round.s
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- /* round.s - Motorola 68040 FP rounding routines (EXC) */
- /* Copyright 1991-1993 Wind River Systems, Inc. */
- .data
- .globl _copyright_wind_river
- .long _copyright_wind_river
- /*
- modification history
- --------------------
- 01g,21jul93,kdl added .text (SPR #2372).
- 01f,23aug92,jcf changed bxxx to jxx.
- 01e,26may92,rrr the tree shuffle
- 01d,10jan92,kdl general cleanup.
- 01c,01jan92,jcf reversed order of cmp <reg>,<reg>
- 01b,17dec91,kdl put in changes from Motorola v3.4 (from FPSP 2.1):
- use register for fixing "lsll 29" problem (01a);
- add check for negative loop count in __x_dnrm_lp.
- 01a,31jul91,kdl original version, from Motorola FPSP v2.0;
- divided "lsll #29" into smaller bit shifts.
- */
- /*
- DESCRIPTION
- roundsa 3.2 2/18/91
- 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- THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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
- NOMANUAL
- */
- #include "fpsp040E.h"
- |
- | __x_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 = 0x0000xxxx
- | sgl = 0x0001xxxx
- | dbl = 0x0002xxxx
- | 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).
- |
- .globl __x_round
- .text
- __x_round:
- | If g=r=s=0 then result is exact and round is done, else set
- | the inex flag in status reg and continue.
- |
- bsrl 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
- jne rnd_cont | lower bits to zero for size
- swap d1 | set up d1:w for round prec.
- jra truncate
- rnd_cont:
- |
- | Use rounding mode as an index into a jump table for these modes.
- |
- orl #inx2a_mask,a6@(USER_FPSR) | 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 a0@(LOCAL_SGN) | check for sign
- jmi 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 a0@(LOCAL_SGN) | check for sign
- jpl 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.
- jra 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
- jcc 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
- jne sgl_or_dbl
- jra end_ext_grs
- sgl_or_dbl:
- moveml d2/d3,a7@- | make some temp registers
- cmpiw #1,d1
- jne grs_dbl
- grs_sgl:
- bfextu a0@(LOCAL_HI){#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 a0@(LOCAL_HI),d2 | get word 2 for s-bit test
- andil #0x0000003f,d2 | s bit is the or of all other
- jne st_stky | bits to the right of g-r
- tstl a0@(LOCAL_LO) | test lower mantissa
- jne st_stky | if any are set, set sticky
- tstl d0 | test original g,r,s
- jne st_stky | if any are set, set sticky
- jra end_sd | if words 3 and 4 are clr, exit
- grs_dbl:
- bfextu a0@(LOCAL_LO){#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 a0@(LOCAL_LO),d2 | get lower mantissa for s-bit test
- andil #0x000001ff,d2 | s bit is the or-ing of all
- jne st_stky | other bits to the right of g-r
- tstl d0 | test word original g,r,s
- jne st_stky | if any are set, set sticky
- jra 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
- #define ad_1_sgl 0x00000100 /* constant to add 1 to l-bit in sgl prec */
- #define 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,a0@(LOCAL_HI)
- jcc scc_clr | no mantissa overflow
- roxrw a0@(LOCAL_HI) | shift v-bit back in
- roxrw a0@(LOCAL_HI+2) | shift v-bit back in
