round.S

|
|	round.sa 3.4 7/29/91
|
|	handle rounding and normalization tasks
|
|
|
|		Copyright (C) Motorola, Inc. 1990
|			All Rights Reserved
|
|       For details on the license for this file, please see the
|       file, README, in this same directory.

|ROUND	idnt    2,1 | Motorola 040 Floating Point Software Package

	|section	8

#include "fpsp.h"

|
|	round --- round result according to precision/mode
|
|	a0 points to the input operand in the internal extended format
|	d1(high word) contains rounding precision:
|		ext = $0000xxxx
|		sgl = $0001xxxx
|		dbl = $0002xxxx
|	d1(low word) contains rounding mode:
|		RN  = $xxxx0000
|		RZ  = $xxxx0001
|		RM  = $xxxx0010
|		RP  = $xxxx0011
|	d0{31:29} contains the g,r,s bits (extended)
|
|	On return the value pointed to by a0 is correctly rounded,
|	a0 is preserved and the g-r-s bits in d0 are cleared.
|	The result is not typed - the tag field is invalid.  The
|	result is still in the internal extended format.
|
|	The INEX bit of USER_FPSR will be set if the rounded result was
|	inexact (i.e. if any of the g-r-s bits were set).
|

	.global	round
round:
| If g=r=s=0 then result is exact and round is done, else set
| the inex flag in status reg and continue.
|
	bsrs	ext_grs			|this subroutine looks at the
|					:rounding precision and sets
|					;the appropriate g-r-s bits.
	tstl	%d0			|if grs are zero, go force
	bne	rnd_cont		|lower bits to zero for size

	swap	%d1			|set up d1.w for round prec.
	bra	truncate

rnd_cont:
|
| Use rounding mode as an index into a jump table for these modes.
|
	orl	#inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
	lea	mode_tab,%a1
	movel	(%a1,%d1.w*4),%a1
	jmp	(%a1)
|
| Jump table indexed by rounding mode in d1.w.  All following assumes
| grs != 0.
|
mode_tab:
	.long	rnd_near
	.long	rnd_zero
	.long	rnd_mnus
	.long	rnd_plus
|
|	ROUND PLUS INFINITY
|
|	If sign of fp number = 0 (positive), then add 1 to l.
|
rnd_plus:
	swap	%d1			|set up d1 for round prec.
	tstb	LOCAL_SGN(%a0)		|check for sign
	bmi	truncate		|if positive then truncate
	movel	#0xffffffff,%d0		|force g,r,s to be all f's
	lea	add_to_l,%a1
	movel	(%a1,%d1.w*4),%a1
	jmp	(%a1)
|
|	ROUND MINUS INFINITY
|
|	If sign of fp number = 1 (negative), then add 1 to l.
|
rnd_mnus:
	swap	%d1			|set up d1 for round prec.
	tstb	LOCAL_SGN(%a0)		|check for sign
	bpl	truncate		|if negative then truncate
	movel	#0xffffffff,%d0		|force g,r,s to be all f's
	lea	add_to_l,%a1
	movel	(%a1,%d1.w*4),%a1
	jmp	(%a1)
|
|	ROUND ZERO
|
|	Always truncate.
rnd_zero:
	swap	%d1			|set up d1 for round prec.
	bra	truncate
|
|
|	ROUND NEAREST
|
|	If (g=1), then add 1 to l and if (r=s=0), then clear l
|	Note that this will round to even in case of a tie.
|
rnd_near:
	swap	%d1			|set up d1 for round prec.
	asll	#1,%d0			|shift g-bit to c-bit
	bcc	truncate		|if (g=1) then
	lea	add_to_l,%a1
	movel	(%a1,%d1.w*4),%a1
	jmp	(%a1)

|
|	ext_grs --- extract guard, round and sticky bits
|
| Input:	d1 =		PREC:ROUND
| Output:	d0{31:29}=	guard, round, sticky
|
| The ext_grs extract the guard/round/sticky bits according to the
| selected rounding precision. It is called by the round subroutine
| only.  All registers except d0 are kept intact. d0 becomes an
| updated guard,round,sticky in d0{31:29}
|
| Notes: the ext_grs uses the round PREC, and therefore has to swap d1
|	 prior to usage, and needs to restore d1 to original.
|
ext_grs:
	swap	%d1			|have d1.w point to round precision
	cmpiw	#0,%d1
	bnes	sgl_or_dbl
	bras	end_ext_grs

