Use the \*(If string provided by mdoc(7), to represent infinity.
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@ -217,10 +217,7 @@ They also provide accurate inverse hyperbolic functions.
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The function
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.Fn pow x 0
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returns x**0 = 1 for all x including x = 0,
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.if n \
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Infinity
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.if t \
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\(if
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\*(If
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(not found on a
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.Tn VAX ) ,
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and
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@ -265,10 +262,7 @@ x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
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.Ed
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.It
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If 0**0 = 1, then
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.if n \
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infinity**0 = 1/0**0 = 1 too; and
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.if t \
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\(if**0 = 1/0**0 = 1 too; and
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\*(If**0 = 1/0**0 = 1 too; and
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then \*(Na**0 = 1 too because x**0 = 1 for all finite
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and infinite x, i.e., independently of x.
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.El
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@ -36,7 +36,6 @@
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.Dt MATH 3
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.Os
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.if n \{\
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.char \[if] "Infinity
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.char \[sr] "sqrt
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.\}
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.Sh NAME
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@ -186,7 +185,7 @@ Range: Overflow threshold = 2.0**1024 = 1.8e308
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Underflow threshold = 0.5**1022 = 2.2e\-308
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.El
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.Bd -ragged -offset indent -compact
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Overflow goes by default to a signed \(if.
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Overflow goes by default to a signed \*(If.
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Underflow is
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.Em Gradual ,
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rounding to the nearest
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@ -204,19 +203,19 @@ sign are division by zero and
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.Fn copysign x \(+-0 .
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In particular, comparison (x > y, x \(>= y, etc.)\&
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cannot be affected by the sign of zero; but if
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finite x = y then \(if = 1/(x\-y) \(!= \-1/(y\-x) = \-\(if.
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finite x = y then \*(If = 1/(x\-y) \(!= \-1/(y\-x) = \-\*(If.
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.Ed
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.Pp
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\(if is signed.
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\*(If is signed.
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.Bd -ragged -offset indent -compact
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It persists when added to itself
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or to any finite number.
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Its sign transforms
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correctly through multiplication and division, and
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(finite)/\(+-\(if\0=\0\(+-0
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(nonzero)/0 = \(+-\(if.
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(finite)/\(+-\*(If\0=\0\(+-0
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(nonzero)/0 = \(+-\*(If.
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But
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\(if\-\(if, \(if\(**0 and \(if/\(if
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\*(If\-\*(If, \*(If\(**0 and \*(If/\*(If
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are, like 0/0 and sqrt(\-3),
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invalid operations that produce \*(Na. ...
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.Ed
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@ -262,7 +261,7 @@ Only rounding like IEEE 754 can do that.
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But no single kind of rounding can be
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proved best for every circumstance, so IEEE 754
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provides rounding towards zero or towards
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+\(if or towards \-\(if
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+\*(If or towards \-\*(If
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at the programmer's option.
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And the
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same kinds of rounding are specified for
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@ -277,8 +276,8 @@ listed below in declining order of probable importance.
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.Bl -column -offset indent "Invalid Operation" "Gradual Underflow"
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.Em "Exception Default Result"
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Invalid Operation \*(Na, or FALSE
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Overflow \(+-\(if
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Divide by Zero \(+-\(if
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Overflow \(+-\*(If
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Divide by Zero \(+-\*(If
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Underflow Gradual Underflow
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Inexact Rounded value
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.El
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