id	sid	tid	token	lemma	pos
ap-1167	1	1	ap-v2.dvi	ap-v2.dvi	PROPN
ap-1167	1	2	acta	acta	PROPN
ap-1167	1	3	polytechnica	polytechnica	PROPN
ap-1167	1	4	vol	vol	NOUN
ap-1167	1	5	.	.	PROPN
ap-1167	2	1	50	50	NUM
ap-1167	2	2	no	no	NOUN
ap-1167	2	3	.	.	PUNCT
ap-1167	3	1	2/2010	2/2010	NUM
ap-1167	3	2	fpu	fpu	NOUN
ap-1167	3	3	-	-	PUNCT
ap-1167	3	4	supported	support	VERB
ap-1167	3	5	running	running	NOUN
ap-1167	3	6	error	error	NOUN
ap-1167	3	7	analysis	analysis	NOUN
ap-1167	3	8	t.	t.	NOUN
ap-1167	3	9	zahradnický	zahradnický	NOUN
ap-1167	3	10	,	,	PUNCT
ap-1167	3	11	r.	r.	PROPN
ap-1167	3	12	lórencz	lórencz	PROPN
ap-1167	3	13	abstract	abstract	ADJ
ap-1167	3	14	a	a	DET
ap-1167	3	15	-	-	PUNCT
ap-1167	3	16	posteriori	posteriori	NOUN
ap-1167	3	17	forward	forward	ADV
ap-1167	3	18	rounding	round	VERB
ap-1167	3	19	error	error	NOUN
ap-1167	3	20	analyses	analysis	NOUN
ap-1167	3	21	tend	tend	VERB
ap-1167	3	22	to	to	PART
ap-1167	3	23	give	give	VERB
ap-1167	3	24	sharper	sharp	ADJ
ap-1167	3	25	error	error	NOUN
ap-1167	3	26	estimates	estimate	NOUN
ap-1167	3	27	than	than	ADP
ap-1167	3	28	a	a	PRON
ap-1167	3	29	-	-	PUNCT
ap-1167	3	30	priori	priori	ADJ
ap-1167	3	31	ones	one	NOUN
ap-1167	3	32	,	,	PUNCT
ap-1167	3	33	as	as	SCONJ
ap-1167	3	34	they	they	PRON
ap-1167	3	35	use	use	VERB
ap-1167	3	36	actual	actual	ADJ
ap-1167	3	37	data	datum	NOUN
ap-1167	3	38	quantities	quantity	NOUN
ap-1167	3	39	.	.	PUNCT
ap-1167	4	1	one	one	NUM
ap-1167	4	2	of	of	ADP
ap-1167	4	3	such	such	DET
ap-1167	4	4	a	a	DET
ap-1167	4	5	-	-	PUNCT
ap-1167	4	6	posteriori	posteriori	NOUN
ap-1167	4	7	analysis	analysis	NOUN
ap-1167	4	8	–	–	PUNCT
ap-1167	4	9	running	run	VERB
ap-1167	4	10	error	error	NOUN
ap-1167	4	11	analysis	analysis	NOUN
ap-1167	4	12	–	–	PUNCT
ap-1167	4	13	uses	use	VERB
ap-1167	4	14	expressions	expression	NOUN
ap-1167	4	15	consisting	consist	VERB
ap-1167	4	16	of	of	ADP
ap-1167	4	17	two	two	NUM
ap-1167	4	18	parts	part	NOUN
ap-1167	4	19	;	;	PUNCT
ap-1167	4	20	one	one	PRON
ap-1167	4	21	generates	generate	VERB
ap-1167	4	22	the	the	DET
ap-1167	4	23	error	error	NOUN
ap-1167	4	24	and	and	CCONJ
ap-1167	4	25	the	the	DET
ap-1167	4	26	other	other	ADJ
ap-1167	4	27	propagates	propagate	VERB
ap-1167	4	28	input	input	ADJ
ap-1167	4	29	errors	error	NOUN
ap-1167	4	30	to	to	ADP
ap-1167	4	31	the	the	DET
ap-1167	4	32	output	output	NOUN
ap-1167	4	33	.	.	PUNCT
ap-1167	5	1	this	this	DET
ap-1167	5	2	paper	paper	NOUN
ap-1167	5	3	suggests	suggest	VERB
ap-1167	5	4	replacing	replace	VERB
ap-1167	5	5	the	the	DET
ap-1167	5	6	error	error	NOUN
ap-1167	5	7	generating	generating	NOUN
ap-1167	5	8	term	term	NOUN
ap-1167	5	9	with	with	ADP
ap-1167	5	10	an	an	DET
ap-1167	5	11	fpu	fpu	NOUN
ap-1167	5	12	-	-	PUNCT
ap-1167	5	13	extracted	extract	VERB
ap-1167	5	14	rounding	rounding	NOUN
ap-1167	5	15	error	error	NOUN
ap-1167	5	16	estimate	estimate	NOUN
ap-1167	5	17	,	,	PUNCT
ap-1167	5	18	which	which	PRON
ap-1167	5	19	produces	produce	VERB
ap-1167	5	20	a	a	DET
ap-1167	5	21	sharper	sharp	ADJ
ap-1167	5	22	error	error	NOUN
ap-1167	5	23	bound	bind	VERB
ap-1167	5	24	.	.	PUNCT
ap-1167	6	1	keywords	keyword	NOUN
ap-1167	6	2	:	:	PUNCT
ap-1167	6	3	analysis	analysis	NOUN
ap-1167	6	4	of	of	ADP
ap-1167	6	5	algorithms	algorithm	NOUN
ap-1167	6	6	,	,	PUNCT
ap-1167	6	7	a	a	DET
ap-1167	6	8	-	-	PUNCT
ap-1167	6	9	posteriori	posteriori	NOUN
ap-1167	6	10	error	error	NOUN
ap-1167	6	11	estimates	estimate	NOUN
ap-1167	6	12	,	,	PUNCT
ap-1167	6	13	running	run	VERB
ap-1167	6	14	error	error	NOUN
ap-1167	6	15	analysis	analysis	NOUN
ap-1167	6	16	,	,	PUNCT
ap-1167	6	17	floating	float	VERB
ap-1167	6	18	point	point	NOUN
ap-1167	6	19	,	,	PUNCT
ap-1167	6	20	numerical	numerical	ADJ
ap-1167	6	21	stability	stability	NOUN
ap-1167	6	22	.	.	PUNCT
ap-1167	7	1	1	1	NUM
ap-1167	7	2	introduction	introduction	NOUN
ap-1167	7	3	rounding	round	VERB
ap-1167	7	4	error	error	NOUN
ap-1167	7	5	analyses	analysis	NOUN
ap-1167	7	6	are	be	AUX
ap-1167	7	7	used	use	VERB
ap-1167	7	8	to	to	PART
ap-1167	7	9	discover	discover	VERB
ap-1167	7	10	the	the	DET
ap-1167	7	11	stability	stability	NOUN
ap-1167	7	12	of	of	ADP
ap-1167	7	13	numerical	numerical	ADJ
ap-1167	7	14	algorithms	algorithm	NOUN
ap-1167	7	15	and	and	CCONJ
ap-1167	7	16	provide	provide	VERB
ap-1167	7	17	information	information	NOUN
ap-1167	7	18	on	on	ADP
ap-1167	7	19	whether	whether	SCONJ
ap-1167	7	20	the	the	DET
ap-1167	7	21	computed	compute	VERB
ap-1167	7	22	result	result	NOUN
ap-1167	7	23	is	be	AUX
ap-1167	7	24	valid	valid	ADJ
ap-1167	7	25	.	.	PUNCT
ap-1167	8	1	they	they	PRON
ap-1167	8	2	are	be	AUX
ap-1167	8	3	typically	typically	ADV
ap-1167	8	4	performed	perform	VERB
ap-1167	8	5	in	in	ADP
ap-1167	8	6	forward	forward	ADV
ap-1167	8	7	or	or	CCONJ
ap-1167	8	8	backward	backward	ADJ
ap-1167	8	9	direction	direction	NOUN
ap-1167	8	10	,	,	PUNCT
ap-1167	8	11	and	and	CCONJ
ap-1167	8	12	either	either	CCONJ
ap-1167	8	13	a	a	X
ap-1167	8	14	-	-	PUNCT
ap-1167	8	15	priori	priori	NOUN
ap-1167	8	16	or	or	CCONJ
ap-1167	8	17	a	a	DET
ap-1167	8	18	-	-	PUNCT
ap-1167	8	19	posteriori	posteriori	NOUN
ap-1167	8	20	.	.	PUNCT
ap-1167	9	1	backward	backward	ADJ
ap-1167	9	2	error	error	NOUN
ap-1167	9	3	analysis	analysis	NOUN
ap-1167	9	4	[	[	X
ap-1167	9	5	6	6	NUM
ap-1167	9	6	]	]	PUNCT
ap-1167	9	7	treats	treat	VERB
ap-1167	9	8	all	all	DET
ap-1167	9	9	operations	operation	NOUN
ap-1167	9	10	as	as	SCONJ
ap-1167	9	11	if	if	SCONJ
ap-1167	9	12	they	they	PRON
ap-1167	9	13	were	be	AUX
ap-1167	9	14	exact	exact	ADJ
ap-1167	9	15	but	but	CCONJ
ap-1167	9	16	with	with	ADP
ap-1167	9	17	a	a	DET
ap-1167	9	18	perturbed	perturb	VERB
ap-1167	9	19	data	datum	NOUN
ap-1167	9	20	,	,	PUNCT
ap-1167	9	21	and	and	CCONJ
ap-1167	9	22	we	we	PRON
ap-1167	9	23	ask	ask	VERB
ap-1167	9	24	for	for	ADP
ap-1167	9	25	which	which	DET
ap-1167	9	26	input	input	NOUN
ap-1167	9	27	data	datum	NOUN
ap-1167	9	28	we	we	PRON
ap-1167	9	29	have	have	AUX
ap-1167	9	30	solved	solve	VERB
ap-1167	9	31	our	our	PRON
ap-1167	9	32	problem	problem	NOUN
ap-1167	9	33	.	.	PUNCT
ap-1167	10	1	using	use	VERB
ap-1167	10	2	backward	backward	ADJ
ap-1167	10	3	error	error	NOUN
ap-1167	10	4	analysis	analysis	NOUN
ap-1167	10	5	is	be	AUX
ap-1167	10	6	preferred	prefer	VERB
ap-1167	10	7	,	,	PUNCT
ap-1167	10	8	as	as	SCONJ
ap-1167	10	9	each	each	DET
ap-1167	10	10	algorithm	algorithm	NOUN
ap-1167	10	11	which	which	PRON
ap-1167	10	12	is	be	AUX
ap-1167	10	13	backward	backward	ADV
ap-1167	10	14	stable	stable	ADJ
ap-1167	10	15	is	be	AUX
ap-1167	10	16	automatically	automatically	ADV
ap-1167	10	17	numerically	numerically	ADV
ap-1167	10	18	stable	stable	ADJ
ap-1167	11	1	[	[	X
ap-1167	11	2	5	5	NUM
ap-1167	11	3	]	]	PUNCT
ap-1167	11	4	,	,	PUNCT
ap-1167	11	5	while	while	SCONJ
ap-1167	11	6	this	this	PRON
ap-1167	11	7	does	do	AUX
ap-1167	11	8	not	not	PART
ap-1167	11	9	hold	hold	VERB
ap-1167	11	10	for	for	ADP
ap-1167	11	11	forward	forward	ADJ
ap-1167	11	12	error	error	NOUN
ap-1167	11	13	analyses	analysis	NOUN
ap-1167	11	14	.	.	PUNCT
ap-1167	12	1	on	on	ADP
ap-1167	12	2	the	the	DET
ap-1167	12	3	other	other	ADJ
ap-1167	12	4	hand	hand	NOUN
ap-1167	12	5	,	,	PUNCT
ap-1167	12	6	forward	forward	ADJ
ap-1167	12	7	error	error	NOUN
ap-1167	12	8	analyses	analysis	NOUN
ap-1167	12	9	treat	treat	VERB
ap-1167	12	10	operations	operation	NOUN
ap-1167	12	11	as	as	ADP
ap-1167	12	12	sources	source	NOUN
ap-1167	12	13	of	of	ADP
ap-1167	12	14	errors	error	NOUN
ap-1167	12	15	,	,	PUNCT
ap-1167	12	16	and	and	CCONJ
ap-1167	12	17	tell	tell	VERB
ap-1167	12	18	us	we	PRON
ap-1167	12	19	about	about	ADP
ap-1167	12	20	the	the	DET
ap-1167	12	21	size	size	NOUN
ap-1167	12	22	of	of	ADP
ap-1167	12	23	the	the	DET
ap-1167	12	24	solution	solution	NOUN
ap-1167	12	25	that	that	PRON
ap-1167	12	26	our	our	PRON
ap-1167	12	27	input	input	NOUN
ap-1167	12	28	data	data	NOUN
ap-1167	12	29	corresponds	correspond	VERB
ap-1167	12	30	to	to	ADP
ap-1167	12	31	.	.	PUNCT
ap-1167	13	1	since	since	SCONJ
ap-1167	13	2	error	error	NOUN
ap-1167	13	3	analyses	analysis	NOUN
ap-1167	13	4	performed	perform	VERB
ap-1167	13	5	a	a	PRON
ap-1167	13	6	-	-	PUNCT
ap-1167	13	7	priori	priori	ADV
ap-1167	13	8	can	can	AUX
ap-1167	13	9	often	often	ADV
ap-1167	13	10	be	be	AUX
ap-1167	13	11	difficult	difficult	ADJ
ap-1167	13	12	if	if	SCONJ
ap-1167	13	13	the	the	DET
ap-1167	13	14	algorithm	algorithm	NOUN
ap-1167	13	15	being	be	AUX
ap-1167	13	16	analyzed	analyze	VERB
ap-1167	13	17	is	be	AUX
ap-1167	13	18	complex	complex	ADJ
ap-1167	13	19	,	,	PUNCT
ap-1167	13	20	a	a	DET
ap-1167	13	21	-	-	PUNCT
ap-1167	13	22	posteriori	posteriori	NOUN
ap-1167	13	23	analyses	analysis	NOUN
ap-1167	13	24	may	may	AUX
ap-1167	13	25	provide	provide	VERB
ap-1167	13	26	a	a	DET
ap-1167	13	27	more	more	ADV
ap-1167	13	28	feasible	feasible	ADJ
ap-1167	13	29	alternative	alternative	NOUN
ap-1167	13	30	(	(	PUNCT
ap-1167	13	31	msc	msc	PROPN
ap-1167	13	32	2000	2000	NUM
ap-1167	13	33	classification	classification	NOUN
ap-1167	13	34	:	:	PUNCT
ap-1167	13	35	65g20	65g20	NUM
ap-1167	13	36	,	,	PUNCT
ap-1167	13	37	65g50	65g50	NUM
ap-1167	13	38	)	)	PUNCT
ap-1167	13	39	.	.	PUNCT
ap-1167	14	1	an	an	DET
ap-1167	14	2	objective	objective	NOUN
ap-1167	14	3	of	of	ADP
ap-1167	14	4	an	an	DET
ap-1167	14	5	a	a	PRON
ap-1167	14	6	-	-	PUNCT
ap-1167	14	7	priori	priori	ADJ
ap-1167	14	8	analysis	analysis	NOUN
ap-1167	14	9	is	be	AUX
ap-1167	14	10	to	to	PART
ap-1167	14	11	find	find	VERB
ap-1167	14	12	the	the	DET
ap-1167	14	13	worst	bad	ADJ
ap-1167	14	14	case	case	NOUN
ap-1167	14	15	bound	bind	VERB
ap-1167	14	16	for	for	ADP
ap-1167	14	17	an	an	DET
ap-1167	14	18	algorithm	algorithm	NOUN
ap-1167	14	19	,	,	PUNCT
ap-1167	14	20	if	if	SCONJ
ap-1167	14	21	it	it	PRON
ap-1167	14	22	exists	exist	VERB
ap-1167	14	23	,	,	PUNCT
ap-1167	14	24	while	while	SCONJ
ap-1167	14	25	a	a	DET
ap-1167	14	26	-	-	PUNCT
ap-1167	14	27	posteriori	posteriori	NOUN
ap-1167	14	28	analyses	analysis	NOUN
ap-1167	14	29	calculate	calculate	VERB
ap-1167	14	30	the	the	DET
ap-1167	14	31	error	error	NOUN
ap-1167	14	32	bound	bind	VERB
ap-1167	14	33	concurrently	concurrently	ADV
ap-1167	14	34	with	with	ADP
ap-1167	14	35	the	the	DET
ap-1167	14	36	evaluation	evaluation	NOUN
ap-1167	14	37	of	of	ADP
ap-1167	14	38	the	the	DET
ap-1167	14	39	result	result	NOUN
ap-1167	14	40	and	and	CCONJ
ap-1167	14	41	work	work	VERB
ap-1167	14	42	with	with	ADP
ap-1167	14	43	actual	actual	ADJ
ap-1167	14	44	data	datum	NOUN
ap-1167	14	45	quantities	quantity	NOUN
ap-1167	14	46	,	,	PUNCT
ap-1167	14	47	providing	provide	VERB
ap-1167	14	48	a	a	DET
ap-1167	14	49	tighter	tight	ADJ
ap-1167	14	50	error	error	NOUN
ap-1167	14	51	bound	bind	VERB
ap-1167	14	52	.	.	PUNCT
ap-1167	15	1	this	this	DET
ap-1167	15	2	paper	paper	NOUN
ap-1167	15	3	presents	present	VERB
ap-1167	15	4	a	a	DET
ap-1167	15	5	replacement	replacement	NOUN
ap-1167	15	6	for	for	ADP
ap-1167	15	7	an	an	DET
ap-1167	15	8	error	error	NOUN
ap-1167	15	9	generating	generating	NOUN
ap-1167	15	10	term	term	NOUN
ap-1167	15	11	in	in	ADP
ap-1167	15	12	error	error	NOUN
ap-1167	15	13	bounds	bound	NOUN
ap-1167	15	14	calculated	calculate	VERB
ap-1167	15	15	with	with	ADP
ap-1167	15	16	forward	forward	ADV
ap-1167	15	17	a	a	DET
ap-1167	15	18	-	-	PUNCT
ap-1167	15	19	posteriori	posteriori	NOUN
ap-1167	15	20	error	error	NOUN
ap-1167	15	21	estimates	estimate	NOUN
ap-1167	15	22	(	(	PUNCT
ap-1167	15	23	also	also	ADV
ap-1167	15	24	known	know	VERB
ap-1167	15	25	as	as	ADP
ap-1167	15	26	running	run	VERB
ap-1167	15	27	error	error	NOUN
ap-1167	15	28	analysis	analysis	NOUN
ap-1167	15	29	)	)	PUNCT
ap-1167	15	30	to	to	PART
ap-1167	15	31	obtain	obtain	VERB
ap-1167	15	32	sharper	sharp	ADJ
ap-1167	15	33	error	error	NOUN
ap-1167	15	34	bounds	bound	NOUN
ap-1167	15	35	by	by	ADP
ap-1167	15	36	exploiting	exploit	VERB
ap-1167	15	37	the	the	DET
ap-1167	15	38	behavior	behavior	NOUN
ap-1167	15	39	of	of	ADP
ap-1167	15	40	the	the	DET
ap-1167	15	41	computer	computer	NOUN
ap-1167	15	42	fpu	fpu	PROPN
ap-1167	15	43	.	.	PUNCT
ap-1167	16	1	we	we	PRON
ap-1167	16	2	expect	expect	VERB
ap-1167	16	3	the	the	DET
ap-1167	16	4	calculation	calculation	NOUN
ap-1167	16	5	to	to	PART
ap-1167	16	6	be	be	AUX
ap-1167	16	7	portable	portable	ADJ
ap-1167	16	8	(	(	PUNCT
ap-1167	16	9	conforming	conform	VERB
ap-1167	16	10	strictly	strictly	ADV
ap-1167	16	11	to	to	ADP
ap-1167	16	12	[	[	X
ap-1167	16	13	3	3	NUM
ap-1167	16	14	]	]	PUNCT
ap-1167	16	15	)	)	PUNCT
ap-1167	16	16	and	and	CCONJ
ap-1167	16	17	assume	assume	VERB
ap-1167	16	18	an	an	DET
ap-1167	16	19	intel	intel	PROPN
ap-1167	16	20	x86	x86	PROPN
ap-1167	16	21	compatible	compatible	PROPN
ap-1167	16	22	fpu	fpu	PROPN
ap-1167	16	23	which	which	PRON
ap-1167	16	24	supports	support	VERB
ap-1167	16	25	double	double	ADJ
ap-1167	16	26	extended	extend	VERB
ap-1167	16	27	precision	precision	NOUN
ap-1167	16	28	(	(	PUNCT
ap-1167	16	29	80	80	NUM
ap-1167	16	30	-	-	PUNCT
ap-1167	16	31	bit	bit	NOUN
ap-1167	16	32	)	)	PUNCT
ap-1167	16	33	floating	float	VERB
ap-1167	16	34	point	point	NOUN
ap-1167	16	35	registers	register	NOUN
ap-1167	16	36	,	,	PUNCT
ap-1167	16	37	which	which	PRON
ap-1167	16	38	are	be	AUX
ap-1167	16	39	essential	essential	ADJ
ap-1167	16	40	for	for	ADP
ap-1167	16	41	this	this	DET
ap-1167	16	42	method	method	NOUN
ap-1167	16	43	.	.	PUNCT
ap-1167	17	1	2	2	NUM
ap-1167	17	2	running	running	NOUN
ap-1167	17	3	error	error	NOUN
ap-1167	17	4	analysis	analysis	NOUN
ap-1167	17	5	and	and	CCONJ
ap-1167	17	6	error	error	NOUN
ap-1167	17	7	bounds	bound	NOUN
ap-1167	17	8	running	run	VERB
ap-1167	17	9	error	error	NOUN
ap-1167	17	10	analysis	analysis	NOUN
ap-1167	17	11	[	[	X
ap-1167	17	12	6	6	NUM
ap-1167	17	13	,	,	PUNCT
ap-1167	17	14	7	7	NUM
ap-1167	17	15	]	]	PUNCT
ap-1167	17	16	is	be	AUX
ap-1167	17	17	a	a	DET
ap-1167	17	18	type	type	NOUN
ap-1167	17	19	of	of	ADP
ap-1167	17	20	a	a	DET
ap-1167	17	21	-	-	PUNCT
ap-1167	17	22	posteriori	posteriori	NOUN
ap-1167	17	23	forward	forward	ADJ
ap-1167	17	24	error	error	NOUN
ap-1167	17	25	analysis	analysis	NOUN
ap-1167	17	26	.	.	PUNCT
ap-1167	18	1	the	the	DET
ap-1167	18	2	algorithm	algorithm	NOUN
ap-1167	18	3	being	be	AUX
ap-1167	18	4	analyzed	analyze	VERB
ap-1167	18	5	is	be	AUX
ap-1167	18	6	extended	extend	VERB
ap-1167	18	7	to	to	PART
ap-1167	18	8	calculate	calculate	VERB
ap-1167	18	9	the	the	DET
ap-1167	18	10	partial	partial	ADJ
ap-1167	18	11	error	error	NOUN
ap-1167	18	12	bound	bind	VERB
ap-1167	18	13	alongside	alongside	ADP
ap-1167	18	14	the	the	DET
ap-1167	18	15	normal	normal	ADJ
ap-1167	18	16	calculation	calculation	NOUN
ap-1167	18	17	.	.	PUNCT
ap-1167	19	1	as	as	SCONJ
ap-1167	19	2	the	the	DET
ap-1167	19	3	algorithm	algorithm	NOUN
ap-1167	19	4	proceeds	proceed	NOUN
ap-1167	19	5	,	,	PUNCT
ap-1167	19	6	bounds	bound	NOUN
ap-1167	19	7	are	be	AUX
ap-1167	19	8	accumulated	accumulate	VERB
ap-1167	19	9	,	,	PUNCT
ap-1167	19	10	making	make	VERB
ap-1167	19	11	a	a	DET
ap-1167	19	12	total	total	ADJ
ap-1167	19	13	error	error	NOUN
ap-1167	19	14	bound	bind	VERB
ap-1167	19	15	estimate	estimate	NOUN
ap-1167	19	16	.	.	PUNCT
ap-1167	20	1	from	from	ADP
ap-1167	20	2	here	here	ADV
ap-1167	20	3	on	on	ADV
ap-1167	20	4	,	,	PUNCT
ap-1167	20	5	a	a	DET
ap-1167	20	6	binary	binary	ADJ
ap-1167	20	7	double	double	ADJ
ap-1167	20	8	precision	precision	NOUN
ap-1167	20	9	floating	float	VERB
ap-1167	20	10	point	point	NOUN
ap-1167	20	11	arithmetic	arithmetic	ADJ
ap-1167	20	12	with	with	ADP
ap-1167	20	13	a	a	DET
ap-1167	20	14	guard	guard	NOUN
ap-1167	20	15	digit	digit	NOUN
ap-1167	20	16	with	with	ADP
ap-1167	20	17	round	round	NOUN
ap-1167	20	18	to	to	ADP
ap-1167	20	19	nearest	near	ADJ
ap-1167	20	20	rounding	round	VERB
ap-1167	20	21	mode	mode	NOUN
ap-1167	20	22	is	be	AUX
ap-1167	20	23	assumed	assume	VERB
ap-1167	20	24	.	.	PUNCT
ap-1167	21	1	definition	definition	NOUN
ap-1167	21	2	1	1	NUM
ap-1167	21	3	let	let	VERB
ap-1167	21	4	ft	ft	AUX
ap-1167	21	5	⊂	⊂	PROPN
ap-1167	21	6	q	q	X
ap-1167	21	7	be	be	AUX
ap-1167	21	8	a	a	DET
ap-1167	21	9	binary	binary	ADJ
ap-1167	21	10	floating	float	VERB
ap-1167	21	11	point	point	NOUN
ap-1167	21	12	set	set	VERB
ap-1167	21	13	with	with	ADP
ap-1167	21	14	a	a	DET
ap-1167	21	15	precision	precision	NOUN
ap-1167	21	16	of	of	ADP
ap-1167	21	17	t	t	PROPN
ap-1167	21	18	,	,	PUNCT
ap-1167	21	19	where	where	SCONJ
ap-1167	21	20	q	q	PROPN
ap-1167	21	21	denotes	denote	VERB
ap-1167	21	22	the	the	DET
ap-1167	21	23	rational	rational	ADJ
ap-1167	21	24	number	number	NOUN
ap-1167	21	25	set	set	VERB
ap-1167	21	26	.	.	PUNCT
ap-1167	22	1	definition	definition	NOUN
ap-1167	22	2	2	2	NUM
ap-1167	22	3	let	let	VERB
ap-1167	22	4	y	y	NOUN
ap-1167	22	5	=	=	PUNCT
ap-1167	22	6	±m	±m	PROPN
ap-1167	22	7	2e−t	2e−t	NOUN
ap-1167	22	8	∈	∈	PROPN
ap-1167	22	9	ft	ft	PART
ap-1167	22	10	be	be	AUX
ap-1167	22	11	a	a	DET
ap-1167	22	12	binary	binary	ADJ
ap-1167	22	13	floating	float	VERB
ap-1167	22	14	point	point	NOUN
ap-1167	22	15	number	number	NOUN
ap-1167	22	16	,	,	PUNCT
ap-1167	22	17	where	where	SCONJ
ap-1167	22	18	m	m	NOUN
ap-1167	22	19	stands	stand	VERB
ap-1167	22	20	for	for	ADP
ap-1167	22	21	mantissa	mantissa	NOUN
ap-1167	22	22	,	,	PUNCT
ap-1167	22	23	e	e	NOUN
ap-1167	22	24	for	for	ADP
ap-1167	22	25	exponent	exponent	NOUN
ap-1167	22	26	,	,	PUNCT
ap-1167	22	27	and	and	CCONJ
ap-1167	22	28	t	t	PROPN
ap-1167	22	29	for	for	ADP
ap-1167	22	30	precision	precision	NOUN
ap-1167	22	31	.	.	PUNCT
ap-1167	23	1	let	let	VERB
ap-1167	23	2	ex(y	ex(y	PUNCT
ap-1167	23	3	)	)	PUNCT
ap-1167	24	1	=	=	SYM
ap-1167	24	2	e.	e.	PROPN
ap-1167	24	3	lemma	lemma	PROPN
ap-1167	24	4	3	3	NUM
ap-1167	24	5	let	let	VERB
ap-1167	24	6	x̂	x̂	PUNCT
ap-1167	25	1	=	=	SYM
ap-1167	25	2	fl(x	fl(x	NOUN
ap-1167	25	3	)	)	PUNCT
ap-1167	25	4	be	be	VERB
ap-1167	25	5	a	a	DET
ap-1167	25	6	floating	float	VERB
ap-1167	25	7	point	point	NOUN
ap-1167	25	8	representation	representation	NOUN
ap-1167	25	9	of	of	ADP
ap-1167	25	10	an	an	DET
ap-1167	25	11	exact	exact	ADJ
ap-1167	25	12	number	number	NOUN
ap-1167	25	13	x	x	NOUN
ap-1167	25	14	,	,	PUNCT
ap-1167	25	15	which	which	PRON
ap-1167	25	16	is	be	AUX
ap-1167	25	17	obtained	obtain	VERB
ap-1167	25	18	by	by	ADP
ap-1167	25	19	rounding	round	VERB
ap-1167	25	20	x	x	PUNCT
ap-1167	25	21	to	to	ADP
ap-1167	25	22	the	the	DET
ap-1167	25	23	nearest	near	ADJ
ap-1167	25	24	element	element	NOUN
ap-1167	25	25	in	in	ADP
ap-1167	25	26	ft	ft	PROPN
ap-1167	25	27	.	.	PUNCT
ap-1167	26	1	the	the	DET
ap-1167	26	2	rounding	round	VERB
ap-1167	26	3	process	process	NOUN
ap-1167	26	4	can	can	AUX
ap-1167	26	5	be	be	AUX
ap-1167	26	6	described	describe	VERB
ap-1167	26	7	as	as	ADP
ap-1167	26	8	:	:	PUNCT
ap-1167	26	9	x̂	x̂	X
ap-1167	26	10	=	=	SYM
ap-1167	26	11	fl(x	fl(x	PROPN
ap-1167	26	12	)	)	PUNCT
ap-1167	26	13	=	=	SYM
ap-1167	27	1	x(1	x(1	PROPN
ap-1167	27	2	+	+	NUM
ap-1167	27	3	δ	δ	PROPN
ap-1167	27	4	)	)	PUNCT
ap-1167	27	5	,	,	PUNCT
ap-1167	27	6	|δ|	|δ|	VERB
ap-1167	27	7	≤	≤	PROPN
ap-1167	27	8	ut	ut	PROPN
ap-1167	27	9	,	,	PUNCT
ap-1167	27	10	(	(	PUNCT
ap-1167	27	11	1	1	X
ap-1167	27	12	)	)	PUNCT
ap-1167	27	13	where	where	SCONJ
ap-1167	27	14	ut	ut	PROPN
ap-1167	27	15	=	=	SYM
ap-1167	27	16	2−t	2−t	PROPN
