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|
|       bindec.sa 3.4 1/3/91
|
|       bindec
|
|       Description:
|               Converts an input in extended precision format
|               to bcd format.
|
|       Input:
|               a0 points to the input extended precision value
|               value in memory; d0 contains the k-factor sign-extended
|               to 32-bits.  The input may be either normalized,
|               unnormalized, or denormalized.
|
|       Output: result in the FP_SCR1 space on the stack.
|
|       Saves and Modifies: D2-D7,A2,FP2
|
|       Algorithm:
|
|       A1.     Set RM and size ext;  Set SIGMA = sign of input.  
|               The k-factor is saved for use in d7. Clear the
|               BINDEC_FLG for separating normalized/denormalized
|               input.  If input is unnormalized or denormalized,
|               normalize it.
|
|       A2.     Set X = abs(input).
|
|       A3.     Compute ILOG.
|               ILOG is the log base 10 of the input value.  It is
|               approximated by adding e + 0.f when the original 
|               value is viewed as 2^^e * 1.f in extended precision.  
|               This value is stored in d6.
|
|       A4.     Clr INEX bit.
|               The operation in A3 above may have set INEX2.  
|
|       A5.     Set ICTR = 0;
|               ICTR is a flag used in A13.  It must be set before the 
|               loop entry A6.
|
|       A6.     Calculate LEN.
|               LEN is the number of digits to be displayed.  The
|               k-factor can dictate either the total number of digits,
|               if it is a positive number, or the number of digits
|               after the decimal point which are to be included as
|               significant.  See the 68882 manual for examples.
|               If LEN is computed to be greater than 17, set OPERR in
|               USER_FPSR.  LEN is stored in d4.
|
|       A7.     Calculate SCALE.
|               SCALE is equal to 10^ISCALE, where ISCALE is the number
|               of decimal places needed to insure LEN integer digits
|               in the output before conversion to bcd. LAMBDA is the
|               sign of ISCALE, used in A9. Fp1 contains
|               10^^(abs(ISCALE)) using a rounding mode which is a
|               function of the original rounding mode and the signs
|               of ISCALE and X.  A table is given in the code.
|
|       A8.     Clr INEX; Force RZ.
|               The operation in A3 above may have set INEX2.  
|               RZ mode is forced for the scaling operation to insure
|               only one rounding error.  The grs bits are collected in 
|               the INEX flag for use in A10.
|
|       A9.     Scale X -> Y.
|               The mantissa is scaled to the desired number of
|               significant digits.  The excess digits are collected
|               in INEX2.
|
|       A10.    Or in INEX.
|               If INEX is set, round error occurred.  This is
|               compensated for by 'or-ing' in the INEX2 flag to
|               the lsb of Y.
|
|       A11.    Restore original FPCR; set size ext.
|               Perform FINT operation in the user's rounding mode.
|               Keep the size to extended.
|
|       A12.    Calculate YINT = FINT(Y) according to user's rounding
|               mode.  The FPSP routine sintd0 is used.  The output
|               is in fp0.
|
|       A13.    Check for LEN digits.
|               If the int operation results in more than LEN digits,
|               or less than LEN -1 digits, adjust ILOG and repeat from
|               A6.  This test occurs only on the first pass.  If the
|               result is exactly 10^LEN, decrement ILOG and divide
|               the mantissa by 10.
|
|       A14.    Convert the mantissa to bcd.
|               The binstr routine is used to convert the LEN digit 
|               mantissa to bcd in memory.  The input to binstr is
|               to be a fraction; i.e. (mantissa)/10^LEN and adjusted
|               such that the decimal point is to the left of bit 63.
|               The bcd digits are stored in the correct position in 
|               the final string area in memory.
|
|       A15.    Convert the exponent to bcd.
|               As in A14 above, the exp is converted to bcd and the
|               digits are stored in the final string.
|               Test the length of the final exponent string.  If the
|               length is 4, set operr.
|
|       A16.    Write sign bits to final string.
|
|       Implementation Notes:
|
|       The registers are used as follows:
|
|               d0: scratch; LEN input to binstr
|               d1: scratch
|               d2: upper 32-bits of mantissa for binstr
|               d3: scratch;lower 32-bits of mantissa for binstr
|               d4: LEN
|               d5: LAMBDA/ICTR
|               d6: ILOG
|               d7: k-factor
|               a0: ptr for original operand/final result
|               a1: scratch pointer
|               a2: pointer to FP_X; abs(original value) in ext
|               fp0: scratch
|               fp1: scratch
|               fp2: scratch
|               F_SCR1:
|               F_SCR2:
|               L_SCR1:
|               L_SCR2:

|               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.