- addw #0x1,a0@(LOCAL_EX) | and incr exponent
- scc_clr:
- tstl d0 | test for rs = 0
- jne sgl_done
- andiw #0xfe00,a0@(LOCAL_HI+2) | clear the l-bit
- sgl_done:
- andil #0xffffff00,a0@(LOCAL_HI) | truncate bits beyond sgl limit
- clrl a0@(LOCAL_LO) | clear d2
- rts
- |
- | ADD EXTENDED
- |
- add_ext:
- addql #1,a0@(LOCAL_LO) | add 1 to l-bit
- jcc xcc_clr | test for carry out
- addql #1,a0@(LOCAL_HI) | propogate carry
- jcc xcc_clr
- roxrw a0@(LOCAL_HI) | mant is 0 so restore v-bit
- roxrw a0@(LOCAL_HI+2) | mant is 0 so restore v-bit
- roxrw a0@(LOCAL_LO)
- roxrw a0@(LOCAL_LO+2)
- addw #0x1,a0@(LOCAL_EX) | and inc exp
- xcc_clr:
- tstl d0 | test rs = 0
- jne add_ext_done
- andib #0xfe,a0@(LOCAL_LO+3) | clear the l bit
- add_ext_done:
- rts
- |
- | ADD DOUBLE
- |
- add_dbl:
- addl #ad_1_dbl,a0@(LOCAL_LO)
- jcc dcc_clr
- addql #1,a0@(LOCAL_HI) | propogate carry
- jcc dcc_clr
- roxrw a0@(LOCAL_HI) | mant is 0 so restore v-bit
- roxrw a0@(LOCAL_HI+2) | mant is 0 so restore v-bit
- roxrw a0@(LOCAL_LO)
- roxrw a0@(LOCAL_LO+2)
- addw #0x1,a0@(LOCAL_EX) | incr exponent
- dcc_clr:
- tstl d0 | test for rs = 0
- jne dbl_done
- andiw #0xf000,a0@(LOCAL_LO+2) | clear the l-bit
- dbl_done:
- andil #0xfffff800,a0@(LOCAL_LO) | 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 # __x_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
- | __x_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
- |
- .globl __x_nrm_zero
- __x_nrm_zero:
- movew a0@(LOCAL_EX),d0
- cmpw #64,d0 | see if exp > 64
- jmi d0_less
- bsrl __x_nrm_set /* | exp > 64 so exp won't exceed 0 */
- rts
- d0_less:
- moveml d2/d3/d5/d6,a7@-
- movel a0@(LOCAL_HI),d1
- movel a0@(LOCAL_LO),d2
- bfffo d1{#0:#32},d3 | get the distance to the first 1
- | | in ms mant
- jeq ms_clr | branch if no bits were set
- cmpw d3,d0 | of X>Y
- jmi greater | then exp will go past 0 (neg) if
- | | it is just shifted
- bsrl __x_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,a0@(LOCAL_EX)
- movel d1,a0@(LOCAL_HI)
- movel d2,a0@(LOCAL_LO)
- moveml a7@+,d2/d3/d5/d6
- rts
- ms_clr:
- bfffo d2{#0:#32},d3 | check if any bits set in ls mant
- jeq all_clr | branch if none set
- addw #32,d3
- cmpw d3,d0 | if X>Y
- jmi greater | then branch
- bsrl __x_nrm_set /* | else exp won't go past 0 */
- moveml a7@+,d2/d3/d5/d6
- rts
- all_clr:
- movew #0,a0@(LOCAL_EX) | no mantissa bits set. Set exp = 0.
- moveml a7@+,d2/d3/d5/d6
- rts
- |
- | NRM_SET
- |
- .globl __x_nrm_set
- __x_nrm_set:
- movel d7,a7@-
- bfffo a0@(LOCAL_HI){#0:#32},d7 | find first 1 in ms mant to d7)
- jeq lower /* | branch if ms mant is all 0's */
- movel d6,a7@-
- subw d7,a0@(LOCAL_EX) | sub exponent by count
- movel a0@(LOCAL_HI),d0 | d0 has ms mant
- movel a0@(LOCAL_LO),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,a0@(LOCAL_LO) | 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,a0@(LOCAL_HI) | 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 a0@(LOCAL_EX),d0 | d0 has exponent
- movel a0@(LOCAL_LO),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,a0@(LOCAL_EX) | store ms mant
- movel d1,a0@(LOCAL_HI) | store exp
- clrl a0@(LOCAL_LO) | clear ls mant
- movel a7@+,d7
- rts
- |
- | __x_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.
