| | |

| 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 |