sgl_or_dbl:
	moveml	%d2/%d3,-(%a7)		|make some temp registers
	cmpiw	#1,%d1
	bnes	grs_dbl
grs_sgl:
	bfextu	LOCAL_HI(%a0){#24:#2},%d3	|sgl prec. g-r are 2 bits right
	movel	#30,%d2			|of the sgl prec. limits
	lsll	%d2,%d3			|shift g-r bits to MSB of d3
	movel	LOCAL_HI(%a0),%d2		|get word 2 for s-bit test
	andil	#0x0000003f,%d2		|s bit is the or of all other
	bnes	st_stky			|bits to the right of g-r
	tstl	LOCAL_LO(%a0)		|test lower mantissa
	bnes	st_stky			|if any are set, set sticky
	tstl	%d0			|test original g,r,s
	bnes	st_stky			|if any are set, set sticky
	bras	end_sd			|if words 3 and 4 are clr, exit
grs_dbl:
	bfextu	LOCAL_LO(%a0){#21:#2},%d3	|dbl-prec. g-r are 2 bits right
	movel	#30,%d2			|of the dbl prec. limits
	lsll	%d2,%d3			|shift g-r bits to the MSB of d3
	movel	LOCAL_LO(%a0),%d2		|get lower mantissa  for s-bit test
	andil	#0x000001ff,%d2		|s bit is the or-ing of all
	bnes	st_stky			|other bits to the right of g-r
	tstl	%d0			|test word original g,r,s
	bnes	st_stky			|if any are set, set sticky
	bras	end_sd			|if clear, exit
st_stky:
	bset	#rnd_stky_bit,%d3
end_sd:
	movel	%d3,%d0			|return grs to d0
	moveml	(%a7)+,%d2/%d3		|restore scratch registers
end_ext_grs:
	swap	%d1			|restore d1 to original
	rts

|*******************  Local Equates
	.set	ad_1_sgl,0x00000100	|  constant to add 1 to l-bit in sgl prec
	.set	ad_1_dbl,0x00000800	|  constant to add 1 to l-bit in dbl prec


|Jump table for adding 1 to the l-bit indexed by rnd prec

add_to_l:
	.long	add_ext
	.long	add_sgl
	.long	add_dbl
	.long	add_dbl
|
|	ADD SINGLE
|
add_sgl:
	addl	#ad_1_sgl,LOCAL_HI(%a0)
	bccs	scc_clr			|no mantissa overflow
	roxrw  LOCAL_HI(%a0)		|shift v-bit back in
	roxrw  LOCAL_HI+2(%a0)		|shift v-bit back in
	addw	#0x1,LOCAL_EX(%a0)	|and incr exponent
scc_clr:
	tstl	%d0			|test for rs = 0
	bnes	sgl_done
	andiw  #0xfe00,LOCAL_HI+2(%a0)	|clear the l-bit
sgl_done:
	andil	#0xffffff00,LOCAL_HI(%a0) |truncate bits beyond sgl limit
	clrl	LOCAL_LO(%a0)		|clear d2
	rts

|
|	ADD EXTENDED
|
add_ext:
	addql  #1,LOCAL_LO(%a0)		|add 1 to l-bit
	bccs	xcc_clr			|test for carry out
	addql  #1,LOCAL_HI(%a0)		|propagate carry
	bccs	xcc_clr
	roxrw  LOCAL_HI(%a0)		|mant is 0 so restore v-bit
	roxrw  LOCAL_HI+2(%a0)		|mant is 0 so restore v-bit
	roxrw	LOCAL_LO(%a0)
	roxrw	LOCAL_LO+2(%a0)
	addw	#0x1,LOCAL_EX(%a0)	|and inc exp
xcc_clr:
	tstl	%d0			|test rs = 0
	bnes	add_ext_done
	andib	#0xfe,LOCAL_LO+3(%a0)	|clear the l bit
add_ext_done:
	rts
|
|	ADD DOUBLE
|
add_dbl:
	addl	#ad_1_dbl,LOCAL_LO(%a0)
	bccs	dcc_clr
	addql	#1,LOCAL_HI(%a0)		|propagate carry
	bccs	dcc_clr
	roxrw	LOCAL_HI(%a0)		|mant is 0 so restore v-bit
	roxrw	LOCAL_HI+2(%a0)		|mant is 0 so restore v-bit
	roxrw	LOCAL_LO(%a0)
	roxrw	LOCAL_LO+2(%a0)
	addw	#0x1,LOCAL_EX(%a0)	|incr exponent
dcc_clr:
	tstl	%d0			|test for rs = 0
	bnes	dbl_done
	andiw	#0xf000,LOCAL_LO+2(%a0)	|clear the l-bit

