|
| 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
