Small wording fixups.
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@ -839,7 +839,7 @@ fixed precision.
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The effects of round-off error can be amplified by the addition or subtraction
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The effects of round-off error can be amplified by the addition or subtraction
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of nearly offsetting quantities resulting in loss of significance. Knuth
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of nearly offsetting quantities resulting in loss of significance. Knuth
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provides two instructive examples where rounded floating point arithmetic with
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provides two instructive examples where rounded floating point arithmetic with
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insufficient precision causes the break down of the associative and
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insufficient precision causes the breakdown of the associative and
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distributive properties of addition:
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distributive properties of addition:
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\begin{verbatim}
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\begin{verbatim}
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@ -893,7 +893,7 @@ The infinities are signed (affine) and can be used in arithmetic operations
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where they get treated as very large, indeterminate numbers. For instance,
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where they get treated as very large, indeterminate numbers. For instance,
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adding a constant to infinity gives another infinite result.
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adding a constant to infinity gives another infinite result.
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Some operations are indeterminate and return \constant{NaN} or when the
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Some operations are indeterminate and return \constant{NaN}, or if the
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\exception{InvalidOperation} signal is trapped, raise an exception. For
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\exception{InvalidOperation} signal is trapped, raise an exception. For
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example, \code{0/0} returns \constant{NaN} which means ``not a number''. This
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example, \code{0/0} returns \constant{NaN} which means ``not a number''. This
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variety of \constant{NaN} is quiet and, once created, will flow through other
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variety of \constant{NaN} is quiet and, once created, will flow through other
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@ -909,11 +909,11 @@ result needs to interrupt a calculation for special handling.
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The signed zeros can result from calculations that underflow.
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The signed zeros can result from calculations that underflow.
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They keep the sign that would have resulted if the calculation had
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They keep the sign that would have resulted if the calculation had
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been carried out to greater precision. Since their magnitude is
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been carried out to greater precision. Since their magnitude is
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zero, the positive and negative zero are treated as equal and their
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zero, both positive and negative zeros are treated as equal and their
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sign is informational.
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sign is informational.
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In addition to the two signed zeros which are distinct, yet equal,
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In addition to the two signed zeros which are distinct yet equal,
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there are various representations of zero with differing precisions,
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there are various representations of zero with differing precisions
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yet equivalent in value. This takes a bit of getting used to. For
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yet equivalent in value. This takes a bit of getting used to. For
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an eye accustomed to normalized floating point representations, it
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an eye accustomed to normalized floating point representations, it
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is not immediately obvious that the following calculation returns
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is not immediately obvious that the following calculation returns
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