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

        .include "fpsp.h"

        |section        8

| Constants in extended precision
LOG2:   .long   0x3FFD0000,0x9A209A84,0xFBCFF798,0x00000000
LOG2UP1:        .long   0x3FFD0000,0x9A209A84,0xFBCFF799,0x00000000

| Constants in single precision
FONE:   .long   0x3F800000,0x00000000,0x00000000,0x00000000
FTWO:   .long   0x40000000,0x00000000,0x00000000,0x00000000
FTEN:   .long   0x41200000,0x00000000,0x00000000,0x00000000
F4933:  .long   0x459A2800,0x00000000,0x00000000,0x00000000

RBDTBL:         .byte   0,0,0,0
        .byte   3,3,2,2
        .byte   3,2,2,3
        .byte   2,3,3,2

        |xref   binstr
        |xref   sintdo
        |xref   ptenrn,ptenrm,ptenrp

        .global bindec
        .global sc_mul
bindec:
        moveml  %d2-%d7/%a2,-(%a7)
        fmovemx %fp0-%fp2,-(%a7)

| A1. Set RM and size ext. Set SIGMA = sign input;
|     The k-factor is saved for use in d7.  Clear BINDEC_FLG for
|     separating  normalized/denormalized input.  If the input
|     is a denormalized number, set the BINDEC_FLG memory word
|     to signal denorm.  If the input is unnormalized, normalize
|     the input and test for denormalized result.  
|
        fmovel  #rm_mode,%FPCR  |set RM and ext
        movel   (%a0),L_SCR2(%a6)       |save exponent for sign check
        movel   %d0,%d7         |move k-factor to d7
        clrb    BINDEC_FLG(%a6) |clr norm/denorm flag
        movew   STAG(%a6),%d0   |get stag
        andiw   #0xe000,%d0     |isolate stag bits
        beq     A2_str          |if zero, input is norm
|
| Normalize the denorm
|
un_de_norm:
        movew   (%a0),%d0
        andiw   #0x7fff,%d0     |strip sign of normalized exp
        movel   4(%a0),%d1
        movel   8(%a0),%d2
norm_loop:
        subw    #1,%d0
        lsll    #1,%d2
        roxll   #1,%d1
        tstl    %d1
        bges    norm_loop
|
| Test if the normalized input is denormalized
|
        tstw    %d0
        bgts    pos_exp         |if greater than zero, it is a norm
        st      BINDEC_FLG(%a6) |set flag for denorm
pos_exp:
        andiw   #0x7fff,%d0     |strip sign of normalized exp
        movew   %d0,(%a0)
        movel   %d1,4(%a0)
        movel   %d2,8(%a0)

| A2. Set X = abs(input).
|
A2_str:
        movel   (%a0),FP_SCR2(%a6) | move input to work space
        movel   4(%a0),FP_SCR2+4(%a6) | move input to work space
        movel   8(%a0),FP_SCR2+8(%a6) | move input to work space
        andil   #0x7fffffff,FP_SCR2(%a6) |create abs(X)

| A3. Compute ILOG.
|     ILOG is the log base 10 of the input value.  It is approx-
|     imated by adding e + 0.f when the original value is viewed
|     as 2^^e * 1.f in extended precision.  This value is stored
|     in d6.
|
| Register usage:
|       Input/Output
|       d0: k-factor/exponent
|       d2: x/x
|       d3: x/x
|       d4: x/x
|       d5: x/x
|       d6: x/ILOG
|       d7: k-factor/Unchanged
|       a0: ptr for original operand/final result
|       a1: x/x
|       a2: x/x
|       fp0: x/float(ILOG)
|       fp1: x/x
|       fp2: x/x
|       F_SCR1:x/x
|       F_SCR2:Abs(X)/Abs(X) with $3fff exponent
|       L_SCR1:x/x
|       L_SCR2:first word of X packed/Unchanged

        tstb    BINDEC_FLG(%a6) |check for denorm
        beqs    A3_cont         |if clr, continue with norm
        movel   #-4933,%d6      |force ILOG = -4933
        bras    A4_str
A3_cont:
        movew   FP_SCR2(%a6),%d0        |move exp to d0
        movew   #0x3fff,FP_SCR2(%a6) |replace exponent with 0x3fff
        fmovex  FP_SCR2(%a6),%fp0       |now fp0 has 1.f
        subw    #0x3fff,%d0     |strip off bias
        faddw   %d0,%fp0                |add in exp
        fsubs   FONE,%fp0       |subtract off 1.0
        fbge    pos_res         |if pos, branch 
        fmulx   LOG2UP1,%fp0    |if neg, mul by LOG2UP1
        fmovel  %fp0,%d6                |put ILOG in d6 as a lword
        bras    A4_str          |go move out ILOG
pos_res:
        fmulx   LOG2,%fp0       |if pos, mul by LOG2
        fmovel  %fp0,%d6                |put ILOG in d6 as a lword


| A4. Clr INEX bit.
|     The operation in A3 above may have set INEX2.  