ap-1167	27	17	is	be	AUX
ap-1167	27	18	unit	unit	NOUN
ap-1167	27	19	roundoff	roundoff	NOUN
ap-1167	27	20	in	in	ADP
ap-1167	27	21	precision	precision	NOUN
ap-1167	27	22	t.	t.	PROPN
ap-1167	27	23	to	to	PART
ap-1167	27	24	conserve	conserve	VERB
ap-1167	27	25	some	some	DET
ap-1167	27	26	space	space	NOUN
ap-1167	27	27	,	,	PUNCT
ap-1167	27	28	and	and	CCONJ
ap-1167	27	29	for	for	ADP
ap-1167	27	30	clarity	clarity	NOUN
ap-1167	27	31	,	,	PUNCT
ap-1167	27	32	u	u	NOUN
ap-1167	27	33	without	without	ADP
ap-1167	27	34	a	a	DET
ap-1167	27	35	subscript	subscript	NOUN
ap-1167	27	36	means	mean	VERB
ap-1167	27	37	u53	u53	NOUN
ap-1167	27	38	.	.	PUNCT
ap-1167	28	1	assumption	assumption	NOUN
ap-1167	28	2	4	4	NUM
ap-1167	28	3	(	(	PUNCT
ap-1167	28	4	standard	standard	ADJ
ap-1167	28	5	model	model	NOUN
ap-1167	28	6	)	)	PUNCT
ap-1167	28	7	we	we	PRON
ap-1167	28	8	assume	assume	VERB
ap-1167	28	9	that	that	SCONJ
ap-1167	28	10	operations	operation	NOUN
ap-1167	28	11	♦	♦	PROPN
ap-1167	28	12	∈	∈	PROPN
ap-1167	28	13	{	{	PUNCT
ap-1167	28	14	+	+	NOUN
ap-1167	28	15	,	,	PUNCT
ap-1167	28	16	−	−	PROPN
ap-1167	28	17	,	,	PUNCT
ap-1167	28	18	·	·	PUNCT
ap-1167	28	19	,	,	PUNCT
ap-1167	28	20	/	/	SYM
ap-1167	28	21	}	}	PUNCT
ap-1167	28	22	and	and	CCONJ
ap-1167	28	23	the	the	DET
ap-1167	28	24	square	square	ADJ
ap-1167	28	25	root	root	NOUN
ap-1167	28	26	follow	follow	VERB
ap-1167	28	27	the	the	DET
ap-1167	28	28	standard	standard	ADJ
ap-1167	28	29	model	model	NOUN
ap-1167	28	30	[	[	X
ap-1167	28	31	5	5	NUM
ap-1167	28	32	]	]	PUNCT
ap-1167	28	33	and	and	CCONJ
ap-1167	28	34	are	be	AUX
ap-1167	28	35	evaluated	evaluate	VERB
ap-1167	28	36	with	with	ADP
ap-1167	28	37	error	error	NOUN
ap-1167	28	38	no	no	ADV
ap-1167	28	39	greater	great	ADJ
ap-1167	28	40	than	than	ADP
ap-1167	28	41	u	u	NOUN
ap-1167	28	42	:	:	PUNCT
ap-1167	28	43	ŝ	ŝ	X
ap-1167	28	44	♦	♦	PROPN
ap-1167	28	45	=	=	PROPN
ap-1167	28	46	fl(â	fl(â	PROPN
ap-1167	28	47	♦	♦	PROPN
ap-1167	28	48	b̂	b̂	NOUN
ap-1167	28	49	)	)	PUNCT
ap-1167	28	50	=	=	PUNCT
ap-1167	28	51	(	(	PUNCT
ap-1167	28	52	â	â	PROPN
ap-1167	28	53	♦	♦	PROPN
ap-1167	28	54	b̂)/(1	b̂)/(1	PROPN
ap-1167	28	55	+	+	PROPN
ap-1167	28	56	δ	δ	PROPN
ap-1167	28	57	♦	♦	PROPN
ap-1167	28	58	)	)	PUNCT
ap-1167	28	59	,	,	PUNCT
ap-1167	28	60	|δ	|δ	PUNCT
ap-1167	28	61	♦	♦	PROPN
ap-1167	28	62	|	|	ADJ
ap-1167	28	63	≤	≤	NUM
ap-1167	28	64	u	u	NOUN
ap-1167	28	65	,	,	PUNCT
ap-1167	28	66	ŝ√	ŝ√	PROPN
ap-1167	28	67	=	=	SYM
ap-1167	28	68	fl	fl	PROPN
ap-1167	28	69	(	(	PUNCT
ap-1167	28	70	√	√	PROPN
ap-1167	28	71	â	â	NUM
ap-1167	28	72	)	)	PUNCT
ap-1167	28	73	=	=	SYM
ap-1167	28	74	√	√	PROPN
ap-1167	28	75	â/(1	â/(1	VERB
ap-1167	28	76	+	+	CCONJ
ap-1167	28	77	δ√	δ√	NOUN
ap-1167	28	78	)	)	PUNCT
ap-1167	28	79	,	,	PUNCT
ap-1167	28	80	|δ√	|δ√	PROPN
ap-1167	29	1	|	|	CCONJ
ap-1167	29	2	≤	≤	NUM
ap-1167	29	3	u	u	NOUN
ap-1167	29	4	,	,	PUNCT
ap-1167	29	5	(	(	PUNCT
ap-1167	29	6	2	2	NUM
ap-1167	29	7	)	)	PUNCT
ap-1167	29	8	where	where	SCONJ
ap-1167	29	9	we	we	PRON
ap-1167	29	10	use	use	VERB
ap-1167	29	11	ŝ	ŝ	NOUN
ap-1167	29	12	as	as	ADP
ap-1167	29	13	a	a	DET
ap-1167	29	14	computed	computed	ADJ
ap-1167	29	15	result	result	NOUN
ap-1167	29	16	of	of	ADP
ap-1167	29	17	an	an	DET
ap-1167	29	18	operation	operation	NOUN
ap-1167	29	19	.	.	PUNCT
ap-1167	30	1	the	the	DET
ap-1167	30	2	standard	standard	ADJ
ap-1167	30	3	model	model	NOUN
ap-1167	30	4	will	will	AUX
ap-1167	30	5	also	also	ADV
ap-1167	30	6	be	be	AUX
ap-1167	30	7	used	use	VERB
ap-1167	30	8	in	in	ADP
ap-1167	30	9	the	the	DET
ap-1167	30	10	form	form	NOUN
ap-1167	30	11	of	of	ADP
ap-1167	30	12	ŝ	ŝ	PROPN
ap-1167	30	13	♦	♦	PROPN
ap-1167	30	14	=	=	PROPN
ap-1167	30	15	fl(â	fl(â	PROPN
ap-1167	30	16	♦	♦	PROPN
ap-1167	30	17	b̂	b̂	NOUN
ap-1167	30	18	)	)	PUNCT
ap-1167	30	19	=	=	PUNCT
ap-1167	30	20	(	(	PUNCT
ap-1167	30	21	â	â	PROPN
ap-1167	30	22	♦	♦	PROPN
ap-1167	30	23	b̂	b̂	NOUN
ap-1167	30	24	)	)	PUNCT
ap-1167	30	25	·	·	PUNCT
ap-1167	31	1	(	(	PUNCT
ap-1167	31	2	1	1	NUM
ap-1167	31	3	+	+	NUM
ap-1167	31	4	δ	δ	PROPN
ap-1167	31	5	♦	♦	PROPN
ap-1167	31	6	)	)	PUNCT
ap-1167	31	7	,	,	PUNCT
ap-1167	32	1	where	where	SCONJ
ap-1167	32	2	useful	useful	ADJ
ap-1167	32	3	.	.	PUNCT
ap-1167	32	4	table	table	NOUN
ap-1167	32	5	1	1	NUM
ap-1167	32	6	summarizes	summarize	NOUN
ap-1167	32	7	the	the	DET
ap-1167	32	8	error	error	NOUN
ap-1167	32	9	bounds	bound	NOUN
ap-1167	32	10	for	for	ADP
ap-1167	32	11	basic	basic	ADJ
ap-1167	32	12	operations	operation	NOUN
ap-1167	32	13	and	and	CCONJ
ap-1167	32	14	the	the	DET
ap-1167	32	15	square	square	ADJ
ap-1167	32	16	root	root	NOUN
ap-1167	32	17	with	with	ADP
ap-1167	32	18	products	product	NOUN
ap-1167	32	19	of	of	ADP
ap-1167	32	20	errors	error	NOUN
ap-1167	32	21	being	be	AUX
ap-1167	32	22	neglected	neglect	VERB
ap-1167	32	23	.	.	PUNCT
ap-1167	33	1	we	we	PRON
ap-1167	33	2	also	also	ADV
ap-1167	33	3	assume	assume	VERB
ap-1167	33	4	that	that	SCONJ
ap-1167	33	5	the	the	DET
ap-1167	33	6	following	follow	VERB
ap-1167	33	7	holds	hold	VERB
ap-1167	33	8	:	:	PUNCT
ap-1167	33	9	ŝ	ŝ	X
ap-1167	33	10	=	=	PUNCT
ap-1167	33	11	s/(1	s/(1	PROPN
ap-1167	34	1	+	+	NUM
ap-1167	34	2	δs	δs	NOUN
ap-1167	34	3	)	)	PUNCT
ap-1167	34	4	=	=	SYM
ap-1167	34	5	s	s	PART
ap-1167	34	6	+	+	X
ap-1167	34	7	σ	σ	PROPN
ap-1167	34	8	,	,	PUNCT
ap-1167	34	9	â	â	X
ap-1167	34	10	=	=	SYM
ap-1167	34	11	a/(1	a/(1	NOUN
ap-1167	34	12	+	+	CCONJ
ap-1167	34	13	δa	δa	NOUN
ap-1167	34	14	)	)	PUNCT
ap-1167	34	15	=	=	PUNCT
ap-1167	35	1	a	a	DET
ap-1167	35	2	+	+	NUM
ap-1167	35	3	α	α	NOUN
ap-1167	35	4	,	,	PUNCT
ap-1167	35	5	and	and	CCONJ
ap-1167	35	6	b̂	b̂	NOUN
ap-1167	35	7	=	=	NOUN
ap-1167	35	8	b/(1	b/(1	NOUN
ap-1167	35	9	+	+	NUM
ap-1167	35	10	δb	δb	NOUN
ap-1167	35	11	)	)	PUNCT
ap-1167	35	12	=	=	SYM
ap-1167	35	13	b	b	PROPN
ap-1167	35	14	+	+	CCONJ
ap-1167	35	15	β	β	X
ap-1167	35	16	,	,	PUNCT
ap-1167	35	17	where	where	SCONJ
ap-1167	35	18	α	α	X
ap-1167	35	19	,	,	PUNCT
ap-1167	35	20	β	β	NOUN
ap-1167	35	21	,	,	PUNCT
ap-1167	35	22	and	and	CCONJ
ap-1167	35	23	σ	σ	NUM
ap-1167	35	24	stand	stand	VERB
ap-1167	35	25	for	for	ADP
ap-1167	35	26	absolute	absolute	ADJ
ap-1167	35	27	(	(	PUNCT
ap-1167	35	28	static	static	ADJ
ap-1167	35	29	)	)	PUNCT
ap-1167	35	30	errors	error	NOUN
ap-1167	35	31	.	.	PUNCT
ap-1167	36	1	30	30	NUM
ap-1167	36	2	acta	acta	PROPN
ap-1167	36	3	polytechnica	polytechnica	PROPN
ap-1167	36	4	vol	vol	NOUN
ap-1167	36	5	.	.	PROPN
ap-1167	37	1	50	50	NUM
ap-1167	37	2	no	no	NOUN
ap-1167	37	3	.	.	PUNCT
ap-1167	38	1	2/2010	2/2010	NUM
ap-1167	38	2	table	table	NOUN
ap-1167	38	3	1	1	NUM
ap-1167	38	4	:	:	PUNCT
ap-1167	38	5	error	error	NOUN
ap-1167	38	6	bound	bind	VERB
ap-1167	38	7	estimates	estimate	NOUN
ap-1167	38	8	for	for	ADP
ap-1167	38	9	basic	basic	ADJ
ap-1167	38	10	operations	operation	NOUN
ap-1167	38	11	operation	operation	NOUN
ap-1167	38	12	error	error	NOUN
ap-1167	38	13	bound	bind	VERB
ap-1167	38	14	addition	addition	NOUN
ap-1167	38	15	and	and	CCONJ
ap-1167	38	16	subtraction	subtraction	NOUN
ap-1167	38	17	|σ±|	|σ±|	NOUN
ap-1167	38	18	≤	≤	NUM
ap-1167	38	19	u	u	PROPN
ap-1167	38	20	|â	|â	NOUN
ap-1167	38	21	±	±	X
ap-1167	38	22	b̂|	b̂|	PROPN
ap-1167	38	23	+	+	CCONJ
ap-1167	38	24	α	α	NOUN
ap-1167	38	25	+	+	X
ap-1167	38	26	β	β	X
ap-1167	38	27	multiplication	multiplication	NOUN
ap-1167	38	28	|σ·|	|σ·|	X
ap-1167	38	29	≤	≤	NUM
ap-1167	38	30	u	u	NOUN
ap-1167	38	31	|âb̂|	|âb̂|	PROPN
ap-1167	38	32	+	+	CCONJ
ap-1167	38	33	α|̂b|	α|̂b|	NUM
ap-1167	38	34	+	+	CCONJ
ap-1167	38	35	β|â|	β|â|	NOUN
ap-1167	38	36	division	division	NOUN
ap-1167	38	37	|σ/|	|σ/|	PROPN
ap-1167	38	38	≤	≤	NUM
ap-1167	38	39	u	u	PROPN
ap-1167	38	40	∣∣∣∣	∣∣∣∣	NOUN
ap-1167	38	41	â	â	X
ap-1167	38	42	b̂	b̂	NOUN
ap-1167	38	43	∣∣∣∣+	∣∣∣∣+	PROPN
ap-1167	38	44	α|̂b|	α|̂b|	PROPN
ap-1167	38	45	+	+	CCONJ
ap-1167	38	46	β|â|	β|â|	NOUN
ap-1167	38	47	b̂2	b̂2	PROPN
ap-1167	38	48	square	square	PROPN
ap-1167	38	49	root	root	PROPN
ap-1167	38	50	|σ√	|σ√	PROPN
ap-1167	38	51	|	|	ADV
ap-1167	38	52	≤	≤	PROPN
ap-1167	38	53	u	u	NOUN
ap-1167	38	54	∣∣∣√â	∣∣∣√â	PROPN
ap-1167	38	55	∣∣∣+	∣∣∣+	PROPN
ap-1167	38	56	α	α	PROPN
ap-1167	38	57	2	2	NUM
ap-1167	38	58	∣∣∣√â	∣∣∣√â	PROPN
ap-1167	38	59	∣∣∣	∣∣∣	NOUN
ap-1167	38	60	the	the	DET
ap-1167	38	61	right	right	ADJ
ap-1167	38	62	-	-	PUNCT
ap-1167	38	63	hand	hand	NOUN
ap-1167	38	64	side	side	NOUN
ap-1167	38	65	of	of	ADP
ap-1167	38	66	each	each	DET
ap-1167	38	67	error	error	NOUN
ap-1167	38	68	bound	bind	VERB
ap-1167	38	69	in	in	ADP
ap-1167	38	70	tab	tab	NOUN
ap-1167	38	71	.	.	PUNCT
ap-1167	38	72	1	1	NUM
ap-1167	38	73	contains	contain	VERB
ap-1167	38	74	an	an	DET
ap-1167	38	75	error	error	NOUN
ap-1167	38	76	generating	generating	NOUN
ap-1167	38	77	term	term	NOUN
ap-1167	38	78	u|	u|	NOUN
ap-1167	38	79	·	·	PUNCT
ap-1167	39	1	|	|	ADV
ap-1167	39	2	,	,	PUNCT
ap-1167	39	3	while	while	SCONJ
ap-1167	39	4	the	the	DET
ap-1167	39	5	rest	rest	NOUN
ap-1167	39	6	of	of	ADP
ap-1167	39	7	each	each	DET
ap-1167	39	8	expression	expression	NOUN
ap-1167	39	9	simply	simply	ADV
ap-1167	39	10	propagates	propagate	VERB
ap-1167	39	11	input	input	PROPN
ap-1167	39	12	error(s	error(s	PROPN
ap-1167	39	13	)	)	PUNCT
ap-1167	39	14	to	to	ADP
ap-1167	39	15	the	the	DET
ap-1167	39	16	output	output	NOUN
ap-1167	39	17	.	.	PUNCT
ap-1167	40	1	when	when	SCONJ
ap-1167	40	2	we	we	PRON
ap-1167	40	3	substitute	substitute	VERB
ap-1167	40	4	u	u	NOUN
ap-1167	40	5	=	=	PROPN
ap-1167	40	6	2−53	2−53	PROPN
ap-1167	40	7	into	into	ADP
ap-1167	40	8	u|ŝ|	u|ŝ|	PRON
ap-1167	40	9	,	,	PUNCT
ap-1167	40	10	multiplying	multiply	VERB
ap-1167	40	11	by	by	ADP
ap-1167	40	12	u	u	NOUN
ap-1167	40	13	reduces	reduce	VERB
ap-1167	40	14	the	the	DET
ap-1167	40	15	exponent	exponent	NOUN
ap-1167	40	16	by	by	ADP
ap-1167	40	17	53	53	NUM
ap-1167	40	18	u|ŝ|	u|ŝ|	NOUN
ap-1167	40	19	=	=	SYM
ap-1167	40	20	1	1	NUM
ap-1167	40	21	,	,	PUNCT
ap-1167	40	22	xx	xx	NUM
ap-1167	40	23	.	.	PUNCT
ap-1167	40	24	.	.	PUNCT
ap-1167	41	1	.	.	PUNCT
ap-1167	42	1	xx︸	xx︸	PROPN
ap-1167	42	2	︷︷	︷︷	PROPN
ap-1167	42	3	︸	︸	ADP
ap-1167	42	4	52	52	NUM
ap-1167	42	5	times	time	NOUN
ap-1167	42	6	·	·	SYM
ap-1167	42	7	2ex(̂s)−2	2ex(̂s)−2	NUM
ap-1167	42	8	t	t	PROPN
ap-1167	42	9	,	,	PUNCT
ap-1167	42	10	(	(	PUNCT
ap-1167	42	11	3	3	X
ap-1167	42	12	)	)	PUNCT
ap-1167	42	13	leaving	leave	VERB
ap-1167	42	14	the	the	DET
ap-1167	42	15	mantissa	mantissa	NOUN
ap-1167	42	16	unchanged	unchanged	ADJ
ap-1167	42	17	if	if	SCONJ
ap-1167	42	18	u|ŝ|	u|ŝ|	ADJ
ap-1167	42	19	is	be	AUX
ap-1167	42	20	normal	normal	ADJ
ap-1167	42	21	.	.	PUNCT
ap-1167	43	1	the	the	DET
ap-1167	43	2	roundoff	roundoff	NOUN
ap-1167	43	3	unit	unit	NOUN
ap-1167	43	4	is	be	AUX
ap-1167	43	5	just	just	ADV
ap-1167	43	6	the	the	DET
ap-1167	43	7	first	first	ADJ
ap-1167	43	8	1	1	NUM
ap-1167	43	9	in	in	ADP
ap-1167	43	10	(	(	PUNCT
ap-1167	43	11	3	3	NUM
ap-1167	43	12	)	)	PUNCT
ap-1167	43	13	,	,	PUNCT
ap-1167	43	14	while	while	SCONJ
ap-1167	43	15	x	x	X
ap-1167	43	16	-	-	PUNCT
ap-1167	43	17	en	en	X
ap-1167	43	18	are	be	AUX
ap-1167	43	19	generally	generally	ADV
ap-1167	43	20	nonzero	nonzero	ADJ
ap-1167	43	21	.	.	PUNCT
ap-1167	44	1	using	use	VERB
ap-1167	44	2	u|ŝ|	u|ŝ|	PRON
ap-1167	44	3	as	as	SCONJ
ap-1167	44	4	a	a	DET
ap-1167	44	5	rounding	round	VERB
ap-1167	44	6	error	error	NOUN
ap-1167	44	7	estimate	estimate	NOUN
ap-1167	44	8	features	feature	VERB
ap-1167	44	9	two	two	NUM
ap-1167	44	10	problems	problem	NOUN
ap-1167	44	11	:	:	PUNCT
ap-1167	44	12	1	1	X
ap-1167	44	13	.	.	PUNCT
ap-1167	44	14	the	the	DET
ap-1167	44	15	calculated	calculate	VERB
ap-1167	44	16	error	error	NOUN
ap-1167	44	17	bound	bind	VERB
ap-1167	44	18	u|ŝ|	u|ŝ|	NOUN
ap-1167	44	19	can	can	AUX
ap-1167	44	20	be	be	AUX
ap-1167	44	21	up	up	ADP
ap-1167	44	22	to	to	ADP
ap-1167	44	23	two	two	NUM
ap-1167	44	24	times	time	NOUN
ap-1167	44	25	larger	large	ADJ
ap-1167	44	26	(	(	PUNCT
ap-1167	44	27	u	u	NOUN
ap-1167	44	28	∑t−1	∑t−1	X
ap-1167	44	29	i=0	i=0	VERB
ap-1167	44	30	ŝi2−i<∼2u	ŝi2−i<∼2u	X
ap-1167	44	31	)	)	PUNCT
ap-1167	44	32	,	,	PUNCT
ap-1167	44	33	assuming	assume	VERB
ap-1167	44	34	that	that	PRON
ap-1167	44	35	ŝi	ŝi	VERB
ap-1167	44	36	refers	refer	VERB
ap-1167	44	37	to	to	ADP
ap-1167	44	38	the	the	DET
ap-1167	44	39	i	i	PROPN
ap-1167	44	40	-	-	PUNCT
ap-1167	44	41	th	th	X
ap-1167	44	42	bit	bit	NOUN
ap-1167	44	43	of	of	ADP
ap-1167	44	44	ŝ.	ŝ.	NOUN
ap-1167	44	45	2	2	NUM
ap-1167	44	46	.	.	PUNCT
ap-1167	45	1	the	the	DET
ap-1167	45	2	error	error	NOUN
ap-1167	45	3	generation	generation	NOUN
ap-1167	45	4	term	term	NOUN
ap-1167	45	5	always	always	ADV
ap-1167	45	6	generates	generate	VERB
ap-1167	45	7	an	an	DET
ap-1167	45	8	error	error	NOUN
ap-1167	45	9	even	even	ADV
ap-1167	45	10	in	in	ADP
ap-1167	45	11	the	the	DET
ap-1167	45	12	case	case	NOUN
ap-1167	45	13	when	when	SCONJ
ap-1167	45	14	no	no	DET
ap-1167	45	15	physical	physical	ADJ
ap-1167	45	16	error	error	NOUN
ap-1167	45	17	was	be	AUX
ap-1167	45	18	committed	commit	VERB
ap-1167	45	19	.	.	PUNCT
ap-1167	46	1	the	the	DET
ap-1167	46	2	expression	expression	NOUN
ap-1167	46	3	u|ŝ|	u|ŝ|	PRON
ap-1167	46	4	tends	tend	VERB
ap-1167	46	5	to	to	PART
ap-1167	46	6	give	give	VERB
ap-1167	46	7	a	a	DET
ap-1167	46	8	higher	high	ADJ
ap-1167	46	9	error	error	NOUN
ap-1167	46	10	bound	bind	VERB
ap-1167	46	11	estimate	estimate	NOUN
ap-1167	46	12	than	than	SCONJ
ap-1167	46	13	we	we	PRON
ap-1167	46	14	would	would	AUX
ap-1167	46	15	need	need	VERB
ap-1167	46	16	.	.	PUNCT
ap-1167	47	1	however	however	ADV
ap-1167	47	2	,	,	PUNCT
ap-1167	47	3	we	we	PRON
ap-1167	47	4	can	can	AUX
ap-1167	47	5	revise	revise	VERB
ap-1167	47	6	this	this	DET
ap-1167	47	7	expression	expression	NOUN
ap-1167	47	8	if	if	SCONJ
ap-1167	47	9	we	we	PRON
ap-1167	47	10	are	be	AUX
ap-1167	47	11	interested	interested	ADJ
ap-1167	47	12	in	in	ADP
ap-1167	47	13	obtaining	obtain	VERB
ap-1167	47	14	a	a	DET
ap-1167	47	15	tighter	tight	ADJ
ap-1167	47	16	error	error	NOUN
ap-1167	47	17	bound	bind	VERB
ap-1167	47	18	estimate	estimate	NOUN
ap-1167	47	19	,	,	PUNCT
ap-1167	47	20	and	and	CCONJ
ap-1167	47	21	we	we	PRON
ap-1167	47	22	can	can	AUX
ap-1167	47	23	do	do	VERB
ap-1167	47	24	so	so	ADV
ap-1167	47	25	by	by	ADP
ap-1167	47	26	exploiting	exploit	VERB
ap-1167	47	27	the	the	DET
ap-1167	47	28	fpu	fpu	NOUN
ap-1167	47	29	.	.	PROPN
ap-1167	47	30	3	3	NUM
ap-1167	47	31	analysis	analysis	NOUN
ap-1167	47	32	many	many	ADJ
ap-1167	47	33	computers	computer	NOUN
ap-1167	47	34	use	use	VERB
ap-1167	47	35	a	a	DET
ap-1167	47	36	processor	processor	NOUN
ap-1167	47	37	with	with	ADP
ap-1167	47	38	intel	intel	PROPN
ap-1167	47	39	x86	x86	NOUN
ap-1167	47	40	architecture	architecture	NOUN
ap-1167	48	1	[	[	X
ap-1167	48	2	4	4	NUM
ap-1167	48	3	]	]	PUNCT
ap-1167	48	4	,	,	PUNCT
ap-1167	48	5	which	which	PRON
ap-1167	48	6	features	feature	VERB
ap-1167	48	7	an	an	DET
ap-1167	48	8	fpu	fpu	NOUN
ap-1167	48	9	with	with	ADP
ap-1167	48	10	8	8	NUM
ap-1167	48	11	double	double	ADJ
ap-1167	48	12	extended	extend	VERB
ap-1167	48	13	precision	precision	NOUN
ap-1167	48	14	floating	float	VERB
ap-1167	48	15	point	point	NOUN
ap-1167	48	16	registers	register	NOUN
ap-1167	48	17	.	.	PUNCT
ap-1167	49	1	once	once	ADV
ap-1167	49	2	a	a	DET
ap-1167	49	3	number	number	NOUN
ap-1167	49	4	is	be	AUX
ap-1167	49	5	loaded	load	VERB
ap-1167	49	6	into	into	ADP
ap-1167	49	7	the	the	DET
ap-1167	49	8	fpu	fpu	NOUN
ap-1167	49	9	,	,	PUNCT
ap-1167	49	10	regardless	regardless	ADV
ap-1167	49	11	of	of	ADP
ap-1167	49	12	its	its	PRON
ap-1167	49	13	precision	precision	NOUN
ap-1167	49	14	,	,	PUNCT
ap-1167	49	15	it	it	PRON
ap-1167	49	16	gets	get	AUX
ap-1167	49	17	automatically	automatically	ADV
ap-1167	49	18	converted	convert	VERB
ap-1167	49	19	into	into	ADP
ap-1167	49	20	the	the	DET
ap-1167	49	21	double	double	ADJ
ap-1167	49	22	extended	extended	ADJ
ap-1167	49	23	precision	precision	NOUN
ap-1167	49	24	format	format	NOUN
ap-1167	49	25	.	.	PUNCT
ap-1167	50	1	further	further	ADJ
ap-1167	50	2	calculations	calculation	NOUN
ap-1167	50	3	are	be	AUX
ap-1167	50	4	performed	perform	VERB
ap-1167	50	5	in	in	ADP
ap-1167	50	6	this	this	DET
ap-1167	50	7	format	format	NOUN
ap-1167	50	8	but	but	CCONJ
ap-1167	50	9	rounded	round	VERB
ap-1167	50	10	to	to	ADP
ap-1167	50	11	a	a	DET
ap-1167	50	12	precision	precision	NOUN
ap-1167	50	13	specified	specify	VERB
ap-1167	50	14	in	in	ADP
ap-1167	50	15	the	the	DET
ap-1167	50	16	floating	float	VERB
ap-1167	50	17	point	point	NOUN
ap-1167	50	18	control	control	NOUN
ap-1167	50	19	word	word	NOUN
ap-1167	50	20	register	register	NOUN
ap-1167	50	21	(	(	PUNCT
ap-1167	50	22	fcw	fcw	PROPN
ap-1167	50	23	)	)	PUNCT
ap-1167	50	24	.	.	PUNCT
ap-1167	51	1	the	the	DET
ap-1167	51	2	default	default	NOUN
ap-1167	51	3	settings	setting	NOUN
ap-1167	51	4	for	for	ADP
ap-1167	51	5	fcw	fcw	NOUN
ap-1167	51	6	specify	specify	VERB
ap-1167	51	7	double	double	ADJ
ap-1167	51	8	extended	extended	ADJ
ap-1167	51	9	precision	precision	NOUN
ap-1167	51	10	,	,	PUNCT
ap-1167	51	11	round	round	ADV
ap-1167	51	12	to	to	ADP
ap-1167	51	13	the	the	DET
ap-1167	51	14	nearest	near	ADJ
ap-1167	51	15	rounding	round	VERB
ap-1167	51	16	mode	mode	NOUN
ap-1167	51	17	and	and	CCONJ
ap-1167	51	18	mask	mask	VERB
ap-1167	51	19	out	out	ADP
ap-1167	51	20	all	all	DET
ap-1167	51	21	floating	float	VERB
ap-1167	51	22	point	point	NOUN
ap-1167	51	23	exceptions	exception	NOUN
ap-1167	51	24	.	.	PUNCT
ap-1167	52	1	if	if	SCONJ
ap-1167	52	2	necessary	necessary	ADJ
ap-1167	52	3	,	,	PUNCT
ap-1167	52	4	they	they	PRON
ap-1167	52	5	can	can	AUX
ap-1167	52	6	be	be	AUX
ap-1167	52	7	changed	change	VERB
ap-1167	52	8	with	with	ADP
ap-1167	52	9	an	an	DET
ap-1167	52	10	fstcw	fstcw	NOUN
ap-1167	52	11	instruction	instruction	NOUN
ap-1167	52	12	.	.	PUNCT
ap-1167	53	1	once	once	SCONJ
ap-1167	53	2	the	the	DET
ap-1167	53	3	result	result	NOUN
ap-1167	53	4	gets	get	AUX
ap-1167	53	5	stored	store	VERB
ap-1167	53	6	back	back	ADV
ap-1167	53	7	into	into	ADP
ap-1167	53	8	a	a	DET
ap-1167	53	9	memory	memory	NOUN
ap-1167	53	10	location	location	NOUN
ap-1167	53	11	,	,	PUNCT
ap-1167	53	12	it	it	PRON
ap-1167	53	13	is	be	AUX
ap-1167	53	14	rounded	rounded	ADJ
ap-1167	53	15	to	to	ADP
ap-1167	53	16	(	(	PUNCT
ap-1167	53	17	or	or	CCONJ
ap-1167	53	18	extended	extend	VERB
ap-1167	53	19	if	if	SCONJ
ap-1167	53	20	fcw	fcw	NOUN
ap-1167	53	21	specified	specify	VERB
ap-1167	53	22	single	single	ADJ
ap-1167	53	23	precision	precision	NOUN
ap-1167	53	24	)	)	PUNCT
ap-1167	53	25	a	a	DET
ap-1167	53	26	defined	define	VERB
ap-1167	53	27	precision	precision	NOUN
ap-1167	53	28	,	,	PUNCT
ap-1167	53	29	depending	depend	VERB
ap-1167	53	30	on	on	ADP
ap-1167	53	31	the	the	DET
ap-1167	53	32	type	type	NOUN
ap-1167	53	33	of	of	ADP
ap-1167	53	34	store	store	NOUN
ap-1167	53	35	instruction	instruction	NOUN
ap-1167	53	36	.	.	PUNCT
ap-1167	54	1	3.1	3.1	NUM
ap-1167	54	2	obtaining	obtain	VERB
ap-1167	54	3	a	a	DET
ap-1167	54	4	tighter	tighter	ADV
ap-1167	54	5	bound	bind	VERB
ap-1167	54	6	from	from	ADP
ap-1167	54	7	the	the	DET
ap-1167	54	8	fpu	fpu	NOUN
ap-1167	54	9	when	when	SCONJ
ap-1167	54	10	rounding	round	VERB
ap-1167	54	11	to	to	ADP
ap-1167	54	12	the	the	DET
ap-1167	54	13	nearest	near	ADJ
