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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
+|
+| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
+| The copyright notice above does not evidence any
+| actual or intended publication of such source code.
+
+|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