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+|
+| 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