ap-1167	54	14	element	element	NOUN
ap-1167	54	15	of	of	ADP
ap-1167	54	16	ft	ft	PROPN
ap-1167	54	17	,	,	PUNCT
ap-1167	54	18	the	the	DET
ap-1167	54	19	relative	relative	ADJ
ap-1167	54	20	error	error	NOUN
ap-1167	54	21	is	be	AUX
ap-1167	54	22	no	no	ADV
ap-1167	54	23	worse	bad	ADJ
ap-1167	54	24	than	than	ADP
ap-1167	54	25	ut	ut	PROPN
ap-1167	54	26	,	,	PUNCT
ap-1167	54	27	and	and	CCONJ
ap-1167	54	28	we	we	PRON
ap-1167	54	29	can	can	AUX
ap-1167	54	30	extract	extract	VERB
ap-1167	54	31	the	the	DET
ap-1167	54	32	static	static	ADJ
ap-1167	54	33	error	error	NOUN
ap-1167	54	34	from	from	ADP
ap-1167	54	35	the	the	DET
ap-1167	54	36	fpu	fpu	NOUN
ap-1167	54	37	by	by	ADP
ap-1167	54	38	subtracting	subtract	VERB
ap-1167	54	39	the	the	DET
ap-1167	54	40	computed	computed	ADJ
ap-1167	54	41	value	value	NOUN
ap-1167	54	42	in	in	ADP
ap-1167	54	43	double	double	ADJ
ap-1167	54	44	extended	extended	ADJ
ap-1167	54	45	precision	precision	NOUN
ap-1167	54	46	from	from	ADP
ap-1167	54	47	its	its	PRON
ap-1167	54	48	rounded	rounded	ADJ
ap-1167	54	49	value	value	NOUN
ap-1167	54	50	.	.	PUNCT
ap-1167	55	1	this	this	DET
ap-1167	55	2	idea	idea	NOUN
ap-1167	55	3	looks	look	VERB
ap-1167	55	4	similar	similar	ADJ
ap-1167	55	5	to	to	ADP
ap-1167	55	6	compensated	compensate	VERB
ap-1167	55	7	summation	summation	NOUN
ap-1167	55	8	[	[	X
ap-1167	55	9	5	5	NUM
ap-1167	55	10	]	]	PUNCT
ap-1167	55	11	,	,	PUNCT
ap-1167	55	12	which	which	PRON
ap-1167	55	13	uses	use	VERB
ap-1167	55	14	an	an	DET
ap-1167	55	15	entirely	entirely	ADV
ap-1167	55	16	software	software	NOUN
ap-1167	55	17	approach	approach	NOUN
ap-1167	55	18	in	in	ADP
ap-1167	55	19	contrast	contrast	NOUN
ap-1167	55	20	to	to	ADP
ap-1167	55	21	our	our	PRON
ap-1167	55	22	paper	paper	NOUN
ap-1167	55	23	.	.	PUNCT
ap-1167	56	1	subtracting	subtract	VERB
ap-1167	56	2	the	the	DET
ap-1167	56	3	values	value	NOUN
ap-1167	56	4	provides	provide	VERB
ap-1167	56	5	an	an	DET
ap-1167	56	6	11	11	NUM
ap-1167	56	7	-	-	PUNCT
ap-1167	56	8	bit	bit	NOUN
ap-1167	56	9	error	error	NOUN
ap-1167	56	10	estimate	estimate	NOUN
ap-1167	56	11	of	of	ADP
ap-1167	56	12	the	the	DET
ap-1167	56	13	real	real	ADJ
ap-1167	56	14	rounding	rounding	NOUN
ap-1167	56	15	error	error	NOUN
ap-1167	56	16	,	,	PUNCT
ap-1167	56	17	which	which	PRON
ap-1167	56	18	is	be	AUX
ap-1167	56	19	no	no	ADV
ap-1167	56	20	greater	great	ADJ
ap-1167	56	21	than	than	ADP
ap-1167	56	22	u.	u.	VERB
ap-1167	56	23	the	the	DET
ap-1167	56	24	entire	entire	ADJ
ap-1167	56	25	idea	idea	NOUN
ap-1167	56	26	can	can	AUX
ap-1167	56	27	be	be	AUX
ap-1167	56	28	written	write	VERB
ap-1167	56	29	as	as	ADP
ap-1167	56	30	:	:	PUNCT
ap-1167	56	31	theorem	theorem	ADJ
ap-1167	56	32	5	5	NUM
ap-1167	56	33	let	let	VERB
ap-1167	56	34	ŝ	ŝ	NOUN
ap-1167	56	35	be	be	AUX
ap-1167	56	36	the	the	DET
ap-1167	56	37	result	result	NOUN
ap-1167	56	38	of	of	ADP
ap-1167	56	39	an	an	DET
ap-1167	56	40	operation	operation	NOUN
ap-1167	56	41	performed	perform	VERB
ap-1167	56	42	in	in	ADP
ap-1167	56	43	double	double	ADJ
ap-1167	56	44	extended	extend	VERB
ap-1167	56	45	precision	precision	NOUN
ap-1167	56	46	and	and	CCONJ
ap-1167	56	47	let	let	VERB
ap-1167	56	48	ŝ	ŝ	NOUN
ap-1167	56	49	be	be	AUX
ap-1167	56	50	the	the	DET
ap-1167	56	51	result	result	NOUN
ap-1167	56	52	in	in	ADP
ap-1167	56	53	double	double	ADJ
ap-1167	56	54	precision	precision	NOUN
ap-1167	56	55	,	,	PUNCT
ap-1167	56	56	which	which	PRON
ap-1167	56	57	we	we	PRON
ap-1167	56	58	obtained	obtain	VERB
ap-1167	56	59	by	by	ADP
ap-1167	56	60	rounding	round	VERB
ap-1167	56	61	ŝ	ŝ	NOUN
ap-1167	56	62	to	to	ADP
ap-1167	56	63	53	53	NUM
ap-1167	56	64	bits	bit	NOUN
ap-1167	56	65	by	by	ADP
ap-1167	56	66	rounding	round	VERB
ap-1167	56	67	to	to	ADP
ap-1167	56	68	the	the	DET
ap-1167	56	69	nearest	near	ADJ
ap-1167	56	70	as	as	SCONJ
ap-1167	56	71	defined	define	VERB
ap-1167	56	72	by	by	ADP
ap-1167	56	73	the	the	DET
ap-1167	56	74	ieee	ieee	NOUN
ap-1167	56	75	754	754	NUM
ap-1167	56	76	standard	standard	NOUN
ap-1167	56	77	.	.	PUNCT
ap-1167	57	1	the	the	DET
ap-1167	57	2	absolute	absolute	ADJ
ap-1167	57	3	rounding	rounding	NOUN
ap-1167	57	4	error	error	NOUN
ap-1167	57	5	for	for	ADP
ap-1167	57	6	an	an	DET
ap-1167	57	7	operation	operation	NOUN
ap-1167	57	8	in	in	ADP
ap-1167	57	9	floating	float	VERB
ap-1167	57	10	point	point	NOUN
ap-1167	57	11	can	can	AUX
ap-1167	57	12	be	be	AUX
ap-1167	57	13	calculated	calculate	VERB
ap-1167	57	14	rather	rather	ADV
ap-1167	57	15	as	as	ADP
ap-1167	57	16	δ	δ	PROPN
ap-1167	57	17	=	=	NOUN
ap-1167	57	18	|ŝ	|ŝ	NOUN
ap-1167	57	19	−	−	NOUN
ap-1167	57	20	ŝ|	ŝ|	PROPN
ap-1167	57	21	,	,	PUNCT
ap-1167	57	22	where	where	SCONJ
ap-1167	57	23	|δ|	|δ|	ADP
ap-1167	57	24	≤	≤	ADJ
ap-1167	57	25	u|ŝ|	u|ŝ|	ADJ
ap-1167	57	26	.	.	PUNCT
ap-1167	58	1	proof	proof	NOUN
ap-1167	58	2	.	.	PUNCT
ap-1167	59	1	we	we	PRON
ap-1167	59	2	can	can	AUX
ap-1167	59	3	extract	extract	VERB
ap-1167	59	4	64	64	NUM
ap-1167	59	5	-	-	PUNCT
ap-1167	59	6	bit	bit	NOUN
ap-1167	59	7	mantissa	mantissa	ADJ
ap-1167	59	8	intermediate	intermediate	ADJ
ap-1167	59	9	results	result	NOUN
ap-1167	59	10	(	(	PUNCT
ap-1167	59	11	ŝ	ŝ	NOUN
ap-1167	59	12	)	)	PUNCT
ap-1167	59	13	from	from	ADP
ap-1167	59	14	the	the	DET
ap-1167	59	15	fpu	fpu	NOUN
ap-1167	59	16	before	before	SCONJ
ap-1167	59	17	they	they	PRON
ap-1167	59	18	get	get	VERB
ap-1167	59	19	rounded	rounded	ADJ
ap-1167	59	20	to	to	ADP
ap-1167	59	21	53	53	NUM
ap-1167	59	22	bits	bit	NOUN
ap-1167	59	23	(	(	PUNCT
ap-1167	59	24	ŝ	ŝ	NOUN
ap-1167	59	25	)	)	PUNCT
ap-1167	59	26	,	,	PUNCT
ap-1167	59	27	and	and	CCONJ
ap-1167	59	28	calculate	calculate	VERB
ap-1167	59	29	δ	δ	PROPN
ap-1167	59	30	=	=	SYM
ap-1167	59	31	|ŝ−	|ŝ−	X
ap-1167	59	32	ŝ|	ŝ|	PROPN
ap-1167	59	33	.	.	PUNCT
ap-1167	60	1	the	the	DET
ap-1167	60	2	quantity	quantity	NOUN
ap-1167	60	3	ŝ	ŝ	VERB
ap-1167	60	4	is	be	AUX
ap-1167	60	5	rounded	round	VERB
ap-1167	60	6	either	either	CCONJ
ap-1167	60	7	down	down	ADV
ap-1167	60	8	to	to	ADP
ap-1167	60	9	f1	f1	PROPN
ap-1167	60	10	∈	∈	PROPN
ap-1167	60	11	f53	f53	NOUN
ap-1167	60	12	or	or	CCONJ
ap-1167	60	13	up	up	ADP
ap-1167	60	14	to	to	ADP
ap-1167	60	15	f2	f2	PROPN
ap-1167	60	16	∈	∈	PROPN
ap-1167	60	17	f53	f53	NOUN
ap-1167	60	18	,	,	PUNCT
ap-1167	60	19	where	where	SCONJ
ap-1167	60	20	f1	f1	NOUN
ap-1167	60	21	,	,	PUNCT
ap-1167	60	22	f2	f2	PROPN
ap-1167	60	23	=	=	SYM
ap-1167	60	24	{	{	PUNCT
ap-1167	60	25	f1	f1	NOUN
ap-1167	60	26	,	,	PUNCT
ap-1167	60	27	f2	f2	PROPN
ap-1167	60	28	∈	∈	PROPN
ap-1167	60	29	f53	f53	NOUN
ap-1167	60	30	:	:	PUNCT
ap-1167	60	31	|f2	|f2	ADP
ap-1167	60	32	−	−	PROPN
ap-1167	60	33	f1|/|f1|	f1|/|f1|	NOUN
ap-1167	60	34	=	=	PUNCT
ap-1167	60	35	2u	2u	PROPN
ap-1167	60	36	}	}	PUNCT
ap-1167	60	37	,	,	PUNCT
ap-1167	60	38	ŝ	ŝ	X
ap-1167	60	39	∈	∈	PROPN
ap-1167	60	40	f64	f64	PROPN
ap-1167	60	41	∧	∧	PROPN
ap-1167	60	42	ŝ	ŝ	NUM
ap-1167	60	43	∈	∈	PROPN
ap-1167	60	44	[	[	X
ap-1167	60	45	f1	f1	NOUN
ap-1167	60	46	,	,	PUNCT
ap-1167	60	47	f2	f2	PROPN
ap-1167	60	48	]	]	PUNCT
ap-1167	60	49	,	,	PUNCT
ap-1167	60	50	ŝ	ŝ	X
ap-1167	60	51	=	=	SYM
ap-1167	60	52	round	round	PROPN
ap-1167	60	53	64→53	64→53	PROPN
ap-1167	60	54	(	(	PUNCT
ap-1167	60	55	ŝ	ŝ	PROPN
ap-1167	60	56	)	)	PUNCT
ap-1167	60	57	⇒	⇒	NOUN
ap-1167	60	58	ŝ	ŝ	ADP
ap-1167	60	59	∈	∈	PROPN
ap-1167	60	60	{	{	PUNCT
ap-1167	60	61	f1	f1	NOUN
ap-1167	60	62	,	,	PUNCT
ap-1167	60	63	f2	f2	PROPN
ap-1167	60	64	}	}	PUNCT
ap-1167	60	65	,	,	PUNCT
ap-1167	60	66	where	where	SCONJ
ap-1167	60	67	ŝ	ŝ	ADV
ap-1167	60	68	=	=	SYM
ap-1167	60	69	round	round	PROPN
ap-1167	60	70	64→53	64→53	PROPN
ap-1167	60	71	(	(	PUNCT
ap-1167	60	72	ŝ	ŝ	PROPN
ap-1167	60	73	)	)	PUNCT
ap-1167	60	74	=	=	SYM
ap-1167	60	75	⎧⎪⎪⎨⎪⎪⎩	⎧⎪⎪⎨⎪⎪⎩	PROPN
ap-1167	60	76	f2	f2	INTJ
ap-1167	60	77	if	if	SCONJ
ap-1167	60	78	|ŝ	|ŝ	NOUN
ap-1167	60	79	−	−	PROPN
ap-1167	60	80	f1|/|f1|	f1|/|f1|	NOUN
ap-1167	60	81	>	>	X
ap-1167	60	82	u	u	NOUN
ap-1167	60	83	f1	f1	NOUN
ap-1167	60	84	or	or	CCONJ
ap-1167	60	85	f2	f2	PROPN
ap-1167	60	86	1	1	NUM
ap-1167	60	87	if	if	SCONJ
ap-1167	60	88	|ŝ	|ŝ	NOUN
ap-1167	60	89	−	−	NOUN
ap-1167	60	90	f1|/|f1|	f1|/|f1|	NOUN
ap-1167	60	91	=	=	SYM
ap-1167	60	92	u	u	NOUN
ap-1167	60	93	f1	f1	NOUN
ap-1167	60	94	if	if	SCONJ
ap-1167	60	95	|ŝ	|ŝ	NOUN
ap-1167	60	96	−	−	NUM
ap-1167	60	97	f1|/|f1|	f1|/|f1|	NOUN
ap-1167	60	98	<	<	X
ap-1167	60	99	u	u	X
ap-1167	60	100	.	.	PUNCT
ap-1167	61	1	(	(	PUNCT
ap-1167	61	2	4	4	X
ap-1167	61	3	)	)	PUNCT
ap-1167	61	4	the	the	DET
ap-1167	61	5	following	follow	VERB
ap-1167	61	6	figure	figure	NOUN
ap-1167	61	7	shows	show	VERB
ap-1167	61	8	the	the	DET
ap-1167	61	9	principle	principle	NOUN
ap-1167	61	10	:	:	PUNCT
ap-1167	61	11	f1	f1	PROPN
ap-1167	61	12	f2	f2	PROPN
ap-1167	61	13	�	�	PROPN
ap-1167	61	14	�	�	PROPN
ap-1167	61	15	2u	2u	PROPN
ap-1167	61	16	�	�	PROPN
ap-1167	61	17	�	�	PROPN
ap-1167	61	18	round	round	VERB
ap-1167	61	19	down	down	ADP
ap-1167	61	20	�	�	PROPN
ap-1167	61	21	�	�	PROPN
ap-1167	61	22	�	�	PROPN
ap-1167	61	23	tie	tie	NOUN
ap-1167	61	24	(	(	PUNCT
ap-1167	61	25	round	round	NOUN
ap-1167	61	26	to	to	ADP
ap-1167	61	27	even	even	ADV
ap-1167	61	28	)	)	PUNCT
ap-1167	61	29	�	�	PROPN
ap-1167	61	30	�	�	PROPN
ap-1167	61	31	round	round	VERB
ap-1167	61	32	up	up	ADP
ap-1167	61	33	fig	fig	NOUN
ap-1167	61	34	.	.	PUNCT
ap-1167	62	1	1	1	NUM
ap-1167	62	2	:	:	PUNCT
ap-1167	62	3	rounding	round	VERB
ap-1167	62	4	a	a	DET
ap-1167	62	5	double	double	ADJ
ap-1167	62	6	extended	extend	VERB
ap-1167	62	7	precision	precision	NOUN
ap-1167	62	8	number	number	NOUN
ap-1167	62	9	to	to	ADP
ap-1167	62	10	double	double	ADJ
ap-1167	62	11	precision	precision	NOUN
ap-1167	62	12	.	.	PUNCT
ap-1167	63	1	in	in	ADP
ap-1167	63	2	all	all	DET
ap-1167	63	3	cases	case	NOUN
ap-1167	63	4	,	,	PUNCT
ap-1167	63	5	the	the	DET
ap-1167	63	6	relative	relative	ADJ
ap-1167	63	7	error	error	NOUN
ap-1167	63	8	can	can	AUX
ap-1167	63	9	be	be	AUX
ap-1167	63	10	computed	compute	VERB
ap-1167	63	11	in	in	ADP
ap-1167	63	12	the	the	DET
ap-1167	63	13	same	same	ADJ
ap-1167	63	14	way	way	NOUN
ap-1167	63	15	as	as	ADP
ap-1167	63	16	|ŝ−	|ŝ−	NOUN
ap-1167	63	17	ŝ|/|ŝ|	ŝ|/|ŝ|	VERB
ap-1167	63	18	≤	≤	NUM
ap-1167	63	19	u	u	NOUN
ap-1167	63	20	and	and	CCONJ
ap-1167	63	21	is	be	AUX
ap-1167	63	22	always	always	ADV
ap-1167	63	23	bounded	bound	VERB
ap-1167	63	24	by	by	ADP
ap-1167	63	25	u.	u.	PROPN
ap-1167	63	26	�	�	PROPN
ap-1167	63	27	1rounding	1rounding	PROPN
ap-1167	63	28	to	to	PART
ap-1167	63	29	even	even	ADV
ap-1167	63	30	as	as	ADP
ap-1167	63	31	in	in	ADP
ap-1167	63	32	[	[	X
ap-1167	63	33	3	3	NUM
ap-1167	63	34	]	]	PUNCT
ap-1167	63	35	applies	apply	VERB
ap-1167	63	36	here	here	ADV
ap-1167	63	37	.	.	PUNCT
ap-1167	64	1	31	31	NUM
ap-1167	64	2	acta	acta	PROPN
ap-1167	64	3	polytechnica	polytechnica	PROPN
ap-1167	64	4	vol	vol	NOUN
ap-1167	64	5	.	.	PROPN
ap-1167	65	1	50	50	NUM
ap-1167	65	2	no	no	NOUN
ap-1167	65	3	.	.	PUNCT
ap-1167	66	1	2/2010	2/2010	PRON
ap-1167	66	2	note	note	NOUN
ap-1167	66	3	1	1	NUM
ap-1167	66	4	theorem	theorem	NOUN
ap-1167	66	5	5	5	NUM
ap-1167	66	6	is	be	AUX
ap-1167	66	7	proved	prove	VERB
ap-1167	66	8	for	for	ADP
ap-1167	66	9	positive	positive	ADJ
ap-1167	66	10	numbers	number	NOUN
ap-1167	66	11	,	,	PUNCT
ap-1167	66	12	but	but	CCONJ
ap-1167	66	13	it	it	PRON
ap-1167	66	14	can	can	AUX
ap-1167	66	15	be	be	AUX
ap-1167	66	16	proved	prove	VERB
ap-1167	66	17	for	for	ADP
ap-1167	66	18	negatives	negative	NOUN
ap-1167	66	19	too	too	ADV
ap-1167	66	20	.	.	PUNCT
ap-1167	67	1	corollary	corollary	ADJ
ap-1167	67	2	6	6	NUM
ap-1167	67	3	the	the	DET
ap-1167	67	4	expression	expression	NOUN
ap-1167	67	5	δ	δ	NOUN
ap-1167	67	6	=	=	PUNCT
ap-1167	67	7	|ŝ	|ŝ	NOUN
ap-1167	67	8	−	−	PROPN
ap-1167	67	9	ŝ|	ŝ|	PROPN
ap-1167	67	10	≤	≤	PRON
ap-1167	67	11	u|ŝ|	u|ŝ|	AUX
ap-1167	67	12	provides	provide	VERB
ap-1167	67	13	an	an	DET
ap-1167	67	14	11	11	NUM
ap-1167	67	15	-	-	PUNCT
ap-1167	67	16	bit	bit	NOUN
ap-1167	67	17	estimate	estimate	NOUN
ap-1167	67	18	of	of	ADP
ap-1167	67	19	the	the	DET
ap-1167	67	20	static	static	ADJ
ap-1167	67	21	rounding	rounding	NOUN
ap-1167	67	22	error	error	NOUN
ap-1167	67	23	and	and	CCONJ
ap-1167	67	24	since	since	SCONJ
ap-1167	67	25	|δ|	|δ|	VERB
ap-1167	67	26	≤	≤	NUM
ap-1167	67	27	u|ŝ|	u|ŝ|	NUM
ap-1167	67	28	,	,	PUNCT
ap-1167	67	29	it	it	PRON
ap-1167	67	30	can	can	AUX
ap-1167	67	31	be	be	AUX
ap-1167	67	32	safely	safely	ADV
ap-1167	67	33	substituted	substitute	VERB
ap-1167	67	34	for	for	ADP
ap-1167	67	35	all	all	DET
ap-1167	67	36	occurrences	occurrence	NOUN
ap-1167	67	37	of	of	ADP
ap-1167	67	38	u|ŝ|	u|ŝ|	NOUN
ap-1167	67	39	in	in	ADP
ap-1167	67	40	tab	tab	NOUN
ap-1167	67	41	.	.	PUNCT
ap-1167	67	42	1	1	NUM
ap-1167	67	43	,	,	PUNCT
ap-1167	67	44	providing	provide	VERB
ap-1167	67	45	a	a	DET
ap-1167	67	46	tighter	tight	ADJ
ap-1167	67	47	error	error	NOUN
ap-1167	67	48	bound	bind	VERB
ap-1167	67	49	.	.	PUNCT
ap-1167	68	1	3.2	3.2	NUM
ap-1167	68	2	implementation	implementation	NOUN
ap-1167	68	3	highlights	highlight	NOUN
ap-1167	68	4	our	our	PRON
ap-1167	68	5	approach	approach	NOUN
ap-1167	68	6	is	be	AUX
ap-1167	68	7	implemented	implement	VERB
ap-1167	68	8	in	in	ADP
ap-1167	68	9	c++	c++	NOUN
ap-1167	68	10	language	language	NOUN
ap-1167	68	11	as	as	ADP
ap-1167	68	12	a	a	DET
ap-1167	68	13	class	class	NOUN
ap-1167	68	14	fdouble	fdouble	ADJ
ap-1167	68	15	with	with	ADP
ap-1167	68	16	gcc	gcc	NOUN
ap-1167	68	17	at&t	at&t	PROPN
ap-1167	68	18	inline	inline	PROPN
ap-1167	68	19	assembly	assembly	PROPN
ap-1167	68	20	language	language	PROPN
ap-1167	68	21	fpu	fpu	PROPN
ap-1167	68	22	statements	statement	NOUN
ap-1167	68	23	[	[	X
ap-1167	68	24	9	9	NUM
ap-1167	68	25	]	]	PUNCT
ap-1167	68	26	.	.	PUNCT
ap-1167	69	1	the	the	DET
ap-1167	69	2	fdouble	fdouble	ADJ
ap-1167	69	3	class	class	NOUN
ap-1167	69	4	overloads	overload	VERB
ap-1167	69	5	most	most	ADJ
ap-1167	69	6	operators	operator	NOUN
ap-1167	69	7	and	and	CCONJ
ap-1167	69	8	some	some	DET
ap-1167	69	9	standard	standard	ADJ
ap-1167	69	10	functions2	functions2	NOUN
ap-1167	69	11	which	which	PRON
ap-1167	69	12	are	be	AUX
ap-1167	69	13	beyond	beyond	ADP
ap-1167	69	14	the	the	DET
ap-1167	69	15	scope	scope	NOUN
ap-1167	69	16	of	of	ADP
ap-1167	69	17	this	this	DET
ap-1167	69	18	paper	paper	NOUN
ap-1167	69	19	,	,	PUNCT
ap-1167	69	20	providing	provide	VERB
ap-1167	69	21	a	a	DET
ap-1167	69	22	handy	handy	ADJ
ap-1167	69	23	replacement	replacement	NOUN
ap-1167	69	24	for	for	ADP
ap-1167	69	25	the	the	DET
ap-1167	69	26	double	double	ADJ
ap-1167	69	27	data	data	NOUN
ap-1167	69	28	type	type	NOUN
ap-1167	69	29	.	.	PUNCT
ap-1167	70	1	the	the	DET
ap-1167	70	2	transition	transition	NOUN
ap-1167	70	3	from	from	ADP
ap-1167	70	4	double	double	ADJ
ap-1167	70	5	data	datum	NOUN
ap-1167	70	6	type	type	NOUN
ap-1167	70	7	to	to	ADP
ap-1167	70	8	fdouble	fdouble	ADJ
ap-1167	70	9	is	be	AUX
ap-1167	70	10	performed	perform	VERB
ap-1167	70	11	just	just	ADV
ap-1167	70	12	by	by	ADP
ap-1167	70	13	changing	change	VERB
ap-1167	70	14	the	the	DET
ap-1167	70	15	name	name	NOUN
ap-1167	70	16	of	of	ADP
ap-1167	70	17	the	the	DET
ap-1167	70	18	data	data	NOUN
ap-1167	70	19	type	type	NOUN
ap-1167	70	20	.	.	PUNCT
ap-1167	71	1	the	the	DET
ap-1167	71	2	rest	rest	NOUN
ap-1167	71	3	is	be	AUX
ap-1167	71	4	handled	handle	VERB
ap-1167	71	5	by	by	ADP
ap-1167	71	6	the	the	DET
ap-1167	71	7	class	class	NOUN
ap-1167	71	8	.	.	PUNCT
ap-1167	72	1	for	for	ADP
ap-1167	72	2	an	an	DET
ap-1167	72	3	illustration	illustration	NOUN
ap-1167	72	4	of	of	ADP
ap-1167	72	5	how	how	SCONJ
ap-1167	72	6	the	the	DET
ap-1167	72	7	class	class	NOUN
ap-1167	72	8	works	work	VERB
ap-1167	72	9	,	,	PUNCT
ap-1167	72	10	the	the	DET
ap-1167	72	11	source	source	NOUN
ap-1167	72	12	of	of	ADP
ap-1167	72	13	a	a	DET
ap-1167	72	14	plus	plus	NOUN
ap-1167	72	15	operator	operator	NOUN
ap-1167	72	16	fdouble::operator+	fdouble::operator+	NOUN
ap-1167	72	17	and	and	CCONJ
ap-1167	72	18	its	its	PRON
ap-1167	72	19	assembly	assembly	NOUN
ap-1167	72	20	portion	portion	NOUN
ap-1167	72	21	op_plus	op_plus	ADV
ap-1167	72	22	performing	perform	VERB
ap-1167	72	23	the	the	DET
ap-1167	72	24	fpu	fpu	NOUN
ap-1167	72	25	-	-	PUNCT
ap-1167	72	26	supported	support	VERB
ap-1167	72	27	running	running	NOUN
ap-1167	72	28	error	error	NOUN
ap-1167	72	29	analysis	analysis	NOUN
ap-1167	72	30	with	with	ADP
ap-1167	72	31	the	the	DET
ap-1167	72	32	terms	term	NOUN
ap-1167	72	33	above	above	ADV
ap-1167	72	34	follows	follow	VERB
ap-1167	72	35	:	:	PUNCT
ap-1167	72	36	fdouble	fdouble	ADJ
ap-1167	72	37	fdouble::operator+(fdouble	fdouble::operator+(fdouble	ADJ
ap-1167	72	38	const	const	PROPN
ap-1167	72	39	&	&	CCONJ
ap-1167	72	40	b	b	NOUN
ap-1167	72	41	)	)	PUNCT
ap-1167	72	42	const	const	NOUN
ap-1167	72	43	{	{	PUNCT
ap-1167	72	44	fdouble	fdouble	ADJ
ap-1167	72	45	r	r	NOUN
ap-1167	72	46	;	;	PUNCT
ap-1167	72	47	op_plus	op_plus	X
ap-1167	72	48	(	(	PUNCT
ap-1167	72	49	r.d	r.d	PROPN
ap-1167	72	50	,	,	PUNCT
ap-1167	72	51	r.e	r.e	PROPN
ap-1167	72	52	,	,	PUNCT
ap-1167	72	53	this->d	this->d	PROPN
ap-1167	72	54	,	,	PUNCT
ap-1167	72	55	this->e	this->e	PROPN
ap-1167	72	56	,	,	PUNCT
ap-1167	72	57	b.d	b.d	PROPN
ap-1167	72	58	,	,	PUNCT
ap-1167	72	59	b.e	b.e	PROPN
ap-1167	72	60	)	)	PUNCT
ap-1167	72	61	;	;	PUNCT
ap-1167	72	62	return	return	VERB
ap-1167	72	63	r	r	NOUN
ap-1167	72	64	;	;	PUNCT
ap-1167	72	65	}	}	PUNCT
ap-1167	72	66	the	the	DET
ap-1167	72	67	fdouble::operator+	fdouble::operator+	NUM
ap-1167	72	68	method	method	NOUN
ap-1167	72	69	calls	call	VERB
ap-1167	72	70	the	the	DET
ap-1167	72	71	op_plus	op_plus	ADJ
ap-1167	72	72	function	function	NOUN
ap-1167	72	73	which	which	PRON
ap-1167	72	74	contains	contain	VERB
ap-1167	72	75	the	the	DET
ap-1167	72	76	assembly	assembly	NOUN
ap-1167	72	77	inline	inline	NOUN
ap-1167	72	78	and	and	CCONJ
ap-1167	72	79	is	be	AUX
ap-1167	72	80	common	common	ADJ
ap-1167	72	81	for	for	SCONJ
ap-1167	72	82	all	all	DET
ap-1167	72	83	other	other	ADJ
ap-1167	72	84	fdouble::operator+	fdouble::operator+	NOUN
ap-1167	72	85	overloads	overload	NOUN
ap-1167	72	86	:	:	PUNCT
ap-1167	72	87	inline	inline	VERB
ap-1167	72	88	void	void	ADJ
ap-1167	72	89	op_plus	op_plus	ADJ
ap-1167	72	90	(	(	PUNCT
ap-1167	72	91	double	double	ADJ
ap-1167	72	92	&	&	CCONJ
ap-1167	72	93	result	result	PROPN
ap-1167	72	94	,	,	PUNCT
ap-1167	72	95	double	double	PROPN
ap-1167	72	96	&	&	CCONJ
ap-1167	72	97	result_err	result_err	NOUN
ap-1167	72	98	,	,	PUNCT
ap-1167	72	99	register	register	VERB
ap-1167	72	100	const	const	NOUN
ap-1167	72	101	double	double	DET
ap-1167	72	102	a	a	PRON
ap-1167	72	103	,	,	PUNCT
ap-1167	72	104	register	register	VERB
ap-1167	72	105	const	const	ADJ
ap-1167	72	106	double	double	PROPN
ap-1167	72	107	a_err	a_err	PROPN
ap-1167	72	108	,	,	PUNCT
ap-1167	72	109	register	register	VERB
ap-1167	72	110	const	const	ADJ
ap-1167	72	111	double	double	PROPN
ap-1167	72	112	b	b	NOUN
ap-1167	72	113	,	,	PUNCT
ap-1167	72	114	register	register	VERB
ap-1167	72	115	const	const	NOUN
ap-1167	72	116	double	double	PROPN
ap-1167	72	117	b_err	b_err	NOUN
ap-1167	72	118	)	)	PUNCT
ap-1167	72	119	{	{	PUNCT
ap-1167	73	1	_	_	PUNCT
ap-1167	73	2	_	_	PUNCT
ap-1167	73	3	asm	asm	NOUN
ap-1167	74	1	_	_	PUNCT
