#LyX 2.4 created this file. For more info see https://www.lyx.org/
\lyxformat 620
\begin_document
\begin_header
\save_transient_properties true
\origin unavailable
\textclass book
\begin_preamble
\input defs
\end_preamble
\use_default_options true
\maintain_unincluded_children no
\language english
\language_package default
\inputencoding utf8
\fontencoding auto
\font_roman "default" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_roman_osf false
\font_sans_osf false
\font_typewriter_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\use_microtype false
\use_dash_ligatures true
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\float_placement class
\float_alignment class
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 1
\use_formatted_ref 0
\use_minted 0
\use_lineno 0
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\is_math_indent 0
\math_numbering_side default
\quotes_style english
\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
\tablestyle default
\tracking_changes false
\output_changes false
\change_bars false
\postpone_fragile_content false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\docbook_table_output 0
\docbook_mathml_prefix 1
\end_header

\begin_body

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
rexerc5[24]
\end_layout

\end_inset

How should Program A be changed so that extra accuracy is achieved,
 essentially by working with a nine-byte accumulator instead of an eight-byte accumulator to the right of the radix point?
 Specify all changes that are required,
 and determine the difference in execution time caused by these changes.
\end_layout

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
answer 
\end_layout

\end_inset

Right now the program adds in pieces of 4 bytes to avoid overflow,
 but we may as well detect the overflow in the lower half and add it to the higher half if needed.
 For this,
 the following changes would be needed:
\end_layout

\begin_layout Enumerate
Add 
\family typewriter
JOV OFLO
\family default
 after line 6.
\end_layout

\begin_layout Enumerate
Change line 23 to 
\family typewriter
SRAX 0,1
\family default
,
 so then 
\family typewriter
ARG:ARGX
\family default
 contains 
\begin_inset Formula $v_{1}\,v_{2}\,\dots\,v_{9}\,0$
\end_inset

.
\end_layout

\begin_layout Enumerate
Change line 31 to 
\family typewriter
SLAX 5
\family default
,
 so rA contains the bytes 
\begin_inset Formula $u_{6}\,u_{7}\,u_{8}\,0\,0$
\end_inset

 and the code below adds 
\begin_inset Formula $0\,u_{6}\,u_{7}\,u_{8}\,0$
\end_inset

 plus 
\begin_inset Formula $0\,v_{6}\,v_{7}\,v_{8}\,v_{9}$
\end_inset

.
\end_layout

\begin_layout Enumerate
Change line 39 to 
\family typewriter
ADD ACC
\family default
 to get 
\begin_inset Formula $u_{1}\,u_{2}\,u_{3}\,u_{4}\,u_{5}$
\end_inset

.
\end_layout

\begin_layout Enumerate
Now line 40 adds 
\begin_inset Formula $v_{1}\,v_{2}\,v_{3}\,v_{4}\,v_{5}$
\end_inset

 to 
\begin_inset Formula $u_{1}\,u_{2}\,u_{3}\,u_{4}\,u_{5}$
\end_inset

,
 so overflow can occur,
 but overflow or a change of sign cannot because 
\begin_inset Formula $|u|\geq|v|$
\end_inset

.
 To handle this overflow and to shift the argument appropriately,
 we add the following after that line:
\begin_inset listings
inline false
status open

\begin_layout Plain Layout

SRAX 1
\end_layout

\begin_layout Plain Layout

JNOV *+3
\end_layout

\begin_layout Plain Layout

STA  *+1(SIGN)
\end_layout

\begin_layout Plain Layout

INCA 1
\end_layout

\end_inset


\end_layout

\begin_layout Standard
This adds 7u of runtime to the program,
 4u if there's no overflow.
 Note that the modified program has not been tested.
 Knuth's solution is slightly faster if there's no overflow.
\end_layout

\end_body
\end_document