dbl_done:
	andil	#0xfffff800,LOCAL_LO(%a0) |truncate bits beyond dbl limit
	rts

error:
	rts
|
| Truncate all other bits
|
trunct:
	.long	end_rnd
	.long	sgl_done
	.long	dbl_done
	.long	dbl_done

truncate:
	lea	trunct,%a1
	movel	(%a1,%d1.w*4),%a1
	jmp	(%a1)

end_rnd:
	rts

|
|	NORMALIZE
|
| These routines (nrm_zero & nrm_set) normalize the unnorm.  This
| is done by shifting the mantissa left while decrementing the
| exponent.
|
| NRM_SET shifts and decrements until there is a 1 set in the integer
| bit of the mantissa (msb in d1).
|
| NRM_ZERO shifts and decrements until there is a 1 set in the integer
| bit of the mantissa (msb in d1) unless this would mean the exponent
| would go less than 0.  In that case the number becomes a denorm - the
| exponent (d0) is set to 0 and the mantissa (d1 & d2) is not
| normalized.
|
| Note that both routines have been optimized (for the worst case) and
| therefore do not have the easy to follow decrement/shift loop.
|
|	NRM_ZERO
|
|	Distance to first 1 bit in mantissa = X
|	Distance to 0 from exponent = Y
|	If X < Y
|	Then
|	  nrm_set
|	Else
|	  shift mantissa by Y
|	  set exponent = 0
|
|input:
|	FP_SCR1 = exponent, ms mantissa part, ls mantissa part
|output:
|	L_SCR1{4} = fpte15 or ete15 bit
|
	.global	nrm_zero
nrm_zero:
	movew	LOCAL_EX(%a0),%d0
	cmpw   #64,%d0          |see if exp > 64
	bmis	d0_less
	bsr	nrm_set		|exp > 64 so exp won't exceed 0
	rts
d0_less:
	moveml	%d2/%d3/%d5/%d6,-(%a7)
	movel	LOCAL_HI(%a0),%d1
	movel	LOCAL_LO(%a0),%d2

	bfffo	%d1{#0:#32},%d3	|get the distance to the first 1
|				;in ms mant
	beqs	ms_clr		|branch if no bits were set
	cmpw	%d3,%d0		|of X>Y
	bmis	greater		|then exp will go past 0 (neg) if
|				;it is just shifted
	bsr	nrm_set		|else exp won't go past 0
	moveml	(%a7)+,%d2/%d3/%d5/%d6
	rts
greater:
	movel	%d2,%d6		|save ls mant in d6
	lsll	%d0,%d2		|shift ls mant by count
	lsll	%d0,%d1		|shift ms mant by count
	movel	#32,%d5
	subl	%d0,%d5		|make op a denorm by shifting bits
	lsrl	%d5,%d6		|by the number in the exp, then
|				;set exp = 0.
	orl	%d6,%d1		|shift the ls mant bits into the ms mant
	movel	#0,%d0		|same as if decremented exp to 0
|				;while shifting
	movew	%d0,LOCAL_EX(%a0)
	movel	%d1,LOCAL_HI(%a0)
	movel	%d2,LOCAL_LO(%a0)
	moveml	(%a7)+,%d2/%d3/%d5/%d6
	rts
ms_clr:
	bfffo	%d2{#0:#32},%d3	|check if any bits set in ls mant
	beqs	all_clr		|branch if none set
	addw	#32,%d3
	cmpw	%d3,%d0		|if X>Y
	bmis	greater		|then branch
	bsr	nrm_set		|else exp won't go past 0
	moveml	(%a7)+,%d2/%d3/%d5/%d6
	rts
all_clr:
	movew	#0,LOCAL_EX(%a0)	|no mantissa bits set. Set exp = 0.
	moveml	(%a7)+,%d2/%d3/%d5/%d6
	rts
|
|	NRM_SET
|
	.global	nrm_set
nrm_set:
	movel	%d7,-(%a7)
	bfffo	LOCAL_HI(%a0){#0:#32},%d7 |find first 1 in ms mant to d7)
	beqs	lower		|branch if ms mant is all 0's

