4.2.3 Double-Precision Calculations

2 files changed, 256 insertions, 3 deletions

diff --git a/vol2/4.2.3.lyx b/vol2/4.2.3.lyx
new file mode 100644
index 0000000..f25be0a
--- /dev/null
+++ b/vol2/4.2.3.lyx
@@ -0,0 +1,245 @@
+#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
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+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
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+\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
diff --git a/vol2/index.lyx b/vol2/index.lyx
index 22d5987..584a80d 100644
--- a/vol2/index.lyx
+++ b/vol2/index.lyx
@@ -1064,13 +1064,21 @@ Double-Precision Calculations
 \end_layout
 
 \begin_layout Standard
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+LatexCommand input
+filename "4.2.3.lyx"
+literal "false"
+
+\end_inset
+
+
 \begin_inset Note Note
 status open
 
 \begin_layout Plain Layout
-7+0;
- 5 (0:28) -> 3d,
- -1/3
+
+\family typewriter
+A10+R25
 \end_layout
 
 \end_inset