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|
|       decbin.sa 3.3 12/19/90
|
|       Description: Converts normalized packed bcd value pointed to by
|       register A6 to extended-precision value in FP0.
|
|       Input: Normalized packed bcd value in ETEMP(a6).
|
|       Output: Exact floating-point representation of the packed bcd value.
|
|       Saves and Modifies: D2-D5
|
|       Speed: The program decbin takes ??? cycles to execute.
|
|       Object Size:
|
|       External Reference(s): None.
|
|       Algorithm:
|       Expected is a normal bcd (i.e. non-exceptional; all inf, zero,
|       and NaN operands are dispatched without entering this routine)
|       value in 68881/882 format at location ETEMP(A6).
|
|       A1.     Convert the bcd exponent to binary by successive adds and muls.
|       Set the sign according to SE. Subtract 16 to compensate
|       for the mantissa which is to be interpreted as 17 integer
|       digits, rather than 1 integer and 16 fraction digits.
|       Note: this operation can never overflow.
|
|       A2. Convert the bcd mantissa to binary by successive
|       adds and muls in FP0. Set the sign according to SM.
|       The mantissa digits will be converted with the decimal point
|       assumed following the least-significant digit.
|       Note: this operation can never overflow.
|
|       A3. Count the number of leading/trailing zeros in the
|       bcd string.  If SE is positive, count the leading zeros;
|       if negative, count the trailing zeros.  Set the adjusted
|       exponent equal to the exponent from A1 and the zero count
|       added if SM = 1 and subtracted if SM = 0.  Scale the
|       mantissa the equivalent of forcing in the bcd value:
|
|       SM = 0  a non-zero digit in the integer position
|       SM = 1  a non-zero digit in Mant0, lsd of the fraction
|
|       this will insure that any value, regardless of its
|       representation (ex. 0.1E2, 1E1, 10E0, 100E-1), is converted
|       consistently.
|
|       A4. Calculate the factor 10^exp in FP1 using a table of
|       10^(2^n) values.  To reduce the error in forming factors
|       greater than 10^27, a directed rounding scheme is used with
|       tables rounded to RN, RM, and RP, according to the table
|       in the comments of the pwrten section.
|
|       A5. Form the final binary number by scaling the mantissa by
|       the exponent factor.  This is done by multiplying the
|       mantissa in FP0 by the factor in FP1 if the adjusted
|       exponent sign is positive, and dividing FP0 by FP1 if
|       it is negative.
|
|       Clean up and return.  Check if the final mul or div resulted
|       in an inex2 exception.  If so, set inex1 in the fpsr and 
|       check if the inex1 exception is enabled.  If so, set d7 upper
|       word to $0100.  This will signal unimp.sa that an enabled inex1
|       exception occurred.  Unimp will fix the stack.
|       

|               Copyright (C) Motorola, Inc. 1990
|                       All Rights Reserved
|
|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 
|       The copyright notice above does not evidence any  
|       actual or intended publication of such source code.

|DECBIN    idnt    2,1 | Motorola 040 Floating Point Software Package

        |section        8

        .include "fpsp.h"

|
|       PTENRN, PTENRM, and PTENRP are arrays of powers of 10 rounded
|       to nearest, minus, and plus, respectively.  The tables include
|       10**{1,2,4,8,16,32,64,128,256,512,1024,2048,4096}.  No rounding
|       is required until the power is greater than 27, however, all
|       tables include the first 5 for ease of indexing.
|
        |xref   PTENRN
        |xref   PTENRM
        |xref   PTENRP

RTABLE: .byte   0,0,0,0
        .byte   2,3,2,3
        .byte   2,3,3,2
        .byte   3,2,2,3

        .global decbin
        .global calc_e
        .global pwrten
        .global calc_m
        .global norm
        .global ap_st_z
        .global ap_st_n
|
        .set    FNIBS,7
        .set    FSTRT,0
|
        .set    ESTRT,4
        .set    EDIGITS,2       | 
|
| Constants in single precision
FZERO:  .long   0x00000000
FONE:   .long   0x3F800000
FTEN:   .long   0x41200000