A4_str: 
        fmovel  #0,%FPSR                |zero all of fpsr - nothing needed


| A5. Set ICTR = 0;
|     ICTR is a flag used in A13.  It must be set before the 
|     loop entry A6. The lower word of d5 is used for ICTR.

        clrw    %d5             |clear ICTR


| A6. Calculate LEN.
|     LEN is the number of digits to be displayed.  The k-factor
|     can dictate either the total number of digits, if it is
|     a positive number, or the number of digits after the
|     original decimal point which are to be included as
|     significant.  See the 68882 manual for examples.
|     If LEN is computed to be greater than 17, set OPERR in
|     USER_FPSR.  LEN is stored in d4.
|
| Register usage:
|       Input/Output
|       d0: exponent/Unchanged
|       d2: x/x/scratch
|       d3: x/x
|       d4: exc picture/LEN
|       d5: ICTR/Unchanged
|       d6: ILOG/Unchanged
|       d7: k-factor/Unchanged
|       a0: ptr for original operand/final result
|       a1: x/x
|       a2: x/x
|       fp0: float(ILOG)/Unchanged
|       fp1: x/x
|       fp2: x/x
|       F_SCR1:x/x
|       F_SCR2:Abs(X) with $3fff exponent/Unchanged
|       L_SCR1:x/x
|       L_SCR2:first word of X packed/Unchanged

A6_str: 
        tstl    %d7             |branch on sign of k
        bles    k_neg           |if k <= 0, LEN = ILOG + 1 - k
        movel   %d7,%d4         |if k > 0, LEN = k
        bras    len_ck          |skip to LEN check
k_neg:
        movel   %d6,%d4         |first load ILOG to d4
        subl    %d7,%d4         |subtract off k
        addql   #1,%d4          |add in the 1
len_ck:
        tstl    %d4             |LEN check: branch on sign of LEN
        bles    LEN_ng          |if neg, set LEN = 1
        cmpl    #17,%d4         |test if LEN > 17
        bles    A7_str          |if not, forget it
        movel   #17,%d4         |set max LEN = 17
        tstl    %d7             |if negative, never set OPERR
        bles    A7_str          |if positive, continue
        orl     #opaop_mask,USER_FPSR(%a6) |set OPERR & AIOP in USER_FPSR
        bras    A7_str          |finished here
LEN_ng:
        moveql  #1,%d4          |min LEN is 1


| A7. Calculate SCALE.
|     SCALE is equal to 10^ISCALE, where ISCALE is the number
|     of decimal places needed to insure LEN integer digits
|     in the output before conversion to bcd. LAMBDA is the sign
|     of ISCALE, used in A9.  Fp1 contains 10^^(abs(ISCALE)) using
|     the rounding mode as given in the following table (see
|     Coonen, p. 7.23 as ref.; however, the SCALE variable is
|     of opposite sign in bindec.sa from Coonen).
|
|       Initial                                 USE
|       FPCR[6:5]       LAMBDA  SIGN(X)         FPCR[6:5]
|       ----------------------------------------------
|        RN     00         0       0            00/0    RN
|        RN     00         0       1            00/0    RN
|        RN     00         1       0            00/0    RN
|        RN     00         1       1            00/0    RN
|        RZ     01         0       0            11/3    RP
|        RZ     01         0       1            11/3    RP
|        RZ     01         1       0            10/2    RM
|        RZ     01         1       1            10/2    RM
|        RM     10         0       0            11/3    RP
|        RM     10         0       1            10/2    RM
|        RM     10         1       0            10/2    RM
|        RM     10         1       1            11/3    RP
|        RP     11         0       0            10/2    RM
|        RP     11         0       1            11/3    RP
|        RP     11         1       0            11/3    RP
|        RP     11         1       1            10/2    RM
|
| Register usage:
|       Input/Output
|       d0: exponent/scratch - final is 0
|       d2: x/0 or 24 for A9
|       d3: x/scratch - offset ptr into PTENRM array
|       d4: LEN/Unchanged
|       d5: 0/ICTR:LAMBDA
|       d6: ILOG/ILOG or k if ((k<=0)&(ILOG<k))
|       d7: k-factor/Unchanged
|       a0: ptr for original operand/final result
|       a1: x/ptr to PTENRM array
|       a2: x/x
|       fp0: float(ILOG)/Unchanged
|       fp1: x/10^ISCALE
|       fp2: x/x
|       F_SCR1:x/x
|       F_SCR2:Abs(X) with $3fff exponent/Unchanged
|       L_SCR1:x/x
|       L_SCR2:first word of X packed/Unchanged

