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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
-|
-| For details on the license for this file, please see the
-| file, README, in this same directory.
-
-|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
- beq 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
- bne 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)
- bra 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