        .set    TEN,10

|
decbin:
        | fmovel        #0,FPCR         ;clr real fpcr
        moveml  %d2-%d5,-(%a7)
|
| Calculate exponent:
|  1. Copy bcd value in memory for use as a working copy.
|  2. Calculate absolute value of exponent in d1 by mul and add.
|  3. Correct for exponent sign.
|  4. Subtract 16 to compensate for interpreting the mant as all integer digits.
|     (i.e., all digits assumed left of the decimal point.)
|
| Register usage:
|
|  calc_e:
|       (*)  d0: temp digit storage
|       (*)  d1: accumulator for binary exponent
|       (*)  d2: digit count
|       (*)  d3: offset pointer
|       ( )  d4: first word of bcd
|       ( )  a0: pointer to working bcd value
|       ( )  a6: pointer to original bcd value
|       (*)  FP_SCR1: working copy of original bcd value
|       (*)  L_SCR1: copy of original exponent word
|
calc_e:
        movel   #EDIGITS,%d2    |# of nibbles (digits) in fraction part
        moveql  #ESTRT,%d3      |counter to pick up digits
        leal    FP_SCR1(%a6),%a0        |load tmp bcd storage address
        movel   ETEMP(%a6),(%a0)        |save input bcd value
        movel   ETEMP_HI(%a6),4(%a0) |save words 2 and 3
        movel   ETEMP_LO(%a6),8(%a0) |and work with these
        movel   (%a0),%d4       |get first word of bcd
        clrl    %d1             |zero d1 for accumulator
e_gd:
        mulul   #TEN,%d1        |mul partial product by one digit place
        bfextu  %d4{%d3:#4},%d0 |get the digit and zero extend into d0
        addl    %d0,%d1         |d1 = d1 + d0
        addqb   #4,%d3          |advance d3 to the next digit
        dbf     %d2,e_gd        |if we have used all 3 digits, exit loop
        btst    #30,%d4         |get SE
        beqs    e_pos           |don't negate if pos
        negl    %d1             |negate before subtracting
e_pos:
        subl    #16,%d1         |sub to compensate for shift of mant
        bges    e_save          |if still pos, do not neg
        negl    %d1             |now negative, make pos and set SE
        orl     #0x40000000,%d4 |set SE in d4,
        orl     #0x40000000,(%a0)       |and in working bcd
e_save:
        movel   %d1,L_SCR1(%a6) |save exp in memory
|
|
| Calculate mantissa:
|  1. Calculate absolute value of mantissa in fp0 by mul and add.
|  2. Correct for mantissa sign.
|     (i.e., all digits assumed left of the decimal point.)
|
| Register usage:
|
|  calc_m:
|       (*)  d0: temp digit storage
|       (*)  d1: lword counter
|       (*)  d2: digit count
|       (*)  d3: offset pointer
|       ( )  d4: words 2 and 3 of bcd
|       ( )  a0: pointer to working bcd value
|       ( )  a6: pointer to original bcd value
|       (*) fp0: mantissa accumulator
|       ( )  FP_SCR1: working copy of original bcd value
|       ( )  L_SCR1: copy of original exponent word
|
calc_m:
        moveql  #1,%d1          |word counter, init to 1
        fmoves  FZERO,%fp0      |accumulator
|
|
|  Since the packed number has a long word between the first & second parts,
|  get the integer digit then skip down & get the rest of the
|  mantissa.  We will unroll the loop once.
|
        bfextu  (%a0){#28:#4},%d0       |integer part is ls digit in long word
        faddb   %d0,%fp0                |add digit to sum in fp0
|
|
|  Get the rest of the mantissa.
|
loadlw:
        movel   (%a0,%d1.L*4),%d4       |load mantissa longword into d4
        moveql  #FSTRT,%d3      |counter to pick up digits
        moveql  #FNIBS,%d2      |reset number of digits per a0 ptr
md2b:
        fmuls   FTEN,%fp0       |fp0 = fp0 * 10
        bfextu  %d4{%d3:#4},%d0 |get the digit and zero extend
        faddb   %d0,%fp0        |fp0 = fp0 + digit
|
|
|  If all the digits (8) in that long word have been converted (d2=0),
|  then inc d1 (=2) to point to the next long word and reset d3 to 0
|  to initialize the digit offset, and set d2 to 7 for the digit count;
|  else continue with this long word.
|
        addqb   #4,%d3          |advance d3 to the next digit
        dbf     %d2,md2b                |check for last digit in this lw
nextlw:
        addql   #1,%d1          |inc lw pointer in mantissa
        cmpl    #2,%d1          |test for last lw
        ble     loadlw          |if not, get last one
        