ap-1167	74	2	_	_	PUNCT
ap-1167	75	1	_	_	PUNCT
ap-1167	76	1	_	_	PUNCT
ap-1167	77	1	volatile	volatile	ADJ
ap-1167	77	2	_	_	PUNCT
ap-1167	78	1	_	_	PUNCT
ap-1167	78	2	(	(	PUNCT
ap-1167	78	3	"	"	PUNCT
ap-1167	78	4	fldl	fldl	ADJ
ap-1167	78	5	%	%	NOUN
ap-1167	78	6	1\n\t	1\n\t	PUNCT
ap-1167	78	7	"	"	PUNCT
ap-1167	78	8	//	//	NUM
ap-1167	78	9	1	1	NUM
ap-1167	78	10	.	.	PUNCT
ap-1167	78	11	load	load	PROPN
ap-1167	78	12	b	b	PROPN
ap-1167	78	13	"	"	PUNCT
ap-1167	78	14	fldl	fldl	ADJ
ap-1167	78	15	%	%	NOUN
ap-1167	78	16	2\n\t	2\n\t	NOUN
ap-1167	78	17	"	"	PUNCT
ap-1167	78	18	//	//	NUM
ap-1167	78	19	2	2	NUM
ap-1167	78	20	.	.	X
ap-1167	78	21	load	load	VERB
ap-1167	78	22	a	a	DET
ap-1167	78	23	"	"	PUNCT
ap-1167	78	24	faddp\n\t	faddp\n\t	PROPN
ap-1167	78	25	"	"	PUNCT
ap-1167	78	26	//	//	NUM
ap-1167	78	27	3	3	NUM
ap-1167	78	28	.	.	PUNCT
ap-1167	78	29	calc	calc	PROPN
ap-1167	78	30	a+b	a+b	PART
ap-1167	78	31	"	"	PUNCT
ap-1167	78	32	fstl	fstl	ADJ
ap-1167	78	33	%	%	NOUN
ap-1167	78	34	3\n\t	3\n\t	NOUN
ap-1167	78	35	"	"	PUNCT
ap-1167	78	36	//	//	NUM
ap-1167	78	37	4	4	NUM
ap-1167	78	38	.	.	X
ap-1167	78	39	store	store	NOUN
ap-1167	78	40	rounded	rounded	ADJ
ap-1167	78	41	result	result	NOUN
ap-1167	78	42	"	"	PUNCT
ap-1167	78	43	fldl	fldl	ADJ
ap-1167	78	44	%	%	NOUN
ap-1167	78	45	3\n\t	3\n\t	NOUN
ap-1167	78	46	"	"	PUNCT
ap-1167	78	47	//	//	NUM
ap-1167	78	48	5	5	NUM
ap-1167	78	49	.	.	PUNCT
ap-1167	78	50	load	load	NOUN
ap-1167	78	51	rounded	rounded	ADJ
ap-1167	78	52	result	result	NOUN
ap-1167	78	53	"	"	PUNCT
ap-1167	78	54	fsubp\n\t	fsubp\n\t	PROPN
ap-1167	78	55	"	"	PUNCT
ap-1167	78	56	//	//	NUM
ap-1167	78	57	6	6	NUM
ap-1167	78	58	.	.	PUNCT
ap-1167	78	59	calc	calc	NOUN
ap-1167	78	60	difference	difference	NOUN
ap-1167	78	61	"	"	PUNCT
ap-1167	78	62	fabs\n\t	fabs\n\t	PROPN
ap-1167	78	63	"	"	PUNCT
ap-1167	78	64	//	//	NUM
ap-1167	78	65	7	7	NUM
ap-1167	78	66	.	.	PUNCT
ap-1167	78	67	calc	calc	VERB
ap-1167	78	68	its	its	PRON
ap-1167	78	69	absolute	absolute	ADJ
ap-1167	78	70	value	value	NOUN
ap-1167	78	71	"	"	PUNCT
ap-1167	78	72	fldl	fldl	ADJ
ap-1167	78	73	%	%	NOUN
ap-1167	78	74	4\n\t	4\n\t	PUNCT
ap-1167	78	75	"	"	PUNCT
ap-1167	78	76	//	//	NUM
ap-1167	78	77	8	8	NUM
ap-1167	78	78	.	.	PUNCT
ap-1167	79	1	load	load	NOUN
ap-1167	79	2	a_err	a_err	PRON
ap-1167	79	3	"	"	PUNCT
ap-1167	79	4	faddp\n\t	faddp\n\t	PROPN
ap-1167	79	5	"	"	PUNCT
ap-1167	79	6	//	//	NUM
ap-1167	79	7	9	9	NUM
ap-1167	79	8	.	.	PUNCT
ap-1167	79	9	calc	calc	NOUN
ap-1167	79	10	diff	diff	PROPN
ap-1167	79	11	+	+	CCONJ
ap-1167	79	12	a_err	a_err	PRON
ap-1167	79	13	"	"	PUNCT
ap-1167	79	14	fldl	fldl	ADJ
ap-1167	79	15	%	%	NOUN
ap-1167	79	16	5\n\t	5\n\t	NUM
ap-1167	79	17	"	"	PUNCT
ap-1167	79	18	//	//	NUM
ap-1167	79	19	10	10	NUM
ap-1167	79	20	.	.	PUNCT
ap-1167	80	1	load	load	NOUN
ap-1167	80	2	b_err	b_err	ADP
ap-1167	80	3	"	"	PUNCT
ap-1167	80	4	faddp	faddp	NOUN
ap-1167	80	5	"	"	PUNCT
ap-1167	80	6	//	//	NUM
ap-1167	80	7	11	11	NUM
ap-1167	80	8	.	.	PUNCT
ap-1167	81	1	calc	calc	NOUN
ap-1167	81	2	diff	diff	PROPN
ap-1167	81	3	+	+	CCONJ
ap-1167	81	4	a_err	a_err	ADP
ap-1167	81	5	+	+	ADV
ap-1167	81	6	b_err	b_err	NOUN
ap-1167	81	7	:	:	PUNCT
ap-1167	81	8	"	"	PUNCT
ap-1167	81	9	=	=	SYM
ap-1167	81	10	t"(result_err	t"(result_err	NOUN
ap-1167	81	11	)	)	PUNCT
ap-1167	81	12	//	//	NOUN
ap-1167	81	13	12	12	NUM
ap-1167	81	14	.	.	PUNCT
ap-1167	82	1	put	put	VERB
ap-1167	82	2	result	result	NOUN
ap-1167	82	3	in	in	ADP
ap-1167	82	4	result_err	result_err	PRON
ap-1167	82	5	:	:	PUNCT
ap-1167	82	6	"	"	PUNCT
ap-1167	82	7	m"(b	m"(b	ADJ
ap-1167	82	8	)	)	PUNCT
ap-1167	82	9	,	,	PUNCT
ap-1167	82	10	//	//	NUM
ap-1167	82	11	13	13	NUM
ap-1167	82	12	.	.	PUNCT
ap-1167	83	1	%	%	INTJ
ap-1167	84	1	1	1	NUM
ap-1167	84	2	=	=	SYM
ap-1167	84	3	b	b	ADJ
ap-1167	84	4	"	"	PUNCT
ap-1167	84	5	m"(a	m"(a	NOUN
ap-1167	84	6	)	)	PUNCT
ap-1167	84	7	,	,	PUNCT
ap-1167	84	8	//	//	NUM
ap-1167	84	9	14	14	NUM
ap-1167	84	10	.	.	PUNCT
ap-1167	85	1	%	%	INTJ
ap-1167	85	2	2	2	NUM
ap-1167	85	3	=	=	NOUN
ap-1167	86	1	a	a	DET
ap-1167	86	2	"	"	PUNCT
ap-1167	86	3	m"(result	m"(result	NOUN
ap-1167	86	4	)	)	PUNCT
ap-1167	86	5	,	,	PUNCT
ap-1167	86	6	//	//	X
ap-1167	86	7	15	15	NUM
ap-1167	86	8	.	.	PUNCT
ap-1167	87	1	%	%	INTJ
ap-1167	87	2	3	3	NUM
ap-1167	87	3	=	=	NOUN
ap-1167	87	4	result	result	NOUN
ap-1167	87	5	"	"	PUNCT
ap-1167	87	6	m"(a_err	m"(a_err	NUM
ap-1167	87	7	)	)	PUNCT
ap-1167	87	8	,	,	PUNCT
ap-1167	87	9	//	//	NUM
ap-1167	87	10	16	16	NUM
ap-1167	87	11	.	.	PUNCT
ap-1167	88	1	%	%	INTJ
ap-1167	89	1	4	4	NUM
ap-1167	89	2	=	=	NOUN
ap-1167	89	3	a_err	a_err	ADP
ap-1167	89	4	"	"	PUNCT
ap-1167	89	5	m"(b_err	m"(b_err	NOUN
ap-1167	89	6	)	)	PUNCT
ap-1167	89	7	//	//	NUM
ap-1167	89	8	17	17	NUM
ap-1167	89	9	.	.	PUNCT
ap-1167	90	1	%	%	INTJ
ap-1167	90	2	5	5	NUM
ap-1167	90	3	=	=	SYM
ap-1167	90	4	b_err	b_err	NOUN
ap-1167	90	5	)	)	PUNCT
ap-1167	90	6	;	;	PUNCT
ap-1167	90	7	}	}	PUNCT
ap-1167	90	8	2currently	2currently	ADV
ap-1167	90	9	only	only	ADV
ap-1167	90	10	logarithm	logarithm	NOUN
ap-1167	90	11	,	,	PUNCT
ap-1167	90	12	power	power	NOUN
ap-1167	90	13	and	and	CCONJ
ap-1167	90	14	exponential	exponential	ADJ
ap-1167	90	15	function	function	NOUN
ap-1167	90	16	,	,	PUNCT
ap-1167	90	17	absolute	absolute	ADJ
ap-1167	90	18	value	value	NOUN
ap-1167	90	19	,	,	PUNCT
ap-1167	90	20	remainder	remainder	NOUN
ap-1167	90	21	and	and	CCONJ
ap-1167	90	22	the	the	DET
ap-1167	90	23	square	square	ADJ
ap-1167	90	24	root	root	NOUN
ap-1167	90	25	are	be	AUX
ap-1167	90	26	available	available	ADJ
ap-1167	90	27	.	.	PUNCT
ap-1167	91	1	32	32	NUM
ap-1167	91	2	acta	acta	PROPN
ap-1167	91	3	polytechnica	polytechnica	PROPN
ap-1167	91	4	vol	vol	NOUN
ap-1167	91	5	.	.	PROPN
ap-1167	92	1	50	50	NUM
ap-1167	92	2	no	no	NOUN
ap-1167	92	3	.	.	PUNCT
ap-1167	93	1	2/2010	2/2010	NUM
ap-1167	93	2	the	the	DET
ap-1167	93	3	op_plus	op_plus	ADJ
ap-1167	93	4	first	first	ADJ
ap-1167	93	5	loads	load	NOUN
ap-1167	93	6	both	both	DET
ap-1167	93	7	double	double	ADJ
ap-1167	93	8	precision	precision	NOUN
ap-1167	93	9	a	a	PRON
ap-1167	93	10	and	and	CCONJ
ap-1167	93	11	b	b	NOUN
ap-1167	93	12	(	(	PUNCT
ap-1167	93	13	lines	line	NOUN
ap-1167	93	14	1	1	NUM
ap-1167	93	15	and	and	CCONJ
ap-1167	93	16	2	2	NUM
ap-1167	93	17	)	)	PUNCT
ap-1167	93	18	on	on	ADP
ap-1167	93	19	the	the	DET
ap-1167	93	20	floating	float	VERB
ap-1167	93	21	point	point	NOUN
ap-1167	93	22	stack	stack	NOUN
ap-1167	93	23	and	and	CCONJ
ap-1167	93	24	the	the	DET
ap-1167	93	25	fpu	fpu	NOUN
ap-1167	93	26	extends	extend	VERB
ap-1167	93	27	them	they	PRON
ap-1167	93	28	to	to	ADP
ap-1167	93	29	the	the	DET
ap-1167	93	30	double	double	ADJ
ap-1167	93	31	extended	extended	ADJ
ap-1167	93	32	precision	precision	NOUN
ap-1167	93	33	.	.	PUNCT
ap-1167	94	1	the	the	DET
ap-1167	94	2	sum	sum	NOUN
ap-1167	94	3	is	be	AUX
ap-1167	94	4	then	then	ADV
ap-1167	94	5	calculated	calculate	VERB
ap-1167	94	6	(	(	PUNCT
ap-1167	94	7	line	line	NOUN
ap-1167	94	8	3	3	NUM
ap-1167	94	9	)	)	PUNCT
ap-1167	94	10	popping	pop	VERB
ap-1167	94	11	a	a	PRON
ap-1167	94	12	from	from	ADP
ap-1167	94	13	the	the	DET
ap-1167	94	14	fpu	fpu	NOUN
ap-1167	94	15	stack	stack	NOUN
ap-1167	94	16	and	and	CCONJ
ap-1167	94	17	replacing	replace	VERB
ap-1167	94	18	b	b	NOUN
ap-1167	94	19	by	by	ADP
ap-1167	94	20	the	the	DET
ap-1167	94	21	sum	sum	NOUN
ap-1167	94	22	.	.	PUNCT
ap-1167	95	1	since	since	SCONJ
ap-1167	95	2	the	the	DET
ap-1167	95	3	result	result	NOUN
ap-1167	95	4	is	be	AUX
ap-1167	95	5	still	still	ADV
ap-1167	95	6	in	in	ADP
ap-1167	95	7	double	double	ADJ
ap-1167	95	8	extended	extended	ADJ
ap-1167	95	9	precision	precision	NOUN
ap-1167	95	10	,	,	PUNCT
ap-1167	95	11	it	it	PRON
ap-1167	95	12	has	have	VERB
ap-1167	95	13	to	to	PART
ap-1167	95	14	be	be	AUX
ap-1167	95	15	stored	store	VERB
ap-1167	95	16	back	back	ADV
ap-1167	95	17	into	into	ADP
ap-1167	95	18	memory	memory	NOUN
ap-1167	95	19	in	in	ADP
ap-1167	95	20	order	order	NOUN
ap-1167	95	21	to	to	PART
ap-1167	95	22	get	get	VERB
ap-1167	95	23	a	a	DET
ap-1167	95	24	rounded	rounded	ADJ
ap-1167	95	25	result	result	NOUN
ap-1167	95	26	according	accord	VERB
ap-1167	95	27	to	to	ADP
ap-1167	95	28	the	the	DET
ap-1167	95	29	standard	standard	NOUN
ap-1167	95	30	that	that	PRON
ap-1167	95	31	we	we	PRON
ap-1167	95	32	have	have	VERB
ap-1167	95	33	to	to	PART
ap-1167	95	34	round	round	VERB
ap-1167	95	35	the	the	DET
ap-1167	95	36	result	result	NOUN
ap-1167	95	37	(	(	PUNCT
ap-1167	95	38	ŝ	ŝ	NOUN
ap-1167	95	39	)	)	PUNCT
ap-1167	95	40	after	after	SCONJ
ap-1167	95	41	each	each	DET
ap-1167	95	42	operation	operation	NOUN
ap-1167	95	43	(	(	PUNCT
ap-1167	95	44	line	line	NOUN
ap-1167	95	45	4	4	NUM
ap-1167	95	46	)	)	PUNCT
ap-1167	95	47	and	and	CCONJ
ap-1167	95	48	rounded	rounded	ADJ
ap-1167	95	49	result	result	NOUN
ap-1167	95	50	(	(	PUNCT
ap-1167	95	51	ŝ	ŝ	NOUN
ap-1167	95	52	)	)	PUNCT
ap-1167	95	53	is	be	AUX
ap-1167	95	54	pushed	push	VERB
ap-1167	95	55	back	back	ADV
ap-1167	95	56	onto	onto	ADP
ap-1167	95	57	the	the	DET
ap-1167	95	58	floating	float	VERB
ap-1167	95	59	point	point	NOUN
ap-1167	95	60	stack	stack	NOUN
ap-1167	95	61	(	(	PUNCT
ap-1167	95	62	line	line	NOUN
ap-1167	95	63	5	5	NUM
ap-1167	95	64	)	)	PUNCT
ap-1167	95	65	.	.	PUNCT
ap-1167	96	1	ŝ	ŝ	PROPN
ap-1167	96	2	−	−	PROPN
ap-1167	96	3	ŝ	ŝ	PROPN
ap-1167	96	4	is	be	AUX
ap-1167	96	5	calculated	calculate	VERB
ap-1167	96	6	(	(	PUNCT
ap-1167	96	7	line	line	NOUN
ap-1167	96	8	6	6	NUM
ap-1167	96	9	)	)	PUNCT
ap-1167	96	10	and	and	CCONJ
ap-1167	96	11	its	its	PRON
ap-1167	96	12	absolute	absolute	ADJ
ap-1167	96	13	value	value	NOUN
ap-1167	96	14	is	be	AUX
ap-1167	96	15	determined	determine	VERB
ap-1167	96	16	(	(	PUNCT
ap-1167	96	17	line	line	NOUN
ap-1167	96	18	7	7	NUM
ap-1167	96	19	)	)	PUNCT
ap-1167	96	20	.	.	PUNCT
ap-1167	97	1	errors	error	NOUN
ap-1167	97	2	are	be	AUX
ap-1167	97	3	propagated	propagate	VERB
ap-1167	97	4	according	accord	VERB
ap-1167	97	5	to	to	ADP
ap-1167	97	6	tab	tab	NOUN
ap-1167	97	7	.	.	PUNCT
ap-1167	98	1	1	1	NUM
ap-1167	99	1	(	(	PUNCT
ap-1167	99	2	lines	line	NOUN
ap-1167	99	3	8	8	NUM
ap-1167	99	4	through	through	ADP
ap-1167	99	5	11	11	NUM
ap-1167	99	6	)	)	PUNCT
ap-1167	99	7	,	,	PUNCT
ap-1167	99	8	and	and	CCONJ
ap-1167	99	9	the	the	DET
ap-1167	99	10	requested	request	VERB
ap-1167	99	11	absolute	absolute	ADJ
ap-1167	99	12	error	error	NOUN
ap-1167	99	13	is	be	AUX
ap-1167	99	14	found	find	VERB
ap-1167	99	15	at	at	ADP
ap-1167	99	16	the	the	DET
ap-1167	99	17	top	top	NOUN
ap-1167	99	18	of	of	ADP
ap-1167	99	19	the	the	DET
ap-1167	99	20	fpu	fpu	PROPN
ap-1167	99	21	stack	stack	NOUN
ap-1167	99	22	(	(	PUNCT
ap-1167	99	23	line	line	NOUN
ap-1167	99	24	12	12	NUM
ap-1167	99	25	)	)	PUNCT
ap-1167	99	26	.	.	PUNCT
ap-1167	100	1	lines	line	NOUN
ap-1167	100	2	13	13	NUM
ap-1167	100	3	through	through	ADP
ap-1167	100	4	17	17	NUM
ap-1167	100	5	specify	specify	NOUN
ap-1167	100	6	input	input	NOUN
ap-1167	100	7	operand	operand	NOUN
ap-1167	100	8	constraints	constraint	NOUN
ap-1167	100	9	for	for	ADP
ap-1167	100	10	the	the	PRON
ap-1167	100	11	_	_	NOUN
ap-1167	100	12	_	_	PUNCT
ap-1167	100	13	asm	asm	NOUN
ap-1167	100	14	_	_	PUNCT
ap-1167	100	15	_	_	PUNCT
ap-1167	101	1	directive	directive	NOUN
ap-1167	101	2	.	.	PUNCT
ap-1167	102	1	other	other	ADJ
ap-1167	102	2	operators	operator	NOUN
ap-1167	102	3	and	and	CCONJ
ap-1167	102	4	functions	function	NOUN
ap-1167	102	5	are	be	AUX
ap-1167	102	6	implemented	implement	VERB
ap-1167	102	7	in	in	ADP
ap-1167	102	8	a	a	DET
ap-1167	102	9	similar	similar	ADJ
ap-1167	102	10	way	way	NOUN
ap-1167	102	11	.	.	PUNCT
ap-1167	103	1	traditional	traditional	ADJ
ap-1167	103	2	running	running	NOUN
ap-1167	103	3	error	error	NOUN
ap-1167	103	4	analysis	analysis	NOUN
ap-1167	103	5	is	be	AUX
ap-1167	103	6	implemented	implement	VERB
ap-1167	103	7	alike	alike	ADV
ap-1167	103	8	,	,	PUNCT
ap-1167	103	9	and	and	CCONJ
ap-1167	103	10	provides	provide	VERB
ap-1167	103	11	class	class	NOUN
ap-1167	103	12	radouble	radouble	NOUN
ap-1167	103	13	.	.	PUNCT
ap-1167	104	1	the	the	DET
ap-1167	104	2	source	source	NOUN
ap-1167	104	3	code	code	NOUN
ap-1167	104	4	for	for	ADP
ap-1167	104	5	radouble::operator+	radouble::operator+	PROPN
ap-1167	104	6	follows	follow	VERB
ap-1167	104	7	:	:	PUNCT
ap-1167	104	8	radouble	radouble	ADJ
ap-1167	104	9	radouble::operator+(radouble	radouble::operator+(radouble	ADJ
ap-1167	104	10	const	const	PROPN
ap-1167	104	11	&	&	CCONJ
ap-1167	104	12	b	b	NOUN
ap-1167	104	13	)	)	PUNCT
ap-1167	104	14	const	const	NOUN
ap-1167	104	15	{	{	PUNCT
ap-1167	104	16	radouble	radouble	ADJ
ap-1167	104	17	r	r	NOUN
ap-1167	104	18	;	;	PUNCT
ap-1167	104	19	r.d	r.d	X
ap-1167	104	20	=	=	SYM
ap-1167	105	1	d	d	PROPN
ap-1167	105	2	+	+	CCONJ
ap-1167	105	3	b.d	b.d	PROPN
ap-1167	105	4	;	;	PUNCT
ap-1167	105	5	r.e	r.e	PROPN
ap-1167	105	6	=	=	PROPN
ap-1167	105	7	fabs(r.d	fabs(r.d	PROPN
ap-1167	105	8	)	)	PUNCT
ap-1167	105	9	*	*	PUNCT
ap-1167	106	1	roundoff_unit	roundoff_unit	VERB
ap-1167	106	2	+	+	CCONJ
ap-1167	106	3	e	e	PROPN
ap-1167	106	4	+	+	CCONJ
ap-1167	106	5	b.e	b.e	PROPN
ap-1167	106	6	;	;	PUNCT
ap-1167	106	7	return	return	VERB
ap-1167	106	8	r	r	NOUN
ap-1167	106	9	;	;	PUNCT
ap-1167	106	10	}	}	PUNCT
ap-1167	106	11	here	here	ADV
ap-1167	106	12	,	,	PUNCT
ap-1167	106	13	we	we	PRON
ap-1167	106	14	can	can	AUX
ap-1167	106	15	see	see	VERB
ap-1167	106	16	that	that	SCONJ
ap-1167	106	17	no	no	DET
ap-1167	106	18	assembly	assembly	NOUN
ap-1167	106	19	language	language	NOUN
ap-1167	106	20	inlines	inline	NOUN
ap-1167	106	21	are	be	AUX
ap-1167	106	22	necessary	necessary	ADJ
ap-1167	106	23	,	,	PUNCT
ap-1167	106	24	but	but	CCONJ
ap-1167	106	25	it	it	PRON
ap-1167	106	26	is	be	AUX
ap-1167	106	27	necessary	necessary	ADJ
ap-1167	106	28	to	to	PART
ap-1167	106	29	provide	provide	VERB
ap-1167	106	30	special	special	ADJ
ap-1167	106	31	compiler	compiler	NOUN
ap-1167	106	32	flags	flag	NOUN
ap-1167	106	33	in	in	ADP
ap-1167	106	34	order	order	NOUN
ap-1167	106	35	to	to	PART
ap-1167	106	36	obtain	obtain	VERB
ap-1167	106	37	the	the	DET
ap-1167	106	38	same	same	ADJ
ap-1167	106	39	results	result	NOUN
ap-1167	106	40	with	with	ADP
ap-1167	106	41	the	the	DET
ap-1167	106	42	fdouble	fdouble	ADJ
ap-1167	106	43	class	class	NOUN
ap-1167	106	44	.	.	PUNCT
ap-1167	107	1	these	these	DET
ap-1167	107	2	gcc	gcc	NOUN
ap-1167	107	3	flags	flag	NOUN
ap-1167	107	4	are	be	AUX
ap-1167	107	5	:	:	PUNCT
ap-1167	107	6	-ffloat	-ffloat	NOUN
ap-1167	107	7	-	-	PUNCT
ap-1167	107	8	store	store	NOUN
ap-1167	107	9	,	,	PUNCT
ap-1167	107	10	which	which	PRON
ap-1167	107	11	ensures	ensure	VERB
ap-1167	107	12	that	that	SCONJ
ap-1167	107	13	the	the	DET
ap-1167	107	14	result	result	NOUN
ap-1167	107	15	of	of	ADP
ap-1167	107	16	each	each	DET
ap-1167	107	17	floating	float	VERB
ap-1167	107	18	point	point	NOUN
ap-1167	107	19	operation	operation	NOUN
ap-1167	107	20	is	be	AUX
ap-1167	107	21	stored	store	VERB
ap-1167	107	22	back	back	ADV
ap-1167	107	23	into	into	ADP
ap-1167	107	24	memory	memory	NOUN
ap-1167	107	25	and	and	CCONJ
ap-1167	107	26	rounded	round	VERB
ap-1167	107	27	to	to	ADP
ap-1167	107	28	a	a	DET
ap-1167	107	29	defined	define	VERB
ap-1167	107	30	precision	precision	NOUN
ap-1167	107	31	(	(	PUNCT
ap-1167	107	32	required	require	VERB
ap-1167	107	33	by	by	ADP
ap-1167	107	34	ieee	ieee	NOUN
ap-1167	107	35	754	754	NUM
ap-1167	107	36	)	)	PUNCT
ap-1167	107	37	,	,	PUNCT
ap-1167	107	38	and	and	CCONJ
ap-1167	107	39	the	the	DET
ap-1167	107	40	second	second	ADJ
ap-1167	107	41	flag	flag	NOUN
ap-1167	107	42	-mfpmath=387	-mfpmath=387	NUM
ap-1167	107	43	,	,	PUNCT
ap-1167	107	44	which	which	PRON
ap-1167	107	45	assures	assure	VERB
ap-1167	107	46	that	that	SCONJ
ap-1167	107	47	the	the	DET
ap-1167	107	48	floating	float	VERB
ap-1167	107	49	point	point	NOUN
ap-1167	107	50	unit	unit	NOUN
ap-1167	107	51	is	be	AUX
ap-1167	107	52	used	use	VERB
ap-1167	107	53	.	.	PUNCT
ap-1167	108	1	without	without	ADP
ap-1167	108	2	the	the	DET
ap-1167	108	3	second	second	ADJ
ap-1167	108	4	flag	flag	NOUN
ap-1167	108	5	,	,	PUNCT
ap-1167	108	6	the	the	DET
ap-1167	108	7	optimization	optimization	NOUN
ap-1167	108	8	could	could	AUX
ap-1167	108	9	use	use	VERB
ap-1167	108	10	sse	sse	NOUN
ap-1167	108	11	instructions	instruction	NOUN
ap-1167	108	12	and	and	CCONJ
ap-1167	108	13	provide	provide	VERB
ap-1167	108	14	less	less	ADV
ap-1167	108	15	accurate	accurate	ADJ
ap-1167	108	16	results	result	NOUN
ap-1167	108	17	.	.	PUNCT
ap-1167	109	1	readers	reader	NOUN
ap-1167	109	2	interested	interested	ADJ
ap-1167	109	3	in	in	ADP
ap-1167	109	4	obtaining	obtain	VERB
ap-1167	109	5	the	the	DET
ap-1167	109	6	complete	complete	ADJ
ap-1167	109	7	source	source	NOUN
ap-1167	109	8	code	code	NOUN
ap-1167	109	9	for	for	ADP
ap-1167	109	10	all	all	DET
ap-1167	109	11	classes	class	NOUN
ap-1167	109	12	should	should	AUX
ap-1167	109	13	refer	refer	VERB
ap-1167	109	14	to	to	ADP
ap-1167	109	15	[	[	X
ap-1167	109	16	9	9	NUM
ap-1167	109	17	]	]	PUNCT
ap-1167	109	18	but	but	CCONJ
ap-1167	109	19	cite	cite	VERB
ap-1167	109	20	this	this	DET
ap-1167	109	21	paper	paper	NOUN
ap-1167	109	22	.	.	PUNCT
ap-1167	110	1	3.3	3.3	NUM
ap-1167	110	2	complexity	complexity	NOUN
ap-1167	110	3	and	and	CCONJ
ap-1167	110	4	implementation	implementation	NOUN
ap-1167	110	5	notes	note	VERB
ap-1167	110	6	the	the	DET
ap-1167	110	7	traditional	traditional	ADJ
ap-1167	110	8	running	running	NOUN
ap-1167	110	9	error	error	NOUN
ap-1167	110	10	analysis	analysis	NOUN
ap-1167	110	11	needs	need	VERB
ap-1167	110	12	to	to	PART
ap-1167	110	13	calculate	calculate	VERB
ap-1167	110	14	u|ŝ|	u|ŝ|	PRON
ap-1167	110	15	,	,	PUNCT
ap-1167	110	16	and	and	CCONJ
ap-1167	110	17	four	four	NUM
ap-1167	110	18	x86	x86	NOUN
ap-1167	110	19	floating	float	VERB
ap-1167	110	20	point	point	NOUN
ap-1167	110	21	instructions	instruction	NOUN
ap-1167	110	22	are	be	AUX
ap-1167	110	23	necessary3	necessary3	PROPN
ap-1167	110	24	.	.	PUNCT
ap-1167	111	1	these	these	PRON
ap-1167	111	2	are	be	AUX
ap-1167	111	3	:	:	PUNCT
ap-1167	111	4	fld	fld	NUM
ap-1167	111	5	instruction	instruction	NOUN
ap-1167	111	6	to	to	PART
ap-1167	111	7	load	load	VERB
ap-1167	111	8	u	u	NOUN
ap-1167	111	9	onto	onto	ADP
ap-1167	111	10	the	the	DET
ap-1167	111	11	floating	float	VERB
ap-1167	111	12	point	point	NOUN
ap-1167	111	13	stack	stack	NOUN
ap-1167	111	14	,	,	PUNCT
ap-1167	111	15	fmul	fmul	NOUN
ap-1167	111	16	to	to	PART
ap-1167	111	17	calculate	calculate	VERB
ap-1167	111	18	uŝ	uŝ	PROPN
ap-1167	111	19	,	,	PUNCT
ap-1167	111	20	fabs	fab	VERB
ap-1167	111	21	to	to	PART
ap-1167	111	22	obtain	obtain	VERB
ap-1167	111	23	|uŝ|	|uŝ|	NOUN
ap-1167	111	24	=	=	SYM
ap-1167	111	25	u|ŝ|	u|ŝ|	ADJ
ap-1167	111	26	,	,	PUNCT
ap-1167	111	27	and	and	CCONJ
ap-1167	111	28	fstl	fstl	NOUN
ap-1167	111	29	to	to	PART
ap-1167	111	30	store	store	VERB
ap-1167	111	31	the	the	DET
ap-1167	111	32	result	result	NOUN
ap-1167	111	33	back	back	ADV
ap-1167	111	34	into	into	ADP
ap-1167	111	35	memory	memory	NOUN
ap-1167	111	36	and	and	CCONJ
ap-1167	111	37	round	round	VERB
ap-1167	111	38	it	it	PRON
ap-1167	111	39	to	to	ADP
ap-1167	111	40	double	double	ADJ
ap-1167	111	41	precision	precision	NOUN
ap-1167	111	42	.	.	PUNCT