A7_str: 
        tstl    %d7             |test sign of k
        bgts    k_pos           |if pos and > 0, skip this
        cmpl    %d6,%d7         |test k - ILOG
        blts    k_pos           |if ILOG >= k, skip this
        movel   %d7,%d6         |if ((k<0) & (ILOG < k)) ILOG = k
k_pos:  
        movel   %d6,%d0         |calc ILOG + 1 - LEN in d0
        addql   #1,%d0          |add the 1
        subl    %d4,%d0         |sub off LEN
        swap    %d5             |use upper word of d5 for LAMBDA
        clrw    %d5             |set it zero initially
        clrw    %d2             |set up d2 for very small case
        tstl    %d0             |test sign of ISCALE
        bges    iscale          |if pos, skip next inst
        addqw   #1,%d5          |if neg, set LAMBDA true
        cmpl    #0xffffecd4,%d0 |test iscale <= -4908
        bgts    no_inf          |if false, skip rest
        addil   #24,%d0         |add in 24 to iscale
        movel   #24,%d2         |put 24 in d2 for A9
no_inf: 
        negl    %d0             |and take abs of ISCALE
iscale: 
        fmoves  FONE,%fp1       |init fp1 to 1
        bfextu  USER_FPCR(%a6){#26:#2},%d1 |get initial rmode bits
        lslw    #1,%d1          |put them in bits 2:1
        addw    %d5,%d1         |add in LAMBDA
        lslw    #1,%d1          |put them in bits 3:1
        tstl    L_SCR2(%a6)     |test sign of original x
        bges    x_pos           |if pos, don't set bit 0
        addql   #1,%d1          |if neg, set bit 0
x_pos:
        leal    RBDTBL,%a2      |load rbdtbl base
        moveb   (%a2,%d1),%d3   |load d3 with new rmode
        lsll    #4,%d3          |put bits in proper position
        fmovel  %d3,%fpcr               |load bits into fpu
        lsrl    #4,%d3          |put bits in proper position
        tstb    %d3             |decode new rmode for pten table
        bnes    not_rn          |if zero, it is RN
        leal    PTENRN,%a1      |load a1 with RN table base
        bras    rmode           |exit decode
not_rn:
        lsrb    #1,%d3          |get lsb in carry
        bccs    not_rp          |if carry clear, it is RM
        leal    PTENRP,%a1      |load a1 with RP table base
        bras    rmode           |exit decode
not_rp:
        leal    PTENRM,%a1      |load a1 with RM table base
rmode:
        clrl    %d3             |clr table index
e_loop: 
        lsrl    #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 pwrten table entry
        tstl    %d0             |test if ISCALE is zero
        bnes    e_loop          |if not, loop


| A8. Clr INEX; Force RZ.
|     The operation in A3 above may have set INEX2.  
|     RZ mode is forced for the scaling operation to insure
|     only one rounding error.  The grs bits are collected in 
|     the INEX flag for use in A10.
|
| Register usage:
|       Input/Output

        fmovel  #0,%FPSR                |clr INEX 
        fmovel  #rz_mode,%FPCR  |set RZ rounding mode


| A9. Scale X -> Y.
|     The mantissa is scaled to the desired number of significant
|     digits.  The excess digits are collected in INEX2. If mul,
|     Check d2 for excess 10 exponential value.  If not zero, 
|     the iscale value would have caused the pwrten calculation
|     to overflow.  Only a negative iscale can cause this, so
|     multiply by 10^(d2), which is now only allowed to be 24,
|     with a multiply by 10^8 and 10^16, which is exact since
|     10^24 is exact.  If the input was denormalized, we must
|     create a busy stack frame with the mul command and the
|     two operands, and allow the fpu to complete the multiply.
|
| Register usage:
|       Input/Output
|       d0: FPCR with RZ mode/Unchanged
|       d2: 0 or 24/unchanged
|       d3: x/x
|       d4: LEN/Unchanged
|       d5: ICTR:LAMBDA
|       d6: ILOG/Unchanged
|       d7: k-factor/Unchanged
|       a0: ptr for original operand/final result
|       a1: ptr to PTENRM array/Unchanged
|       a2: x/x
|       fp0: float(ILOG)/X adjusted for SCALE (Y)
|       fp1: 10^ISCALE/Unchanged
|       fp2: x/x
|       F_SCR1:x/x
|       F_SCR2:Abs(X) with $3fff exponent/Unchanged
|       L_SCR1:x/x
|       L_SCR2:first word of X packed/Unchanged

A9_str: 
        fmovex  (%a0),%fp0      |load X from memory
        fabsx   %fp0            |use abs(X)
        tstw    %d5             |LAMBDA is in lower word of d5
        bnes    sc_mul          |if neg (LAMBDA = 1), scale by mul
        fdivx   %fp1,%fp0               |calculate X / SCALE -> Y to fp0
        bras    A10_st          |branch to A10