	movel	%d6,-(%a7)

	subw	%d7,LOCAL_EX(%a0)	|sub exponent by count
	movel	LOCAL_HI(%a0),%d0	|d0 has ms mant
	movel	LOCAL_LO(%a0),%d1 |d1 has ls mant

	lsll	%d7,%d0		|shift first 1 to j bit position
	movel	%d1,%d6		|copy ls mant into d6
	lsll	%d7,%d6		|shift ls mant by count
	movel	%d6,LOCAL_LO(%a0)	|store ls mant into memory
	moveql	#32,%d6
	subl	%d7,%d6		|continue shift
	lsrl	%d6,%d1		|shift off all bits but those that will
|				;be shifted into ms mant
	orl	%d1,%d0		|shift the ls mant bits into the ms mant
	movel	%d0,LOCAL_HI(%a0)	|store ms mant into memory
	moveml	(%a7)+,%d7/%d6	|restore registers
	rts

|
| We get here if ms mant was = 0, and we assume ls mant has bits
| set (otherwise this would have been tagged a zero not a denorm).
|
lower:
	movew	LOCAL_EX(%a0),%d0	|d0 has exponent
	movel	LOCAL_LO(%a0),%d1	|d1 has ls mant
	subw	#32,%d0		|account for ms mant being all zeros
	bfffo	%d1{#0:#32},%d7	|find first 1 in ls mant to d7)
	subw	%d7,%d0		|subtract shift count from exp
	lsll	%d7,%d1		|shift first 1 to integer bit in ms mant
	movew	%d0,LOCAL_EX(%a0)	|store ms mant
	movel	%d1,LOCAL_HI(%a0)	|store exp
	clrl	LOCAL_LO(%a0)	|clear ls mant
	movel	(%a7)+,%d7
	rts
|
|	denorm --- denormalize an intermediate result
|
|	Used by underflow.
|
| Input:
|	a0	 points to the operand to be denormalized
|		 (in the internal extended format)
|
|	d0:	 rounding precision
| Output:
|	a0	 points to the denormalized result
|		 (in the internal extended format)
|
|	d0	is guard,round,sticky
|
| d0 comes into this routine with the rounding precision. It
| is then loaded with the denormalized exponent threshold for the
| rounding precision.
|

	.global	denorm
denorm:
	btstb	#6,LOCAL_EX(%a0)	|check for exponents between $7fff-$4000
	beqs	no_sgn_ext
	bsetb	#7,LOCAL_EX(%a0)	|sign extend if it is so
no_sgn_ext:

	cmpib	#0,%d0		|if 0 then extended precision
	bnes	not_ext		|else branch

	clrl	%d1		|load d1 with ext threshold
	clrl	%d0		|clear the sticky flag
	bsr	dnrm_lp		|denormalize the number
	tstb	%d1		|check for inex
	beq	no_inex		|if clr, no inex
	bras	dnrm_inex	|if set, set inex

not_ext:
	cmpil	#1,%d0		|if 1 then single precision
	beqs	load_sgl	|else must be 2, double prec

load_dbl:
	movew	#dbl_thresh,%d1	|put copy of threshold in d1
	movel	%d1,%d0		|copy d1 into d0
	subw	LOCAL_EX(%a0),%d0	|diff = threshold - exp
	cmpw	#67,%d0		|if diff > 67 (mant + grs bits)
	bpls	chk_stky	|then branch (all bits would be
|				; shifted off in denorm routine)
	clrl	%d0		|else clear the sticky flag
	bsr	dnrm_lp		|denormalize the number
	tstb	%d1		|check flag
	beqs	no_inex		|if clr, no inex
	bras	dnrm_inex	|if set, set inex