ap-1167	112	1	our	our	PRON
ap-1167	112	2	approach	approach	NOUN
ap-1167	112	3	suggests	suggest	VERB
ap-1167	112	4	to	to	PART
ap-1167	112	5	substitute	substitute	VERB
ap-1167	112	6	|ŝ−	|ŝ−	NOUN
ap-1167	112	7	ŝ|	ŝ|	PROPN
ap-1167	112	8	for	for	ADP
ap-1167	112	9	u|ŝ|	u|ŝ|	PRON
ap-1167	112	10	and	and	CCONJ
ap-1167	112	11	a	a	DET
ap-1167	112	12	typical	typical	ADJ
ap-1167	112	13	evaluation	evaluation	NOUN
ap-1167	112	14	requires	require	VERB
ap-1167	112	15	an	an	DET
ap-1167	112	16	fldl	fldl	ADJ
ap-1167	112	17	instruction	instruction	NOUN
ap-1167	112	18	to	to	PART
ap-1167	112	19	load	load	VERB
ap-1167	112	20	ŝ	ŝ	NOUN
ap-1167	112	21	onto	onto	ADP
ap-1167	112	22	the	the	DET
ap-1167	112	23	floating	float	VERB
ap-1167	112	24	point	point	NOUN
ap-1167	112	25	stack	stack	NOUN
ap-1167	112	26	,	,	PUNCT
ap-1167	112	27	fsub	fsub	NOUN
ap-1167	112	28	to	to	PART
ap-1167	112	29	calculate	calculate	VERB
ap-1167	112	30	ŝ−ŝ	ŝ−ŝ	PROPN
ap-1167	112	31	,	,	PUNCT
ap-1167	112	32	fabs	fab	VERB
ap-1167	112	33	to	to	PART
ap-1167	112	34	obtain	obtain	VERB
ap-1167	112	35	its	its	PRON
ap-1167	112	36	absolute	absolute	ADJ
ap-1167	112	37	value	value	NOUN
ap-1167	112	38	|ŝ−ŝ|	|ŝ−ŝ|	NOUN
ap-1167	112	39	,	,	PUNCT
ap-1167	112	40	and	and	CCONJ
ap-1167	112	41	fstl	fstl	NOUN
ap-1167	112	42	to	to	PART
ap-1167	112	43	store	store	VERB
ap-1167	112	44	the	the	DET
ap-1167	112	45	result	result	NOUN
ap-1167	112	46	into	into	ADP
ap-1167	112	47	memory	memory	NOUN
ap-1167	112	48	while	while	SCONJ
ap-1167	112	49	rounding	round	VERB
ap-1167	112	50	it	it	PRON
ap-1167	112	51	to	to	ADP
ap-1167	112	52	double	double	ADJ
ap-1167	112	53	precision	precision	NOUN
ap-1167	112	54	.	.	PUNCT
ap-1167	113	1	according	accord	VERB
ap-1167	113	2	to	to	ADP
ap-1167	113	3	instruction	instruction	NOUN
ap-1167	113	4	latency	latency	NOUN
ap-1167	113	5	tables	table	NOUN
ap-1167	113	6	[	[	X
ap-1167	113	7	1	1	NUM
ap-1167	113	8	]	]	PUNCT
ap-1167	113	9	,	,	PUNCT
ap-1167	113	10	fsub	fsub	PROPN
ap-1167	113	11	instruction	instruction	NOUN
ap-1167	113	12	latency	latency	NOUN
ap-1167	113	13	is	be	AUX
ap-1167	113	14	3	3	NUM
ap-1167	113	15	cycles	cycle	NOUN
ap-1167	113	16	,	,	PUNCT
ap-1167	113	17	while	while	SCONJ
ap-1167	113	18	fmul	fmul	NOUN
ap-1167	113	19	latency	latency	NOUN
ap-1167	113	20	is	be	AUX
ap-1167	113	21	5	5	NUM
ap-1167	113	22	.	.	PUNCT
ap-1167	114	1	the	the	DET
ap-1167	114	2	following	follow	VERB
ap-1167	114	3	table	table	NOUN
ap-1167	114	4	compares	compare	VERB
ap-1167	114	5	the	the	DET
ap-1167	114	6	two	two	NUM
ap-1167	114	7	approaches	approach	NOUN
ap-1167	114	8	from	from	ADP
ap-1167	114	9	the	the	DET
ap-1167	114	10	latency	latency	NOUN
ap-1167	114	11	point	point	NOUN
ap-1167	114	12	of	of	ADP
ap-1167	114	13	view	view	NOUN
ap-1167	114	14	,	,	PUNCT
ap-1167	114	15	proving	prove	VERB
ap-1167	114	16	that	that	SCONJ
ap-1167	114	17	there	there	PRON
ap-1167	114	18	is	be	VERB
ap-1167	114	19	a	a	DET
ap-1167	114	20	speed	speed	NOUN
ap-1167	114	21	enhancement	enhancement	NOUN
ap-1167	114	22	:	:	PUNCT
ap-1167	114	23	table	table	NOUN
ap-1167	114	24	2	2	NUM
ap-1167	114	25	:	:	PUNCT
ap-1167	114	26	comparing	compare	VERB
ap-1167	114	27	the	the	DET
ap-1167	114	28	fpu	fpu	PROPN
ap-1167	114	29	instructions	instruction	NOUN
ap-1167	114	30	necessary	necessary	ADJ
ap-1167	114	31	to	to	PART
ap-1167	114	32	evaluate	evaluate	VERB
ap-1167	114	33	the	the	DET
ap-1167	114	34	absolute	absolute	ADJ
ap-1167	114	35	error	error	NOUN
ap-1167	114	36	traditional	traditional	ADJ
ap-1167	114	37	approach	approach	NOUN
ap-1167	114	38	our	our	PRON
ap-1167	114	39	approach	approach	NOUN
ap-1167	114	40	instructions	instruction	NOUN
ap-1167	114	41	latency	latency	NOUN
ap-1167	114	42	instructions	instruction	NOUN
ap-1167	114	43	latency	latency	PROPN
ap-1167	114	44	fldl	fldl	VERB
ap-1167	114	45	3	3	NUM
ap-1167	114	46	fldl	fldl	PROPN
ap-1167	114	47	3	3	NUM
ap-1167	114	48	fmul	fmul	PROPN
ap-1167	114	49	5	5	NUM
ap-1167	114	50	fsub	fsub	NOUN
ap-1167	114	51	3	3	NUM
ap-1167	114	52	fabs	fab	NOUN
ap-1167	114	53	1	1	NUM
ap-1167	114	54	fabs	fab	NOUN
ap-1167	114	55	1	1	NUM
ap-1167	114	56	fstl	fstl	NOUN
ap-1167	114	57	3	3	NUM
ap-1167	114	58	fstl	fstl	NOUN
ap-1167	114	59	3	3	NUM
ap-1167	114	60	total	total	NOUN
ap-1167	114	61	12	12	NUM
ap-1167	114	62	total	total	NOUN
ap-1167	114	63	10	10	NUM
ap-1167	114	64	our	our	PRON
ap-1167	114	65	approach	approach	NOUN
ap-1167	114	66	not	not	PART
ap-1167	114	67	only	only	ADV
ap-1167	114	68	provides	provide	VERB
ap-1167	114	69	a	a	DET
ap-1167	114	70	better	well	ADJ
ap-1167	114	71	error	error	NOUN
ap-1167	114	72	bound	bind	VERB
ap-1167	114	73	estimate	estimate	NOUN
ap-1167	114	74	,	,	PUNCT
ap-1167	114	75	but	but	CCONJ
ap-1167	114	76	also	also	ADV
ap-1167	114	77	at	at	ADP
ap-1167	114	78	a	a	DET
ap-1167	114	79	higher	high	ADJ
ap-1167	114	80	speed	speed	NOUN
ap-1167	114	81	and	and	CCONJ
ap-1167	114	82	we	we	PRON
ap-1167	114	83	should	should	AUX
ap-1167	114	84	expect	expect	VERB
ap-1167	114	85	about	about	ADP
ap-1167	114	86	20	20	NUM
ap-1167	114	87	per	per	NOUN
ap-1167	114	88	cent	cent	NOUN
ap-1167	114	89	speed	speed	NOUN
ap-1167	114	90	up	up	ADP
ap-1167	114	91	.	.	PUNCT
ap-1167	115	1	3.4	3.4	NUM
ap-1167	115	2	case	case	NOUN
ap-1167	115	3	study	study	VERB
ap-1167	115	4	the	the	DET
ap-1167	115	5	case	case	NOUN
ap-1167	115	6	study	study	NOUN
ap-1167	115	7	compares	compare	VERB
ap-1167	115	8	the	the	DET
ap-1167	115	9	presented	present	VERB
ap-1167	115	10	approach	approach	NOUN
ap-1167	115	11	to	to	ADP
ap-1167	115	12	traditional	traditional	ADJ
ap-1167	115	13	running	running	NOUN
ap-1167	115	14	error	error	NOUN
ap-1167	115	15	analysis	analysis	NOUN
ap-1167	115	16	,	,	PUNCT
ap-1167	115	17	and	and	CCONJ
ap-1167	115	18	also	also	ADV
ap-1167	115	19	compares	compare	VERB
ap-1167	115	20	it	it	PRON
ap-1167	115	21	to	to	ADP
ap-1167	115	22	a	a	DET
ap-1167	115	23	forward	forward	ADJ
ap-1167	115	24	error	error	NOUN
ap-1167	115	25	bound	bind	VERB
ap-1167	115	26	determined	determine	VERB
ap-1167	115	27	a	a	DET
ap-1167	115	28	-	-	PUNCT
ap-1167	115	29	priori	priori	ADJ
ap-1167	115	30	on	on	ADP
ap-1167	115	31	the	the	DET
ap-1167	115	32	following	following	ADJ
ap-1167	115	33	mathematical	mathematical	ADJ
ap-1167	115	34	identity	identity	NOUN
ap-1167	115	35	:	:	PUNCT
ap-1167	115	36	y∞	y∞	NUM
ap-1167	115	37	=	=	SYM
ap-1167	115	38	log	log	NOUN
ap-1167	115	39	2	2	NUM
ap-1167	115	40	=	=	SYM
ap-1167	115	41	∞∑	∞∑	NUM
ap-1167	115	42	k=1	k=1	PUNCT
ap-1167	116	1	(	(	PUNCT
ap-1167	116	2	−1)k−1	−1)k−1	ADV
ap-1167	116	3	k	k	X
ap-1167	116	4	.	.	PUNCT
ap-1167	117	1	(	(	PUNCT
ap-1167	117	2	5	5	NUM
ap-1167	117	3	)	)	PUNCT
ap-1167	117	4	c++	c++	NOUN
ap-1167	117	5	and	and	CCONJ
ap-1167	117	6	mathematica	mathematica	PROPN
ap-1167	117	7	[	[	X
ap-1167	117	8	8	8	NUM
ap-1167	117	9	]	]	X
ap-1167	117	10	software	software	NOUN
ap-1167	117	11	are	be	AUX
ap-1167	117	12	used	use	VERB
ap-1167	117	13	to	to	PART
ap-1167	117	14	verify	verify	VERB
ap-1167	117	15	the	the	DET
ap-1167	117	16	results	result	NOUN
ap-1167	117	17	.	.	PUNCT
ap-1167	118	1	a	a	DET
ap-1167	118	2	rounding	round	VERB
ap-1167	118	3	error	error	NOUN
ap-1167	118	4	analysis	analysis	NOUN
ap-1167	118	5	of	of	ADP
ap-1167	118	6	(	(	PUNCT
ap-1167	118	7	5	5	NUM
ap-1167	118	8	)	)	PUNCT
ap-1167	118	9	for	for	ADP
ap-1167	118	10	a	a	DET
ap-1167	118	11	double	double	ADJ
ap-1167	118	12	precision	precision	NOUN
ap-1167	118	13	floating	float	VERB
ap-1167	118	14	point	point	NOUN
ap-1167	118	15	arithmetic	arithmetic	ADJ
ap-1167	118	16	for	for	ADP
ap-1167	118	17	n	n	PROPN
ap-1167	118	18	addends	addend	NOUN
ap-1167	118	19	is	be	AUX
ap-1167	118	20	given	give	VERB
ap-1167	118	21	with	with	ADP
ap-1167	118	22	the	the	DET
ap-1167	118	23	following	follow	VERB
ap-1167	118	24	assumptions	assumption	NOUN
ap-1167	118	25	:	:	PUNCT
ap-1167	118	26	3this	3this	NUM
ap-1167	118	27	approach	approach	NOUN
ap-1167	118	28	works	work	VERB
ap-1167	118	29	only	only	ADV
ap-1167	118	30	with	with	ADP
ap-1167	118	31	fpu	fpu	PROPN
ap-1167	118	32	,	,	PUNCT
ap-1167	118	33	not	not	PART
ap-1167	118	34	sse2	sse2	NOUN
ap-1167	118	35	/	/	SYM
ap-1167	118	36	sse3	sse3	NOUN
ap-1167	118	37	,	,	PUNCT
ap-1167	118	38	as	as	SCONJ
ap-1167	118	39	sse	sse	NOUN
ap-1167	118	40	does	do	AUX
ap-1167	118	41	not	not	PART
ap-1167	118	42	support	support	VERB
ap-1167	118	43	double	double	ADJ
ap-1167	118	44	extended	extend	VERB
ap-1167	118	45	precision	precision	NOUN
ap-1167	118	46	and	and	CCONJ
ap-1167	118	47	we	we	PRON
ap-1167	118	48	are	be	AUX
ap-1167	118	49	unable	unable	ADJ
ap-1167	118	50	to	to	PART
ap-1167	118	51	calculate	calculate	VERB
ap-1167	118	52	|ŝ	|ŝ	NOUN
ap-1167	118	53	−	−	DET
ap-1167	118	54	ŝ|	ŝ|	PROPN
ap-1167	118	55	.	.	PUNCT
ap-1167	119	1	33	33	NUM
ap-1167	119	2	acta	acta	PROPN
ap-1167	119	3	polytechnica	polytechnica	PROPN
ap-1167	119	4	vol	vol	NOUN
ap-1167	119	5	.	.	PROPN
ap-1167	119	6	50	50	NUM
ap-1167	119	7	no	no	NOUN
ap-1167	119	8	.	.	PUNCT
ap-1167	120	1	2/2010	2/2010	NUM
ap-1167	120	2	−8	−8	NOUN
ap-1167	121	1	−6	−6	INTJ
ap-1167	121	2	−2	−2	NOUN
ap-1167	121	3	−4	−4	X
ap-1167	121	4	0	0	PUNCT
ap-1167	122	1	l	l	NOUN
ap-1167	122	2	og	og	INTJ
ap-1167	122	3	ar	ar	PROPN
ap-1167	122	4	it	it	PRON
ap-1167	122	5	hm	hm	INTJ
ap-1167	122	6	of	of	ADP
ap-1167	122	7	er	er	INTJ
ap-1167	122	8	ro	ro	INTJ
ap-1167	122	9	r	r	NOUN
ap-1167	122	10	running	running	NOUN
ap-1167	122	11	error	error	NOUN
ap-1167	122	12	our	our	PRON
ap-1167	122	13	approach	approach	NOUN
ap-1167	122	14	result	result	VERB
ap-1167	122	15	error	error	NOUN
ap-1167	122	16	forward	forward	NOUN
ap-1167	122	17	error	error	NOUN
ap-1167	122	18	bound	bind	VERB
ap-1167	122	19	log2	log2	PROPN
ap-1167	122	20	n	n	CCONJ
ap-1167	122	21	−18	−18	NUM
ap-1167	122	22	−16	−16	PROPN
ap-1167	122	23	−14	−14	NUM
ap-1167	122	24	−12	−12	NUM
ap-1167	123	1	−10	−10	NOUN
ap-1167	123	2	−8	−8	X
ap-1167	124	1	−6	−6	INTJ
ap-1167	124	2	−4	−4	X
ap-1167	125	1	−2	−2	NOUN
ap-1167	125	2	0	0	NUM
ap-1167	125	3	0	0	NUM
ap-1167	125	4	4	4	NUM
ap-1167	125	5	8	8	NUM
ap-1167	125	6	12	12	NUM
ap-1167	125	7	16	16	NUM
ap-1167	125	8	20	20	NUM
ap-1167	125	9	24	24	NUM
ap-1167	125	10	28	28	NUM
ap-1167	125	11	32	32	NUM
ap-1167	125	12	36	36	NUM
ap-1167	125	13	−18	−18	NUM
ap-1167	125	14	−16	−16	PROPN
ap-1167	125	15	−14	−14	NUM
ap-1167	125	16	−12	−12	NUM
ap-1167	125	17	−10	−10	PROPN
ap-1167	125	18	fig	fig	NOUN
ap-1167	125	19	.	.	PUNCT
ap-1167	126	1	2	2	NUM
ap-1167	126	2	:	:	PUNCT
ap-1167	126	3	calculated	calculate	VERB
ap-1167	126	4	value	value	NOUN
ap-1167	126	5	of	of	ADP
ap-1167	126	6	ŷn	ŷn	PROPN
ap-1167	126	7	and	and	CCONJ
ap-1167	126	8	its	its	PRON
ap-1167	126	9	error	error	NOUN
ap-1167	126	10	bounds	bound	NOUN
ap-1167	126	11	(	(	PUNCT
ap-1167	126	12	forward	forward	ADJ
ap-1167	126	13	sum	sum	NOUN
ap-1167	126	14	direction	direction	NOUN
ap-1167	126	15	)	)	PUNCT
ap-1167	126	16	1	1	X
ap-1167	126	17	.	.	PUNCT
ap-1167	127	1	the	the	DET
ap-1167	127	2	first	first	ADJ
ap-1167	127	3	two	two	NUM
ap-1167	127	4	addends	addend	NOUN
ap-1167	127	5	(	(	PUNCT
ap-1167	127	6	1	1	NUM
ap-1167	127	7	and	and	CCONJ
ap-1167	127	8	1/2	1/2	NUM
ap-1167	127	9	)	)	PUNCT
ap-1167	127	10	of	of	ADP
ap-1167	127	11	the	the	DET
ap-1167	127	12	sum	sum	NOUN
ap-1167	127	13	are	be	AUX
ap-1167	127	14	exact	exact	ADJ
ap-1167	127	15	as	as	SCONJ
ap-1167	127	16	we	we	PRON
ap-1167	127	17	use	use	VERB
ap-1167	127	18	a	a	DET
ap-1167	127	19	binary	binary	ADJ
ap-1167	127	20	floating	float	VERB
ap-1167	127	21	point	point	NOUN
ap-1167	127	22	arithmetic	arithmetic	ADJ
ap-1167	127	23	,	,	PUNCT
ap-1167	127	24	2	2	NUM
ap-1167	127	25	.	.	PUNCT
ap-1167	128	1	(	(	PUNCT
ap-1167	128	2	−1)k−1	−1)k−1	NOUN
ap-1167	128	3	is	be	AUX
ap-1167	128	4	evaluated	evaluate	VERB
ap-1167	128	5	as	as	ADP
ap-1167	128	6	(	(	PUNCT
ap-1167	128	7	−1)k−1	−1)k−1	NOUN
ap-1167	128	8	=	=	SYM
ap-1167	128	9	⎧⎨⎩	⎧⎨⎩	NUM
ap-1167	128	10	1	1	NUM
ap-1167	128	11	when	when	SCONJ
ap-1167	128	12	k	k	PROPN
ap-1167	128	13	is	be	AUX
ap-1167	128	14	odd	odd	ADJ
ap-1167	128	15	−1	−1	NOUN
ap-1167	128	16	otherwise	otherwise	ADV
ap-1167	128	17	rather	rather	ADV
ap-1167	128	18	than	than	ADP
ap-1167	128	19	using	use	VERB
ap-1167	128	20	pow	pow	NOUN
ap-1167	128	21	function	function	NOUN
ap-1167	128	22	from	from	ADP
ap-1167	128	23	libm	libm	NOUN
ap-1167	128	24	thus	thus	ADV
ap-1167	128	25	the	the	DET
ap-1167	128	26	result	result	NOUN
ap-1167	128	27	is	be	AUX
ap-1167	128	28	always	always	ADV
ap-1167	128	29	exact	exact	ADJ
ap-1167	128	30	,	,	PUNCT
ap-1167	128	31	3	3	X
ap-1167	128	32	.	.	X
ap-1167	129	1	all	all	DET
ap-1167	129	2	operations	operation	NOUN
ap-1167	129	3	follow	follow	VERB
ap-1167	129	4	the	the	DET
ap-1167	129	5	standard	standard	ADJ
ap-1167	129	6	model	model	NOUN
ap-1167	129	7	.	.	PUNCT
ap-1167	130	1	the	the	DET
ap-1167	130	2	computed	compute	VERB
ap-1167	130	3	ŷn	ŷn	PROPN
ap-1167	130	4	is	be	AUX
ap-1167	130	5	expressed	express	VERB
ap-1167	130	6	as	as	ADP
ap-1167	130	7	:	:	PUNCT
ap-1167	130	8	ŷn	ŷn	PROPN
ap-1167	130	9	=	=	SYM
ap-1167	130	10	[	[	PUNCT
ap-1167	130	11	·	·	PUNCT
ap-1167	130	12	·	·	PUNCT
ap-1167	130	13	·	·	PUNCT
ap-1167	131	1	[	[	X
ap-1167	131	2	(	(	PUNCT
ap-1167	131	3	1	1	NUM
ap-1167	131	4	−	−	NUM
ap-1167	131	5	1	1	NUM
ap-1167	131	6	2	2	NUM
ap-1167	131	7	)	)	PUNCT
ap-1167	131	8	(	(	PUNCT
ap-1167	131	9	1	1	NUM
ap-1167	131	10	+	+	NUM
ap-1167	131	11	δ1	δ1	NOUN
ap-1167	131	12	)	)	PUNCT
ap-1167	132	1	+	+	CCONJ
ap-1167	132	2	1	1	NUM
ap-1167	132	3	3	3	NUM
ap-1167	132	4	(	(	PUNCT
ap-1167	132	5	1	1	NUM
ap-1167	132	6	+	+	CCONJ
ap-1167	132	7	δ2	δ2	VERB
ap-1167	132	8	)	)	PUNCT
ap-1167	132	9	]	]	PUNCT
ap-1167	132	10	(	(	PUNCT
ap-1167	132	11	1	1	NUM
ap-1167	132	12	+	+	CCONJ
ap-1167	132	13	δ3	δ3	PROPN
ap-1167	132	14	)	)	PUNCT
ap-1167	132	15	−	−	PROPN
ap-1167	132	16	·	·	PUNCT
ap-1167	132	17	·	·	PUNCT
ap-1167	132	18	·	·	PUNCT
ap-1167	132	19	]	]	X
ap-1167	132	20	(	(	PUNCT
ap-1167	132	21	1	1	NUM
ap-1167	132	22	+	+	CCONJ
ap-1167	132	23	δ2n−3	δ2n−3	ADJ
ap-1167	132	24	)	)	PUNCT
ap-1167	132	25	=	=	PUNCT
ap-1167	133	1	(	(	PUNCT
ap-1167	133	2	6	6	NUM
ap-1167	133	3	)	)	PUNCT
ap-1167	133	4	=	=	SYM
ap-1167	133	5	1(1	1(1	NUM
ap-1167	133	6	+	+	SYM
ap-1167	133	7	θn	θn	NOUN
ap-1167	133	8	)	)	PUNCT
ap-1167	133	9	−	−	PROPN
ap-1167	133	10	1	1	NUM
ap-1167	133	11	2	2	NUM
ap-1167	133	12	(	(	PUNCT
ap-1167	133	13	1	1	NUM
ap-1167	133	14	+	+	CCONJ
ap-1167	133	15	θn	θn	NOUN
ap-1167	133	16	)	)	PUNCT
ap-1167	133	17	+	+	CCONJ
ap-1167	133	18	1	1	NUM
ap-1167	133	19	3	3	NUM
ap-1167	133	20	(	(	PUNCT
ap-1167	133	21	1	1	NUM
ap-1167	133	22	+	+	NUM
ap-1167	133	23	θn	θn	NOUN
ap-1167	133	24	)	)	PUNCT
ap-1167	133	25	−	−	PROPN
ap-1167	133	26	.	.	PUNCT
ap-1167	133	27	.	.	PUNCT
ap-1167	133	28	.	.	PUNCT
ap-1167	134	1	+	+	CCONJ
ap-1167	134	2	(	(	PUNCT
ap-1167	134	3	−1)n−1	−1)n−1	PRON
ap-1167	134	4	n	n	CCONJ
ap-1167	134	5	(	(	PUNCT
ap-1167	134	6	1	1	NUM
ap-1167	134	7	+	+	NUM
ap-1167	134	8	θ2	θ2	PROPN
ap-1167	134	9	)	)	PUNCT
ap-1167	134	10	≤	≤	NOUN
ap-1167	134	11	(	(	PUNCT
ap-1167	134	12	7	7	NUM
ap-1167	134	13	)	)	PUNCT
ap-1167	134	14	≤	≤	NOUN
ap-1167	134	15	(	(	PUNCT
ap-1167	134	16	1	1	NUM
ap-1167	134	17	−	−	NUM
ap-1167	134	18	1	1	NUM
ap-1167	134	19	2	2	NUM
ap-1167	134	20	+	+	CCONJ
ap-1167	134	21	1	1	NUM
ap-1167	134	22	3	3	NUM
ap-1167	134	23	−	−	NOUN
ap-1167	134	24	1	1	NUM
ap-1167	134	25	4	4	NUM
ap-1167	134	26	+	+	CCONJ
ap-1167	134	27	−	−	PROPN
ap-1167	134	28	·	·	PUNCT
ap-1167	134	29	·	·	PUNCT
ap-1167	134	30	·	·	PUNCT
ap-1167	135	1	+	+	CCONJ
ap-1167	135	2	(	(	PUNCT
ap-1167	135	3	−1)n−1	−1)n−1	PRON
ap-1167	135	4	n	n	NOUN
ap-1167	135	5	)	)	PUNCT
ap-1167	135	6	(	(	PUNCT
ap-1167	135	7	1	1	NUM
ap-1167	135	8	+	+	CCONJ
ap-1167	135	9	θn	θn	NOUN
ap-1167	135	10	)	)	PUNCT
ap-1167	135	11	=	=	PUNCT
ap-1167	135	12	(	(	PUNCT
ap-1167	135	13	1	1	NUM
ap-1167	135	14	+	+	CCONJ
ap-1167	135	15	θn	θn	ADJ
ap-1167	135	16	)	)	PUNCT
ap-1167	135	17	n∑	n∑	NOUN
ap-1167	135	18	k=1	k=1	PUNCT
ap-1167	135	19	(	(	PUNCT
ap-1167	135	20	−1)k−1	−1)k−1	INTJ
ap-1167	135	21	k	k	X
ap-1167	135	22	,	,	PUNCT
ap-1167	135	23	(	(	PUNCT
ap-1167	135	24	8)	8)	NUM
ap-1167	135	25	where	where	SCONJ
ap-1167	135	26	|δi|	|δi|	PROPN
ap-1167	135	27	≤	≤	PROPN
ap-1167	135	28	u	u	PROPN
ap-1167	135	29	,	,	PUNCT
ap-1167	135	30	n∏	n∏	PROPN
ap-1167	135	31	i=1	i=1	PROPN
ap-1167	135	32	(	(	PUNCT
ap-1167	135	33	1	1	NUM
ap-1167	135	34	+	+	NUM
ap-1167	135	35	δi)ρi	δi)ρi	NOUN
ap-1167	135	36	=	=	SYM
ap-1167	135	37	1	1	NUM
ap-1167	135	38	+	+	SYM
ap-1167	135	39	θn	θn	NOUN
ap-1167	135	40	,	,	PUNCT
ap-1167	135	41	where	where	SCONJ
ap-1167	135	42	ρi	ρi	NOUN
ap-1167	135	43	=	=	NOUN
ap-1167	135	44	±1	±1	VERB
ap-1167	135	45	,	,	PUNCT
ap-1167	135	46	and	and	CCONJ
ap-1167	135	47	|θn|	|θn|	PROPN
ap-1167	135	48	≤	≤	NUM
ap-1167	135	49	nu	nu	INTJ
ap-1167	135	50	1	1	NUM
ap-1167	135	51	−	−	PROPN
ap-1167	135	52	nu	nu	NOUN
ap-1167	135	53	=	=	PUNCT
ap-1167	135	54	γn	γn	PROPN
ap-1167	135	55	,	,	PUNCT
ap-1167	135	56	and	and	CCONJ
ap-1167	135	57	nu	nu	X
ap-1167	135	58	<	<	X
ap-1167	135	59	1	1	NUM
ap-1167	135	60	[	[	X
ap-1167	135	61	5	5	NUM
ap-1167	135	62	]	]	PUNCT
ap-1167	135	63	.	.	PUNCT
ap-1167	136	1	the	the	DET
ap-1167	136	2	backward	backward	ADJ
ap-1167	136	3	error	error	NOUN
ap-1167	136	4	is	be	AUX
ap-1167	136	5	immediately	immediately	ADV
ap-1167	136	6	visible	visible	ADJ
ap-1167	136	7	from	from	ADP
ap-1167	136	8	equation	equation	NOUN
ap-1167	136	9	(	(	PUNCT
ap-1167	136	10	7	7	NUM
ap-1167	136	11	)	)	PUNCT
ap-1167	136	12	,	,	PUNCT
ap-1167	136	13	in	in	ADP
ap-1167	136	14	which	which	PRON
ap-1167	136	15	we	we	PRON
ap-1167	136	16	can	can	AUX
ap-1167	136	17	consider	consider	VERB
ap-1167	136	18	the	the	DET
ap-1167	136	19	sum	sum	NOUN
ap-1167	136	20	as	as	ADP
ap-1167	136	21	an	an	DET
ap-1167	136	22	exact	exact	ADJ
ap-1167	136	23	sum	sum	NOUN
ap-1167	136	24	of	of	ADP
ap-1167	136	25	perturbed	perturb	VERB
ap-1167	136	26	data	datum	NOUN
ap-1167	136	27	entries	entry	NOUN
ap-1167	136	28	by	by	ADP
ap-1167	136	29	a	a	DET
ap-1167	136	30	relative	relative	ADJ
ap-1167	136	31	value	value	NOUN
ap-1167	136	32	certainly	certainly	ADV
ap-1167	136	33	bounded	bound	VERB
ap-1167	136	34	by	by	ADP
ap-1167	136	35	γn	γn	PRON
ap-1167	136	36	.	.	PUNCT
ap-1167	137	1	the	the	DET
ap-1167	137	2	forward	forward	ADJ
ap-1167	137	3	a	a	PRON
ap-1167	137	4	-	-	PUNCT
ap-1167	137	5	priori	priori	ADJ
ap-1167	137	6	error	error	NOUN
ap-1167	137	7	bound	bind	VERB
ap-1167	137	8	is	be	AUX
ap-1167	137	9	then	then	ADV
ap-1167	137	10	calculated	calculate	VERB
ap-1167	137	11	as	as	ADP
ap-1167	137	12	:	:	PUNCT
ap-1167	137	13	|ŷn	|ŷn	PROPN
ap-1167	137	14	−	−	PROPN
ap-1167	137	15	yn	yn	INTJ
ap-1167	138	1	|	|	ADV
ap-1167	138	2	≤	≤	X
ap-1167	138	3	γn	γn	ADP
ap-1167	138	4	n∑	n∑	NOUN
ap-1167	138	5	k=1	k=1	PROPN
ap-1167	139	1	(	(	PUNCT
ap-1167	139	2	−1)k−1	−1)k−1	INTJ
ap-1167	139	3	k	k	X
ap-1167	139	4	,	,	PUNCT
ap-1167	139	5	(	(	PUNCT
ap-1167	139	6	9	9	NUM
ap-1167	139	7	)	)	PUNCT
ap-1167	139	8	and	and	CCONJ
ap-1167	139	9	presents	present	VERB
ap-1167	139	10	the	the	DET
ap-1167	139	11	worst	bad	ADJ
ap-1167	139	12	case	case	NOUN
