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| round.sa 3.4 7/29/91
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| handle rounding and normalization tasks
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| Copyright (C) Motorola, Inc. 1990
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| All Rights Reserved
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| For details on the license for this file, please see the
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| file, README, in this same directory.
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|
|ROUND idnt 2,1 | Motorola 040 Floating Point Software Package
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|
|section 8
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|
#include "fpsp.h"
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|
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| round --- round result according to precision/mode
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| a0 points to the input operand in the internal extended format
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| d1(high word) contains rounding precision:
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| ext = $0000xxxx
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| sgl = $0001xxxx
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| dbl = $0002xxxx
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| d1(low word) contains rounding mode:
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| RN = $xxxx0000
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| RZ = $xxxx0001
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| RM = $xxxx0010
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| RP = $xxxx0011
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| d0{31:29} contains the g,r,s bits (extended)
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|
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| On return the value pointed to by a0 is correctly rounded,
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| a0 is preserved and the g-r-s bits in d0 are cleared.
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| The result is not typed - the tag field is invalid. The
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| result is still in the internal extended format.
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| The INEX bit of USER_FPSR will be set if the rounded result was
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| inexact (i.e. if any of the g-r-s bits were set).
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.global round
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round:
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| If g=r=s=0 then result is exact and round is done, else set
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| the inex flag in status reg and continue.
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bsrs ext_grs |this subroutine looks at the
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| :rounding precision and sets
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| ;the appropriate g-r-s bits.
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tstl %d0 |if grs are zero, go force
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bne rnd_cont |lower bits to zero for size
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swap %d1 |set up d1.w for round prec.
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bra truncate
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rnd_cont:
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| Use rounding mode as an index into a jump table for these modes.
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orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
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lea mode_tab,%a1
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movel (%a1,%d1.w*4),%a1
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jmp (%a1)
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| Jump table indexed by rounding mode in d1.w. All following assumes
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| grs != 0.
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mode_tab:
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.long rnd_near
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.long rnd_zero
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.long rnd_mnus
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.long rnd_plus
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| ROUND PLUS INFINITY
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| If sign of fp number = 0 (positive), then add 1 to l.
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rnd_plus:
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swap %d1 |set up d1 for round prec.
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tstb LOCAL_SGN(%a0) |check for sign
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bmi truncate |if positive then truncate
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movel #0xffffffff,%d0 |force g,r,s to be all f's
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lea add_to_l,%a1
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movel (%a1,%d1.w*4),%a1
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jmp (%a1)
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| ROUND MINUS INFINITY
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| If sign of fp number = 1 (negative), then add 1 to l.
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rnd_mnus:
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swap %d1 |set up d1 for round prec.
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tstb LOCAL_SGN(%a0) |check for sign
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bpl truncate |if negative then truncate
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movel #0xffffffff,%d0 |force g,r,s to be all f's
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lea add_to_l,%a1
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movel (%a1,%d1.w*4),%a1
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jmp (%a1)
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| ROUND ZERO
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| Always truncate.
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rnd_zero:
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swap %d1 |set up d1 for round prec.
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bra truncate
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| ROUND NEAREST
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| If (g=1), then add 1 to l and if (r=s=0), then clear l
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| Note that this will round to even in case of a tie.
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rnd_near:
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swap %d1 |set up d1 for round prec.
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asll #1,%d0 |shift g-bit to c-bit
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bcc truncate |if (g=1) then
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lea add_to_l,%a1
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movel (%a1,%d1.w*4),%a1
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jmp (%a1)
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| ext_grs --- extract guard, round and sticky bits
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| Input: d1 = PREC:ROUND
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| Output: d0{31:29}= guard, round, sticky
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| The ext_grs extract the guard/round/sticky bits according to the
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| selected rounding precision. It is called by the round subroutine
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| only. All registers except d0 are kept intact. d0 becomes an
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| updated guard,round,sticky in d0{31:29}
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| Notes: the ext_grs uses the round PREC, and therefore has to swap d1
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| prior to usage, and needs to restore d1 to original.
