Document exp2() and exp2f(), and make other minor tweaks and updates.
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@ -32,12 +32,15 @@
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.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
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.\" $FreeBSD$
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.\"
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.Dd January 14, 2005
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.Dd April 5, 2005
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.Dt EXP 3
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.Os
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.Sh NAME
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.Nm exp ,
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.Nm expf ,
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.\" The sorting error is intentional. exp and expf should be adjacent.
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.Nm exp2 ,
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.Nm exp2f ,
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.Nm expm1 ,
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.Nm expm1f ,
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.Nm log ,
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@ -58,6 +61,10 @@
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.Ft float
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.Fn expf "float x"
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.Ft double
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.Fn exp2 "double x"
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.Ft float
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.Fn exp2f "float x"
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.Ft double
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.Fn expm1 "double x"
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.Ft float
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.Fn expm1f "float x"
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@ -82,7 +89,16 @@ The
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.Fn exp
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and the
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.Fn expf
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functions compute the exponential value of the given argument
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functions compute the base
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.Ms e
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exponential value of the given argument
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.Fa x .
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.Pp
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The
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.Fn exp2
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and the
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.Fn exp2f
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functions compute the base 2 exponential of the given argument
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.Fa x .
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.Pp
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The
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@ -125,57 +141,16 @@ of
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to the exponent
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.Ar y .
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.Sh ERROR (due to Roundoff etc.)
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.Fn exp x ,
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.Fn log x ,
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.Fn expm1 x
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The values of
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.Fn exp 0 ,
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.Fn expm1 0 ,
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.Fn exp2 integer ,
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and
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.Fn log1p x
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are accurate to within
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an
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.Em ulp ,
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and
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.Fn log10 x
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to within about 2
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.Em ulps ;
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an
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.Em ulp
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is one
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.Em Unit
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in the
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.Em Last
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.Em Place .
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The error in
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.Fn pow x y
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is below about 2
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.Em ulps
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when its
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magnitude is moderate, but increases as
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.Fn pow x y
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approaches
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the over/underflow thresholds until almost as many bits could be
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lost as are occupied by the floating\-point format's exponent
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field; that is 8 bits for
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.Tn "VAX D"
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and 11 bits for IEEE 754 Double.
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No such drastic loss has been exposed by testing; the worst
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errors observed have been below 20
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.Em ulps
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for
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.Tn "VAX D" ,
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300
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.Em ulps
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for
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.Tn IEEE
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754 Double.
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Moderate values of
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.Fn pow
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are accurate enough that
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.Fn pow integer integer
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is exact until it is bigger than 2**56 on a
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.Tn VAX ,
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2**53 for
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.Tn IEEE
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754.
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are exact provided that they are representable.
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.\" XXX Is this really true for pow()?
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Otherwise the error in these functions is generally below one
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.Em ulp .
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.Sh RETURN VALUES
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These functions will return the appropriate computation unless an error
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occurs or an argument is out of range.
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@ -214,15 +189,7 @@ They also provide accurate inverse hyperbolic functions.
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.Pp
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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
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(not found on a
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.Tn VAX ) ,
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and
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.Em NaN
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(the reserved
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operand on a
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.Tn VAX ) .
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returns x**0 = 1 for all x including x = 0, \*(If, and \*(Na .
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Previous implementations of pow may
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have defined x**0 to be undefined in some or all of these
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cases.
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@ -267,23 +234,3 @@ and infinite x, i.e., independently of x.
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.Sh SEE ALSO
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.Xr fenv 3 ,
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.Xr math 3
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.Sh HISTORY
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A
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.Fn exp ,
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.Fn log
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and
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.Fn pow
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functions
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appeared in
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.At v6 .
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A
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.Fn log10
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function
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appeared in
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.At v7 .
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The
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.Fn log1p
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and
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.Fn expm1
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functions appeared in
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.Bx 4.3 .
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@ -32,7 +32,7 @@
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.\" from: @(#)math.3 6.10 (Berkeley) 5/6/91
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.\" $FreeBSD$
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.\"
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.Dd March 24, 2005
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.Dd April 5, 2005
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.Dt MATH 3
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.Os
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.if n \{\
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@ -174,7 +174,7 @@ cosh hyperbolic cosine
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erf error function
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erfc complementary error function
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exp exponential base e
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.\" exp2 exponential base 2
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exp2 exponential base 2
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expm1 exp(x)\-1
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j0 Bessel function of the first kind of the order 0
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j1 Bessel function of the first kind of the order 1
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@ -196,10 +196,10 @@ yn Bessel function of the second kind of the order n
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.El
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.Pp
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Unlike the algebraic functions listed earlier, the routines
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in this section may not produce a result that is correctly rounded.
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In general, an unbounded number of digits of a value taken by a
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transcendental function may be needed to determine the correctly rounded
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result.
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in this section may not produce a result that is correctly rounded,
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so reproducible results cannot be guaranteed across platforms.
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For most of these functions, however, incorrect rounding occurs
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rarely, and then only in very-close-to-halfway cases.
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.Sh SEE ALSO
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.Xr fenv 3 ,
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.Xr ieee 3
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@ -221,14 +221,16 @@ and
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values, were written for or imported into subsequent versions of FreeBSD.
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.Sh BUGS
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The
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.Fn exp2 ,
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.Fn log2 ,
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.Fn log2
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and
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.Fn nan
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functions are missing, and many functions are not available in their
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.Vt "long double"
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variants.
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.Pp
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Many of the routines to compute transcendental functions produce
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inaccurate results in other than the default rounding mode.
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.Pp
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On some architectures, trigonometric argument reduction is not
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performed accurately, resulting in errors greater than 1
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.Em ulp
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