Changed layout for more manageable volumes

1 files changed, 0 insertions, 496 deletions

diff --git a/3.6.lyx b/3.6.lyx
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-#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
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-\begin_preamble
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-\use_default_options true
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-\language english
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-\index Index
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-\color #008000
-\end_index
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-\end_header
-
-\begin_body
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-rexerc2[15]
-\end_layout
-
-\end_inset
-
-some people have been afraid that computers will someday take over the world;
- but they are reassured by the statement that a machine cannot do anything really new,
- since it is only obeying the commands of its master,
- the programmer.
- Lady Lovelace wrote in 1844,
- 
-\begin_inset Quotes eld
-\end_inset
-
-The Analytical Engine has no pretensions to 
-\emph on
-originate
-\emph default
- anything.
- It can do 
-\emph on
-whatever we know how to order it
-\emph default
- to perform.
-\begin_inset Quotes erd
-\end_inset
-
- Her statement has been elaborated further by many philosophers.
- Discuss this topic,
- with random number generators in mind.
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-answer 
-\end_layout
-
-\end_inset
-
-While it is true that a machine cannot do anything that a programmer doesn't tell it to do,
- there are a number of caveats here.
- First is that the programmer,
- or their boss,
- may not have other people's best interests in mind.
- Another one is that what the programmer tells the machine to do is not the same thing as what they 
-\emph on
-expects
-\emph default
- them to do;
- the software may have bugs,
- although the bugs are unlikely to make the computer take over the world.
- Finally,
- if a random number generator is being used,
- the programmer is telling the machine to do one of a number of actions,
- chosen with some given distribution,
- without telling it which one to choose.
- These actions are typically limited to a given scope,
- and the programmer still controls the family of actions that the machine may take.
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-rexerc11[M25]
-\end_layout
-
-\end_inset
-
-Assuming that floating point arithmetic on numbers of type 
-\family typewriter
-double
-\family default
- is properly rounded in the sense of Section 4.2.2 (hence exact when the values are suitably restricted),
- convert the C routines 
-\emph on
-ran_array
-\emph default
- and 
-\emph on
-ran_start
-\emph default
- to similar programs that deliver double-precision random fractions in the range 
-\begin_inset Formula $[0..1)$
-\end_inset
-
-,
- instead of 30-bit integers.
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-answer 
-\end_layout
-
-\end_inset
-
-Technically this does the work:
-\begin_inset listings
-lstparams "language=C,numbers=left,basicstyle={\small\sffamily},breaklines=true"
-inline false
-status open
-
-\begin_layout Plain Layout
-
-#include <math.h>
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-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-static double ran_u[KK];
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-void ranf_array(double out[],
- size_t n)
-\end_layout
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\begin_layout Plain Layout
-
-	size_t i,
- j;
-\end_layout
-
-\begin_layout Plain Layout
-
-	assert(n >= KK);
-\end_layout
-
-\begin_layout Plain Layout
-
-	for (j = 0;
- j < KK;
- j++)
-\end_layout
-
-\begin_layout Plain Layout
-
-		out[j] = ran_u[j];
-\end_layout
-
-\begin_layout Plain Layout
-
-	for (;
- j < n;
- j++)
-\end_layout
-
-\begin_layout Plain Layout
-
-		out[j] = fmod(1.
- + out[j-KK] - out[j-LL],
- 1.);
-\end_layout
-
-\begin_layout Plain Layout
-
-	for (i = 0;
- i < LL;
- i++,
- j++)
-\end_layout
-
-\begin_layout Plain Layout
-
-		ran_u[i] = fmod(1.
- + out[j-KK] - out[j-LL],
- 1.);
-\end_layout
-
-\begin_layout Plain Layout
-
-	for (;
- i < KK;
- i++,
- j++)
-\end_layout
-
-\begin_layout Plain Layout
-
-		ran_u[i] = fmod(1.
- + out[j-KK] - ran_x[j-LL],
- 1.);
-\end_layout
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\begin_layout Plain Layout
-
-\end_layout
-
-\begin_layout Plain Layout
-
-void ranf_start(long seed)
-\end_layout
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\begin_layout Plain Layout
-
-	ranf_start(seed);
-\end_layout
-
-\begin_layout Plain Layout
-
-	for (size_t i = 0;
- i < KK;
- i++)
-\end_layout
-
-\begin_layout Plain Layout
-
-		ran_u[i] = (double)ran_x[i] / MM;
-\end_layout
-
-\begin_layout Plain Layout
-
-}
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-rexerc12[M21]
-\end_layout
-
-\end_inset
-
-What random number generator would be suitable for a minicomputer that does arithmetic only on integers in the range 
-\begin_inset Formula $[-32768..32767]$
-\end_inset
-
-?
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-answer 
-\end_layout
-
-\end_inset
-
-We could use one of the generators with very large moduli from exercise 3.2.1.1–14.
- We could also use running generators like the one in the text 
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-rexerc15[25]
-\end_layout
-
-\end_inset
-
-Write C code that makes it convenient to generate the random integers obtained from 
-\emph on
-ran_array
-\emph default
- by discarding all but the first 100 of every 1009 elements,
- as recommended in the text.
-\end_layout
-
-\begin_layout Standard
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-answer
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-
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-
-
-\end_layout
-
-\begin_layout Standard
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-lstparams "language=C,numbers=left,basicstyle={\normalsize\sffamily},breaklines=true"
-inline false
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-\begin_layout Plain Layout
-
-long next()
-\end_layout
-
-\begin_layout Plain Layout
-
-{
-\end_layout
-
-\begin_layout Plain Layout
-
-	static long buf[1009],
- next = 100;
-\end_layout
-
-\begin_layout Plain Layout
-
-	if (next == 100) {
-\end_layout
-
-\begin_layout Plain Layout
-
-		ran_array(buf,
- sizeof(buf) / sizeof(buf[0]));
-\end_layout
-
-\begin_layout Plain Layout
-
-		next = 0;
-\end_layout
-
-\begin_layout Plain Layout
-
-	}
-\end_layout
-
-\begin_layout Plain Layout
-
-	return buf[next++];
-\end_layout
-
-\begin_layout Plain Layout
-
-}
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-
-\end_inset
-
-
-\end_layout
-
-\end_body
-\end_document