sc_mul:
        tstb    BINDEC_FLG(%a6) |check for denorm
        beqs    A9_norm         |if norm, continue with mul
        fmovemx %fp1-%fp1,-(%a7)        |load ETEMP with 10^ISCALE
        movel   8(%a0),-(%a7)   |load FPTEMP with input arg
        movel   4(%a0),-(%a7)
        movel   (%a0),-(%a7)
        movel   #18,%d3         |load count for busy stack
A9_loop:
        clrl    -(%a7)          |clear lword on stack
        dbf     %d3,A9_loop     
        moveb   VER_TMP(%a6),(%a7) |write current version number
        moveb   #BUSY_SIZE-4,1(%a7) |write current busy size 
        moveb   #0x10,0x44(%a7) |set fcefpte[15] bit
        movew   #0x0023,0x40(%a7)       |load cmdreg1b with mul command
        moveb   #0xfe,0x8(%a7)  |load all 1s to cu savepc
        frestore (%a7)+         |restore frame to fpu for completion
        fmulx   36(%a1),%fp0    |multiply fp0 by 10^8
        fmulx   48(%a1),%fp0    |multiply fp0 by 10^16
        bras    A10_st
A9_norm:
        tstw    %d2             |test for small exp case
        beqs    A9_con          |if zero, continue as normal
        fmulx   36(%a1),%fp0    |multiply fp0 by 10^8
        fmulx   48(%a1),%fp0    |multiply fp0 by 10^16
A9_con:
        fmulx   %fp1,%fp0               |calculate X * SCALE -> Y to fp0


| A10. Or in INEX.
|      If INEX is set, round error occurred.  This is compensated
|      for by 'or-ing' in the INEX2 flag to the lsb of Y.
|
| Register usage:
|       Input/Output
|       d0: FPCR with RZ mode/FPSR with INEX2 isolated
|       d2: x/x
|       d3: x/x
|       d4: LEN/Unchanged
|       d5: ICTR:LAMBDA
|       d6: ILOG/Unchanged
|       d7: k-factor/Unchanged
|       a0: ptr for original operand/final result
|       a1: ptr to PTENxx array/Unchanged
|       a2: x/ptr to FP_SCR2(a6)
|       fp0: Y/Y with lsb adjusted
|       fp1: 10^ISCALE/Unchanged
|       fp2: x/x

A10_st: 
        fmovel  %FPSR,%d0               |get FPSR
        fmovex  %fp0,FP_SCR2(%a6)       |move Y to memory
        leal    FP_SCR2(%a6),%a2        |load a2 with ptr to FP_SCR2
        btstl   #9,%d0          |check if INEX2 set
        beqs    A11_st          |if clear, skip rest
        oril    #1,8(%a2)       |or in 1 to lsb of mantissa
        fmovex  FP_SCR2(%a6),%fp0       |write adjusted Y back to fpu


| A11. Restore original FPCR; set size ext.
|      Perform FINT operation in the user's rounding mode.  Keep
|      the size to extended.  The sintdo entry point in the sint
|      routine expects the FPCR value to be in USER_FPCR for
|      mode and precision.  The original FPCR is saved in L_SCR1.

A11_st: 
        movel   USER_FPCR(%a6),L_SCR1(%a6) |save it for later
        andil   #0x00000030,USER_FPCR(%a6) |set size to ext, 
|                                       ;block exceptions


| A12. Calculate YINT = FINT(Y) according to user's rounding mode.
|      The FPSP routine sintd0 is used.  The output is in fp0.
|
| Register usage:
|       Input/Output
|       d0: FPSR with AINEX cleared/FPCR with size set to ext
|       d2: x/x/scratch
|       d3: x/x
|       d4: LEN/Unchanged
|       d5: ICTR:LAMBDA/Unchanged
|       d6: ILOG/Unchanged
|       d7: k-factor/Unchanged
|       a0: ptr for original operand/src ptr for sintdo
|       a1: ptr to PTENxx array/Unchanged
|       a2: ptr to FP_SCR2(a6)/Unchanged
|       a6: temp pointer to FP_SCR2(a6) - orig value saved and restored
|       fp0: Y/YINT
|       fp1: 10^ISCALE/Unchanged
|       fp2: x/x
|       F_SCR1:x/x
|       F_SCR2:Y adjusted for inex/Y with original exponent
|       L_SCR1:x/original USER_FPCR
|       L_SCR2:first word of X packed/Unchanged

A12_st:
        moveml  %d0-%d1/%a0-%a1,-(%a7)  |save regs used by sintd0       
        movel   L_SCR1(%a6),-(%a7)
        movel   L_SCR2(%a6),-(%a7)
        leal    FP_SCR2(%a6),%a0                |a0 is ptr to F_SCR2(a6)
        fmovex  %fp0,(%a0)              |move Y to memory at FP_SCR2(a6)
        tstl    L_SCR2(%a6)             |test sign of original operand
        bges    do_fint                 |if pos, use Y 
        orl     #0x80000000,(%a0)               |if neg, use -Y
do_fint:
        movel   USER_FPSR(%a6),-(%a7)
        bsr     sintdo                  |sint routine returns int in fp0
        moveb   (%a7),USER_FPSR(%a6)
        addl    #4,%a7
        movel   (%a7)+,L_SCR2(%a6)
        movel   (%a7)+,L_SCR1(%a6)
        moveml  (%a7)+,%d0-%d1/%a0-%a1  |restore regs used by sint      
        movel   L_SCR2(%a6),FP_SCR2(%a6)        |restore original exponent
        movel   L_SCR1(%a6),USER_FPCR(%a6) |restore user's FPCR