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ext_grs:
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swap %d1 |have d1.w point to round precision
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cmpiw #0,%d1
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bnes sgl_or_dbl
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bras end_ext_grs
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sgl_or_dbl:
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moveml %d2/%d3,-(%a7) |make some temp registers
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cmpiw #1,%d1
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bnes grs_dbl
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grs_sgl:
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bfextu LOCAL_HI(%a0){#24:#2},%d3 |sgl prec. g-r are 2 bits right
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movel #30,%d2 |of the sgl prec. limits
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lsll %d2,%d3 |shift g-r bits to MSB of d3
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movel LOCAL_HI(%a0),%d2 |get word 2 for s-bit test
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andil #0x0000003f,%d2 |s bit is the or of all other
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bnes st_stky |bits to the right of g-r
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tstl LOCAL_LO(%a0) |test lower mantissa
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bnes st_stky |if any are set, set sticky
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tstl %d0 |test original g,r,s
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bnes st_stky |if any are set, set sticky
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bras end_sd |if words 3 and 4 are clr, exit
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grs_dbl:
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bfextu LOCAL_LO(%a0){#21:#2},%d3 |dbl-prec. g-r are 2 bits right
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movel #30,%d2 |of the dbl prec. limits
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lsll %d2,%d3 |shift g-r bits to the MSB of d3
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movel LOCAL_LO(%a0),%d2 |get lower mantissa for s-bit test
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andil #0x000001ff,%d2 |s bit is the or-ing of all
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bnes st_stky |other bits to the right of g-r
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tstl %d0 |test word original g,r,s
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bnes st_stky |if any are set, set sticky
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bras end_sd |if clear, exit
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st_stky:
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bset #rnd_stky_bit,%d3
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end_sd:
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movel %d3,%d0 |return grs to d0
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moveml (%a7)+,%d2/%d3 |restore scratch registers
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end_ext_grs:
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swap %d1 |restore d1 to original
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rts
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|******************* Local Equates
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.set ad_1_sgl,0x00000100 | constant to add 1 to l-bit in sgl prec
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.set ad_1_dbl,0x00000800 | constant to add 1 to l-bit in dbl prec
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|Jump table for adding 1 to the l-bit indexed by rnd prec
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add_to_l:
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.long add_ext
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.long add_sgl
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.long add_dbl
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.long add_dbl
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| ADD SINGLE
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add_sgl:
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addl #ad_1_sgl,LOCAL_HI(%a0)
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bccs scc_clr |no mantissa overflow
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roxrw LOCAL_HI(%a0) |shift v-bit back in
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roxrw LOCAL_HI+2(%a0) |shift v-bit back in
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addw #0x1,LOCAL_EX(%a0) |and incr exponent
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scc_clr:
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tstl %d0 |test for rs = 0
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bnes sgl_done
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andiw #0xfe00,LOCAL_HI+2(%a0) |clear the l-bit
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sgl_done:
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andil #0xffffff00,LOCAL_HI(%a0) |truncate bits beyond sgl limit
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clrl LOCAL_LO(%a0) |clear d2
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rts
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| ADD EXTENDED
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add_ext:
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addql #1,LOCAL_LO(%a0) |add 1 to l-bit
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bccs xcc_clr |test for carry out
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addql #1,LOCAL_HI(%a0) |propagate carry
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bccs xcc_clr
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roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit
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roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit
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roxrw LOCAL_LO(%a0)
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roxrw LOCAL_LO+2(%a0)
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addw #0x1,LOCAL_EX(%a0) |and inc exp
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xcc_clr:
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tstl %d0 |test rs = 0
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bnes add_ext_done
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andib #0xfe,LOCAL_LO+3(%a0) |clear the l bit
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add_ext_done:
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rts
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| ADD DOUBLE
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add_dbl:
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addl #ad_1_dbl,LOCAL_LO(%a0)
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bccs dcc_clr
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addql #1,LOCAL_HI(%a0) |propagate carry
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bccs dcc_clr
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roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit
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roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit
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roxrw LOCAL_LO(%a0)
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roxrw LOCAL_LO+2(%a0)
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addw #0x1,LOCAL_EX(%a0) |incr exponent
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dcc_clr:
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tstl %d0 |test for rs = 0
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bnes dbl_done
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andiw #0xf000,LOCAL_LO+2(%a0) |clear the l-bit
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dbl_done:
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andil #0xfffff800,LOCAL_LO(%a0) |truncate bits beyond dbl limit
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rts
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error:
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rts
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| Truncate all other bits
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trunct:
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.long end_rnd
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.long sgl_done
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.long dbl_done
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.long dbl_done
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truncate:
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lea trunct,%a1
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movel (%a1,%d1.w*4),%a1
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jmp (%a1)
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end_rnd:
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rts
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| NORMALIZE
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| These routines (nrm_zero & nrm_set) normalize the unnorm. This
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| is done by shifting the mantissa left while decrementing the
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| exponent.