- |
- .globl __x_denorm
- __x_denorm:
- btst #6,a0@(LOCAL_EX) | check for exponents between 0x7fff-0x4000
- jeq no_sgn_ext
- bset #7,a0@(LOCAL_EX) | sign extend if it is so
- no_sgn_ext:
- cmpib #0,d0 | if 0 then extended precision
- jne not_ext | else branch
- clrl d1 | load d1 with ext threshold
- clrl d0 | clear the sticky flag
- bsrl __x_dnrm_lp | denormalize the number
- tstb d1 | check for inex
- jeq no_inex | if clr, no inex
- jra dnrm_inex | if set, set inex
- not_ext:
- cmpil #1,d0 | if 1 then single precision
- jeq 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 a0@(LOCAL_EX),d0 | diff = threshold - exp
- cmpw #67,d0 | if diff > 67 (mant + grs bits)
- jpl chk_stky | then branch (all bits would be
- | | shifted off in denorm routine)
- clrl d0 | else clear the sticky flag
- bsrl __x_dnrm_lp | denormalize the number
- tstb d1 | check flag
- jeq no_inex | if clr, no inex
- jra 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 a0@(LOCAL_EX),d0 | diff = threshold - exp
- cmpw #67,d0 | if diff > 67 (mant + grs bits)
- jpl chk_stky | then branch (all bits would be
- | | shifted off in __x_denorm routine)
- clrl d0 | else clear the sticky flag
- bsrl __x_dnrm_lp | denormalize the number
- tstb d1 | check flag
- jeq no_inex | if clr, no inex
- jra dnrm_inex | if set, set inex
- chk_stky:
- tstl a0@(LOCAL_HI) | check for any bits set
- jne set_stky
- tstl a0@(LOCAL_LO) | check for any bits set
- jne set_stky
- jra clr_mant
- set_stky:
- orl #inx2a_mask,a6@(USER_FPSR) | set inex2/ainex
- movel #0x20000000,d0 | set sticky bit in return value
- clr_mant:
- movew d1,a0@(LOCAL_EX) | load exp with threshold
- movel #0,a0@(LOCAL_HI) | set d1 = 0 (ms mantissa)
- movel #0,a0@(LOCAL_LO) | set d2 = 0 (ms mantissa)
- rts
- dnrm_inex:
- orl #inx2a_mask,a6@(USER_FPSR) | set inex2/ainex
- no_inex:
- rts
- |
- | __x_dnrm_lp --- normalize exponent/mantissa to specified threshhold
- |
- | 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
- | d1b 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.
- |
- .globl __x_dnrm_lp
- __x_dnrm_lp:
- movel d2,a7@- | save d2 for temp use
- btst #E3,a6@(E_BYTE) | test for type E3 exception
- jeq not_E3 | not type E3 exception
- clrl d0 | guard,round,sticky init.
- bfextu a6@(WBTEMP_GRS){#6:#3},d2 | extract guard,round, sticky bit
- | The following bit shift specifies a larger number of bits than actually
- | allowed (8). So, it was divided into a series of smaller shifts.
- | lsll #29,d2 | original shift g,r,s to their postions
- |
- |
- | lsll #8,d2 | shift g,r,s 8 bits
- | lsll #8,d2 | shift g,r,s 8 bits (total 16)
- | lsll #8,d2 | shift g,r,s 8 bits (total 24)
- | lsll #5,d2 | shift g,r,s 5 bits (total 29)
- | orl d2,d0 | in d0
- movel #29,d0
- lsll d0,d2 | shift g,r,s to their postions
- movel d2,d0
- not_E3:
- movel a7@+,d2 | restore d2
- movel a0@(LOCAL_LO),a6@(FP_SCR2+LOCAL_LO)
- movel d0,a6@(FP_SCR2+LOCAL_GRS)
