//
// $Id$
//
// 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// THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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<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
