|
| 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
bne 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
