xref: /src/sys/arch/m68k/fpsp/decbin.sa

*	MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP
*	M68000 Hi-Performance Microprocessor Division
*	M68040 Software Package 
*
*	M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc.
*	All rights reserved.
*
*	THE SOFTWARE is provided on an "AS IS" basis and without warranty.
*	To the maximum extent permitted by applicable law,
*	MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED,
*	INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A
*	PARTICULAR PURPOSE and any warranty against infringement with
*	regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF)
*	and any accompanying written materials. 
*
*	To the maximum extent permitted by applicable law,
*	IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER
*	(INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS
*	PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR
*	OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE
*	SOFTWARE.  Motorola assumes no responsibility for the maintenance
*	and support of the SOFTWARE.  
*
*	You are hereby granted a copyright license to use, modify, and
*	distribute the SOFTWARE so long as this entire notice is retained
*	without alteration in any modified and/or redistributed versions,
*	and that such modified versions are clearly identified as such.
*	No licenses are granted by implication, estoppel or otherwise
*	under any patents or trademarks of Motorola, Inc.

*
*	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 occured.  Unimp will fix the stack.
*	

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	dc.b	0,0,0,0
	dc.b	2,3,2,3
	dc.b	2,3,3,2
	dc.b	3,2,2,3

	xdef	decbin
	xdef	calc_e
	xdef	pwrten
	xdef	calc_m
	xdef	norm
	xdef	ap_st_z
	xdef	ap_st_n
*
FNIBS	equ	7
FSTRT	equ	0
*
ESTRT	equ	4
EDIGITS equ	2	
*
* Constants in single precision
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:
	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:
	moveq.l	#1,d1		;word counter, init to 1
	fmove.s	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
	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
	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:
	addq.l	#1,d1		;inc lw pointer in mantissa
	cmp.l	#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.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	#$40000000,(a0)	; and in memory
*
* Calculate the mantissa multiplier to compensate for the striping of
* zeros from the mantissa.
*
ap_p_fm:
	move.l	#PTENRN,a1	;get address of power-of-ten table
	clr.l	d3		;init table index
	fmove.s	FONE,fp1	;init fp1 to 1
	moveq.l	#3,d2		;init d2 to count bits in counter
ap_p_el:
	asr.l	#1,d0		;shift lsb into carry
	bcc.b	ap_p_en		;if 1, mul fp1 by pwrten factor
	fmul.x	(a1,d3),fp1	;mul by 10**(d3_bit_no)
ap_p_en:
	add.l	#12,d3		;inc d3 to next rtable entry
	tst.l	d0		;check if d0 is zero
	bne.b	ap_p_el		;if not, get next bit
	fmul.x	fp1,fp0		;mul mantissa by 10**(no_bits_shifted)
	bra.b	pwrten		;go calc pwrten
*
* This section handles a negative adjusted exponent.
*
ap_st_n:
	clr.l	d1		;clr counter
	moveq.l	#2,d5		;set up d5 to point to lword 3
	move.l	(a0,d5.L*4),d4	;get lword 3
	bne.b	ap_n_cl		;if not zero, check digits
	sub.l	#1,d5		;dec d5 to point to lword 2
	addq.l	#8,d1		;inc counter by 8
	move.l	(a0,d5.L*4),d4	;get lword 2
ap_n_cl:
	move.l	#28,d3		;point to last digit
	moveq.l	#7,d2		;init digit counter
ap_n_gd:
	bfextu	d4{d3:4},d0	;get digit
	bne.b	ap_n_fx		;if non-zero, go to exp fix
	subq.l	#4,d3		;point to previous digit
	addq.l	#1,d1		;inc digit counter
	dbf.w	d2,ap_n_gd	;get next digit
ap_n_fx:
	move.l	d1,d0		;copy counter to d0
	move.l	L_SCR1(a6),d1	;get adjusted exp from memory
	sub.l	d0,d1		;subtract count from exp
	bgt.b	ap_n_fm		;if still pos, go fix mantissa
	neg.l	d1		;take abs of exp and clr SE
	move.l	(a0),d4		;load lword 1 to d4
	and.l	#$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
	clr.l	d3		;init table index
	fmove.s	FONE,fp1	;init fp1 to 1
	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
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:
	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
	or.l	#inx1a_mask,USER_FPSR(a6) ;set inex1/ainex
no_exc:
	movem.l	(a7)+,d2-d5
	rts
	end