506 lines
15 KiB
ArmAsm
506 lines
15 KiB
ArmAsm
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| decbin.sa 3.3 12/19/90
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| Description: Converts normalized packed bcd value pointed to by
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| register A6 to extended-precision value in FP0.
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| Input: Normalized packed bcd value in ETEMP(a6).
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| Output: Exact floating-point representation of the packed bcd value.
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| Saves and Modifies: D2-D5
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| Speed: The program decbin takes ??? cycles to execute.
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| Object Size:
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| External Reference(s): None.
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| Algorithm:
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| Expected is a normal bcd (i.e. non-exceptional; all inf, zero,
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| and NaN operands are dispatched without entering this routine)
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| value in 68881/882 format at location ETEMP(A6).
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| A1. Convert the bcd exponent to binary by successive adds and muls.
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| Set the sign according to SE. Subtract 16 to compensate
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| for the mantissa which is to be interpreted as 17 integer
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| digits, rather than 1 integer and 16 fraction digits.
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| Note: this operation can never overflow.
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| A2. Convert the bcd mantissa to binary by successive
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| adds and muls in FP0. Set the sign according to SM.
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| The mantissa digits will be converted with the decimal point
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| assumed following the least-significant digit.
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| Note: this operation can never overflow.
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| A3. Count the number of leading/trailing zeros in the
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| bcd string. If SE is positive, count the leading zeros;
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| if negative, count the trailing zeros. Set the adjusted
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| exponent equal to the exponent from A1 and the zero count
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| added if SM = 1 and subtracted if SM = 0. Scale the
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| mantissa the equivalent of forcing in the bcd value:
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| SM = 0 a non-zero digit in the integer position
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| SM = 1 a non-zero digit in Mant0, lsd of the fraction
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| this will insure that any value, regardless of its
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| representation (ex. 0.1E2, 1E1, 10E0, 100E-1), is converted
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| consistently.
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| A4. Calculate the factor 10^exp in FP1 using a table of
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| 10^(2^n) values. To reduce the error in forming factors
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| greater than 10^27, a directed rounding scheme is used with
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| tables rounded to RN, RM, and RP, according to the table
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| in the comments of the pwrten section.
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| A5. Form the final binary number by scaling the mantissa by
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| the exponent factor. This is done by multiplying the
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| mantissa in FP0 by the factor in FP1 if the adjusted
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| exponent sign is positive, and dividing FP0 by FP1 if
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| it is negative.
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| Clean up and return. Check if the final mul or div resulted
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| in an inex2 exception. If so, set inex1 in the fpsr and
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| check if the inex1 exception is enabled. If so, set d7 upper
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| word to $0100. This will signal unimp.sa that an enabled inex1
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| exception occurred. Unimp will fix the stack.
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| Copyright (C) Motorola, Inc. 1990
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| All Rights Reserved
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| For details on the license for this file, please see the
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| file, README, in this same directory.
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|DECBIN idnt 2,1 | Motorola 040 Floating Point Software Package
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|section 8
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#include "fpsp.h"
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| PTENRN, PTENRM, and PTENRP are arrays of powers of 10 rounded
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| to nearest, minus, and plus, respectively. The tables include
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| 10**{1,2,4,8,16,32,64,128,256,512,1024,2048,4096}. No rounding
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| is required until the power is greater than 27, however, all
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| tables include the first 5 for ease of indexing.
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|xref PTENRN
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|xref PTENRM
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|xref PTENRP
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RTABLE: .byte 0,0,0,0
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.byte 2,3,2,3
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.byte 2,3,3,2
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.byte 3,2,2,3
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.global decbin
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.global calc_e
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.global pwrten
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.global calc_m
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.global norm
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.global ap_st_z
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.global ap_st_n
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.set FNIBS,7
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.set FSTRT,0
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.set ESTRT,4
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.set EDIGITS,2 |
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| Constants in single precision
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FZERO: .long 0x00000000
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FONE: .long 0x3F800000
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FTEN: .long 0x41200000
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.set TEN,10
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decbin:
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| fmovel #0,FPCR ;clr real fpcr
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moveml %d2-%d5,-(%a7)
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| Calculate exponent:
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| 1. Copy bcd value in memory for use as a working copy.
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| 2. Calculate absolute value of exponent in d1 by mul and add.
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| 3. Correct for exponent sign.
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| 4. Subtract 16 to compensate for interpreting the mant as all integer digits.