| A13. Check for LEN digits.
|      If the int operation results in more than LEN digits,
|      or less than LEN -1 digits, adjust ILOG and repeat from
|      A6.  This test occurs only on the first pass.  If the
|      result is exactly 10^LEN, decrement ILOG and divide
|      the mantissa by 10.  The calculation of 10^LEN cannot
|      be inexact, since all powers of ten upto 10^27 are exact
|      in extended precision, so the use of a previous power-of-ten
|      table will introduce no error.
|
|
| Register usage:
|       Input/Output
|       d0: FPCR with size set to ext/scratch final = 0
|       d2: x/x
|       d3: x/scratch final = x
|       d4: LEN/LEN adjusted
|       d5: ICTR:LAMBDA/LAMBDA:ICTR
|       d6: ILOG/ILOG adjusted
|       d7: k-factor/Unchanged
|       a0: pointer into memory for packed bcd string formation
|       a1: ptr to PTENxx array/Unchanged
|       a2: ptr to FP_SCR2(a6)/Unchanged
|       fp0: int portion of Y/abs(YINT) adjusted
|       fp1: 10^ISCALE/Unchanged
|       fp2: x/10^LEN
|       F_SCR1:x/x
|       F_SCR2:Y with original exponent/Unchanged
|       L_SCR1:original USER_FPCR/Unchanged
|       L_SCR2:first word of X packed/Unchanged

A13_st: 
        swap    %d5             |put ICTR in lower word of d5
        tstw    %d5             |check if ICTR = 0
        bne     not_zr          |if non-zero, go to second test
|
| Compute 10^(LEN-1)
|
        fmoves  FONE,%fp2       |init fp2 to 1.0
        movel   %d4,%d0         |put LEN in d0
        subql   #1,%d0          |d0 = LEN -1
        clrl    %d3             |clr table index
l_loop: 
        lsrl    #1,%d0          |shift next bit into carry
        bccs    l_next          |if zero, skip the mul
        fmulx   (%a1,%d3),%fp2  |mul by 10**(d3_bit_no)
l_next:
        addl    #12,%d3         |inc d3 to next pwrten table entry
        tstl    %d0             |test if LEN is zero
        bnes    l_loop          |if not, loop
|
| 10^LEN-1 is computed for this test and A14.  If the input was
| denormalized, check only the case in which YINT > 10^LEN.
|
        tstb    BINDEC_FLG(%a6) |check if input was norm
        beqs    A13_con         |if norm, continue with checking
        fabsx   %fp0            |take abs of YINT
        bra     test_2
|
| Compare abs(YINT) to 10^(LEN-1) and 10^LEN
|
A13_con:
        fabsx   %fp0            |take abs of YINT
        fcmpx   %fp2,%fp0               |compare abs(YINT) with 10^(LEN-1)
        fbge    test_2          |if greater, do next test
        subql   #1,%d6          |subtract 1 from ILOG
        movew   #1,%d5          |set ICTR
        fmovel  #rm_mode,%FPCR  |set rmode to RM
        fmuls   FTEN,%fp2       |compute 10^LEN 
        bra     A6_str          |return to A6 and recompute YINT
test_2:
        fmuls   FTEN,%fp2       |compute 10^LEN
        fcmpx   %fp2,%fp0               |compare abs(YINT) with 10^LEN
        fblt    A14_st          |if less, all is ok, go to A14
        fbgt    fix_ex          |if greater, fix and redo
        fdivs   FTEN,%fp0       |if equal, divide by 10
        addql   #1,%d6          | and inc ILOG
        bras    A14_st          | and continue elsewhere
fix_ex:
        addql   #1,%d6          |increment ILOG by 1
        movew   #1,%d5          |set ICTR
        fmovel  #rm_mode,%FPCR  |set rmode to RM
        bra     A6_str          |return to A6 and recompute YINT
|
| Since ICTR <> 0, we have already been through one adjustment, 
| and shouldn't have another; this is to check if abs(YINT) = 10^LEN
| 10^LEN is again computed using whatever table is in a1 since the
| value calculated cannot be inexact.
|
not_zr:
        fmoves  FONE,%fp2       |init fp2 to 1.0
        movel   %d4,%d0         |put LEN in d0
        clrl    %d3             |clr table index
z_loop:
        lsrl    #1,%d0          |shift next bit into carry
        bccs    z_next          |if zero, skip the mul
        fmulx   (%a1,%d3),%fp2  |mul by 10**(d3_bit_no)
z_next:
        addl    #12,%d3         |inc d3 to next pwrten table entry
        tstl    %d0             |test if LEN is zero
        bnes    z_loop          |if not, loop
        fabsx   %fp0            |get abs(YINT)
        fcmpx   %fp2,%fp0               |check if abs(YINT) = 10^LEN
        fbne    A14_st          |if not, skip this
        fdivs   FTEN,%fp0       |divide abs(YINT) by 10
        addql   #1,%d6          |and inc ILOG by 1
        addql   #1,%d4          | and inc LEN
        fmuls   FTEN,%fp2       | if LEN++, the get 10^^LEN