load_sgl:
	movew	#sgl_thresh,%d1	|put copy of threshold in d1
	movel	%d1,%d0		|copy d1 into d0
	subw	LOCAL_EX(%a0),%d0	|diff = threshold - exp
	cmpw	#67,%d0		|if diff > 67 (mant + grs bits)
	bpls	chk_stky	|then branch (all bits would be
|				; shifted off in denorm routine)
	clrl	%d0		|else clear the sticky flag
	bsr	dnrm_lp		|denormalize the number
	tstb	%d1		|check flag
	beqs	no_inex		|if clr, no inex
	bras	dnrm_inex	|if set, set inex

chk_stky:
	tstl	LOCAL_HI(%a0)	|check for any bits set
	bnes	set_stky
	tstl	LOCAL_LO(%a0)	|check for any bits set
	bnes	set_stky
	bras	clr_mant
set_stky:
	orl	#inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
	movel	#0x20000000,%d0	|set sticky bit in return value
clr_mant:
	movew	%d1,LOCAL_EX(%a0)		|load exp with threshold
	movel	#0,LOCAL_HI(%a0)	|set d1 = 0 (ms mantissa)
	movel	#0,LOCAL_LO(%a0)		|set d2 = 0 (ms mantissa)
	rts
dnrm_inex:
	orl	#inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
no_inex:
	rts

