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28 .\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
29 .\" $FreeBSD: head/lib/msun/man/exp.3 251343 2013-06-03 19:51:32Z kargl $
38 .\" The sorting error is intentional. exp, expf, and expl should be adjacent.
47 .Nd exponential and power functions
57 .Fn expl "long double x"
63 .Fn exp2l "long double x"
69 .Fn expm1l "long double x"
71 .Fn pow "double x" "double y"
73 .Fn powf "float x" "float y"
80 functions compute the base
82 exponential value of the given argument
90 functions compute the base 2 exponential of the given argument
98 functions compute the value exp(x)\-1 accurately even for tiny argument
105 functions compute the value
110 .Sh ERROR (due to Roundoff etc.)
116 .Fn pow integer integer
117 are exact provided that they are representable.
118 .\" XXX Is this really true for pow()?
119 Otherwise the error in these functions is generally below one
122 These functions will return the appropriate computation unless an error
123 occurs or an argument is out of range.
128 raise an invalid exception and return an \*(Na if
136 returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na .
137 Previous implementations of pow may
138 have defined x**0 to be undefined in some or all of these
140 Here are reasons for returning x**0 = 1 always:
141 .Bl -enum -width indent
143 Any program that already tests whether x is zero (or
144 infinite or \*(Na) before computing x**0 cannot care
145 whether 0**0 = 1 or not.
146 Any program that depends
147 upon 0**0 to be invalid is dubious anyway since that
148 expression's meaning and, if invalid, its consequences
149 vary from one computer system to another.
151 Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for
152 all x, including x = 0.
153 This is compatible with the convention that accepts a[0]
154 as the value of polynomial
155 .Bd -literal -offset indent
156 p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n
159 at x = 0 rather than reject a[0]\(**0**0 as invalid.
161 Analysts will accept 0**0 = 1 despite that x**y can
162 approach anything or nothing as x and y approach 0
164 The reason for setting 0**0 = 1 anyway is this:
165 .Bd -ragged -offset indent
168 functions analytic (expandable
169 in power series) in z around z = 0, and if there
170 x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
174 \*(If**0 = 1/0**0 = 1 too; and
175 then \*(Na**0 = 1 too because x**0 = 1 for all finite
176 and infinite x, i.e., independently of x.
184 These functions conform to