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28 .\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
37 .\" The sorting error is intentional. exp and expf should be adjacent.
45 .Nd exponential and power functions
59 .Fn exp2l "long double x"
65 .Fn pow "double x" "double y"
67 .Fn powf "float x" "float y"
73 functions compute the base
75 exponential value of the given argument
83 functions compute the base 2 exponential of the given argument
90 functions compute the value exp(x)\-1 accurately even for tiny argument
97 functions compute the value
102 .Sh ERROR (due to Roundoff etc.)
108 .Fn pow integer integer
109 are exact provided that they are representable.
110 .\" XXX Is this really true for pow()?
111 Otherwise the error in these functions is generally below one
114 These functions will return the appropriate computation unless an error
115 occurs or an argument is out of range.
120 raise an invalid exception and return an \*(Na if
128 returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na .
129 Previous implementations of pow may
130 have defined x**0 to be undefined in some or all of these
132 Here are reasons for returning x**0 = 1 always:
133 .Bl -enum -width indent
135 Any program that already tests whether x is zero (or
136 infinite or \*(Na) before computing x**0 cannot care
137 whether 0**0 = 1 or not.
138 Any program that depends
139 upon 0**0 to be invalid is dubious anyway since that
140 expression's meaning and, if invalid, its consequences
141 vary from one computer system to another.
143 Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for
144 all x, including x = 0.
145 This is compatible with the convention that accepts a[0]
146 as the value of polynomial
147 .Bd -literal -offset indent
148 p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n
151 at x = 0 rather than reject a[0]\(**0**0 as invalid.
153 Analysts will accept 0**0 = 1 despite that x**y can
154 approach anything or nothing as x and y approach 0
156 The reason for setting 0**0 = 1 anyway is this:
157 .Bd -ragged -offset indent
160 functions analytic (expandable
161 in power series) in z around z = 0, and if there
162 x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
166 \*(If**0 = 1/0**0 = 1 too; and
167 then \*(Na**0 = 1 too because x**0 = 1 for all finite
168 and infinite x, i.e., independently of x.
176 These functions conform to