ap-1167	139	13	error	error	NOUN
ap-1167	139	14	estimate	estimate	NOUN
ap-1167	139	15	,	,	PUNCT
ap-1167	139	16	which	which	PRON
ap-1167	139	17	can	can	AUX
ap-1167	139	18	be	be	AUX
ap-1167	139	19	far	far	ADV
ap-1167	139	20	from	from	ADP
ap-1167	139	21	true	true	ADJ
ap-1167	139	22	error	error	NOUN
ap-1167	139	23	bound	bind	VERB
ap-1167	139	24	.	.	PUNCT
ap-1167	140	1	the	the	DET
ap-1167	140	2	following	follow	VERB
ap-1167	140	3	section	section	NOUN
ap-1167	140	4	demonstrates	demonstrate	VERB
ap-1167	140	5	this	this	DET
ap-1167	140	6	statement	statement	NOUN
ap-1167	140	7	.	.	PUNCT
ap-1167	141	1	3.4.1	3.4.1	NUM
ap-1167	141	2	results	result	NOUN
ap-1167	141	3	results	result	NOUN
ap-1167	141	4	are	be	AUX
ap-1167	141	5	provided	provide	VERB
ap-1167	141	6	for	for	ADP
ap-1167	141	7	two	two	NUM
ap-1167	141	8	summation	summation	NOUN
ap-1167	141	9	orders	order	NOUN
ap-1167	141	10	.	.	PUNCT
ap-1167	142	1	the	the	DET
ap-1167	142	2	first	first	ADJ
ap-1167	142	3	case	case	NOUN
ap-1167	142	4	performs	perform	VERB
ap-1167	142	5	the	the	DET
ap-1167	142	6	summation	summation	NOUN
ap-1167	142	7	in	in	ADP
ap-1167	142	8	decreasing	decrease	VERB
ap-1167	142	9	order	order	NOUN
ap-1167	142	10	of	of	ADP
ap-1167	142	11	magnitude	magnitude	NOUN
ap-1167	142	12	,	,	PUNCT
ap-1167	142	13	where	where	SCONJ
ap-1167	142	14	a	a	DET
ap-1167	142	15	poor	poor	ADJ
ap-1167	142	16	,	,	PUNCT
ap-1167	142	17	insufficiently	insufficiently	ADV
ap-1167	142	18	accurate	accurate	ADJ
ap-1167	142	19	result	result	NOUN
ap-1167	142	20	is	be	AUX
ap-1167	142	21	quickly	quickly	ADV
ap-1167	142	22	visible	visible	ADJ
ap-1167	142	23	.	.	PUNCT
ap-1167	143	1	the	the	DET
ap-1167	143	2	figure	figure	NOUN
ap-1167	143	3	2	2	NUM
ap-1167	143	4	depicts	depict	VERB
ap-1167	143	5	this	this	DET
ap-1167	143	6	scenario	scenario	NOUN
ap-1167	143	7	,	,	PUNCT
ap-1167	143	8	where	where	SCONJ
ap-1167	143	9	n	n	PRON
ap-1167	143	10	stands	stand	VERB
ap-1167	143	11	for	for	ADP
ap-1167	143	12	number	number	NOUN
ap-1167	143	13	of	of	ADP
ap-1167	143	14	iterations	iteration	NOUN
ap-1167	143	15	and	and	CCONJ
ap-1167	143	16	the	the	DET
ap-1167	143	17	y	y	ADJ
ap-1167	143	18	-	-	PUNCT
ap-1167	143	19	axis	axis	NOUN
ap-1167	143	20	shows	show	VERB
ap-1167	143	21	a	a	DET
ap-1167	143	22	base	base	NOUN
ap-1167	143	23	10	10	NUM
ap-1167	143	24	logarithm	logarithm	NOUN
ap-1167	143	25	of	of	ADP
ap-1167	143	26	the	the	DET
ap-1167	143	27	order	order	NOUN
ap-1167	143	28	of	of	ADP
ap-1167	143	29	the	the	DET
ap-1167	143	30	error	error	NOUN
ap-1167	143	31	.	.	PUNCT
ap-1167	144	1	the	the	DET
ap-1167	144	2	first	first	ADJ
ap-1167	144	3	line	line	NOUN
ap-1167	144	4	,	,	PUNCT
ap-1167	144	5	marked	mark	VERB
ap-1167	144	6	with	with	ADP
ap-1167	144	7	�	�	PROPN
ap-1167	144	8	,	,	PUNCT
ap-1167	144	9	presents	present	VERB
ap-1167	144	10	the	the	DET
ap-1167	144	11	absolute	absolute	ADJ
ap-1167	144	12	error	error	NOUN
ap-1167	144	13	,	,	PUNCT
ap-1167	144	14	which	which	PRON
ap-1167	144	15	is	be	AUX
ap-1167	144	16	log10	log10	PROPN
ap-1167	144	17	(	(	PUNCT
ap-1167	144	18	|ŷn	|ŷn	PROPN
ap-1167	144	19	−	−	PROPN
ap-1167	144	20	log	log	NOUN
ap-1167	144	21	2|	2|	NUM
ap-1167	144	22	)	)	PUNCT
ap-1167	144	23	and	and	CCONJ
ap-1167	144	24	it	it	PRON
ap-1167	144	25	gets	get	VERB
ap-1167	144	26	smaller	small	ADJ
ap-1167	144	27	with	with	ADP
ap-1167	144	28	each	each	DET
ap-1167	144	29	further	further	ADJ
ap-1167	144	30	accumulation	accumulation	NOUN
ap-1167	144	31	of	of	ADP
ap-1167	144	32	the	the	DET
ap-1167	144	33	sum	sum	NOUN
ap-1167	144	34	.	.	PUNCT
ap-1167	145	1	rounding	round	VERB
ap-1167	145	2	errors	error	NOUN
ap-1167	145	3	go	go	VERB
ap-1167	145	4	against	against	ADP
ap-1167	145	5	this	this	DET
ap-1167	145	6	error	error	NOUN
ap-1167	145	7	from	from	ADP
ap-1167	145	8	bottom	bottom	NOUN
ap-1167	145	9	to	to	ADP
ap-1167	145	10	top	top	NOUN
ap-1167	145	11	,	,	PUNCT
ap-1167	145	12	and	and	CCONJ
ap-1167	145	13	are	be	AUX
ap-1167	145	14	represented	represent	VERB
ap-1167	145	15	with	with	ADP
ap-1167	145	16	the	the	DET
ap-1167	145	17	remaining	remain	VERB
ap-1167	145	18	three	three	NUM
ap-1167	145	19	lines	line	NOUN
ap-1167	145	20	.	.	PUNCT
ap-1167	146	1	from	from	ADP
ap-1167	146	2	top	top	NOUN
ap-1167	146	3	to	to	ADP
ap-1167	146	4	bottom	bottom	NOUN
ap-1167	146	5	:	:	PUNCT
ap-1167	146	6	the	the	DET
ap-1167	146	7	×+line	×+line	PROPN
ap-1167	146	8	presents	present	VERB
ap-1167	146	9	the	the	DET
ap-1167	146	10	worst	bad	ADJ
ap-1167	146	11	case	case	NOUN
ap-1167	146	12	,	,	PUNCT
ap-1167	146	13	that	that	ADV
ap-1167	146	14	is	is	ADV
ap-1167	146	15	,	,	PUNCT
ap-1167	146	16	the	the	DET
ap-1167	146	17	a	a	ADV
ap-1167	146	18	-	-	PUNCT
ap-1167	146	19	priori	priori	NOUN
ap-1167	146	20	forward	forward	ADJ
ap-1167	146	21	error	error	NOUN
ap-1167	146	22	bound	bind	VERB
ap-1167	146	23	which	which	PRON
ap-1167	146	24	is	be	AUX
ap-1167	146	25	obtained	obtain	VERB
ap-1167	146	26	from	from	ADP
ap-1167	146	27	the	the	DET
ap-1167	146	28	right	right	ADJ
ap-1167	146	29	hand	hand	NOUN
ap-1167	146	30	side	side	NOUN
ap-1167	146	31	of	of	ADP
ap-1167	146	32	(	(	PUNCT
ap-1167	146	33	9	9	NUM
ap-1167	146	34	)	)	PUNCT
ap-1167	146	35	.	.	PUNCT
ap-1167	147	1	the	the	DET
ap-1167	147	2	second	second	ADJ
ap-1167	147	3	line	line	NOUN
ap-1167	147	4	,	,	PUNCT
ap-1167	147	5	marked	mark	VERB
ap-1167	147	6	with	with	ADP
ap-1167	147	7	+	+	PROPN
ap-1167	147	8	,	,	PUNCT
ap-1167	147	9	stands	stand	VERB
ap-1167	147	10	for	for	ADP
ap-1167	147	11	an	an	DET
ap-1167	147	12	a	a	DET
ap-1167	147	13	-	-	PUNCT
ap-1167	147	14	posteriori	posteriori	NOUN
ap-1167	147	15	running	run	VERB
ap-1167	147	16	error	error	NOUN
ap-1167	147	17	bound	bind	VERB
ap-1167	147	18	.	.	PUNCT
ap-1167	148	1	we	we	PRON
ap-1167	148	2	can	can	AUX
ap-1167	148	3	see	see	VERB
ap-1167	148	4	that	that	SCONJ
ap-1167	148	5	it	it	PRON
ap-1167	148	6	is	be	AUX
ap-1167	148	7	slightly	slightly	ADV
ap-1167	148	8	better	well	ADJ
ap-1167	148	9	than	than	ADP
ap-1167	148	10	the	the	DET
ap-1167	148	11	a	a	PRON
ap-1167	148	12	-	-	PUNCT
ap-1167	148	13	priori	priori	NOUN
ap-1167	148	14	bound	bind	VERB
ap-1167	148	15	,	,	PUNCT
ap-1167	148	16	and	and	CCONJ
ap-1167	148	17	the	the	DET
ap-1167	148	18	last	last	ADJ
ap-1167	148	19	line	line	NOUN
ap-1167	148	20	(	(	PUNCT
ap-1167	148	21	×	×	NOUN
ap-1167	148	22	)	)	PUNCT
ap-1167	148	23	presents	present	VERB
ap-1167	148	24	our	our	PRON
ap-1167	148	25	approach	approach	NOUN
ap-1167	148	26	,	,	PUNCT
ap-1167	148	27	which	which	PRON
ap-1167	148	28	accounts	account	VERB
ap-1167	148	29	real	real	ADJ
ap-1167	148	30	rounding	rounding	NOUN
ap-1167	148	31	errors	error	NOUN
ap-1167	148	32	,	,	PUNCT
ap-1167	148	33	and	and	CCONJ
ap-1167	148	34	that	that	PRON
ap-1167	148	35	is	be	AUX
ap-1167	148	36	the	the	DET
ap-1167	148	37	reason	reason	NOUN
ap-1167	148	38	why	why	SCONJ
ap-1167	148	39	the	the	DET
ap-1167	148	40	first	first	ADJ
ap-1167	148	41	two	two	NUM
ap-1167	148	42	iterations	iteration	NOUN
ap-1167	148	43	have	have	VERB
ap-1167	148	44	no	no	DET
ap-1167	148	45	error	error	NOUN
ap-1167	148	46	(	(	PUNCT
ap-1167	148	47	cf	cf	NOUN
ap-1167	148	48	.	.	PUNCT
ap-1167	149	1	the	the	DET
ap-1167	149	2	×	×	NOUN
ap-1167	149	3	at	at	ADP
ap-1167	149	4	the	the	DET
ap-1167	149	5	top	top	NOUN
ap-1167	149	6	)	)	PUNCT
ap-1167	149	7	.	.	PUNCT
ap-1167	150	1	we	we	PRON
ap-1167	150	2	can	can	AUX
ap-1167	150	3	also	also	ADV
ap-1167	150	4	observe	observe	VERB
ap-1167	150	5	that	that	SCONJ
ap-1167	150	6	if	if	SCONJ
ap-1167	150	7	we	we	PRON
ap-1167	150	8	use	use	VERB
ap-1167	150	9	an	an	DET
ap-1167	150	10	a	a	PRON
ap-1167	150	11	-	-	PUNCT
ap-1167	150	12	priori	priori	NOUN
ap-1167	150	13	bound	bind	VERB
ap-1167	150	14	,	,	PUNCT
ap-1167	150	15	we	we	PRON
ap-1167	150	16	will	will	AUX
ap-1167	150	17	have	have	VERB
ap-1167	150	18	to	to	PART
ap-1167	150	19	terminate	terminate	VERB
ap-1167	150	20	the	the	DET
ap-1167	150	21	accumulation	accumulation	NOUN
ap-1167	150	22	somewhere	somewhere	ADV
ap-1167	150	23	after	after	ADP
ap-1167	150	24	226	226	NUM
ap-1167	150	25	iterations	iteration	NOUN
ap-1167	150	26	,	,	PUNCT
ap-1167	150	27	and	and	CCONJ
ap-1167	150	28	after	after	ADP
ap-1167	150	29	227	227	NUM
ap-1167	150	30	iterations	iteration	NOUN
ap-1167	150	31	with	with	ADP
ap-1167	150	32	the	the	DET
ap-1167	150	33	running	running	NOUN
ap-1167	150	34	error	error	NOUN
ap-1167	150	35	bound	bind	VERB
ap-1167	150	36	and	and	CCONJ
ap-1167	150	37	approximately	approximately	ADV
ap-1167	150	38	228	228	NUM
ap-1167	150	39	iterations	iteration	NOUN
ap-1167	150	40	with	with	ADP
ap-1167	150	41	our	our	PRON
ap-1167	150	42	approach	approach	NOUN
ap-1167	150	43	.	.	PUNCT
ap-1167	151	1	calculating	calculate	VERB
ap-1167	151	2	more	more	ADJ
ap-1167	151	3	iterations	iteration	NOUN
ap-1167	151	4	beyond	beyond	ADP
ap-1167	151	5	the	the	DET
ap-1167	151	6	bound	bind	VERB
ap-1167	151	7	does	do	AUX
ap-1167	151	8	not	not	PART
ap-1167	151	9	make	make	VERB
ap-1167	151	10	sense	sense	NOUN
ap-1167	151	11	in	in	ADP
ap-1167	151	12	this	this	DET
ap-1167	151	13	case	case	NOUN
ap-1167	151	14	,	,	PUNCT
ap-1167	151	15	because	because	SCONJ
ap-1167	151	16	each	each	DET
ap-1167	151	17	accumulant	accumulant	NOUN
ap-1167	151	18	is	be	AUX
ap-1167	151	19	smaller	small	ADJ
ap-1167	151	20	than	than	ADP
ap-1167	151	21	the	the	DET
ap-1167	151	22	error	error	NOUN
ap-1167	151	23	of	of	ADP
ap-1167	151	24	the	the	DET
ap-1167	151	25	result	result	NOUN
ap-1167	151	26	.	.	PUNCT
ap-1167	152	1	34	34	NUM
ap-1167	152	2	acta	acta	PROPN
ap-1167	152	3	polytechnica	polytechnica	PROPN
ap-1167	152	4	vol	vol	NOUN
ap-1167	152	5	.	.	PROPN
ap-1167	153	1	50	50	NUM
ap-1167	153	2	no	no	NOUN
ap-1167	153	3	.	.	PUNCT
ap-1167	154	1	2/2010	2/2010	NUM
ap-1167	154	2	444036322824	444036322824	NUM
ap-1167	154	3	result	result	VERB
ap-1167	154	4	error	error	NOUN
ap-1167	154	5	forward	forward	NOUN
ap-1167	154	6	error	error	NOUN
ap-1167	154	7	bound	bind	VERB
ap-1167	154	8	our	our	PRON
ap-1167	154	9	approach	approach	NOUN
ap-1167	154	10	20	20	NUM
ap-1167	154	11	running	running	NOUN
ap-1167	154	12	error	error	NOUN
ap-1167	154	13	−18	−18	NUM
ap-1167	154	14	8	8	NUM
ap-1167	154	15	1612	1612	NUM
ap-1167	154	16	0	0	NUM
ap-1167	155	1	−2	−2	NOUN
ap-1167	155	2	−4	−4	X
ap-1167	155	3	−6	−6	NOUN
ap-1167	156	1	−8	−8	X
ap-1167	156	2	−10	−10	X
ap-1167	156	3	−12	−12	NOUN
ap-1167	156	4	−14	−14	NOUN
ap-1167	156	5	−16	−16	DET
ap-1167	156	6	−14	−14	NUM
ap-1167	156	7	−12	−12	NUM
ap-1167	157	1	−10	−10	NOUN
ap-1167	157	2	−8	−8	X
ap-1167	158	1	−6	−6	INTJ
ap-1167	158	2	−4	−4	X
ap-1167	159	1	−2	−2	NOUN
ap-1167	159	2	0	0	NUM
ap-1167	159	3	0	0	NUM
ap-1167	159	4	4	4	NUM
ap-1167	159	5	48	48	NUM
ap-1167	159	6	−18	−18	NUM
ap-1167	159	7	log2	log2	PROPN
ap-1167	159	8	n	n	ADP
ap-1167	159	9	l	l	NOUN
ap-1167	159	10	og	og	INTJ
ap-1167	159	11	ar	ar	PROPN
ap-1167	160	1	it	it	PRON
ap-1167	160	2	hm	hm	INTJ
ap-1167	160	3	of	of	ADP
ap-1167	160	4	er	er	INTJ
ap-1167	160	5	ro	ro	INTJ
ap-1167	160	6	r	r	NOUN
ap-1167	160	7	52	52	NUM
ap-1167	160	8	−16	−16	DET
ap-1167	160	9	fig	fig	NOUN
ap-1167	160	10	.	.	PUNCT
ap-1167	161	1	3	3	NUM
ap-1167	161	2	:	:	PUNCT
ap-1167	161	3	calculated	calculate	VERB
ap-1167	161	4	value	value	NOUN
ap-1167	161	5	of	of	ADP
ap-1167	161	6	ŷn	ŷn	PROPN
ap-1167	161	7	and	and	CCONJ
ap-1167	161	8	its	its	PRON
ap-1167	161	9	error	error	NOUN
ap-1167	161	10	bounds	bound	NOUN
ap-1167	161	11	(	(	PUNCT
ap-1167	161	12	reverse	reverse	ADJ
ap-1167	161	13	sum	sum	NOUN
ap-1167	161	14	direction	direction	NOUN
ap-1167	161	15	)	)	PUNCT
ap-1167	161	16	the	the	DET
ap-1167	161	17	second	second	ADJ
ap-1167	161	18	case	case	NOUN
ap-1167	161	19	performs	perform	VERB
ap-1167	161	20	the	the	DET
ap-1167	161	21	sum	sum	NOUN
ap-1167	161	22	in	in	ADP
ap-1167	161	23	the	the	DET
ap-1167	161	24	reverse	reverse	ADJ
ap-1167	161	25	order	order	NOUN
ap-1167	161	26	,	,	PUNCT
ap-1167	161	27	i.e.	i.e.	X
ap-1167	161	28	going	go	VERB
ap-1167	161	29	from	from	ADP
ap-1167	161	30	numbers	number	NOUN
ap-1167	161	31	of	of	ADP
ap-1167	161	32	the	the	DET
ap-1167	161	33	smallest	small	ADJ
ap-1167	161	34	magnitude	magnitude	NOUN
ap-1167	161	35	towards	towards	ADP
ap-1167	161	36	greater	great	ADJ
ap-1167	161	37	numbers	number	NOUN
ap-1167	161	38	(	(	PUNCT
ap-1167	161	39	see	see	VERB
ap-1167	161	40	figure	figure	NOUN
ap-1167	161	41	3	3	NUM
ap-1167	161	42	)	)	PUNCT
ap-1167	161	43	.	.	PUNCT
ap-1167	162	1	note	note	VERB
ap-1167	162	2	that	that	SCONJ
ap-1167	162	3	this	this	DET
ap-1167	162	4	scenario	scenario	NOUN
ap-1167	162	5	demonstrates	demonstrate	VERB
ap-1167	162	6	the	the	DET
ap-1167	162	7	claim	claim	NOUN
ap-1167	162	8	that	that	SCONJ
ap-1167	162	9	an	an	DET
ap-1167	162	10	error	error	NOUN
ap-1167	162	11	bound	bind	VERB
ap-1167	162	12	obtained	obtain	VERB
ap-1167	162	13	a	a	DET
ap-1167	162	14	-	-	PUNCT
ap-1167	162	15	priori	priori	ADJ
ap-1167	162	16	(	(	PUNCT
ap-1167	162	17	i.e.	i.e.	X
ap-1167	162	18	the	the	DET
ap-1167	162	19	forward	forward	ADJ
ap-1167	162	20	error	error	NOUN
ap-1167	162	21	bound	bind	VERB
ap-1167	162	22	)	)	PUNCT
ap-1167	162	23	is	be	AUX
ap-1167	162	24	often	often	ADV
ap-1167	162	25	too	too	ADV
ap-1167	162	26	pessimistic	pessimistic	ADJ
ap-1167	162	27	and	and	CCONJ
ap-1167	162	28	presents	present	VERB
ap-1167	162	29	the	the	DET
ap-1167	162	30	worst	bad	ADJ
ap-1167	162	31	case	case	NOUN
ap-1167	162	32	.	.	PUNCT
ap-1167	163	1	using	use	VERB
ap-1167	163	2	it	it	PRON
ap-1167	163	3	would	would	AUX
ap-1167	163	4	lead	lead	VERB
ap-1167	163	5	to	to	ADP
ap-1167	163	6	premature	premature	ADJ
ap-1167	163	7	termination	termination	NOUN
ap-1167	163	8	of	of	ADP
ap-1167	163	9	the	the	DET
ap-1167	163	10	sum	sum	NOUN
ap-1167	163	11	evaluation	evaluation	NOUN
ap-1167	163	12	.	.	PUNCT
ap-1167	164	1	one	one	NUM
ap-1167	164	2	more	more	ADJ
ap-1167	164	3	thing	thing	NOUN
ap-1167	164	4	is	be	AUX
ap-1167	164	5	demonstrated	demonstrate	VERB
ap-1167	164	6	,	,	PUNCT
ap-1167	164	7	i.e.	i.e.	X
ap-1167	164	8	,	,	PUNCT
ap-1167	164	9	that	that	SCONJ
ap-1167	164	10	we	we	PRON
ap-1167	164	11	should	should	AUX
ap-1167	164	12	accumulate	accumulate	VERB
ap-1167	164	13	numbers	number	NOUN
ap-1167	164	14	in	in	ADP
ap-1167	164	15	increasing	increase	VERB
ap-1167	164	16	order	order	NOUN
ap-1167	164	17	of	of	ADP
ap-1167	164	18	magnitude	magnitude	NOUN
ap-1167	164	19	.	.	PUNCT
ap-1167	165	1	if	if	SCONJ
ap-1167	165	2	we	we	PRON
ap-1167	165	3	do	do	AUX
ap-1167	165	4	not	not	PART
ap-1167	165	5	do	do	VERB
ap-1167	165	6	that	that	PRON
ap-1167	165	7	,	,	PUNCT
ap-1167	165	8	numbers	number	NOUN
ap-1167	165	9	with	with	ADP
ap-1167	165	10	small	small	ADJ
ap-1167	165	11	magnitude	magnitude	NOUN
ap-1167	165	12	start	start	VERB
ap-1167	165	13	to	to	PART
ap-1167	165	14	contribute	contribute	VERB
ap-1167	165	15	less	less	ADV
ap-1167	165	16	and	and	CCONJ
ap-1167	165	17	less	less	ADJ
ap-1167	165	18	to	to	ADP
ap-1167	165	19	a	a	DET
ap-1167	165	20	proportionally	proportionally	ADV
ap-1167	165	21	huge	huge	ADJ
ap-1167	165	22	sum	sum	NOUN
ap-1167	165	23	value	value	NOUN
ap-1167	165	24	,	,	PUNCT
ap-1167	165	25	and	and	CCONJ
ap-1167	165	26	we	we	PRON
ap-1167	165	27	sooner	soon	ADV
ap-1167	165	28	or	or	CCONJ
ap-1167	165	29	later	later	ADV
ap-1167	165	30	find	find	VERB
ap-1167	165	31	that	that	SCONJ
ap-1167	165	32	further	further	ADJ
ap-1167	165	33	additions	addition	NOUN
ap-1167	165	34	do	do	AUX
ap-1167	165	35	not	not	PART
ap-1167	165	36	change	change	VERB
ap-1167	165	37	the	the	DET
ap-1167	165	38	value	value	NOUN
ap-1167	165	39	of	of	ADP
ap-1167	165	40	the	the	DET
ap-1167	165	41	sum	sum	NOUN
ap-1167	165	42	.	.	PUNCT
ap-1167	166	1	due	due	ADP
ap-1167	166	2	to	to	ADP
ap-1167	166	3	this	this	DET
ap-1167	166	4	fact	fact	NOUN
ap-1167	166	5	,	,	PUNCT
ap-1167	166	6	the	the	DET
ap-1167	166	7	harmonic	harmonic	ADJ
ap-1167	166	8	sequence	sequence	NOUN
ap-1167	166	9	∞∑	∞∑	NOUN
ap-1167	166	10	k=1	k=1	ADP
ap-1167	166	11	1	1	NUM
ap-1167	166	12	k	k	NOUN
ap-1167	166	13	=	=	SYM
ap-1167	166	14	∞	∞	NUM
ap-1167	166	15	converges	converge	VERB
ap-1167	166	16	in	in	ADP
ap-1167	166	17	finite	finite	ADJ
ap-1167	166	18	arithmetics	arithmetic	NOUN
ap-1167	166	19	,	,	PUNCT
ap-1167	166	20	and	and	CCONJ
ap-1167	166	21	has	have	VERB
ap-1167	166	22	a	a	DET
ap-1167	166	23	finite	finite	ADJ
ap-1167	166	24	sum	sum	NOUN
ap-1167	166	25	depending	depend	VERB
ap-1167	166	26	on	on	ADP
ap-1167	166	27	the	the	DET
ap-1167	166	28	type	type	NOUN
ap-1167	166	29	of	of	ADP
ap-1167	166	30	arithmetic	arithmetic	NOUN
ap-1167	166	31	.	.	PUNCT
ap-1167	167	1	the	the	DET
ap-1167	167	2	following	follow	VERB
ap-1167	167	3	table	table	NOUN
ap-1167	167	4	presents	present	VERB
ap-1167	167	5	selected	select	VERB
ap-1167	167	6	portions	portion	NOUN
ap-1167	167	7	of	of	ADP
ap-1167	167	8	the	the	DET
ap-1167	167	9	evaluation	evaluation	NOUN
ap-1167	167	10	time	time	NOUN
ap-1167	167	11	for	for	ADP
ap-1167	167	12	all	all	DET
ap-1167	167	13	two	two	NUM
ap-1167	167	14	a	a	DET
ap-1167	167	15	-	-	PUNCT
ap-1167	167	16	posteriori	posteriori	NOUN
ap-1167	167	17	error	error	NOUN
ap-1167	167	18	analyses	analysis	NOUN
ap-1167	167	19	including	include	VERB
ap-1167	167	20	the	the	DET
ap-1167	167	21	original	original	ADJ
ap-1167	167	22	computation	computation	NOUN
ap-1167	167	23	.	.	PUNCT
ap-1167	168	1	in	in	ADP
ap-1167	168	2	addition	addition	NOUN
ap-1167	168	3	,	,	PUNCT
ap-1167	168	4	the	the	DET
ap-1167	168	5	table	table	NOUN
ap-1167	168	6	shows	show	VERB
ap-1167	168	7	the	the	DET
ap-1167	168	8	run	run	ADJ
ap-1167	168	9	time	time	NOUN
ap-1167	168	10	for	for	ADP
ap-1167	168	11	the	the	DET
ap-1167	168	12	objdouble	objdouble	ADJ
ap-1167	168	13	class	class	NOUN
ap-1167	168	14	,	,	PUNCT
ap-1167	168	15	which	which	PRON
ap-1167	168	16	wraps	wrap	VERB
ap-1167	168	17	the	the	DET
ap-1167	168	18	double	double	ADJ
ap-1167	168	19	data	datum	NOUN
ap-1167	168	20	class	class	NOUN
ap-1167	168	21	that	that	PRON
ap-1167	168	22	is	be	AUX
ap-1167	168	23	used	use	VERB
ap-1167	168	24	after	after	ADP
ap-1167	168	25	subtracting	subtract	VERB
ap-1167	168	26	the	the	DET
ap-1167	168	27	double	double	ADJ
ap-1167	168	28	column	column	NOUN
ap-1167	168	29	to	to	PART
ap-1167	168	30	determine	determine	VERB
ap-1167	168	31	the	the	DET
ap-1167	168	32	amount	amount	NOUN
ap-1167	168	33	of	of	ADP
ap-1167	168	34	the	the	DET
ap-1167	168	35	c++	c++	NOUN
ap-1167	168	36	object	object	VERB
ap-1167	168	37	overhead	overhead	ADV
ap-1167	168	38	.	.	PUNCT
ap-1167	169	1	the	the	DET
ap-1167	169	2	results	result	NOUN
ap-1167	169	3	were	be	AUX
ap-1167	169	4	obtained	obtain	VERB
ap-1167	169	5	with	with	ADP
ap-1167	169	6	the	the	DET
ap-1167	169	7	posix	posix	ADJ
ap-1167	169	8	getrusageapi	getrusageapi	NOUN
ap-1167	169	9	which	which	PRON
ap-1167	169	10	provides	provide	VERB
ap-1167	169	11	,	,	PUNCT
ap-1167	169	12	besides	besides	SCONJ
ap-1167	169	13	other	other	ADJ
ap-1167	169	14	information	information	NOUN
ap-1167	169	15	,	,	PUNCT
ap-1167	169	16	the	the	DET
ap-1167	169	17	amount	amount	NOUN
ap-1167	169	18	of	of	ADP
ap-1167	169	19	used	use	VERB
ap-1167	169	20	time	time	NOUN