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| NRM_SET shifts and decrements until there is a 1 set in the integer
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| bit of the mantissa (msb in d1).
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| NRM_ZERO shifts and decrements until there is a 1 set in the integer
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| bit of the mantissa (msb in d1) unless this would mean the exponent
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| would go less than 0. In that case the number becomes a denorm - the
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| exponent (d0) is set to 0 and the mantissa (d1 & d2) is not
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| normalized.
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| Note that both routines have been optimized (for the worst case) and
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| therefore do not have the easy to follow decrement/shift loop.
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| NRM_ZERO
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| Distance to first 1 bit in mantissa = X
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| Distance to 0 from exponent = Y
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| If X < Y
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| Then
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| nrm_set
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| Else
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| shift mantissa by Y
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| set exponent = 0
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|input:
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| FP_SCR1 = exponent, ms mantissa part, ls mantissa part
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|output:
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| L_SCR1{4} = fpte15 or ete15 bit
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.global nrm_zero
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nrm_zero:
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movew LOCAL_EX(%a0),%d0
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cmpw #64,%d0 |see if exp > 64
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bmis d0_less
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bsr nrm_set |exp > 64 so exp won't exceed 0
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rts
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d0_less:
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moveml %d2/%d3/%d5/%d6,-(%a7)
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movel LOCAL_HI(%a0),%d1
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movel LOCAL_LO(%a0),%d2
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bfffo %d1{#0:#32},%d3 |get the distance to the first 1
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| ;in ms mant
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beqs ms_clr |branch if no bits were set
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cmpw %d3,%d0 |of X>Y
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bmis greater |then exp will go past 0 (neg) if
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| ;it is just shifted
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bsr nrm_set |else exp won't go past 0
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moveml (%a7)+,%d2/%d3/%d5/%d6
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rts
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greater:
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movel %d2,%d6 |save ls mant in d6
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lsll %d0,%d2 |shift ls mant by count
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lsll %d0,%d1 |shift ms mant by count
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movel #32,%d5
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subl %d0,%d5 |make op a denorm by shifting bits
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lsrl %d5,%d6 |by the number in the exp, then
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| ;set exp = 0.
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orl %d6,%d1 |shift the ls mant bits into the ms mant
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movel #0,%d0 |same as if decremented exp to 0
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| ;while shifting
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movew %d0,LOCAL_EX(%a0)
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movel %d1,LOCAL_HI(%a0)
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movel %d2,LOCAL_LO(%a0)
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moveml (%a7)+,%d2/%d3/%d5/%d6
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rts
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ms_clr:
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bfffo %d2{#0:#32},%d3 |check if any bits set in ls mant
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beqs all_clr |branch if none set
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addw #32,%d3
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cmpw %d3,%d0 |if X>Y
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bmis greater |then branch
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bsr nrm_set |else exp won't go past 0
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moveml (%a7)+,%d2/%d3/%d5/%d6
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rts
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all_clr:
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movew #0,LOCAL_EX(%a0) |no mantissa bits set. Set exp = 0.
