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Chapter 1: Introduction
1.3 Because of round-off errors, it is customary to specify the number of decimal places that should be included in the output and round up accordingly. Otherwise, numbers e out looking strange. We assume error checks have already been performed; the routine SeparateO is left to the reader. Code is shown in Fig. 1.1.
1.4 The general way to do this is to write a procedure with heading void ProcessFile( const char *FileName );
which opensFileName,O does whatever processing is needed, and then closes it. If a line of the form
#include SomeFile
is detected, then the call ProcessFile( SomeFile );
is made recursively. Self-referential includes can be detected by keeping a list of files for which a call toProcessFileO has not yet terminated, and checking this list before making a new call toProcessFile.O
1.5 (a) The proof is by induction. The theorem is clearly true for 0 <XO ≤ 1, since it is true for XO = 1, and forXO < 1, logXO is negative. It is also easy to see that the theorem holds for 1 <XO ≤ 2, since it is true forXO = 2, and forXO < 2, logXO is at most 1. Suppose the theorem is true for pO <XO ≤ 2pO (where pO is a positive integer), and consider any 2pO <YO ≤ 4pO (pO ≥ 1). Then logYO = 1 + log (YO/ 2) < 1 +YO/ 2 <YO/ 2 +YO/ 2 ≤YO, where the first inequality follows by the inductive hypothesis.
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