ap-1167	169	21	in	in	ADP
ap-1167	169	22	seconds	second	NOUN
ap-1167	169	23	and	and	CCONJ
ap-1167	169	24	microseconds	microsecond	NOUN
ap-1167	169	25	since	since	SCONJ
ap-1167	169	26	the	the	DET
ap-1167	169	27	start	start	NOUN
ap-1167	169	28	of	of	ADP
ap-1167	169	29	the	the	DET
ap-1167	169	30	process	process	NOUN
ap-1167	169	31	.	.	PUNCT
ap-1167	170	1	for	for	ADP
ap-1167	170	2	measuring	measure	VERB
ap-1167	170	3	purposes	purpose	NOUN
ap-1167	170	4	,	,	PUNCT
ap-1167	170	5	these	these	PRON
ap-1167	170	6	are	be	AUX
ap-1167	170	7	internally	internally	ADV
ap-1167	170	8	converted	convert	VERB
ap-1167	170	9	into	into	ADP
ap-1167	170	10	milliseconds	millisecond	NOUN
ap-1167	170	11	and	and	CCONJ
ap-1167	170	12	a	a	DET
ap-1167	170	13	difference	difference	NOUN
ap-1167	170	14	of	of	ADP
ap-1167	170	15	two	two	NUM
ap-1167	170	16	millisecond	millisecond	NOUN
ap-1167	170	17	values	value	NOUN
ap-1167	170	18	performs	perform	VERB
ap-1167	170	19	a	a	DET
ap-1167	170	20	measurement	measurement	NOUN
ap-1167	170	21	without	without	ADP
ap-1167	170	22	interference	interference	NOUN
ap-1167	170	23	with	with	ADP
ap-1167	170	24	other	other	ADJ
ap-1167	170	25	processes	process	NOUN
ap-1167	170	26	and	and	CCONJ
ap-1167	170	27	the	the	DET
ap-1167	170	28	operating	operating	NOUN
ap-1167	170	29	system	system	NOUN
ap-1167	170	30	.	.	PUNCT
ap-1167	171	1	each	each	DET
ap-1167	171	2	value	value	NOUN
ap-1167	171	3	was	be	AUX
ap-1167	171	4	measured	measure	VERB
ap-1167	171	5	50	50	NUM
ap-1167	171	6	times	time	NOUN
ap-1167	171	7	and	and	CCONJ
ap-1167	171	8	the	the	DET
ap-1167	171	9	results	result	NOUN
ap-1167	171	10	were	be	AUX
ap-1167	171	11	statistically	statistically	ADV
ap-1167	171	12	evaluated	evaluate	VERB
ap-1167	171	13	[	[	X
ap-1167	171	14	2	2	NUM
ap-1167	171	15	]	]	PUNCT
ap-1167	171	16	.	.	PUNCT
ap-1167	172	1	when	when	SCONJ
ap-1167	172	2	we	we	PRON
ap-1167	172	3	compare	compare	VERB
ap-1167	172	4	the	the	DET
ap-1167	172	5	traditional	traditional	ADJ
ap-1167	172	6	running	running	NOUN
ap-1167	172	7	error	error	NOUN
ap-1167	172	8	analysis	analysis	NOUN
ap-1167	172	9	run	run	VERB
ap-1167	172	10	time	time	NOUN
ap-1167	172	11	to	to	ADP
ap-1167	172	12	a	a	DET
ap-1167	172	13	simple	simple	ADJ
ap-1167	172	14	evaluation	evaluation	NOUN
ap-1167	172	15	in	in	ADP
ap-1167	172	16	double	double	ADJ
ap-1167	172	17	precision	precision	NOUN
ap-1167	172	18	,	,	PUNCT
ap-1167	172	19	we	we	PRON
ap-1167	172	20	obtain	obtain	VERB
ap-1167	172	21	that	that	DET
ap-1167	172	22	object	object	NOUN
ap-1167	172	23	-	-	PUNCT
ap-1167	172	24	oriented	orient	VERB
ap-1167	172	25	running	running	NOUN
ap-1167	172	26	error	error	NOUN
ap-1167	172	27	analysis	analysis	NOUN
ap-1167	172	28	with	with	ADP
ap-1167	172	29	the	the	DET
ap-1167	172	30	radouble	radouble	ADJ
ap-1167	172	31	class	class	NOUN
ap-1167	172	32	is	be	AUX
ap-1167	172	33	approximately	approximately	ADV
ap-1167	172	34	2.81	2.81	NUM
ap-1167	172	35	times	time	NOUN
ap-1167	172	36	slower	slow	ADJ
ap-1167	172	37	.	.	PUNCT
ap-1167	173	1	this	this	DET
ap-1167	173	2	slowdown	slowdown	NOUN
ap-1167	173	3	includes	include	VERB
ap-1167	173	4	the	the	DET
ap-1167	173	5	c++	c++	NOUN
ap-1167	173	6	overhead	overhead	NOUN
ap-1167	173	7	,	,	PUNCT
ap-1167	173	8	consisting	consist	VERB
ap-1167	173	9	of	of	ADP
ap-1167	173	10	object	object	NOUN
ap-1167	173	11	construction	construction	NOUN
ap-1167	173	12	and	and	CCONJ
ap-1167	173	13	operator	operator	NOUN
ap-1167	173	14	calls	call	NOUN
ap-1167	173	15	.	.	PUNCT
ap-1167	174	1	the	the	DET
ap-1167	174	2	overhead	overhead	NOUN
ap-1167	174	3	was	be	AUX
ap-1167	174	4	measured	measure	VERB
ap-1167	174	5	with	with	ADP
ap-1167	174	6	the	the	DET
ap-1167	174	7	objdouble	objdouble	ADJ
ap-1167	174	8	class	class	NOUN
ap-1167	174	9	and	and	CCONJ
ap-1167	174	10	the	the	DET
ap-1167	174	11	results	result	NOUN
ap-1167	174	12	show	show	VERB
ap-1167	174	13	that	that	SCONJ
ap-1167	174	14	the	the	DET
ap-1167	174	15	evaluation	evaluation	NOUN
ap-1167	174	16	with	with	ADP
ap-1167	174	17	objdouble	objdouble	ADJ
ap-1167	174	18	class	class	NOUN
ap-1167	174	19	took	take	VERB
ap-1167	174	20	2	2	NUM
ap-1167	174	21	times	time	NOUN
ap-1167	174	22	longer	long	ADJ
ap-1167	174	23	than	than	ADP
ap-1167	174	24	with	with	ADP
ap-1167	174	25	the	the	DET
ap-1167	174	26	double	double	ADJ
ap-1167	174	27	data	data	NOUN
ap-1167	174	28	type	type	NOUN
ap-1167	174	29	.	.	PUNCT
ap-1167	175	1	our	our	PRON
ap-1167	175	2	approach	approach	NOUN
ap-1167	175	3	is	be	AUX
ap-1167	175	4	only	only	ADV
ap-1167	175	5	2.35	2.35	NUM
ap-1167	175	6	times	time	NOUN
ap-1167	175	7	slower	slow	ADJ
ap-1167	175	8	than	than	ADP
ap-1167	175	9	the	the	DET
ap-1167	175	10	original	original	ADJ
ap-1167	175	11	approach	approach	NOUN
ap-1167	175	12	with	with	ADP
ap-1167	175	13	the	the	DET
ap-1167	175	14	double	double	ADJ
ap-1167	175	15	data	data	NOUN
ap-1167	175	16	type	type	NOUN
ap-1167	175	17	,	,	PUNCT
ap-1167	175	18	and	and	CCONJ
ap-1167	175	19	it	it	PRON
ap-1167	175	20	is	be	AUX
ap-1167	175	21	1.19	1.19	NUM
ap-1167	175	22	times	time	NOUN
ap-1167	175	23	faster	fast	ADJ
ap-1167	175	24	than	than	ADP
ap-1167	175	25	the	the	DET
ap-1167	175	26	traditional	traditional	ADJ
ap-1167	175	27	approach	approach	NOUN
ap-1167	175	28	.	.	PUNCT
ap-1167	176	1	this	this	DET
ap-1167	176	2	speed	speed	NOUN
ap-1167	176	3	up	up	ADP
ap-1167	176	4	is	be	AUX
ap-1167	176	5	what	what	PRON
ap-1167	176	6	we	we	PRON
ap-1167	176	7	have	have	AUX
ap-1167	176	8	been	be	AUX
ap-1167	176	9	expecting	expect	VERB
ap-1167	176	10	from	from	ADP
ap-1167	176	11	tab	tab	NOUN
ap-1167	176	12	.	.	PUNCT
ap-1167	177	1	2	2	NUM
ap-1167	177	2	.	.	NOUN
ap-1167	177	3	table	table	NOUN
ap-1167	177	4	3	3	NUM
ap-1167	177	5	:	:	PUNCT
ap-1167	177	6	run	run	VERB
ap-1167	177	7	times	time	NOUN
ap-1167	177	8	for	for	ADP
ap-1167	177	9	reverse	reverse	ADJ
ap-1167	177	10	sum	sum	NOUN
ap-1167	177	11	evaluations	evaluation	NOUN
ap-1167	177	12	of	of	ADP
ap-1167	177	13	selected	select	VERB
ap-1167	177	14	n	n	PRON
ap-1167	177	15	operations	operation	NOUN
ap-1167	177	16	with	with	ADP
ap-1167	177	17	four	four	NUM
ap-1167	177	18	data	datum	NOUN
ap-1167	177	19	types	type	NOUN
ap-1167	177	20	.	.	PUNCT
ap-1167	178	1	these	these	PRON
ap-1167	178	2	are	be	AUX
ap-1167	178	3	double	double	ADJ
ap-1167	178	4	data	data	NOUN
ap-1167	178	5	type	type	NOUN
ap-1167	178	6	with	with	ADP
ap-1167	178	7	no	no	DET
ap-1167	178	8	error	error	NOUN
ap-1167	178	9	analysis	analysis	NOUN
ap-1167	178	10	,	,	PUNCT
ap-1167	178	11	the	the	DET
ap-1167	178	12	radouble	radouble	ADJ
ap-1167	178	13	data	data	NOUN
ap-1167	178	14	type	type	NOUN
ap-1167	178	15	,	,	PUNCT
ap-1167	178	16	an	an	DET
ap-1167	178	17	object	object	NOUN
ap-1167	178	18	-	-	PUNCT
ap-1167	178	19	oriented	orient	VERB
ap-1167	178	20	traditional	traditional	ADJ
ap-1167	178	21	running	running	NOUN
ap-1167	178	22	error	error	NOUN
ap-1167	178	23	analysis	analysis	NOUN
ap-1167	178	24	,	,	PUNCT
ap-1167	178	25	fdouble	fdouble	ADJ
ap-1167	178	26	data	datum	NOUN
ap-1167	178	27	type	type	NOUN
ap-1167	178	28	which	which	PRON
ap-1167	178	29	performs	perform	VERB
ap-1167	178	30	fpu	fpu	NOUN
ap-1167	178	31	-	-	PUNCT
ap-1167	178	32	supported	support	VERB
ap-1167	178	33	running	running	NOUN
ap-1167	178	34	error	error	NOUN
ap-1167	178	35	analysis	analysis	NOUN
ap-1167	178	36	,	,	PUNCT
ap-1167	178	37	and	and	CCONJ
ap-1167	178	38	the	the	DET
ap-1167	178	39	objdouble	objdouble	ADJ
ap-1167	178	40	class	class	NOUN
ap-1167	178	41	,	,	PUNCT
ap-1167	178	42	which	which	PRON
ap-1167	178	43	wraps	wrap	VERB
ap-1167	178	44	double	double	ADJ
ap-1167	178	45	data	data	NOUN
ap-1167	178	46	type	type	NOUN
ap-1167	178	47	and	and	CCONJ
ap-1167	178	48	is	be	AUX
ap-1167	178	49	used	use	VERB
ap-1167	178	50	to	to	PART
ap-1167	178	51	measure	measure	VERB
ap-1167	178	52	the	the	DET
ap-1167	178	53	c++	c++	NOUN
ap-1167	178	54	overhead	overhead	ADV
ap-1167	178	55	.	.	PUNCT
ap-1167	179	1	all	all	DET
ap-1167	179	2	values	value	NOUN
ap-1167	179	3	are	be	AUX
ap-1167	179	4	rounded	rounded	ADJ
ap-1167	179	5	to	to	ADP
ap-1167	179	6	whole	whole	ADJ
ap-1167	179	7	milliseconds	millisecond	NOUN
ap-1167	179	8	log2n	log2n	PROPN
ap-1167	179	9	double	double	ADJ
ap-1167	179	10	radouble	radouble	ADJ
ap-1167	179	11	fdouble	fdouble	ADJ
ap-1167	179	12	objdouble	objdouble	ADJ
ap-1167	179	13	16	16	NUM
ap-1167	179	14	1	1	NUM
ap-1167	179	15	3	3	NUM
ap-1167	179	16	3	3	NUM
ap-1167	179	17	2	2	NUM
ap-1167	179	18	20	20	NUM
ap-1167	179	19	8	8	NUM
ap-1167	179	20	50	50	NUM
ap-1167	179	21	42	42	NUM
ap-1167	179	22	36	36	NUM
ap-1167	179	23	24	24	NUM
ap-1167	179	24	285	285	NUM
ap-1167	179	25	803	803	NUM
ap-1167	179	26	672	672	NUM
ap-1167	179	27	573	573	NUM
ap-1167	179	28	28	28	NUM
ap-1167	179	29	4	4	NUM
ap-1167	179	30	568	568	NUM
ap-1167	179	31	12	12	NUM
ap-1167	179	32	849	849	NUM
ap-1167	179	33	10	10	NUM
ap-1167	179	34	777	777	NUM
ap-1167	179	35	9	9	NUM
ap-1167	179	36	178	178	NUM
ap-1167	179	37	32	32	NUM
ap-1167	179	38	73	73	NUM
ap-1167	179	39	120	120	NUM
ap-1167	179	40	205	205	NUM
ap-1167	179	41	726	726	NUM
ap-1167	179	42	172	172	NUM
ap-1167	179	43	538	538	NUM
ap-1167	179	44	146	146	NUM
ap-1167	179	45	847	847	NUM
ap-1167	179	46	4	4	NUM
ap-1167	179	47	conclusions	conclusion	NOUN
ap-1167	179	48	the	the	DET
ap-1167	179	49	traditional	traditional	ADJ
ap-1167	179	50	running	running	NOUN
ap-1167	179	51	error	error	NOUN
ap-1167	179	52	analysis	analysis	NOUN
ap-1167	179	53	approach	approach	NOUN
ap-1167	179	54	uses	use	VERB
ap-1167	179	55	the	the	DET
ap-1167	179	56	u|ŝ|	u|ŝ|	NOUN
ap-1167	179	57	term	term	NOUN
ap-1167	179	58	to	to	PART
ap-1167	179	59	get	get	VERB
ap-1167	179	60	a	a	DET
ap-1167	179	61	rounding	round	VERB
ap-1167	179	62	error	error	NOUN
ap-1167	179	63	estimate	estimate	NOUN
ap-1167	179	64	and	and	CCONJ
ap-1167	179	65	,	,	PUNCT
ap-1167	179	66	as	as	SCONJ
ap-1167	179	67	we	we	PRON
ap-1167	179	68	have	have	AUX
ap-1167	179	69	shown	show	VERB
ap-1167	179	70	,	,	PUNCT
ap-1167	179	71	this	this	DET
ap-1167	179	72	estimate	estimate	NOUN
ap-1167	179	73	can	can	AUX
ap-1167	179	74	be	be	AUX
ap-1167	179	75	up	up	ADP
ap-1167	179	76	to	to	ADP
ap-1167	179	77	two	two	NUM
ap-1167	179	78	times	time	NOUN
ap-1167	179	79	35	35	NUM
ap-1167	179	80	acta	acta	PROPN
ap-1167	179	81	polytechnica	polytechnica	PROPN
ap-1167	179	82	vol	vol	NOUN
ap-1167	179	83	.	.	PROPN
ap-1167	180	1	50	50	NUM
ap-1167	180	2	no	no	NOUN
ap-1167	180	3	.	.	PUNCT
ap-1167	181	1	2/2010	2/2010	NUM
ap-1167	181	2	larger	large	ADJ
ap-1167	181	3	than	than	ADP
ap-1167	181	4	the	the	DET
ap-1167	181	5	actual	actual	ADJ
ap-1167	181	6	rounding	rounding	NOUN
ap-1167	181	7	error	error	NOUN
ap-1167	181	8	.	.	PUNCT
ap-1167	182	1	moreover	moreover	ADV
ap-1167	182	2	,	,	PUNCT
ap-1167	182	3	this	this	DET
ap-1167	182	4	term	term	NOUN
ap-1167	182	5	always	always	ADV
ap-1167	182	6	generates	generate	VERB
ap-1167	182	7	an	an	DET
ap-1167	182	8	error	error	NOUN
ap-1167	182	9	,	,	PUNCT
ap-1167	182	10	regardless	regardless	ADV
ap-1167	182	11	of	of	ADP
ap-1167	182	12	whether	whether	SCONJ
ap-1167	182	13	an	an	DET
ap-1167	182	14	error	error	NOUN
ap-1167	182	15	was	be	AUX
ap-1167	182	16	physically	physically	ADV
ap-1167	182	17	committed	commit	VERB
ap-1167	182	18	.	.	PUNCT
ap-1167	183	1	by	by	ADP
ap-1167	183	2	exploiting	exploit	VERB
ap-1167	183	3	the	the	DET
ap-1167	183	4	floating	float	VERB
ap-1167	183	5	point	point	NOUN
ap-1167	183	6	unit	unit	NOUN
ap-1167	183	7	’s	’s	PART
ap-1167	183	8	behavior	behavior	NOUN
ap-1167	183	9	of	of	ADP
ap-1167	183	10	the	the	DET
ap-1167	183	11	intel	intel	PROPN
ap-1167	183	12	x86	x86	NOUN
ap-1167	183	13	platform	platform	NOUN
ap-1167	183	14	,	,	PUNCT
ap-1167	183	15	we	we	PRON
ap-1167	183	16	are	be	AUX
ap-1167	183	17	able	able	ADJ
ap-1167	183	18	to	to	PART
ap-1167	183	19	obtain	obtain	VERB
ap-1167	183	20	an	an	DET
ap-1167	183	21	11bit	11bit	NOUN
ap-1167	183	22	error	error	NOUN
ap-1167	183	23	estimate	estimate	NOUN
ap-1167	183	24	by	by	ADP
ap-1167	183	25	subtracting	subtract	VERB
ap-1167	183	26	the	the	DET
ap-1167	183	27	rounded	rounded	ADJ
ap-1167	183	28	result	result	NOUN
ap-1167	183	29	ŝ	ŝ	NOUN
ap-1167	183	30	from	from	ADP
ap-1167	183	31	its	its	PRON
ap-1167	183	32	not	not	PART
ap-1167	183	33	yet	yet	ADV
ap-1167	183	34	rounded	rounded	ADJ
ap-1167	183	35	equivalent	equivalent	ADJ
ap-1167	183	36	ŝ	ŝ	NOUN
ap-1167	183	37	,	,	PUNCT
ap-1167	183	38	and	and	CCONJ
ap-1167	183	39	when	when	SCONJ
ap-1167	183	40	divided	divide	VERB
ap-1167	183	41	by	by	ADP
ap-1167	183	42	ŝ	ŝ	NOUN
ap-1167	183	43	,	,	PUNCT
ap-1167	183	44	this	this	DET
ap-1167	183	45	estimate	estimate	NOUN
ap-1167	183	46	is	be	AUX
ap-1167	183	47	always	always	ADV
ap-1167	183	48	less	less	ADJ
ap-1167	183	49	than	than	ADP
ap-1167	183	50	or	or	CCONJ
ap-1167	183	51	equal	equal	ADJ
ap-1167	183	52	to	to	ADP
ap-1167	183	53	the	the	DET
ap-1167	183	54	unit	unit	NOUN
ap-1167	183	55	roundoff	roundoff	VERB
ap-1167	183	56	u.	u.	VERB
ap-1167	183	57	our	our	PRON
ap-1167	183	58	approach	approach	NOUN
ap-1167	183	59	is	be	AUX
ap-1167	183	60	very	very	ADV
ap-1167	183	61	similar	similar	ADJ
ap-1167	183	62	to	to	ADP
ap-1167	183	63	the	the	DET
ap-1167	183	64	traditional	traditional	ADJ
ap-1167	183	65	approach	approach	NOUN
ap-1167	183	66	;	;	PUNCT
ap-1167	183	67	it	it	PRON
ap-1167	183	68	also	also	ADV
ap-1167	183	69	needs	need	VERB
ap-1167	183	70	four	four	NUM
ap-1167	183	71	fpu	fpu	NOUN
ap-1167	183	72	instructions	instruction	NOUN
ap-1167	183	73	,	,	PUNCT
ap-1167	183	74	but	but	CCONJ
ap-1167	183	75	it	it	PRON
ap-1167	183	76	replaces	replace	VERB
ap-1167	183	77	multiplication	multiplication	NOUN
ap-1167	183	78	by	by	ADP
ap-1167	183	79	subtraction	subtraction	NOUN
ap-1167	183	80	and	and	CCONJ
ap-1167	183	81	that	that	PRON
ap-1167	183	82	saves	save	VERB
ap-1167	183	83	2	2	NUM
ap-1167	183	84	cpu	cpu	NOUN
ap-1167	183	85	cycles	cycle	NOUN
ap-1167	183	86	per	per	ADP
ap-1167	183	87	evaluation	evaluation	NOUN
ap-1167	183	88	,	,	PUNCT
ap-1167	183	89	obtaining	obtain	VERB
ap-1167	183	90	almost	almost	ADV
ap-1167	183	91	20	20	NUM
ap-1167	183	92	per	per	NOUN
ap-1167	183	93	cent	cent	NOUN
ap-1167	183	94	speedup	speedup	NOUN
ap-1167	183	95	over	over	ADP
ap-1167	183	96	traditional	traditional	ADJ
ap-1167	183	97	running	running	NOUN
ap-1167	183	98	error	error	NOUN
ap-1167	183	99	analysis	analysis	NOUN
ap-1167	183	100	.	.	PUNCT
ap-1167	184	1	we	we	PRON
ap-1167	184	2	encourage	encourage	VERB
ap-1167	184	3	the	the	DET
ap-1167	184	4	use	use	NOUN
ap-1167	184	5	of	of	ADP
ap-1167	184	6	running	run	VERB
ap-1167	184	7	error	error	NOUN
ap-1167	184	8	analysis	analysis	NOUN
ap-1167	184	9	in	in	ADP
ap-1167	184	10	all	all	DET
ap-1167	184	11	iterative	iterative	NOUN
ap-1167	184	12	tasks	task	NOUN
ap-1167	184	13	where	where	SCONJ
ap-1167	184	14	critical	critical	ADJ
ap-1167	184	15	cancellation	cancellation	NOUN
ap-1167	184	16	can	can	AUX
ap-1167	184	17	occur	occur	VERB
ap-1167	184	18	,	,	PUNCT
ap-1167	184	19	such	such	ADJ
ap-1167	184	20	as	as	ADP
ap-1167	184	21	during	during	ADP
ap-1167	184	22	evaluation	evaluation	NOUN
ap-1167	184	23	of	of	ADP
ap-1167	184	24	a	a	DET
ap-1167	184	25	numeric	numeric	ADJ
ap-1167	184	26	derivative	derivative	NOUN
ap-1167	184	27	.	.	PUNCT
ap-1167	185	1	as	as	SCONJ
ap-1167	185	2	we	we	PRON
ap-1167	185	3	have	have	AUX
ap-1167	185	4	seen	see	VERB
ap-1167	185	5	in	in	ADP
ap-1167	185	6	the	the	DET
ap-1167	185	7	case	case	NOUN
ap-1167	185	8	study	study	NOUN
ap-1167	185	9	,	,	PUNCT
ap-1167	185	10	an	an	DET
ap-1167	185	11	error	error	NOUN
ap-1167	185	12	bound	bind	VERB
ap-1167	185	13	determined	determine	VERB
ap-1167	185	14	a	a	PRON
ap-1167	185	15	-	-	PUNCT
ap-1167	185	16	priori	priori	ADV
ap-1167	185	17	can	can	AUX
ap-1167	185	18	be	be	AUX
ap-1167	185	19	far	far	ADV
ap-1167	185	20	from	from	ADP
ap-1167	185	21	the	the	DET
ap-1167	185	22	actual	actual	ADJ
ap-1167	185	23	error	error	NOUN
ap-1167	185	24	and	and	CCONJ
ap-1167	185	25	,	,	PUNCT
ap-1167	185	26	especially	especially	ADV
ap-1167	185	27	with	with	ADP
ap-1167	185	28	the	the	DET
ap-1167	185	29	provided	provide	VERB
ap-1167	185	30	classes	class	NOUN
ap-1167	185	31	,	,	PUNCT
ap-1167	185	32	running	run	VERB
ap-1167	185	33	error	error	NOUN
ap-1167	185	34	analysis	analysis	NOUN
ap-1167	185	35	provides	provide	VERB
ap-1167	185	36	a	a	DET
ap-1167	185	37	very	very	ADV
ap-1167	185	38	quick	quick	ADJ
ap-1167	185	39	and	and	CCONJ
ap-1167	185	40	feasible	feasible	ADJ
ap-1167	185	41	replacement	replacement	NOUN
ap-1167	185	42	.	.	PUNCT
ap-1167	186	1	this	this	PRON
ap-1167	186	2	,	,	PUNCT
ap-1167	186	3	however	however	ADV
ap-1167	186	4	,	,	PUNCT
ap-1167	186	5	costs	cost	VERB
ap-1167	186	6	2.85	2.85	NUM
ap-1167	186	7	times	time	NOUN
ap-1167	186	8	the	the	DET
ap-1167	186	9	evaluation	evaluation	NOUN
ap-1167	186	10	time	time	NOUN
ap-1167	186	11	,	,	PUNCT
ap-1167	186	12	but	but	CCONJ
ap-1167	186	13	when	when	SCONJ
ap-1167	186	14	replaced	replace	VERB
ap-1167	186	15	by	by	ADP
ap-1167	186	16	fpu	fpu	NOUN
ap-1167	186	17	-	-	PUNCT
ap-1167	186	18	supported	support	VERB
ap-1167	186	19	running	running	NOUN
ap-1167	186	20	error	error	NOUN
ap-1167	186	21	analysis	analysis	NOUN
ap-1167	186	22	,	,	PUNCT
ap-1167	186	23	the	the	DET
ap-1167	186	24	cost	cost	NOUN
ap-1167	186	25	is	be	AUX
ap-1167	186	26	2.35	2.35	NUM
ap-1167	186	27	while	while	SCONJ
ap-1167	186	28	providing	provide	VERB
ap-1167	186	29	a	a	DET
ap-1167	186	30	yet	yet	ADV
ap-1167	186	31	tighter	tight	ADJ
ap-1167	186	32	bound	bind	VERB
ap-1167	186	33	.	.	PUNCT
ap-1167	187	1	with	with	ADP
ap-1167	187	2	a	a	DET
ap-1167	187	3	tighter	tighter	ADV
ap-1167	187	4	bound	bind	VERB
ap-1167	187	5	,	,	PUNCT
ap-1167	187	6	we	we	PRON
ap-1167	187	7	are	be	AUX
ap-1167	187	8	able	able	ADJ
ap-1167	187	9	to	to	PART
ap-1167	187	10	calculate	calculate	VERB
ap-1167	187	11	more	more	ADJ
ap-1167	187	12	iterations	iteration	NOUN
ap-1167	187	13	and	and	CCONJ
ap-1167	187	14	be	be	AUX
ap-1167	187	15	sure	sure	ADJ
ap-1167	187	16	that	that	SCONJ
ap-1167	187	17	the	the	DET
ap-1167	187	18	result	result	NOUN
ap-1167	187	19	is	be	AUX
ap-1167	187	20	still	still	ADV
ap-1167	187	21	valid	valid	ADJ
ap-1167	187	22	.	.	PUNCT
ap-1167	188	1	acknowledgement	acknowledgement	NOUN
ap-1167	188	2	this	this	DET
ap-1167	188	3	research	research	NOUN
ap-1167	188	4	has	have	AUX
ap-1167	188	5	been	be	AUX
ap-1167	188	6	partially	partially	ADV
ap-1167	188	7	supported	support	VERB
ap-1167	188	8	by	by	ADP
ap-1167	188	9	the	the	DET
ap-1167	188	10	ministry	ministry	PROPN
ap-1167	188	11	of	of	ADP
ap-1167	188	12	education	education	PROPN
ap-1167	188	13	,	,	PUNCT
ap-1167	188	14	youth	youth	NOUN
ap-1167	188	15	,	,	PUNCT
ap-1167	188	16	and	and	CCONJ
ap-1167	188	17	sport	sport	NOUN
ap-1167	188	18	of	of	ADP
ap-1167	188	19	the	the	DET
ap-1167	188	20	czech	czech	PROPN
ap-1167	188	21	republic	republic	NOUN
ap-1167	188	22	,	,	PUNCT
ap-1167	188	23	under	under	ADP
ap-1167	188	24	research	research	NOUN
ap-1167	188	25	program	program	NOUN
ap-1167	188	26	msm	msm	NOUN
