EXP(3) BSD Library Functions Manual EXP(3)[top]NAMEexp, expf, exp2, exp2f, exp2l, expm1, expm1f, pow, powf — exponential and power functionsLIBRARYMath Library (libm, -lm)SYNOPSIS#include <math.h> double exp(double x); float expf(float x); double exp2(double x); float exp2f(float x); long double exp2l(long double x); double expm1(double x); float expm1f(float x); double pow(double x, double y); float powf(float x, float y);DESCRIPTIONThe exp() and the expf() functions compute the base e exponential value of the given argument x. The exp2(), exp2f(), and exp2l() functions compute the base 2 exponential of the given argument x. The expm1() and the expm1f() functions compute the value exp(x)-1 accu‐ rately even for tiny argument x. The pow() and the powf() functions compute the value of x to the exponent y.ERROR (due to Roundoff etc.)The values of exp(0), expm1(0), exp2(integer), and pow(integer, integer) are exact provided that they are representable. Otherwise the error in these functions is generally below one ulp.RETURN VALUESThese functions will return the appropriate computation unless an error occurs or an argument is out of range. The functions pow(x, y) and powf(x, y) raise an invalid exception and return an NaN if x < 0 and y is not an integer.NOTESThe function pow(x, 0) returns x**0 = 1 for all x including x = 0, ∞, and NaN . Previous implementations ofpowmay have defined x**0 to be unde‐ fined in some or all of these cases. Here are reasons for returning x**0 = 1 always: 1. Any program that already tests whether x is zero (or infinite or NaN) before computing x**0 cannot care whether 0**0 = 1 or not. Any program that depends upon 0**0 to be invalid is dubious any‐ way since that expression's meaning and, if invalid, its conse‐ quences vary from one computer system to another. 2. Some Algebra texts (e.g. Sigler's) define x**0 = 1 for all x, including x = 0. This is compatible with the convention that accepts a[0] as the value of polynomial p(x) = a[0]∗x**0 + a[1]∗x**1 + a[2]∗x**2 +...+ a[n]∗x**n at x = 0 rather than reject a[0]∗0**0 as invalid. 3. Analysts will accept 0**0 = 1 despite that x**y can approach any‐ thing or nothing as x and y approach 0 independently. The reason for setting 0**0 = 1 anyway is this: If x(z) and y(z) are any functions analytic (expandable in power series) in z around z = 0, and if there x(0) = y(0) = 0, then x(z)**y(z) → 1 as z → 0. 4. If 0**0 = 1, then ∞**0 = 1/0**0 = 1 too; and then NaN**0 = 1 too because x**0 = 1 for all finite and infinite x, i.e., indepen‐ dently of x.SEE ALSOfenv(3), ldexp(3), log(3), math(3)STANDARDSThese functions conform to ISO/IEC 9899:1999 (“ISO C99”).BSDJanuary 17, 2008 BSD

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