|
|  Check the sign of the mant and make the value in fp0 the same sign.
|
m_sign:
        btst    #31,(%a0)       |test sign of the mantissa
        beqs    ap_st_z         |if clear, go to append/strip zeros
        fnegx   %fp0            |if set, negate fp0
        
|
| Append/strip zeros:
|
|  For adjusted exponents which have an absolute value greater than 27*,
|  this routine calculates the amount needed to normalize the mantissa
|  for the adjusted exponent.  That number is subtracted from the exp
|  if the exp was positive, and added if it was negative.  The purpose
|  of this is to reduce the value of the exponent and the possibility
|  of error in calculation of pwrten.
|
|  1. Branch on the sign of the adjusted exponent.
|  2p.(positive exp)
|   2. Check M16 and the digits in lwords 2 and 3 in descending order.
|   3. Add one for each zero encountered until a non-zero digit.
|   4. Subtract the count from the exp.
|   5. Check if the exp has crossed zero in #3 above; make the exp abs
|          and set SE.
|       6. Multiply the mantissa by 10**count.
|  2n.(negative exp)
|   2. Check the digits in lwords 3 and 2 in descending order.
|   3. Add one for each zero encountered until a non-zero digit.
|   4. Add the count to the exp.
|   5. Check if the exp has crossed zero in #3 above; clear SE.
|   6. Divide the mantissa by 10**count.
|
|  *Why 27?  If the adjusted exponent is within -28 < expA < 28, than
|   any adjustment due to append/strip zeros will drive the resultant
|   exponent towards zero.  Since all pwrten constants with a power
|   of 27 or less are exact, there is no need to use this routine to
|   attempt to lessen the resultant exponent.
|
| Register usage:
|
|  ap_st_z:
|       (*)  d0: temp digit storage
|       (*)  d1: zero count
|       (*)  d2: digit count
|       (*)  d3: offset pointer
|       ( )  d4: first word of bcd
|       (*)  d5: lword counter
|       ( )  a0: pointer to working bcd value
|       ( )  FP_SCR1: working copy of original bcd value
|       ( )  L_SCR1: copy of original exponent word
|
|
| First check the absolute value of the exponent to see if this
| routine is necessary.  If so, then check the sign of the exponent
| and do append (+) or strip (-) zeros accordingly.
| This section handles a positive adjusted exponent.
|
ap_st_z:
        movel   L_SCR1(%a6),%d1 |load expA for range test
        cmpl    #27,%d1         |test is with 27
        ble     pwrten          |if abs(expA) <28, skip ap/st zeros
        btst    #30,(%a0)       |check sign of exp
        bnes    ap_st_n         |if neg, go to neg side
        clrl    %d1             |zero count reg
        movel   (%a0),%d4               |load lword 1 to d4
        bfextu  %d4{#28:#4},%d0 |get M16 in d0
        bnes    ap_p_fx         |if M16 is non-zero, go fix exp
        addql   #1,%d1          |inc zero count
        moveql  #1,%d5          |init lword counter
        movel   (%a0,%d5.L*4),%d4       |get lword 2 to d4
        bnes    ap_p_cl         |if lw 2 is zero, skip it
        addql   #8,%d1          |and inc count by 8
        addql   #1,%d5          |inc lword counter
        movel   (%a0,%d5.L*4),%d4       |get lword 3 to d4
ap_p_cl:
        clrl    %d3             |init offset reg
        moveql  #7,%d2          |init digit counter
ap_p_gd:
        bfextu  %d4{%d3:#4},%d0 |get digit
        bnes    ap_p_fx         |if non-zero, go to fix exp
        addql   #4,%d3          |point to next digit
        addql   #1,%d1          |inc digit counter
        dbf     %d2,ap_p_gd     |get next digit
ap_p_fx:
        movel   %d1,%d0         |copy counter to d2
        movel   L_SCR1(%a6),%d1 |get adjusted exp from memory