ap-1167	188	27	6840770014	6840770014	NUM
ap-1167	188	28	,	,	PUNCT
ap-1167	188	29	and	and	CCONJ
ap-1167	188	30	by	by	ADP
ap-1167	188	31	the	the	DET
ap-1167	188	32	czech	czech	PROPN
ap-1167	188	33	science	science	NOUN
ap-1167	188	34	foundation	foundation	PROPN
ap-1167	188	35	as	as	ADP
ap-1167	188	36	project	project	NOUN
ap-1167	188	37	no	no	NOUN
ap-1167	188	38	.	.	PUNCT
ap-1167	189	1	201/06/1039	201/06/1039	NOUN
ap-1167	189	2	.	.	PUNCT
ap-1167	190	1	references	reference	NOUN
ap-1167	190	2	[	[	X
ap-1167	190	3	1	1	NUM
ap-1167	190	4	]	]	X
ap-1167	190	5	fog	fog	PROPN
ap-1167	190	6	,	,	PUNCT
ap-1167	190	7	a.	a.	NOUN
ap-1167	190	8	:	:	PUNCT
ap-1167	190	9	instruction	instruction	NOUN
ap-1167	190	10	tables	table	NOUN
ap-1167	190	11	:	:	PUNCT
ap-1167	190	12	lists	list	NOUN
ap-1167	190	13	of	of	ADP
ap-1167	190	14	instruction	instruction	NOUN
ap-1167	190	15	latencies	latency	NOUN
ap-1167	190	16	,	,	PUNCT
ap-1167	190	17	throughputs	throughput	NOUN
ap-1167	190	18	and	and	CCONJ
ap-1167	190	19	micro	micro	NOUN
ap-1167	190	20	-	-	NOUN
ap-1167	190	21	operation	operation	NOUN
ap-1167	190	22	breakdowns	breakdown	NOUN
ap-1167	190	23	for	for	ADP
ap-1167	190	24	intel	intel	PROPN
ap-1167	190	25	and	and	CCONJ
ap-1167	190	26	amd	amd	PROPN
ap-1167	190	27	cpu	cpu	PROPN
ap-1167	190	28	’s	’s	PART
ap-1167	190	29	,	,	PUNCT
ap-1167	190	30	copenhagen	copenhagen	PROPN
ap-1167	190	31	university	university	PROPN
ap-1167	190	32	college	college	PROPN
ap-1167	190	33	of	of	ADP
ap-1167	190	34	engineering	engineering	PROPN
ap-1167	190	35	,	,	PUNCT
ap-1167	190	36	available	available	ADJ
ap-1167	190	37	online	online	ADV
ap-1167	190	38	as	as	ADP
ap-1167	190	39	a	a	DET
ap-1167	190	40	part	part	NOUN
ap-1167	190	41	of	of	ADP
ap-1167	190	42	software	software	NOUN
ap-1167	190	43	optimization	optimization	NOUN
ap-1167	190	44	resources	resource	NOUN
ap-1167	190	45	,	,	PUNCT
ap-1167	190	46	http://www.agner.org/optimize/	http://www.agner.org/optimize/	NOUN
ap-1167	190	47	,	,	PUNCT
ap-1167	190	48	2008	2008	NUM
ap-1167	190	49	.	.	PUNCT
ap-1167	191	1	[	[	X
ap-1167	191	2	2	2	NUM
ap-1167	191	3	]	]	X
ap-1167	191	4	bevington	bevington	PROPN
ap-1167	191	5	,	,	PUNCT
ap-1167	191	6	p.	p.	PROPN
ap-1167	191	7	,	,	PUNCT
ap-1167	191	8	robinson	robinson	PROPN
ap-1167	191	9	,	,	PUNCT
ap-1167	191	10	d.	d.	PROPN
ap-1167	191	11	k.	k.	PROPN
ap-1167	191	12	:	:	PUNCT
ap-1167	191	13	data	datum	NOUN
ap-1167	191	14	reduction	reduction	NOUN
ap-1167	191	15	and	and	CCONJ
ap-1167	191	16	error	error	NOUN
ap-1167	191	17	analysis	analysis	NOUN
ap-1167	191	18	for	for	ADP
ap-1167	191	19	the	the	DET
ap-1167	191	20	physical	physical	ADJ
ap-1167	191	21	sciences	sciences	PROPN
ap-1167	191	22	,	,	PUNCT
ap-1167	191	23	mcgraw	mcgraw	NOUN
ap-1167	191	24	-	-	PUNCT
ap-1167	191	25	hill	hill	NOUN
ap-1167	191	26	science	science	NOUN
ap-1167	191	27	/	/	SYM
ap-1167	191	28	engineering	engineering	NOUN
ap-1167	191	29	/	/	SYM
ap-1167	191	30	math	math	NOUN
ap-1167	191	31	,	,	PUNCT
ap-1167	191	32	2002	2002	NUM
ap-1167	191	33	.	.	PUNCT
ap-1167	192	1	[	[	X
ap-1167	192	2	3	3	X
ap-1167	192	3	]	]	X
ap-1167	192	4	ieee	ieee	NOUN
ap-1167	192	5	computer	computer	NOUN
ap-1167	192	6	society	society	PROPN
ap-1167	192	7	standards	standard	NOUN
ap-1167	192	8	committee	committee	NOUN
ap-1167	192	9	.	.	PUNCT
ap-1167	193	1	working	working	NOUN
ap-1167	193	2	group	group	NOUN
ap-1167	193	3	of	of	ADP
ap-1167	193	4	the	the	DET
ap-1167	193	5	microprocessor	microprocessor	NOUN
ap-1167	193	6	standards	standard	NOUN
ap-1167	193	7	subcommittee	subcommittee	NOUN
ap-1167	193	8	and	and	CCONJ
ap-1167	193	9	american	american	PROPN
ap-1167	193	10	national	national	PROPN
ap-1167	193	11	standards	standards	PROPN
ap-1167	193	12	institute	institute	PROPN
ap-1167	193	13	:	:	PUNCT
ap-1167	193	14	ieee	ieee	PROPN
ap-1167	193	15	standard	standard	PROPN
ap-1167	193	16	for	for	ADP
ap-1167	193	17	binary	binary	ADJ
ap-1167	193	18	floatingpoint	floatingpoint	PROPN
ap-1167	193	19	arithmetic	arithmetic	ADJ
ap-1167	193	20	,	,	PUNCT
ap-1167	193	21	ser	ser	PROPN
ap-1167	193	22	.	.	PUNCT
ap-1167	194	1	ansi	ansi	PROPN
ap-1167	194	2	/	/	SYM
ap-1167	194	3	ieee	ieee	NOUN
ap-1167	194	4	std	std	NOUN
ap-1167	194	5	754	754	NUM
ap-1167	194	6	-	-	SYM
ap-1167	194	7	1985	1985	NUM
ap-1167	194	8	.	.	PUNCT
ap-1167	195	1	ieee	ieee	PROPN
ap-1167	195	2	computer	computer	PROPN
ap-1167	195	3	society	society	PROPN
ap-1167	195	4	press	press	NOUN
ap-1167	195	5	,	,	PUNCT
ap-1167	195	6	1985	1985	NUM
ap-1167	195	7	.	.	PUNCT
ap-1167	196	1	[	[	X
ap-1167	196	2	4	4	X
ap-1167	196	3	]	]	X
ap-1167	196	4	intel	intel	PROPN
ap-1167	196	5	corporation	corporation	NOUN
ap-1167	196	6	:	:	PUNCT
ap-1167	196	7	intel	intel	PROPN
ap-1167	196	8	r	r	PROPN
ap-1167	196	9	©	©	PROPN
ap-1167	196	10	64	64	NUM
ap-1167	196	11	and	and	CCONJ
ap-1167	196	12	ia-32	ia-32	NOUN
ap-1167	196	13	architectures	architecture	NOUN
ap-1167	196	14	software	software	NOUN
ap-1167	196	15	developer	developer	NOUN
ap-1167	196	16	’s	’s	PART
ap-1167	196	17	manual	manual	NOUN
ap-1167	196	18	,	,	PUNCT
ap-1167	196	19	vol	vol	NOUN
ap-1167	196	20	.	.	PUNCT
ap-1167	196	21	3a	3a	NUM
ap-1167	196	22	,	,	PUNCT
ap-1167	196	23	system	system	NOUN
ap-1167	196	24	programming	programming	NOUN
ap-1167	196	25	guide	guide	NOUN
ap-1167	196	26	,	,	PUNCT
ap-1167	196	27	part	part	NOUN
ap-1167	196	28	1	1	NUM
ap-1167	196	29	,	,	PUNCT
ap-1167	196	30	11/2007	11/2007	NUM
ap-1167	196	31	.	.	PUNCT
ap-1167	197	1	[	[	X
ap-1167	197	2	5	5	NUM
ap-1167	197	3	]	]	X
ap-1167	197	4	higham	higham	PROPN
ap-1167	197	5	,	,	PUNCT
ap-1167	197	6	n.	n.	PROPN
ap-1167	197	7	j.	j.	PROPN
ap-1167	197	8	:	:	PUNCT
ap-1167	197	9	accuracy	accuracy	NOUN
ap-1167	197	10	and	and	CCONJ
ap-1167	197	11	stability	stability	NOUN
ap-1167	197	12	of	of	ADP
ap-1167	197	13	numerical	numerical	ADJ
ap-1167	197	14	algorithms	algorithm	NOUN
ap-1167	197	15	,	,	PUNCT
ap-1167	197	16	2nd	2nd	PROPN
ap-1167	197	17	edition	edition	NOUN
ap-1167	197	18	,	,	PUNCT
ap-1167	197	19	society	society	NOUN
ap-1167	197	20	for	for	ADP
ap-1167	197	21	industrial	industrial	ADJ
ap-1167	197	22	and	and	CCONJ
ap-1167	197	23	applied	applied	ADJ
ap-1167	197	24	mathematics	mathematic	NOUN
ap-1167	197	25	,	,	PUNCT
ap-1167	197	26	2002	2002	NUM
ap-1167	197	27	.	.	PUNCT
ap-1167	198	1	[	[	X
ap-1167	198	2	6	6	NUM
ap-1167	198	3	]	]	X
ap-1167	198	4	wilkinson	wilkinson	PROPN
ap-1167	198	5	,	,	PUNCT
ap-1167	198	6	j.	j.	PROPN
ap-1167	198	7	h.	h.	PROPN
ap-1167	198	8	:	:	PUNCT
ap-1167	198	9	the	the	DET
ap-1167	198	10	state	state	NOUN
ap-1167	198	11	of	of	ADP
ap-1167	198	12	the	the	DET
ap-1167	198	13	art	art	NOUN
ap-1167	198	14	in	in	ADP
ap-1167	198	15	error	error	NOUN
ap-1167	198	16	analysis	analysis	NOUN
ap-1167	198	17	,	,	PUNCT
ap-1167	198	18	nag	nag	VERB
ap-1167	198	19	newsletter	newsletter	NOUN
ap-1167	198	20	,	,	PUNCT
ap-1167	198	21	vol	vol	NOUN
ap-1167	198	22	.	.	PUNCT
ap-1167	198	23	2/85	2/85	NUM
ap-1167	198	24	,	,	PUNCT
ap-1167	198	25	1985	1985	NUM
ap-1167	198	26	.	.	PUNCT
ap-1167	199	1	[	[	X
ap-1167	199	2	7	7	NUM
ap-1167	199	3	]	]	X
ap-1167	199	4	wilkinson	wilkinson	PROPN
ap-1167	199	5	,	,	PUNCT
ap-1167	199	6	j.	j.	PROPN
ap-1167	199	7	h.	h.	PROPN
ap-1167	199	8	:	:	PUNCT
ap-1167	199	9	error	error	NOUN
ap-1167	199	10	analysis	analysis	NOUN
ap-1167	199	11	revisited	revisit	VERB
ap-1167	199	12	,	,	PUNCT
ap-1167	199	13	i	i	PRON
ap-1167	199	14	m	m	VERB
ap-1167	199	15	a	a	DET
ap-1167	199	16	bulletin	bulletin	NOUN
ap-1167	199	17	,	,	PUNCT
ap-1167	199	18	vol	vol	NOUN
ap-1167	199	19	.	.	PROPN
ap-1167	199	20	22	22	NUM
ap-1167	199	21	,	,	PUNCT
ap-1167	199	22	no	no	INTJ
ap-1167	199	23	.	.	NOUN
ap-1167	199	24	11/12	11/12	NUM
ap-1167	199	25	,	,	PUNCT
ap-1167	199	26	pp	pp	ADJ
ap-1167	199	27	.	.	PUNCT
ap-1167	200	1	192–200	192–200	NUM
ap-1167	200	2	,	,	PUNCT
ap-1167	200	3	1986	1986	NUM
ap-1167	200	4	.	.	PUNCT
ap-1167	201	1	[	[	X
ap-1167	201	2	8	8	NUM
ap-1167	201	3	]	]	PUNCT
ap-1167	201	4	wolfram	wolfram	PROPN
ap-1167	201	5	research	research	PROPN
ap-1167	201	6	,	,	PUNCT
ap-1167	201	7	inc	inc	PROPN
ap-1167	201	8	.	.	PROPN
ap-1167	201	9	:	:	PUNCT
ap-1167	201	10	mathematica	mathematica	PROPN
ap-1167	201	11	7	7	NUM
ap-1167	201	12	,	,	PUNCT
ap-1167	201	13	http://www.wolfram.com/	http://www.wolfram.com/	NOUN
ap-1167	201	14	,	,	PUNCT
ap-1167	201	15	2008	2008	NUM
ap-1167	201	16	.	.	PUNCT
ap-1167	202	1	[	[	X
ap-1167	202	2	9	9	NUM
ap-1167	202	3	]	]	PUNCT
ap-1167	202	4	zahradnický	zahradnický	NOUN
ap-1167	202	5	,	,	PUNCT
ap-1167	202	6	t.	t.	PROPN
ap-1167	202	7	:	:	PUNCT
ap-1167	202	8	fdouble	fdouble	ADJ
ap-1167	202	9	class	class	NOUN
ap-1167	202	10	,	,	PUNCT
ap-1167	202	11	a	a	DET
ap-1167	202	12	double	double	ADJ
ap-1167	202	13	data	data	NOUN
ap-1167	202	14	type	type	NOUN
ap-1167	202	15	replacement	replacement	NOUN
ap-1167	202	16	c++	c++	NOUN
ap-1167	202	17	class	class	NOUN
ap-1167	202	18	with	with	ADP
ap-1167	202	19	the	the	DET
ap-1167	202	20	fpusupported	fpusupported	ADJ
ap-1167	202	21	running	running	NOUN
ap-1167	202	22	error	error	NOUN
ap-1167	202	23	analysis	analysis	NOUN
ap-1167	202	24	.	.	PUNCT
ap-1167	203	1	accessible	accessible	ADJ
ap-1167	203	2	online	online	ADV
ap-1167	203	3	at	at	ADP
ap-1167	203	4	http://service.felk.cvut.cz/anc/zahradt/	http://service.felk.cvut.cz/anc/zahradt/	PROPN
ap-1167	203	5	fdouble.tar.gz	fdouble.tar.gz	PROPN
ap-1167	203	6	,	,	PUNCT
ap-1167	203	7	2007	2007	NUM
ap-1167	203	8	.	.	PUNCT
ap-1167	204	1	ing	ing	ADJ
ap-1167	204	2	.	.	PUNCT
ap-1167	205	1	tomáš	tomáš	PROPN
ap-1167	205	2	zahradnický	zahradnický	PROPN
ap-1167	205	3	was	be	AUX
ap-1167	205	4	born	bear	VERB
ap-1167	205	5	on	on	ADP
ap-1167	205	6	9th	9th	ADJ
ap-1167	205	7	march	march	PROPN
ap-1167	205	8	1979	1979	NUM
ap-1167	205	9	,	,	PUNCT
ap-1167	205	10	in	in	ADP
ap-1167	205	11	prague	prague	PROPN
ap-1167	205	12	,	,	PUNCT
ap-1167	205	13	czech	czech	PROPN
ap-1167	205	14	republic	republic	NOUN
ap-1167	205	15	.	.	PUNCT
ap-1167	206	1	in	in	ADP
ap-1167	206	2	2003	2003	NUM
ap-1167	206	3	he	he	PRON
ap-1167	206	4	graduated	graduate	VERB
ap-1167	206	5	(	(	PUNCT
ap-1167	206	6	msc	msc	PROPN
ap-1167	206	7	)	)	PUNCT
ap-1167	206	8	from	from	ADP
ap-1167	206	9	the	the	DET
ap-1167	206	10	department	department	NOUN
ap-1167	206	11	of	of	ADP
ap-1167	206	12	computer	computer	NOUN
ap-1167	206	13	science	science	NOUN
ap-1167	206	14	and	and	CCONJ
ap-1167	206	15	engineering	engineering	NOUN
ap-1167	206	16	of	of	ADP
ap-1167	206	17	the	the	DET
ap-1167	206	18	faculty	faculty	NOUN
ap-1167	206	19	of	of	ADP
ap-1167	206	20	electrical	electrical	ADJ
ap-1167	206	21	engineering	engineering	NOUN
ap-1167	206	22	at	at	ADP
ap-1167	206	23	the	the	DET
ap-1167	206	24	czech	czech	PROPN
ap-1167	206	25	technical	technical	PROPN
ap-1167	206	26	university	university	PROPN
ap-1167	206	27	in	in	ADP
ap-1167	206	28	prague	prague	PROPN
ap-1167	206	29	.	.	PUNCT
ap-1167	207	1	since	since	SCONJ
ap-1167	207	2	2004	2004	NUM
ap-1167	207	3	he	he	PRON
ap-1167	207	4	has	have	AUX
ap-1167	207	5	been	be	AUX
ap-1167	207	6	a	a	DET
ap-1167	207	7	postgraduate	postgraduate	NOUN
ap-1167	207	8	student	student	NOUN
ap-1167	207	9	at	at	ADP
ap-1167	207	10	the	the	DET
ap-1167	207	11	same	same	ADJ
ap-1167	207	12	department	department	NOUN
ap-1167	207	13	,	,	PUNCT
ap-1167	207	14	where	where	SCONJ
ap-1167	207	15	he	he	PRON
ap-1167	207	16	became	become	VERB
ap-1167	207	17	an	an	DET
ap-1167	207	18	assistant	assistant	ADJ
ap-1167	207	19	professor	professor	NOUN
ap-1167	207	20	in	in	ADP
ap-1167	207	21	2007	2007	NUM
ap-1167	207	22	.	.	PUNCT
ap-1167	208	1	since	since	SCONJ
ap-1167	208	2	2009	2009	NUM
ap-1167	208	3	he	he	PRON
ap-1167	208	4	has	have	AUX
ap-1167	208	5	been	be	AUX
ap-1167	208	6	an	an	DET
ap-1167	208	7	assistant	assistant	ADJ
ap-1167	208	8	professor	professor	NOUN
ap-1167	208	9	at	at	ADP
ap-1167	208	10	the	the	DET
ap-1167	208	11	department	department	PROPN
ap-1167	208	12	of	of	ADP
ap-1167	208	13	computer	computer	NOUN
ap-1167	208	14	systems	system	NOUN
ap-1167	208	15	at	at	ADP
ap-1167	208	16	the	the	DET
ap-1167	208	17	faculty	faculty	NOUN
ap-1167	208	18	of	of	ADP
ap-1167	208	19	information	information	NOUN
ap-1167	208	20	technologies	technology	NOUN
ap-1167	208	21	at	at	ADP
ap-1167	208	22	the	the	DET
ap-1167	208	23	czech	czech	PROPN
ap-1167	208	24	technical	technical	PROPN
ap-1167	208	25	university	university	PROPN
ap-1167	208	26	in	in	ADP
ap-1167	208	27	prague	prague	PROPN
ap-1167	208	28	.	.	PUNCT
ap-1167	209	1	his	his	PRON
ap-1167	209	2	scientific	scientific	ADJ
ap-1167	209	3	research	research	NOUN
ap-1167	209	4	focuses	focus	VERB
ap-1167	209	5	on	on	ADP
ap-1167	209	6	system	system	NOUN
ap-1167	209	7	optimization	optimization	NOUN
ap-1167	209	8	,	,	PUNCT
ap-1167	209	9	and	and	CCONJ
ap-1167	209	10	on	on	ADP
ap-1167	209	11	parameter	parameter	NOUN
ap-1167	209	12	extraction	extraction	NOUN
ap-1167	209	13	.	.	PUNCT
ap-1167	210	1	doc	doc	PROPN
ap-1167	210	2	.	.	PROPN
ap-1167	211	1	ing	ing	PROPN
ap-1167	211	2	.	.	PUNCT
ap-1167	212	1	róbert	róbert	PROPN
ap-1167	212	2	lórencz	lórencz	PROPN
ap-1167	212	3	,	,	PUNCT
ap-1167	212	4	csc	csc	PROPN
ap-1167	212	5	.	.	PROPN
ap-1167	212	6	was	be	AUX
ap-1167	212	7	born	bear	VERB
ap-1167	212	8	on	on	ADP
ap-1167	212	9	10th	10th	ADJ
ap-1167	212	10	august	august	PROPN
ap-1167	212	11	1957	1957	NUM
ap-1167	212	12	in	in	ADP
ap-1167	212	13	prešov	prešov	NOUN
ap-1167	212	14	,	,	PUNCT
ap-1167	212	15	slovak	slovak	ADJ
ap-1167	212	16	republic	republic	NOUN
ap-1167	212	17	.	.	PUNCT
ap-1167	213	1	in	in	ADP
ap-1167	213	2	1981	1981	NUM
ap-1167	213	3	he	he	PRON
ap-1167	213	4	graduated	graduate	VERB
ap-1167	213	5	(	(	PUNCT
ap-1167	213	6	msc	msc	PROPN
ap-1167	213	7	)	)	PUNCT
ap-1167	213	8	from	from	ADP
ap-1167	213	9	the	the	DET
ap-1167	213	10	faculty	faculty	NOUN
ap-1167	213	11	of	of	ADP
ap-1167	213	12	electrical	electrical	ADJ
ap-1167	213	13	engineering	engineering	NOUN
ap-1167	213	14	at	at	ADP
ap-1167	213	15	the	the	DET
ap-1167	213	16	czech	czech	PROPN
ap-1167	213	17	technical	technical	PROPN
ap-1167	213	18	university	university	PROPN
ap-1167	213	19	in	in	ADP
ap-1167	213	20	prague	prague	PROPN
ap-1167	213	21	.	.	PUNCT
ap-1167	214	1	he	he	PRON
ap-1167	214	2	received	receive	VERB
ap-1167	214	3	his	his	PRON
ap-1167	214	4	ph.d	ph.d	PROPN
ap-1167	214	5	.	.	PROPN
ap-1167	214	6	degree	degree	NOUN
ap-1167	214	7	in	in	ADP
ap-1167	214	8	1990	1990	NUM
ap-1167	214	9	from	from	ADP
ap-1167	214	10	the	the	DET
ap-1167	214	11	slovak	slovak	ADJ
ap-1167	214	12	academy	academy	NOUN
ap-1167	214	13	of	of	ADP
ap-1167	214	14	sciences	sciences	PROPN
ap-1167	214	15	.	.	PUNCT
ap-1167	215	1	in	in	ADP
ap-1167	215	2	1998	1998	NUM
ap-1167	215	3	he	he	PRON
ap-1167	215	4	became	become	VERB
ap-1167	215	5	an	an	DET
ap-1167	215	6	assistant	assistant	ADJ
ap-1167	215	7	professor	professor	NOUN
ap-1167	215	8	at	at	ADP
ap-1167	215	9	the	the	DET
ap-1167	215	10	department	department	NOUN
ap-1167	215	11	of	of	ADP
ap-1167	215	12	computer	computer	NOUN
ap-1167	215	13	science	science	NOUN
ap-1167	215	14	and	and	CCONJ
ap-1167	215	15	engineering	engineering	NOUN
ap-1167	215	16	at	at	ADP
ap-1167	215	17	the	the	DET
ap-1167	215	18	faculty	faculty	NOUN
ap-1167	215	19	of	of	ADP
ap-1167	215	20	electrical	electrical	ADJ
ap-1167	215	21	engineering	engineering	NOUN
ap-1167	215	22	at	at	ADP
ap-1167	215	23	the	the	DET
ap-1167	215	24	czech	czech	PROPN
ap-1167	215	25	technical	technical	PROPN
ap-1167	215	26	university	university	PROPN
ap-1167	215	27	in	in	ADP
ap-1167	215	28	prague	prague	PROPN
ap-1167	215	29	.	.	PUNCT
ap-1167	216	1	in	in	ADP
ap-1167	216	2	2005	2005	NUM
ap-1167	216	3	he	he	PRON
ap-1167	216	4	defended	defend	VERB
ap-1167	216	5	his	his	PRON
ap-1167	216	6	habilitation	habilitation	NOUN
ap-1167	216	7	thesis	thesis	NOUN
ap-1167	216	8	and	and	CCONJ
ap-1167	216	9	became	become	VERB
ap-1167	216	10	an	an	DET
ap-1167	216	11	associate	associate	ADJ
ap-1167	216	12	professor	professor	NOUN
ap-1167	216	13	at	at	ADP
ap-1167	216	14	the	the	DET
ap-1167	216	15	same	same	ADJ
ap-1167	216	16	department	department	NOUN
ap-1167	216	17	.	.	PUNCT
ap-1167	217	1	since	since	SCONJ
ap-1167	217	2	2009	2009	NUM
ap-1167	217	3	,	,	PUNCT
ap-1167	217	4	he	he	PRON
ap-1167	217	5	has	have	AUX
ap-1167	217	6	worked	work	VERB
ap-1167	217	7	as	as	ADP
ap-1167	217	8	an	an	DET
ap-1167	217	9	associate	associate	ADJ
ap-1167	217	10	professor	professor	NOUN
ap-1167	217	11	at	at	ADP
ap-1167	217	12	the	the	DET
ap-1167	217	13	department	department	PROPN
ap-1167	217	14	of	of	ADP
ap-1167	217	15	computer	computer	NOUN
ap-1167	217	16	systems	system	NOUN
ap-1167	217	17	at	at	ADP
ap-1167	217	18	the	the	DET
ap-1167	217	19	faculty	faculty	NOUN
ap-1167	217	20	of	of	ADP
ap-1167	217	21	information	information	NOUN
ap-1167	217	22	technologies	technology	NOUN
ap-1167	217	23	at	at	ADP
ap-1167	217	24	the	the	DET
ap-1167	217	25	czech	czech	PROPN
ap-1167	217	26	technical	technical	PROPN
ap-1167	217	27	university	university	PROPN
ap-1167	217	28	in	in	ADP
ap-1167	217	29	prague	prague	PROPN
ap-1167	217	30	.	.	PUNCT
ap-1167	218	1	his	his	PRON
ap-1167	218	2	scientific	scientific	ADJ
ap-1167	218	3	research	research	NOUN
ap-1167	218	4	focuses	focus	VERB
ap-1167	218	5	on	on	ADP
ap-1167	218	6	arithmetics	arithmetic	NOUN
ap-1167	218	7	for	for	ADP
ap-1167	218	8	numerical	numerical	ADJ
ap-1167	218	9	algorithms	algorithm	NOUN
ap-1167	218	10	,	,	PUNCT
ap-1167	218	11	residual	residual	ADJ
ap-1167	218	12	arithmetic	arithmetic	ADJ
ap-1167	218	13	,	,	PUNCT
ap-1167	218	14	error	error	NOUN
ap-1167	218	15	-	-	PUNCT
ap-1167	218	16	free	free	ADJ
ap-1167	218	17	computation	computation	NOUN
ap-1167	218	18	and	and	CCONJ
ap-1167	218	19	cryptography	cryptography	NOUN
ap-1167	218	20	.	.	PUNCT
ap-1167	219	1	ing	ing	ADJ
ap-1167	219	2	.	.	PUNCT
ap-1167	220	1	tomáš	tomáš	PROPN
ap-1167	220	2	zahradnický	zahradnický	PROPN
ap-1167	220	3	doc	doc	PROPN
ap-1167	220	4	.	.	PROPN
ap-1167	221	1	ing	ing	PROPN
ap-1167	221	2	.	.	PUNCT
ap-1167	222	1	róbert	róbert	PROPN
ap-1167	222	2	lórencz	lórencz	PROPN
ap-1167	222	3	,	,	PUNCT
ap-1167	222	4	csc	csc	PROPN
ap-1167	222	5	.	.	PUNCT
ap-1167	223	1	e	e	X
ap-1167	223	2	-	-	NOUN
ap-1167	223	3	mail	mail	NOUN
ap-1167	223	4	:	:	PUNCT
ap-1167	223	5	zahradt|lorencz@fit.cvut.cz	zahradt|lorencz@fit.cvut.cz	PROPN
ap-1167	223	6	department	department	PROPN
ap-1167	223	7	of	of	ADP
ap-1167	223	8	computer	computer	NOUN
ap-1167	223	9	systems	system	NOUN
ap-1167	223	10	faculty	faculty	NOUN
ap-1167	223	11	of	of	ADP
ap-1167	223	12	information	information	NOUN
ap-1167	223	13	technologies	technology	NOUN
ap-1167	223	14	czech	czech	PROPN
ap-1167	223	15	technical	technical	PROPN
ap-1167	223	16	university	university	PROPN
ap-1167	223	17	in	in	ADP
ap-1167	223	18	prague	prague	PROPN
ap-1167	223	19	kolejńı	kolejńı	PROPN
ap-1167	223	20	550/2	550/2	PROPN
ap-1167	223	21	,	,	PUNCT
ap-1167	223	22	160	160	NUM
ap-1167	223	23	00	00	NUM
ap-1167	223	24	prague	prague	PROPN
ap-1167	223	25	,	,	PUNCT
ap-1167	223	26	czech	czech	PROPN
ap-1167	223	27	republic	republic	NOUN
ap-1167	223	28	36	36	NUM