| A14. Convert the mantissa to bcd.
|      The binstr routine is used to convert the LEN digit 
|      mantissa to bcd in memory.  The input to binstr is
|      to be a fraction; i.e. (mantissa)/10^LEN and adjusted
|      such that the decimal point is to the left of bit 63.
|      The bcd digits are stored in the correct position in 
|      the final string area in memory.
|
|
| Register usage:
|       Input/Output
|       d0: x/LEN call to binstr - final is 0
|       d1: x/0
|       d2: x/ms 32-bits of mant of abs(YINT)
|       d3: x/ls 32-bits of mant of abs(YINT)
|       d4: LEN/Unchanged
|       d5: ICTR:LAMBDA/LAMBDA:ICTR
|       d6: ILOG
|       d7: k-factor/Unchanged
|       a0: pointer into memory for packed bcd string formation
|           /ptr to first mantissa byte in result string
|       a1: ptr to PTENxx array/Unchanged
|       a2: ptr to FP_SCR2(a6)/Unchanged
|       fp0: int portion of Y/abs(YINT) adjusted
|       fp1: 10^ISCALE/Unchanged
|       fp2: 10^LEN/Unchanged
|       F_SCR1:x/Work area for final result
|       F_SCR2:Y with original exponent/Unchanged
|       L_SCR1:original USER_FPCR/Unchanged
|       L_SCR2:first word of X packed/Unchanged

A14_st: 
        fmovel  #rz_mode,%FPCR  |force rz for conversion
        fdivx   %fp2,%fp0               |divide abs(YINT) by 10^LEN
        leal    FP_SCR1(%a6),%a0
        fmovex  %fp0,(%a0)      |move abs(YINT)/10^LEN to memory
        movel   4(%a0),%d2      |move 2nd word of FP_RES to d2
        movel   8(%a0),%d3      |move 3rd word of FP_RES to d3
        clrl    4(%a0)          |zero word 2 of FP_RES
        clrl    8(%a0)          |zero word 3 of FP_RES
        movel   (%a0),%d0               |move exponent to d0
        swap    %d0             |put exponent in lower word
        beqs    no_sft          |if zero, don't shift
        subil   #0x3ffd,%d0     |sub bias less 2 to make fract
        tstl    %d0             |check if > 1
        bgts    no_sft          |if so, don't shift
        negl    %d0             |make exp positive
m_loop:
        lsrl    #1,%d2          |shift d2:d3 right, add 0s 
        roxrl   #1,%d3          |the number of places
        dbf     %d0,m_loop      |given in d0
no_sft:
        tstl    %d2             |check for mantissa of zero
        bnes    no_zr           |if not, go on
        tstl    %d3             |continue zero check
        beqs    zer_m           |if zero, go directly to binstr
no_zr:
        clrl    %d1             |put zero in d1 for addx
        addil   #0x00000080,%d3 |inc at bit 7
        addxl   %d1,%d2         |continue inc
        andil   #0xffffff80,%d3 |strip off lsb not used by 882
zer_m:
        movel   %d4,%d0         |put LEN in d0 for binstr call
        addql   #3,%a0          |a0 points to M16 byte in result
        bsr     binstr          |call binstr to convert mant


| A15. Convert the exponent to bcd.
|      As in A14 above, the exp is converted to bcd and the
|      digits are stored in the final string.
|
|      Digits are stored in L_SCR1(a6) on return from BINDEC as:
|
|        32               16 15                0
|       -----------------------------------------
|       |  0 | e3 | e2 | e1 | e4 |  X |  X |  X |
|       -----------------------------------------
|
| And are moved into their proper places in FP_SCR1.  If digit e4
| is non-zero, OPERR is signaled.  In all cases, all 4 digits are
| written as specified in the 881/882 manual for packed decimal.
|
| Register usage:
|       Input/Output
|       d0: x/LEN call to binstr - final is 0
|       d1: x/scratch (0);shift count for final exponent packing
|       d2: x/ms 32-bits of exp fraction/scratch
|       d3: x/ls 32-bits of exp fraction
|       d4: LEN/Unchanged
|       d5: ICTR:LAMBDA/LAMBDA:ICTR
|       d6: ILOG
|       d7: k-factor/Unchanged
|       a0: ptr to result string/ptr to L_SCR1(a6)
|       a1: ptr to PTENxx array/Unchanged
|       a2: ptr to FP_SCR2(a6)/Unchanged
|       fp0: abs(YINT) adjusted/float(ILOG)
|       fp1: 10^ISCALE/Unchanged
|       fp2: 10^LEN/Unchanged
|       F_SCR1:Work area for final result/BCD result
|       F_SCR2:Y with original exponent/ILOG/10^4
|       L_SCR1:original USER_FPCR/Exponent digits on return from binstr
|       L_SCR2:first word of X packed/Unchanged

