Use the \*(If string provided by mdoc(7), to represent infinity.

This commit is contained in:
ru 2005-01-16 16:49:10 +00:00
parent 9bccb183eb
commit 8f12d81a1c
2 changed files with 11 additions and 18 deletions

View File

@ -217,10 +217,7 @@ They also provide accurate inverse hyperbolic functions.
The function
.Fn pow x 0
returns x**0 = 1 for all x including x = 0,
.if n \
Infinity
.if t \
\(if
\*(If
(not found on a
.Tn VAX ) ,
and
@ -265,10 +262,7 @@ x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
.Ed
.It
If 0**0 = 1, then
.if n \
infinity**0 = 1/0**0 = 1 too; and
.if t \
\(if**0 = 1/0**0 = 1 too; and
\*(If**0 = 1/0**0 = 1 too; and
then \*(Na**0 = 1 too because x**0 = 1 for all finite
and infinite x, i.e., independently of x.
.El

View File

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