
* ;be shifted into ms mant
or.l d1,d0 ;shift the ls mant bits into the ms mant
move.l d0,LOCAL_HI(a0) ;store ms mant into memory
movem.l (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:
move.w LOCAL_EX(a0),d0 ;d0 has exponent
move.l LOCAL_LO(a0),d1 ;d1 has ls mant
sub.w #32,d0 ;account for ms mant being all zeros
bfffo d1{0:32},d7 ;find first 1 in ls mant to d7)
sub.w d7,d0 ;subtract shift count from exp
lsl.l d7,d1 ;shift first 1 to integer bit in ms mant
move.w d0,LOCAL_EX(a0) ;store ms mant
move.l d1,LOCAL_HI(a0) ;store exp
clr.l LOCAL_LO(a0) ;clear ls mant
move.l (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.
*
xdef denorm
denorm:
btst.b #6,LOCAL_EX(a0) ;check for exponents between $7fff-$4000
beq.b no_sgn_ext
bset.b #7,LOCAL_EX(a0) ;sign extend if it is so
no_sgn_ext:
tst.b d0 ;if 0 then extended precision
bne.b not_ext ;else branch
clr.l d1 ;load d1 with ext threshold
clr.l d0 ;clear the sticky flag
bsr dnrm_lp ;denormalize the number
tst.b d1 ;check for inex
beq.w no_inex ;if clr, no inex
bra.b dnrm_inex ;if set, set inex
not_ext:
cmpi.l #1,d0 ;if 1 then single precision
beq.b load_sgl ;else must be 2, double prec
load_dbl:
move.w #dbl_thresh,d1 ;put copy of threshold in d1
move.l d1,d0 ;copy d1 into d0
sub.w LOCAL_EX(a0),d0 ;diff = threshold - exp
cmp.w #67,d0 ;if diff > 67 (mant + grs bits)
bpl.b chk_stky ;then branch (all bits would be
* ; shifted off in denorm routine)
clr.l d0 ;else clear the sticky flag
bsr dnrm_lp ;denormalize the number
tst.b d1 ;check flag
beq.b no_inex ;if clr, no inex
bra.b dnrm_inex ;if set, set inex
load_sgl:
move.w #sgl_thresh,d1 ;put copy of threshold in d1
move.l d1,d0 ;copy d1 into d0
sub.w LOCAL_EX(a0),d0 ;diff = threshold - exp
cmp.w #67,d0 ;if diff > 67 (mant + grs bits)
bpl.b chk_stky ;then branch (all bits would be
* ; shifted off in denorm routine)
clr.l d0 ;else clear the sticky flag
bsr dnrm_lp ;denormalize the number
tst.b d1 ;check flag
beq.b no_inex ;if clr, no inex
bra.b dnrm_inex ;if set, set inex
chk_stky:
tst.l LOCAL_HI(a0) ;check for any bits set
bne.b set_stky
tst.l LOCAL_LO(a0) ;check for any bits set
bne.b set_stky
bra.b clr_mant
set_stky:
or.l #inx2a_mask,USER_FPSR(a6) ;set inex2/ainex
move.l #$20000000,d0 ;set sticky bit in return value
clr_mant:
move.w d1,LOCAL_EX(a0) ;load exp with threshold
clr.l LOCAL_HI(a0) ;set d1 = 0 (ms mantissa)
clr.l LOCAL_LO(a0) ;set d2 = 0 (ms mantissa)
rts
dnrm_inex:
or.l #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.