A15_st: 
        tstb    BINDEC_FLG(%a6) |check for denorm
        beqs    not_denorm
        ftstx   %fp0            |test for zero
        fbeq    den_zero        |if zero, use k-factor or 4933
        fmovel  %d6,%fp0                |float ILOG
        fabsx   %fp0            |get abs of ILOG
        bras    convrt
den_zero:
        tstl    %d7             |check sign of the k-factor
        blts    use_ilog        |if negative, use ILOG
        fmoves  F4933,%fp0      |force exponent to 4933
        bras    convrt          |do it
use_ilog:
        fmovel  %d6,%fp0                |float ILOG
        fabsx   %fp0            |get abs of ILOG
        bras    convrt
not_denorm:
        ftstx   %fp0            |test for zero
        fbne    not_zero        |if zero, force exponent
        fmoves  FONE,%fp0       |force exponent to 1
        bras    convrt          |do it
not_zero:       
        fmovel  %d6,%fp0                |float ILOG
        fabsx   %fp0            |get abs of ILOG
convrt:
        fdivx   24(%a1),%fp0    |compute ILOG/10^4
        fmovex  %fp0,FP_SCR2(%a6)       |store fp0 in memory
        movel   4(%a2),%d2      |move word 2 to d2
        movel   8(%a2),%d3      |move word 3 to d3
        movew   (%a2),%d0               |move exp to d0
        beqs    x_loop_fin      |if zero, skip the shift
        subiw   #0x3ffd,%d0     |subtract off bias
        negw    %d0             |make exp positive
x_loop:
        lsrl    #1,%d2          |shift d2:d3 right 
        roxrl   #1,%d3          |the number of places
        dbf     %d0,x_loop      |given in d0
x_loop_fin:
        clrl    %d1             |put zero in d1 for addx
        addil   #0x00000080,%d3 |inc at bit 6
        addxl   %d1,%d2         |continue inc
        andil   #0xffffff80,%d3 |strip off lsb not used by 882
        movel   #4,%d0          |put 4 in d0 for binstr call
        leal    L_SCR1(%a6),%a0 |a0 is ptr to L_SCR1 for exp digits
        bsr     binstr          |call binstr to convert exp
        movel   L_SCR1(%a6),%d0 |load L_SCR1 lword to d0 
        movel   #12,%d1         |use d1 for shift count
        lsrl    %d1,%d0         |shift d0 right by 12
        bfins   %d0,FP_SCR1(%a6){#4:#12} |put e3:e2:e1 in FP_SCR1
        lsrl    %d1,%d0         |shift d0 right by 12
        bfins   %d0,FP_SCR1(%a6){#16:#4} |put e4 in FP_SCR1 
        tstb    %d0             |check if e4 is zero
        beqs    A16_st          |if zero, skip rest
        orl     #opaop_mask,USER_FPSR(%a6) |set OPERR & AIOP in USER_FPSR


| A16. Write sign bits to final string.
|          Sigma is bit 31 of initial value; RHO is bit 31 of d6 (ILOG).
|
| Register usage:
|       Input/Output
|       d0: x/scratch - final is x
|       d2: x/x
|       d3: x/x
|       d4: LEN/Unchanged
|       d5: ICTR:LAMBDA/LAMBDA:ICTR
|       d6: ILOG/ILOG adjusted
|       d7: k-factor/Unchanged
|       a0: ptr to L_SCR1(a6)/Unchanged
|       a1: ptr to PTENxx array/Unchanged
|       a2: ptr to FP_SCR2(a6)/Unchanged
|       fp0: float(ILOG)/Unchanged
|       fp1: 10^ISCALE/Unchanged
|       fp2: 10^LEN/Unchanged
|       F_SCR1:BCD result with correct signs
|       F_SCR2:ILOG/10^4
|       L_SCR1:Exponent digits on return from binstr
|       L_SCR2:first word of X packed/Unchanged

A16_st:
        clrl    %d0             |clr d0 for collection of signs
        andib   #0x0f,FP_SCR1(%a6) |clear first nibble of FP_SCR1 
        tstl    L_SCR2(%a6)     |check sign of original mantissa
        bges    mant_p          |if pos, don't set SM
        moveql  #2,%d0          |move 2 in to d0 for SM
mant_p:
        tstl    %d6             |check sign of ILOG
        bges    wr_sgn          |if pos, don't set SE
        addql   #1,%d0          |set bit 0 in d0 for SE 
wr_sgn:
        bfins   %d0,FP_SCR1(%a6){#0:#2} |insert SM and SE into FP_SCR1

| Clean up and restore all registers used.

        fmovel  #0,%FPSR                |clear possible inex2/ainex bits
        fmovemx (%a7)+,%fp0-%fp2
        moveml  (%a7)+,%d2-%d7/%a2
        rts

        |end