round.s

RTEMS (Real-Time Executive for Multiprocessor Systems) is a free open source real-time operating sys

//
//      $Id: round.S,v 1.1 1998/12/14 23:15:23 joel Exp $
//
//	round.sa 3.4 7/29/91
//
//	handle rounding and normalization tasks
//
//
//
//		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//	THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA 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.

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

	|section	8

#include "fpsp.defs"

//
//	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