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supermario/base/SuperMarioProj.1994-02-09/OS/FPUEmulation/DecBin.a
Elliot Nunn 2e16381318 Bring in sources, and document
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;
; File: DecBin.a
;
; Contains: Packed Decimal to Binary conversion code
;
; Originally Written by: Motorola Inc.
; Adapted to Apple/MPW: Jon Okada
;
; Copyright: © 1990, 1991 by Apple Computer, Inc., all rights reserved.
;
; This file is used in these builds: Mac32
;
; Change History (most recent first):
;
; <2> 3/30/91 BG Rolling in Jon Okada's latest changes.
; <1> 12/14/90 BG First checked into TERROR/BBS.
; decbin.a
; Based upon Motorola file 'decbin.sa'
; CHANGE LOG:
; 02 Jan 91 JPO Removed constants FZERO, FONE, and FTEN; embedded
; constant values in instructions.
;
*
* decbin.sa 3.1 12/10/90
*
* 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 occured. 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
*
* 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.
*
RTABLE dc.b 0,0,0,0
dc.b 2,3,2,3
dc.b 2,3,3,2
dc.b 3,2,2,3
*
FNIBS equ 7
FSTRT equ 0
*
ESTRT equ 4
EDIGITS equ 2
*
* Constants in single precision - removed <1/2/91, JPO>
;FZERO dc.l $00000000
;FONE dc.l $3F800000
;FTEN dc.l $41200000
TEN equ 10
*
decbin:
fmove.l #0,FPCR ;clr real fpcr
movem.l 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: ; label not referenced <1/2/91, JPO>
move.l #EDIGITS,d2 ;# of nibbles (digits) in fraction part
moveq.l #ESTRT,d3 ;counter to pick up digits
lea.l FP_SCR1(a6),a0 ;load tmp bcd storage address
move.l ETEMP(a6),(a0) ;save input bcd value
move.l ETEMP_HI(a6),4(a0) ;save words 2 and 3
move.l ETEMP_LO(a6),8(a0) ;and work with these
move.l (a0),d4 ;get first word of bcd
clr.l d1 ;zero d1 for accumulator
e_gd:
mulu.l #TEN,d1 ;mul partial product by one digit place
bfextu d4{d3:4},d0 ;get the digit and zero extend into d0
add.l d0,d1 ;d1 = d1 + d0
addq.b #4,d3 ;advance d3 to the next digit
dbf.w d2,e_gd ;if we have used all 3 digits, exit loop
btst #30,d4 ;get SE
beq.b e_pos ;don't negate if pos
neg.l d1 ;negate before subtracting
e_pos:
sub.l #16,d1 ;sub to compensate for shift of mant
bge.b e_save ;if still pos, do not neg
neg.l d1 ;now negative, make pos and set SE
or.l #$40000000,d4 ;set SE in d4,
or.l #$40000000,(a0) ;and in working bcd
e_save:
move.l 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: ; label not referenced <1/2/91, JPO>
moveq.l #1,d1 ;word counter, init to 1
; fmove.s FZERO,fp0 ;accumulator <1/2/91, JPO>
fmove.b #0,fp0 ; <1/2/91, JPO>
*
*
* 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
fadd.b d0,fp0 ;add digit to sum in fp0
*
*
* Get the rest of the mantissa.
*
loadlw:
move.l (a0,d1.L*4),d4 ;load mantissa lonqword into d4
moveq.l #FSTRT,d3 ;counter to pick up digits
moveq.l #FNIBS,d2 ;reset number of digits per a0 ptr
md2b:
; fmul.s FTEN,fp0 ;fp0 = fp0 * 10 <1/2/91, JPO>
fmul.b #TEN,fp0 ; <1/2/91, JPO>
bfextu d4{d3:4},d0 ;get the digit and zero extend
fadd.b 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.
*
addq.b #4,d3 ;advance d3 to the next digit
dbf.w d2,md2b ;check for last digit in this lw
;nextlw: ; label not referenced <1/2/91, JPO>
addq.l #1,d1 ;inc lw pointer in mantissa
cmp.l #2,d1 ;test for last lw
ble.b loadlw ;if not, get last one - short branch <1/2/91, JPO>
*
* Check the sign of the mant and make the value in fp0 the same sign.
