bindec.S
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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
- 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