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moveml (%a7)+,%d2/%d3/%d5/%d6
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rts
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| NRM_SET
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.global nrm_set
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nrm_set:
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movel %d7,-(%a7)
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bfffo LOCAL_HI(%a0){#0:#32},%d7 |find first 1 in ms mant to d7)
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beqs lower |branch if ms mant is all 0's
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movel %d6,-(%a7)
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subw %d7,LOCAL_EX(%a0) |sub exponent by count
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movel LOCAL_HI(%a0),%d0 |d0 has ms mant
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movel LOCAL_LO(%a0),%d1 |d1 has ls mant
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lsll %d7,%d0 |shift first 1 to j bit position
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movel %d1,%d6 |copy ls mant into d6
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lsll %d7,%d6 |shift ls mant by count
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movel %d6,LOCAL_LO(%a0) |store ls mant into memory
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moveql #32,%d6
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subl %d7,%d6 |continue shift
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lsrl %d6,%d1 |shift off all bits but those that will
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| ;be shifted into ms mant
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orl %d1,%d0 |shift the ls mant bits into the ms mant
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movel %d0,LOCAL_HI(%a0) |store ms mant into memory
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moveml (%a7)+,%d7/%d6 |restore registers
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rts
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| We get here if ms mant was = 0, and we assume ls mant has bits
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| set (otherwise this would have been tagged a zero not a denorm).
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lower:
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movew LOCAL_EX(%a0),%d0 |d0 has exponent
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movel LOCAL_LO(%a0),%d1 |d1 has ls mant
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subw #32,%d0 |account for ms mant being all zeros
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bfffo %d1{#0:#32},%d7 |find first 1 in ls mant to d7)
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subw %d7,%d0 |subtract shift count from exp
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lsll %d7,%d1 |shift first 1 to integer bit in ms mant
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movew %d0,LOCAL_EX(%a0) |store ms mant
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movel %d1,LOCAL_HI(%a0) |store exp
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clrl LOCAL_LO(%a0) |clear ls mant
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movel (%a7)+,%d7
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rts
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| denorm --- denormalize an intermediate result
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| Used by underflow.
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| Input:
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| a0 points to the operand to be denormalized
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| (in the internal extended format)
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| d0: rounding precision
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| Output:
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| a0 points to the denormalized result
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| (in the internal extended format)
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| d0 is guard,round,sticky
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| d0 comes into this routine with the rounding precision. It
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| is then loaded with the denormalized exponent threshold for the
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| rounding precision.
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.global denorm
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denorm:
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btstb #6,LOCAL_EX(%a0) |check for exponents between $7fff-$4000
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beqs no_sgn_ext
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bsetb #7,LOCAL_EX(%a0) |sign extend if it is so
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no_sgn_ext:
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cmpib #0,%d0 |if 0 then extended precision
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bnes not_ext |else branch
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clrl %d1 |load d1 with ext threshold
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clrl %d0 |clear the sticky flag
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bsr dnrm_lp |denormalize the number
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tstb %d1 |check for inex
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beq no_inex |if clr, no inex
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bras dnrm_inex |if set, set inex
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not_ext:
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cmpil #1,%d0 |if 1 then single precision
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beqs load_sgl |else must be 2, double prec
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load_dbl:
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movew #dbl_thresh,%d1 |put copy of threshold in d1
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movel %d1,%d0 |copy d1 into d0
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subw LOCAL_EX(%a0),%d0 |diff = threshold - exp
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cmpw #67,%d0 |if diff > 67 (mant + grs bits)
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bpls chk_stky |then branch (all bits would be
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| ; shifted off in denorm routine)
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clrl %d0 |else clear the sticky flag
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bsr dnrm_lp |denormalize the number
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tstb %d1 |check flag
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beqs no_inex |if clr, no inex
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bras dnrm_inex |if set, set inex
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load_sgl:
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movew #sgl_thresh,%d1 |put copy of threshold in d1
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movel %d1,%d0 |copy d1 into d0
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subw LOCAL_EX(%a0),%d0 |diff = threshold - exp
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cmpw #67,%d0 |if diff > 67 (mant + grs bits)
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bpls chk_stky |then branch (all bits would be