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| (i.e., all digits assumed left of the decimal point.)
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| Register usage:
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| calc_e:
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| (*) d0: temp digit storage
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| (*) d1: accumulator for binary exponent
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| (*) d2: digit count
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| (*) d3: offset pointer
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| ( ) d4: first word of bcd
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| ( ) a0: pointer to working bcd value
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| ( ) a6: pointer to original bcd value
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| (*) FP_SCR1: working copy of original bcd value
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| (*) L_SCR1: copy of original exponent word
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calc_e:
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movel #EDIGITS,%d2 |# of nibbles (digits) in fraction part
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moveql #ESTRT,%d3 |counter to pick up digits
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leal FP_SCR1(%a6),%a0 |load tmp bcd storage address
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movel ETEMP(%a6),(%a0) |save input bcd value
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movel ETEMP_HI(%a6),4(%a0) |save words 2 and 3
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movel ETEMP_LO(%a6),8(%a0) |and work with these
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movel (%a0),%d4 |get first word of bcd
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clrl %d1 |zero d1 for accumulator
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e_gd:
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mulul #TEN,%d1 |mul partial product by one digit place
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bfextu %d4{%d3:#4},%d0 |get the digit and zero extend into d0
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addl %d0,%d1 |d1 = d1 + d0
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addqb #4,%d3 |advance d3 to the next digit
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dbf %d2,e_gd |if we have used all 3 digits, exit loop
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btst #30,%d4 |get SE
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beqs e_pos |don't negate if pos
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negl %d1 |negate before subtracting
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e_pos:
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subl #16,%d1 |sub to compensate for shift of mant
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bges e_save |if still pos, do not neg
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negl %d1 |now negative, make pos and set SE
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orl #0x40000000,%d4 |set SE in d4,
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orl #0x40000000,(%a0) |and in working bcd
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e_save:
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movel %d1,L_SCR1(%a6) |save exp in memory
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| Calculate mantissa:
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| 1. Calculate absolute value of mantissa in fp0 by mul and add.
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| 2. Correct for mantissa sign.
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| (i.e., all digits assumed left of the decimal point.)
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| Register usage:
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| calc_m:
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| (*) d0: temp digit storage
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| (*) d1: lword counter
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| (*) d2: digit count
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| (*) d3: offset pointer
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| ( ) d4: words 2 and 3 of bcd
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| ( ) a0: pointer to working bcd value
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| ( ) a6: pointer to original bcd value
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| (*) fp0: mantissa accumulator
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| ( ) FP_SCR1: working copy of original bcd value
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| ( ) L_SCR1: copy of original exponent word
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calc_m:
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moveql #1,%d1 |word counter, init to 1
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fmoves FZERO,%fp0 |accumulator
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| Since the packed number has a long word between the first & second parts,
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| get the integer digit then skip down & get the rest of the
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| mantissa. We will unroll the loop once.
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bfextu (%a0){#28:#4},%d0 |integer part is ls digit in long word
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faddb %d0,%fp0 |add digit to sum in fp0
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| Get the rest of the mantissa.
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loadlw:
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movel (%a0,%d1.L*4),%d4 |load mantissa longword into d4
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moveql #FSTRT,%d3 |counter to pick up digits
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moveql #FNIBS,%d2 |reset number of digits per a0 ptr
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md2b:
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fmuls FTEN,%fp0 |fp0 = fp0 * 10
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bfextu %d4{%d3:#4},%d0 |get the digit and zero extend
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faddb %d0,%fp0 |fp0 = fp0 + digit
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| If all the digits (8) in that long word have been converted (d2=0),
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| then inc d1 (=2) to point to the next long word and reset d3 to 0
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| to initialize the digit offset, and set d2 to 7 for the digit count;
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| else continue with this long word.
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addqb #4,%d3 |advance d3 to the next digit
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dbf %d2,md2b |check for last digit in this lw
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nextlw:
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addql #1,%d1 |inc lw pointer in mantissa
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cmpl #2,%d1 |test for last lw
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ble loadlw |if not, get last one
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| Check the sign of the mant and make the value in fp0 the same sign.
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m_sign:
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btst #31,(%a0) |test sign of the mantissa
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beq ap_st_z |if clear, go to append/strip zeros
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fnegx %fp0 |if set, negate fp0
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| Append/strip zeros:
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| For adjusted exponents which have an absolute value greater than 27*,
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| this routine calculates the amount needed to normalize the mantissa
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| for the adjusted exponent. That number is subtracted from the exp
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| if the exp was positive, and added if it was negative. The purpose
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| of this is to reduce the value of the exponent and the possibility
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| of error in calculation of pwrten.
