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648 lines
16 KiB
648 lines
16 KiB
| |
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| round.sa 3.4 7/29/91 |
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| |
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| handle rounding and normalization tasks |
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| |
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| Copyright (C) Motorola, Inc. 1990 |
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| All Rights Reserved |
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| |
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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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|
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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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| |
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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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| |
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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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| |
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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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| |
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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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| |
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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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| |
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| ROUND MINUS INFINITY |
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| |
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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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| |
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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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| |
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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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| |
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| Input: d1 = PREC:ROUND |
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| Output: d0{31:29}= guard, round, sticky |
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| |
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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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| |
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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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| |
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| ADD SINGLE |
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| |
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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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| |
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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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| |
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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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| |
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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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| |
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| denorm --- denormalize an intermediate result |
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| Used by underflow. |
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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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| (in the internal extended format) |
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| |
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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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| |
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| d0 is guard,round,sticky |
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| |
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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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| |
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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 |
|
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
|
|
|