//
// $Id$
//
// 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.defs"
//
// 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
