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28 .\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
38 .\" The sorting error is intentional. exp, expf, and expl should be adjacent.
48 .Nd exponential and power functions
58 .Fn expl "long double x"
64 .Fn exp2l "long double x"
70 .Fn expm1l "long double x"
72 .Fn pow "double x" "double y"
74 .Fn powf "float x" "float y"
76 .Fn powl "long double x" "long double y"
83 functions compute the base
85 exponential value of the given argument
93 functions compute the base 2 exponential of the given argument
101 functions compute the value exp(x)\-1 accurately even for tiny argument
109 functions compute the value
114 .Sh ERROR (due to Roundoff etc.)
120 .Fn pow integer integer
121 are exact provided that they are representable.
122 .\" XXX Is this really true for pow()?
123 Otherwise the error in these functions is generally below one
126 These functions will return the appropriate computation unless an error
127 occurs or an argument is out of range.
133 raise an invalid exception and return an \*(Na if
141 returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na .
142 Previous implementations of pow may
143 have defined x**0 to be undefined in some or all of these
145 Here are reasons for returning x**0 = 1 always:
146 .Bl -enum -width indent
148 Any program that already tests whether x is zero (or
149 infinite or \*(Na) before computing x**0 cannot care
150 whether 0**0 = 1 or not.
151 Any program that depends
152 upon 0**0 to be invalid is dubious anyway since that
153 expression's meaning and, if invalid, its consequences
154 vary from one computer system to another.
156 Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for
157 all x, including x = 0.
158 This is compatible with the convention that accepts a[0]
159 as the value of polynomial
160 .Bd -literal -offset indent
161 p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n
164 at x = 0 rather than reject a[0]\(**0**0 as invalid.
166 Analysts will accept 0**0 = 1 despite that x**y can
167 approach anything or nothing as x and y approach 0
169 The reason for setting 0**0 = 1 anyway is this:
170 .Bd -ragged -offset indent
173 functions analytic (expandable
174 in power series) in z around z = 0, and if there
175 x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
179 \*(If**0 = 1/0**0 = 1 too; and
180 then \*(Na**0 = 1 too because x**0 = 1 for all finite
181 and infinite x, i.e., independently of x.
184 To conform with newer C/C++ standards, a stub implementation for
186 was committed to the math library, where
190 Thus, the numerical accuracy is at most that of the 53-bit double
191 precision implementation.
198 These functions conform to