        subl    %d0,%d1         |subtract count from exp
        bges    ap_p_fm         |if still pos, go to pwrten
        negl    %d1             |now its neg; get abs
        movel   (%a0),%d4               |load lword 1 to d4
        orl     #0x40000000,%d4 | and set SE in d4
        orl     #0x40000000,(%a0)       | and in memory
|
| Calculate the mantissa multiplier to compensate for the striping of
| zeros from the mantissa.
|
ap_p_fm:
        movel   #PTENRN,%a1     |get address of power-of-ten table
        clrl    %d3             |init table index
        fmoves  FONE,%fp1       |init fp1 to 1
        moveql  #3,%d2          |init d2 to count bits in counter
ap_p_el:
        asrl    #1,%d0          |shift lsb into carry
        bccs    ap_p_en         |if 1, mul fp1 by pwrten factor
        fmulx   (%a1,%d3),%fp1  |mul by 10**(d3_bit_no)
ap_p_en:
        addl    #12,%d3         |inc d3 to next rtable entry
        tstl    %d0             |check if d0 is zero
        bnes    ap_p_el         |if not, get next bit
        fmulx   %fp1,%fp0               |mul mantissa by 10**(no_bits_shifted)
        bras    pwrten          |go calc pwrten
|
| This section handles a negative adjusted exponent.
|
ap_st_n:
        clrl    %d1             |clr counter
        moveql  #2,%d5          |set up d5 to point to lword 3
        movel   (%a0,%d5.L*4),%d4       |get lword 3
        bnes    ap_n_cl         |if not zero, check digits
        subl    #1,%d5          |dec d5 to point to lword 2
        addql   #8,%d1          |inc counter by 8
        movel   (%a0,%d5.L*4),%d4       |get lword 2
ap_n_cl:
        movel   #28,%d3         |point to last digit
        moveql  #7,%d2          |init digit counter
ap_n_gd:
        bfextu  %d4{%d3:#4},%d0 |get digit
        bnes    ap_n_fx         |if non-zero, go to exp fix
        subql   #4,%d3          |point to previous digit
        addql   #1,%d1          |inc digit counter
        dbf     %d2,ap_n_gd     |get next digit
ap_n_fx:
        movel   %d1,%d0         |copy counter to d0
        movel   L_SCR1(%a6),%d1 |get adjusted exp from memory
        subl    %d0,%d1         |subtract count from exp
        bgts    ap_n_fm         |if still pos, go fix mantissa
        negl    %d1             |take abs of exp and clr SE
        movel   (%a0),%d4               |load lword 1 to d4
        andl    #0xbfffffff,%d4 | and clr SE in d4
        andl    #0xbfffffff,(%a0)       | and in memory
|
| Calculate the mantissa multiplier to compensate for the appending of
| zeros to the mantissa.
|
ap_n_fm:
        movel   #PTENRN,%a1     |get address of power-of-ten table
        clrl    %d3             |init table index
        fmoves  FONE,%fp1       |init fp1 to 1
        moveql  #3,%d2          |init d2 to count bits in counter
ap_n_el:
        asrl    #1,%d0          |shift lsb into carry
        bccs    ap_n_en         |if 1, mul fp1 by pwrten factor
        fmulx   (%a1,%d3),%fp1  |mul by 10**(d3_bit_no)
ap_n_en:
        addl    #12,%d3         |inc d3 to next rtable entry
        tstl    %d0             |check if d0 is zero
        bnes    ap_n_el         |if not, get next bit
        fdivx   %fp1,%fp0               |div mantissa by 10**(no_bits_shifted)
|
|
| Calculate power-of-ten factor from adjusted and shifted exponent.
|
| Register usage:
|
|  pwrten:
|       (*)  d0: temp
|       ( )  d1: exponent
|       (*)  d2: {FPCR[6:5],SM,SE} as index in RTABLE; temp
|       (*)  d3: FPCR work copy
|       ( )  d4: first word of bcd
|       (*)  a1: RTABLE pointer
|  calc_p:
|       (*)  d0: temp
|       ( )  d1: exponent
|       (*)  d3: PWRTxx table index
|       ( )  a0: pointer to working copy of bcd