|
|	dnrm_lp --- normalize exponent/mantissa to specified threshold
|
| Input:
|	a0		points to the operand to be denormalized
|	d0{31:29}	initial guard,round,sticky
|	d1{15:0}	denormalization threshold
| Output:
|	a0		points to the denormalized operand
|	d0{31:29}	final guard,round,sticky
|	d1.b		inexact flag:  all ones means inexact result
|
| The LOCAL_LO and LOCAL_GRS parts of the value are copied to FP_SCR2
| so that bfext can be used to extract the new low part of the mantissa.
| Dnrm_lp can be called with a0 pointing to ETEMP or WBTEMP and there
| is no LOCAL_GRS scratch word following it on the fsave frame.
|
	.global	dnrm_lp
dnrm_lp:
	movel	%d2,-(%sp)		|save d2 for temp use
	btstb	#E3,E_BYTE(%a6)		|test for type E3 exception
	beqs	not_E3			|not type E3 exception
	bfextu	WBTEMP_GRS(%a6){#6:#3},%d2	|extract guard,round, sticky  bit
	movel	#29,%d0
	lsll	%d0,%d2			|shift g,r,s to their positions
	movel	%d2,%d0
not_E3:
	movel	(%sp)+,%d2		|restore d2
	movel	LOCAL_LO(%a0),FP_SCR2+LOCAL_LO(%a6)
	movel	%d0,FP_SCR2+LOCAL_GRS(%a6)
	movel	%d1,%d0			|copy the denorm threshold
	subw	LOCAL_EX(%a0),%d1		|d1 = threshold - uns exponent
	bles	no_lp			|d1 <= 0
	cmpw	#32,%d1
	blts	case_1			|0 = d1 < 32
	cmpw	#64,%d1
	blts	case_2			|32 <= d1 < 64
	bra	case_3			|d1 >= 64
|
| No normalization necessary
|
no_lp:
	clrb	%d1			|set no inex2 reported
	movel	FP_SCR2+LOCAL_GRS(%a6),%d0	|restore original g,r,s
	rts
|
| case (0<d1<32)
|
case_1:
	movel	%d2,-(%sp)
	movew	%d0,LOCAL_EX(%a0)		|exponent = denorm threshold
	movel	#32,%d0
	subw	%d1,%d0			|d0 = 32 - d1
	bfextu	LOCAL_EX(%a0){%d0:#32},%d2
	bfextu	%d2{%d1:%d0},%d2		|d2 = new LOCAL_HI
	bfextu	LOCAL_HI(%a0){%d0:#32},%d1	|d1 = new LOCAL_LO
	bfextu	FP_SCR2+LOCAL_LO(%a6){%d0:#32},%d0	|d0 = new G,R,S
	movel	%d2,LOCAL_HI(%a0)		|store new LOCAL_HI
	movel	%d1,LOCAL_LO(%a0)		|store new LOCAL_LO
	clrb	%d1
	bftst	%d0{#2:#30}
	beqs	c1nstky
	bsetl	#rnd_stky_bit,%d0
	st	%d1
c1nstky:
	movel	FP_SCR2+LOCAL_GRS(%a6),%d2	|restore original g,r,s
	andil	#0xe0000000,%d2		|clear all but G,R,S
	tstl	%d2			|test if original G,R,S are clear
	beqs	grs_clear
	orl	#0x20000000,%d0		|set sticky bit in d0
grs_clear:
	andil	#0xe0000000,%d0		|clear all but G,R,S
	movel	(%sp)+,%d2
	rts
|
| case (32<=d1<64)
|
case_2:
	movel	%d2,-(%sp)
	movew	%d0,LOCAL_EX(%a0)		|unsigned exponent = threshold
	subw	#32,%d1			|d1 now between 0 and 32
	movel	#32,%d0
	subw	%d1,%d0			|d0 = 32 - d1
	bfextu	LOCAL_EX(%a0){%d0:#32},%d2
	bfextu	%d2{%d1:%d0},%d2		|d2 = new LOCAL_LO
	bfextu	LOCAL_HI(%a0){%d0:#32},%d1	|d1 = new G,R,S
	bftst	%d1{#2:#30}
	bnes	c2_sstky		|bra if sticky bit to be set
	bftst	FP_SCR2+LOCAL_LO(%a6){%d0:#32}
	bnes	c2_sstky		|bra if sticky bit to be set
	movel	%d1,%d0
	clrb	%d1
	bras	end_c2
c2_sstky:
	movel	%d1,%d0
	bsetl	#rnd_stky_bit,%d0
	st	%d1
end_c2:
	clrl	LOCAL_HI(%a0)		|store LOCAL_HI = 0
	movel	%d2,LOCAL_LO(%a0)		|store LOCAL_LO
	movel	FP_SCR2+LOCAL_GRS(%a6),%d2	|restore original g,r,s
	andil	#0xe0000000,%d2		|clear all but G,R,S
	tstl	%d2			|test if original G,R,S are clear
	beqs	clear_grs
	orl	#0x20000000,%d0		|set sticky bit in d0
clear_grs:
	andil	#0xe0000000,%d0		|get rid of all but G,R,S
	movel	(%sp)+,%d2
	rts
|
| d1 >= 64 Force the exponent to be the denorm threshold with the
| correct sign.
|
case_3:
	movew	%d0,LOCAL_EX(%a0)
	tstw	LOCAL_SGN(%a0)
	bges	c3con
c3neg:
	orl	#0x80000000,LOCAL_EX(%a0)
c3con:
	cmpw	#64,%d1
	beqs	sixty_four
	cmpw	#65,%d1
	beqs	sixty_five
|
| Shift value is out of range.  Set d1 for inex2 flag and
| return a zero with the given threshold.
|
	clrl	LOCAL_HI(%a0)
	clrl	LOCAL_LO(%a0)
	movel	#0x20000000,%d0
	st	%d1
	rts

sixty_four:
	movel	LOCAL_HI(%a0),%d0
	bfextu	%d0{#2:#30},%d1
	andil	#0xc0000000,%d0
	bras	c3com

sixty_five:
	movel	LOCAL_HI(%a0),%d0
	bfextu	%d0{#1:#31},%d1
	andil	#0x80000000,%d0
	lsrl	#1,%d0			|shift high bit into R bit

c3com:
	tstl	%d1
	bnes	c3ssticky
	tstl	LOCAL_LO(%a0)
	bnes	c3ssticky
	tstb	FP_SCR2+LOCAL_GRS(%a6)
	bnes	c3ssticky
	clrb	%d1
	bras	c3end

c3ssticky:
	bsetl	#rnd_stky_bit,%d0
	st	%d1
c3end:
	clrl	LOCAL_HI(%a0)
	clrl	LOCAL_LO(%a0)
	rts

	|end