- movel d1,d0 | copy the denorm threshold
- subw a0@(LOCAL_EX),d1 | d1 = threshold - uns exponent
- jle no_lp | d1 <= 0
- cmpw #32,d1
- jlt case_1 | 0 = d1 < 32
- cmpw #64,d1
- jlt case_2 | 32 <= d1 < 64
- jra case_3 | d1 >= 64
- |
- | No normalization necessary
- |
- no_lp:
- clrb d1 | set no inex2 reported
- movel a6@(FP_SCR2+LOCAL_GRS),d0 | restore original g,r,s
- rts
- |
- | case (0<d1<32)
- |
- case_1:
- movel d2,a7@-
- movew d0,a0@(LOCAL_EX) | exponent = denorm threshold
- movel #32,d0
- subw d1,d0 | d0 = 32 - d1
- bfextu a0@(LOCAL_EX){d0:#32},d2
- bfextu d2{d1:d0},d2 | d2 = new LOCAL_HI
- bfextu a0@(LOCAL_HI){d0:#32},d1 | d1 = new LOCAL_LO
- bfextu a6@(FP_SCR2+LOCAL_LO){d0:#32},d0 | d0 = new G,R,S
- movel d2,a0@(LOCAL_HI) | store new LOCAL_HI
- movel d1,a0@(LOCAL_LO) | store new LOCAL_LO
- clrb d1
- bftst d0{#2:#30}
- jeq c1nstky
- bset #rnd_stky_bit,d0
- st d1
- c1nstky:
- movel a6@(FP_SCR2+LOCAL_GRS),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
- jeq grs_clear
- orl #0x20000000,d0 | set sticky bit in d0
- grs_clear:
- andil #0xe0000000,d0 | clear all but G,R,S
- movel a7@+,d2
- rts
- |
- | case (32<=d1<64)
- |
- case_2:
- movel d2,a7@-
- movew d0,a0@(LOCAL_EX) | unsigned exponent = threshold
- subw #32,d1 | d1 now between 0 and 32
- movel #32,d0
- subw d1,d0 | d0 = 32 - d1
- bfextu a0@(LOCAL_EX){d0:#32},d2
- bfextu d2{d1:d0},d2 | d2 = new LOCAL_LO
- bfextu a0@(LOCAL_HI){d0:#32},d1 | d1 = new G,R,S
- bftst d1{#2:#30}
- jne c2_sstky | jra if sticky bit to be set
- bftst a6@(FP_SCR2+LOCAL_LO){d0:#32}
- jne c2_sstky | jra if sticky bit to be set
- movel d1,d0
- clrb d1
- jra end_c2
- c2_sstky:
- movel d1,d0
- bset #rnd_stky_bit,d0
- st d1
- end_c2:
- clrl a0@(LOCAL_HI) | store LOCAL_HI = 0
- movel d2,a0@(LOCAL_LO) | store LOCAL_LO
- movel a6@(FP_SCR2+LOCAL_GRS),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
- jeq clear_grs
- orl #0x20000000,d0 | set sticky bit in d0
- clear_grs:
- andil #0xe0000000,d0 | get rid of all but G,R,S
- movel a7@+,d2
- rts
- |
- | d1 >= 64 Force the exponent to be the denorm threshold with the
- | correct sign.
- |
- case_3:
- movew d0,a0@(LOCAL_EX)
- tstw a0@(LOCAL_SGN)
- jge c3con
- c3neg:
- orl #0x80000000,a0@(LOCAL_EX)
- c3con:
- cmpw #64,d1
- jeq sixty_four
- cmpw #65,d1
- jeq sixty_five
- |
- | Shift value is out of range. Set d1 for inex2 flag and
- | return a zero with the given threshold.
- |
- clrl a0@(LOCAL_HI)
- clrl a0@(LOCAL_LO)
- movel #0x20000000,d0
- st d1
- rts
- sixty_four:
- movel a0@(LOCAL_HI),d0
- bfextu d0{#2:#30},d1
- andil #0xc0000000,d0
- jra c3com
- sixty_five:
- movel a0@(LOCAL_HI),d0
- bfextu d0{#1:#31},d1
- andil #0x80000000,d0
- lsrl #1,d0 | shift high bit into R bit
- c3com:
- tstl d1
- jne c3ssticky
- tstl a0@(LOCAL_LO)
- jne c3ssticky
- tstb a6@(FP_SCR2+LOCAL_GRS)
- jne c3ssticky
- clrb d1
- jra c3end
- c3ssticky:
- bset #rnd_stky_bit,d0
- st d1
- c3end:
- clrl a0@(LOCAL_HI)
- clrl a0@(LOCAL_LO)
- rts
- | end