|       (*)  a1: PWRTxx pointer
|       (*) fp1: power-of-ten accumulator
|
| Pwrten calculates the exponent factor in the selected rounding mode
| according to the following table:
|       
|       Sign of Mant  Sign of Exp  Rounding Mode  PWRTEN Rounding Mode
|
|       ANY       ANY   RN      RN
|
|        +         +    RP      RP
|        -         +    RP      RM
|        +         -    RP      RM
|        -         -    RP      RP
|
|        +         +    RM      RM
|        -         +    RM      RP
|        +         -    RM      RP
|        -         -    RM      RM
|
|        +         +    RZ      RM
|        -         +    RZ      RM
|        +         -    RZ      RP
|        -         -    RZ      RP
|
|
pwrten:
        movel   USER_FPCR(%a6),%d3 |get user's FPCR
        bfextu  %d3{#26:#2},%d2 |isolate rounding mode bits
        movel   (%a0),%d4               |reload 1st bcd word to d4
        asll    #2,%d2          |format d2 to be
        bfextu  %d4{#0:#2},%d0  | {FPCR[6],FPCR[5],SM,SE}
        addl    %d0,%d2         |in d2 as index into RTABLE
        leal    RTABLE,%a1      |load rtable base
        moveb   (%a1,%d2),%d0   |load new rounding bits from table
        clrl    %d3                     |clear d3 to force no exc and extended
        bfins   %d0,%d3{#26:#2} |stuff new rounding bits in FPCR
        fmovel  %d3,%FPCR               |write new FPCR
        asrl    #1,%d0          |write correct PTENxx table
        bccs    not_rp          |to a1
        leal    PTENRP,%a1      |it is RP
        bras    calc_p          |go to init section
not_rp:
        asrl    #1,%d0          |keep checking
        bccs    not_rm
        leal    PTENRM,%a1      |it is RM
        bras    calc_p          |go to init section
not_rm:
        leal    PTENRN,%a1      |it is RN
calc_p:
        movel   %d1,%d0         |copy exp to d0;use d0
        bpls    no_neg          |if exp is negative,
        negl    %d0             |invert it
        orl     #0x40000000,(%a0)       |and set SE bit
no_neg:
        clrl    %d3             |table index
        fmoves  FONE,%fp1       |init fp1 to 1
e_loop:
        asrl    #1,%d0          |shift next bit into carry
        bccs    e_next          |if zero, skip the mul
        fmulx   (%a1,%d3),%fp1  |mul by 10**(d3_bit_no)
e_next:
        addl    #12,%d3         |inc d3 to next rtable entry
        tstl    %d0             |check if d0 is zero
        bnes    e_loop          |not zero, continue shifting
|
|
|  Check the sign of the adjusted exp and make the value in fp0 the
|  same sign. If the exp was pos then multiply fp1*fp0;
|  else divide fp0/fp1.
|
| Register Usage:
|  norm:
|       ( )  a0: pointer to working bcd value
|       (*) fp0: mantissa accumulator
|       ( ) fp1: scaling factor - 10**(abs(exp))
|
norm:
        btst    #30,(%a0)       |test the sign of the exponent
        beqs    mul             |if clear, go to multiply
div:
        fdivx   %fp1,%fp0               |exp is negative, so divide mant by exp
        bras    end_dec
mul:
        fmulx   %fp1,%fp0               |exp is positive, so multiply by exp
|
|
| Clean up and return with result in fp0.
|
| If the final mul/div in decbin incurred an inex exception,
| it will be inex2, but will be reported as inex1 by get_op.
|
end_dec:
        fmovel  %FPSR,%d0               |get status register    
        bclrl   #inex2_bit+8,%d0        |test for inex2 and clear it
        fmovel  %d0,%FPSR               |return status reg w/o inex2
        beqs    no_exc          |skip this if no exc
        orl     #inx1a_mask,USER_FPSR(%a6) |set inex1/ainex
no_exc:
        moveml  (%a7)+,%d2-%d5
        rts
        |end