*
;m_sign: ; label not referenced <1/2/91, JPO>
btst #31,(a0) ;test sign of the mantissa
beq.b ap_st_z ;if clear, go to append/strip zeros
fneg.x 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 decending 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 decending 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 resultane
* 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:
move.l L_SCR1(a6),d1 ;load expA for range test
cmp.l #27,d1 ;test is with 27
ble.w pwrten ;if abs(expA) <28, skip ap/st zeros
btst #30,(a0) ;check sign of exp
bne.b ap_st_n ;if neg, go to neg side
clr.l d1 ;zero count reg
move.l (a0),d4 ;load lword 1 to d4
bfextu d4{28:4},d0 ;get M16 in d0
bne.b ap_p_fx ;if M16 is non-zero, go fix exp
addq.l #1,d1 ;inc zero count
moveq.l #1,d5 ;init lword counter
move.l (a0,d5.L*4),d4 ;get lword 2 to d4
bne.b ap_p_cl ;if lw 2 is zero, skip it
addq.l #8,d1 ;and inc count by 8
addq.l #1,d5 ;inc lword counter
move.l (a0,d5.L*4),d4 ;get lword 3 to d4
ap_p_cl:
clr.l d3 ;init offset reg
moveq.l #7,d2 ;init digit counter
ap_p_gd:
bfextu d4{d3:4},d0 ;get digit
bne.b ap_p_fx ;if non-zero, go to fix exp
addq.l #4,d3 ;point to next digit
addq.l #1,d1 ;inc digit counter
dbf.w d2,ap_p_gd ;get next digit
ap_p_fx:
move.l d1,d0 ;copy counter to d2
move.l L_SCR1(a6),d1 ;get adjusted exp from memory
sub.l d0,d1 ;subtract count from exp
bge.b ap_p_fm ;if still pos, go to pwrten
neg.l d1 ;now its neg; get abs
move.l (a0),d4 ;load lword 1 to d4
or.l #$40000000,d4 ; and set SE in d4
or.l #$40000000,(a0) ; and in memory
*
* Calculate the mantissa multiplier to compensate for the striping of
* zeros from the mantissa.
*
ap_p_fm:
; move.l #PTENRN,a1 ;get address of power-of-ten table - deleted <1/2/91, JPO>
lea PTENRN,a1 ; <1/2/91, JPO>
clr.l d3 ;init table index
; fmove.s FONE,fp1 ;init fp1 to 1 <1/2/91, JPO>
fmove.b #1,fp1 ; <1/2/91, JPO>
moveq.l #3,d2 ;init d2 to count bits in counter
ap_p_el:
asr.l #1,d0 ;shift lsb into carry
bcc.b ap_p_en ;if 1, mul fp1 by pwrten factor
fmul.x (a1,d3),fp1 ;mul by 10**(d3_bit_no)
ap_p_en:
add.l #12,d3 ;inc d3 to next rtable entry
tst.l d0 ;check if d0 is zero
bne.b ap_p_el ;if not, get next bit
fmul.x fp1,fp0 ;mul mantissa by 10**(no_bits_shifted)
bra.b pwrten ;go calc pwrten
*
* This section handles a negative adjusted exponent.
*
ap_st_n:
clr.l d1 ;clr counter
moveq.l #2,d5 ;set up d5 to point to lword 3
move.l (a0,d5.L*4),d4 ;get lword 3
bne.b ap_n_cl ;if not zero, check digits
sub.l #1,d5 ;dec d5 to point to lword 2
addq.l #8,d1 ;inc counter by 8
move.l (a0,d5.L*4),d4 ;get lword 2
ap_n_cl:
move.l #28,d3 ;point to last digit
moveq.l #7,d2 ;init digit counter
ap_n_gd:
bfextu d4{d3:4},d0 ;get digit
bne.b ap_n_fx ;if non-zero, go to exp fix
subq.l #4,d3 ;point to previous digit
addq.l #1,d1 ;inc digit counter
dbf.w d2,ap_n_gd ;get next digit
ap_n_fx:
move.l d1,d0 ;copy counter to d0
move.l L_SCR1(a6),d1 ;get adjusted exp from memory
sub.l d0,d1 ;subtract count from exp
bgt.b ap_n_fm ;if still pos, go fix mantissa
neg.l d1 ;take abs of exp and clr SE
move.l (a0),d4 ;load lword 1 to d4
and.l #$bfffffff,d4 ; and clr SE in d4
and.l #$bfffffff,(a0) ; and in memory
*
* Calculate the mantissa multiplier to compensate for the appending of
* zeros to the mantissa.