*
xdef dnrm_lp
dnrm_lp:
move.l d2,-(sp) ;save d2 for temp use
btst.b #E3,E_BYTE(a6) ;test for type E3 exception
beq.b not_E3 ;not type E3 exception
bfextu WBTEMP_GRS(a6){6:3},d2 ;extract guard,round, sticky bit
move.l #29,d0
lsl.l d0,d2 ;shift g,r,s to their postions
move.l d2,d0
not_E3:
move.l (sp)+,d2 ;restore d2
move.l LOCAL_LO(a0),FP_SCR2+LOCAL_LO(a6)
move.l d0,FP_SCR2+LOCAL_GRS(a6)
move.l d1,d0 ;copy the denorm threshold
sub.w LOCAL_EX(a0),d1 ;d1 = threshold - uns exponent
ble.b no_lp ;d1 <= 0
cmp.w #32,d1
blt.b case_1 ;0 = d1 < 32
cmp.w #64,d1
blt.b case_2 ;32 <= d1 < 64
bra.w case_3 ;d1 >= 64
*
* No normalization necessary
*
no_lp:
clr.b d1 ;set no inex2 reported
move.l FP_SCR2+LOCAL_GRS(a6),d0 ;restore original g,r,s
rts
*
* case (0<d1<32)
*
case_1:
move.l d2,-(sp)
move.w d0,LOCAL_EX(a0) ;exponent = denorm threshold
move.l #32,d0
sub.w 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
move.l d2,LOCAL_HI(a0) ;store new LOCAL_HI
move.l d1,LOCAL_LO(a0) ;store new LOCAL_LO
clr.b d1
bftst d0{2:30}
beq.b c1nstky
bset.l #rnd_stky_bit,d0
st.b d1
c1nstky:
move.l FP_SCR2+LOCAL_GRS(a6),d2 ;restore original g,r,s
andi.l #$e0000000,d2 ;clear all but G,R,S
tst.l d2 ;test if original G,R,S are clear
beq.b grs_clear
or.l #$20000000,d0 ;set sticky bit in d0
grs_clear:
andi.l #$e0000000,d0 ;clear all but G,R,S
move.l (sp)+,d2
rts
*
* case (32<=d1<64)
*
case_2:
move.l d2,-(sp)
move.w d0,LOCAL_EX(a0) ;unsigned exponent = threshold
sub.w #32,d1 ;d1 now between 0 and 32
move.l #32,d0
sub.w 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}
bne.b c2_sstky ;bra if sticky bit to be set
bftst FP_SCR2+LOCAL_LO(a6){d0:32}
bne.b c2_sstky ;bra if sticky bit to be set
move.l d1,d0
clr.b d1
bra.b end_c2
c2_sstky:
move.l d1,d0
bset.l #rnd_stky_bit,d0
st.b d1
end_c2:
clr.l LOCAL_HI(a0) ;store LOCAL_HI = 0
move.l d2,LOCAL_LO(a0) ;store LOCAL_LO
move.l FP_SCR2+LOCAL_GRS(a6),d2 ;restore original g,r,s
andi.l #$e0000000,d2 ;clear all but G,R,S
tst.l d2 ;test if original G,R,S are clear
beq.b clear_grs
or.l #$20000000,d0 ;set sticky bit in d0
clear_grs:
andi.l #$e0000000,d0 ;get rid of all but G,R,S
move.l (sp)+,d2
rts
*
* d1 >= 64 Force the exponent to be the denorm threshold with the
* correct sign.
*
case_3:
move.w d0,LOCAL_EX(a0)
tst.w LOCAL_SGN(a0)
bge.b c3con
c3neg:
or.l #$80000000,LOCAL_EX(a0)
c3con:
cmp.w #64,d1
beq.b sixty_four
cmp.w #65,d1
beq.b sixty_five
*
* Shift value is out of range. Set d1 for inex2 flag and
* return a zero with the given threshold.
*
clr.l LOCAL_HI(a0)
clr.l LOCAL_LO(a0)
move.l #$20000000,d0
st.b d1
rts
sixty_four:
move.l LOCAL_HI(a0),d0
bfextu d0{2:30},d1
andi.l #$c0000000,d0
bra.b c3com
sixty_five:
move.l LOCAL_HI(a0),d0
bfextu d0{1:31},d1
andi.l #$80000000,d0
lsr.l #1,d0 ;shift high bit into R bit
c3com:
tst.l d1
bne.b c3ssticky
tst.l LOCAL_LO(a0)
bne.b c3ssticky
tst.b FP_SCR2+LOCAL_GRS(a6)
bne.b c3ssticky
clr.b d1
bra.b c3end
c3ssticky:
bset.l #rnd_stky_bit,d0
st.b d1
c3end:
clr.l LOCAL_HI(a0)
clr.l LOCAL_LO(a0)
rts
end
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