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| 1. Branch on the sign of the adjusted exponent.
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| 2p.(positive exp)
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| 2. Check M16 and the digits in lwords 2 and 3 in descending order.
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| 3. Add one for each zero encountered until a non-zero digit.
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| 4. Subtract the count from the exp.
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| 5. Check if the exp has crossed zero in #3 above; make the exp abs
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| and set SE.
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| 6. Multiply the mantissa by 10**count.
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| 2n.(negative exp)
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| 2. Check the digits in lwords 3 and 2 in descending order.
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| 3. Add one for each zero encountered until a non-zero digit.
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| 4. Add the count to the exp.
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| 5. Check if the exp has crossed zero in #3 above; clear SE.
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| 6. Divide the mantissa by 10**count.
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| *Why 27? If the adjusted exponent is within -28 < expA < 28, than
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| any adjustment due to append/strip zeros will drive the resultant
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| exponent towards zero. Since all pwrten constants with a power
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| of 27 or less are exact, there is no need to use this routine to
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| attempt to lessen the resultant exponent.
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| Register usage:
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| ap_st_z:
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| (*) d0: temp digit storage
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| (*) d1: zero count
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| (*) d2: digit count
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| (*) d3: offset pointer
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| ( ) d4: first word of bcd
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| (*) d5: lword counter
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| ( ) a0: pointer to working bcd value
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| ( ) FP_SCR1: working copy of original bcd value
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| ( ) L_SCR1: copy of original exponent word
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| First check the absolute value of the exponent to see if this
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| routine is necessary. If so, then check the sign of the exponent
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| and do append (+) or strip (-) zeros accordingly.
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| This section handles a positive adjusted exponent.
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ap_st_z:
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movel L_SCR1(%a6),%d1 |load expA for range test
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cmpl #27,%d1 |test is with 27
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ble pwrten |if abs(expA) <28, skip ap/st zeros
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btst #30,(%a0) |check sign of exp
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bne ap_st_n |if neg, go to neg side
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clrl %d1 |zero count reg
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movel (%a0),%d4 |load lword 1 to d4
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bfextu %d4{#28:#4},%d0 |get M16 in d0
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bnes ap_p_fx |if M16 is non-zero, go fix exp
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addql #1,%d1 |inc zero count
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moveql #1,%d5 |init lword counter
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movel (%a0,%d5.L*4),%d4 |get lword 2 to d4
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bnes ap_p_cl |if lw 2 is zero, skip it
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addql #8,%d1 |and inc count by 8
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addql #1,%d5 |inc lword counter
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movel (%a0,%d5.L*4),%d4 |get lword 3 to d4
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ap_p_cl:
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clrl %d3 |init offset reg
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moveql #7,%d2 |init digit counter
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ap_p_gd:
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bfextu %d4{%d3:#4},%d0 |get digit
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bnes ap_p_fx |if non-zero, go to fix exp
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addql #4,%d3 |point to next digit
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addql #1,%d1 |inc digit counter
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dbf %d2,ap_p_gd |get next digit
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ap_p_fx:
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movel %d1,%d0 |copy counter to d2
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movel L_SCR1(%a6),%d1 |get adjusted exp from memory
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subl %d0,%d1 |subtract count from exp
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bges ap_p_fm |if still pos, go to pwrten
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negl %d1 |now its neg; get abs
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movel (%a0),%d4 |load lword 1 to d4
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orl #0x40000000,%d4 | and set SE in d4
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orl #0x40000000,(%a0) | and in memory
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| Calculate the mantissa multiplier to compensate for the striping of
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| zeros from the mantissa.
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ap_p_fm:
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movel #PTENRN,%a1 |get address of power-of-ten table
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clrl %d3 |init table index
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fmoves FONE,%fp1 |init fp1 to 1
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moveql #3,%d2 |init d2 to count bits in counter
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ap_p_el:
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asrl #1,%d0 |shift lsb into carry
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bccs ap_p_en |if 1, mul fp1 by pwrten factor
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fmulx (%a1,%d3),%fp1 |mul by 10**(d3_bit_no)
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ap_p_en:
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addl #12,%d3 |inc d3 to next rtable entry
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tstl %d0 |check if d0 is zero
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bnes ap_p_el |if not, get next bit
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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
|