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| ; shifted off in denorm routine)
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clrl %d0 |else clear the sticky flag
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bsr dnrm_lp |denormalize the number
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tstb %d1 |check flag
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beqs no_inex |if clr, no inex
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bras dnrm_inex |if set, set inex
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chk_stky:
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tstl LOCAL_HI(%a0) |check for any bits set
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bnes set_stky
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tstl LOCAL_LO(%a0) |check for any bits set
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bnes set_stky
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bras clr_mant
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set_stky:
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orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
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movel #0x20000000,%d0 |set sticky bit in return value
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clr_mant:
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movew %d1,LOCAL_EX(%a0) |load exp with threshold
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movel #0,LOCAL_HI(%a0) |set d1 = 0 (ms mantissa)
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movel #0,LOCAL_LO(%a0) |set d2 = 0 (ms mantissa)
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rts
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dnrm_inex:
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orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
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no_inex:
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rts
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| dnrm_lp --- normalize exponent/mantissa to specified threshold
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|
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| Input:
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| a0 points to the operand to be denormalized
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| d0{31:29} initial guard,round,sticky
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| d1{15:0} denormalization threshold
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| Output:
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| a0 points to the denormalized operand
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| d0{31:29} final guard,round,sticky
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| d1.b inexact flag: all ones means inexact result
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|
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| The LOCAL_LO and LOCAL_GRS parts of the value are copied to FP_SCR2
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| so that bfext can be used to extract the new low part of the mantissa.
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| Dnrm_lp can be called with a0 pointing to ETEMP or WBTEMP and there
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| is no LOCAL_GRS scratch word following it on the fsave frame.
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|
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.global dnrm_lp
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dnrm_lp:
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movel %d2,-(%sp) |save d2 for temp use
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btstb #E3,E_BYTE(%a6) |test for type E3 exception
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beqs not_E3 |not type E3 exception
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bfextu WBTEMP_GRS(%a6){#6:#3},%d2 |extract guard,round, sticky bit
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movel #29,%d0
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lsll %d0,%d2 |shift g,r,s to their positions
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movel %d2,%d0
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not_E3:
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movel (%sp)+,%d2 |restore d2
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movel LOCAL_LO(%a0),FP_SCR2+LOCAL_LO(%a6)
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movel %d0,FP_SCR2+LOCAL_GRS(%a6)
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movel %d1,%d0 |copy the denorm threshold
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subw LOCAL_EX(%a0),%d1 |d1 = threshold - uns exponent
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bles no_lp |d1 <= 0
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cmpw #32,%d1
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blts case_1 |0 = d1 < 32
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cmpw #64,%d1
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blts case_2 |32 <= d1 < 64
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bra case_3 |d1 >= 64
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|
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| No normalization necessary
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no_lp:
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clrb %d1 |set no inex2 reported
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movel FP_SCR2+LOCAL_GRS(%a6),%d0 |restore original g,r,s
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rts
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|
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| case (0<d1<32)
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|
|
case_1:
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movel %d2,-(%sp)
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movew %d0,LOCAL_EX(%a0) |exponent = denorm threshold
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movel #32,%d0
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subw %d1,%d0 |d0 = 32 - d1
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bfextu LOCAL_EX(%a0){%d0:#32},%d2
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bfextu %d2{%d1:%d0},%d2 |d2 = new LOCAL_HI
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bfextu LOCAL_HI(%a0){%d0:#32},%d1 |d1 = new LOCAL_LO
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bfextu FP_SCR2+LOCAL_LO(%a6){%d0:#32},%d0 |d0 = new G,R,S
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movel %d2,LOCAL_HI(%a0) |store new LOCAL_HI
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movel %d1,LOCAL_LO(%a0) |store new LOCAL_LO
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clrb %d1
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bftst %d0{#2:#30}
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beqs c1nstky
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bsetl #rnd_stky_bit,%d0
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st %d1
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c1nstky:
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movel FP_SCR2+LOCAL_GRS(%a6),%d2 |restore original g,r,s
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andil #0xe0000000,%d2 |clear all but G,R,S
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tstl %d2 |test if original G,R,S are clear
|
beqs grs_clear
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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
|