*
ap_n_fm:
; move.l #PTENRN,a1 ;get address of power-of-ten table - deleted <1/2/91, JPO>
lea PTENRN,a1 ; <1/2/91, JPO>
clr.l d3 ;init table index
; fmove.s FONE,fp1 ;init fp1 to 1 <1/2/91, JPO>
fmove.b #1,fp1 ; <1/2/91, JPO>
moveq.l #3,d2 ;init d2 to count bits in counter
ap_n_el:
asr.l #1,d0 ;shift lsb into carry
bcc.b ap_n_en ;if 1, mul fp1 by pwrten factor
fmul.x (a1,d3),fp1 ;mul by 10**(d3_bit_no)
ap_n_en:
add.l #12,d3 ;inc d3 to next rtable entry
tst.l d0 ;check if d0 is zero
bne.b ap_n_el ;if not, get next bit
fdiv.x 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:
move.l USER_FPCR(a6),d3 ;get user's FPCR
bfextu d3{26:2},d2 ;isolate rounding mode bits
move.l (a0),d4 ;reload 1st bcd word to d4
asl.l #2,d2 ;format d2 to be
bfextu d4{0:2},d0 ; {FPCR[6],FPCR[5],SM,SE}
add.l d0,d2 ;in d2 as index into RTABLE
lea.l RTABLE,a1 ;load rtable base
move.b (a1,d2),d0 ;load new rounding bits from table
clr.l d3 ;clear d3 to force no exc and extended
bfins d0,d3{26:2} ;stuff new rounding bits in FPCR
fmove.l d3,FPCR ;write new FPCR
asr.l #1,d0 ;write correct PTENxx table
bcc.b not_rp ;to a1
lea.l PTENRP,a1 ;it is RP
bra.b calc_p ;go to init section
not_rp:
asr.l #1,d0 ;keep checking
bcc.b not_rm
lea.l PTENRM,a1 ;it is RM
bra.b calc_p ;go to init section
not_rm:
lea.l PTENRN,a1 ;it is RN
calc_p:
move.l d1,d0 ;copy exp to d0;use d0
bpl.b no_neg ;if exp is negative,
neg.l d0 ;invert it
or.l #$40000000,(a0) ;and set SE bit
no_neg:
clr.l d3 ;table index
; fmove.s FONE,fp1 ;init fp1 to 1 <1/2/91, JPO>
fmove.b #1,fp1 ; <1/2/91, JPO>
e_loop:
asr.l #1,d0 ;shift next bit into carry
bcc.b e_next ;if zero, skip the mul
fmul.x (a1,d3),fp1 ;mul by 10**(d3_bit_no)
e_next:
add.l #12,d3 ;inc d3 to next rtable entry
tst.l d0 ;check if d0 is zero
bne.b 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
beq.b mul ;if clear, go to multiply
;div: ; label not referenced <1/2/91, JPO>
fdiv.x fp1,fp0 ;exp is negative, so divide mant by exp
bra.b end_dec
mul:
fmul.x 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:
fmove.l FPSR,d0 ;get status register
bclr.l #inex2_bit+8,d0 ;test for inex2 and clear it
fmove.l d0,FPSR ;return status reg w/o inex2
; beq.b no_exc ;skip this if no exc - label changed <1/2/91, JPO>
beq.b dbno_exc ; <1/2/91, JPO>
or.l #inx1a_mask,USER_FPSR(a6) ;set inex1/ainex
;no_exc: ; label changed <1/2/91, JPO>
dbno_exc: ; <1/2/91, JPO>
movem.l (a7)+,d2-d5
rts
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