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## exp(3)

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 ```EXP(3) OpenBSD Programmer's Manual EXP(3) NAME exp, expf, expm1, expm1f, log, logf, log10, log10f, log1p, log1pf, pow, powf - exponential, logarithm, power functions SYNOPSIS #include double exp(double x); float expf(float x); double expm1(double x); float expm1f(float x); double log(double x); float logf(float x); double log10(double x); float log10f(float x); double log1p(double x); float log1pf(float x); double pow(double x, double y); float powf(float x, float y); DESCRIPTION The exp() function computes the exponential value of the given argument x. The expm1() function computes the value exp(x)-1 accurately even for tiny argument x. The log() function computes the value of the natural logarithm of argu- ment x. The log10() function computes the value of the logarithm of argument x to base 10. The log1p() function computes the value of log(1+x) accurately even for tiny argument x. The pow() computes the value of x to the exponent y. ERROR (due to Roundoff etc.) exp(x), log(x), expm1(x) and log1p(x) are accurate to within an ulp, and log10(x) to within about 2 ulps; an ulp is one Unit in the Last Place. The error in pow(x, y) is below about 2 ulps when its magnitude is moder- ate, but increases as pow(x, y) approaches the over/underflow thresholds until almost as many bits could be lost as are occupied by the float- ing-point format's exponent field; that is 8 bits for VAX D and 11 bits for IEEE 754 Double. No such drastic loss has been exposed by testing; the worst errors observed have been below 20 ulps for VAX D, 300 ulps for IEEE 754 Double. Moderate values of pow() are accurate enough that pow(integer, integer) is exact until it is bigger than 2**56 on a VAX, 2**53 for IEEE 754. RETURN VALUES These functions will return the appropriate computation unless an error occurs or an argument is out of range. The functions exp(), expm1() and pow() detect if the computed value will overflow, set the global variable errno to ERANGE and cause a reserved operand fault on a VAX or Tahoe. The function pow(x, y) checks to see if x < 0 and y is not an integer, in the event this is true, the global variable errno is set to EDOM and on the VAX and Tahoe generate a reserved operand fault. On a VAX and Tahoe, errno is set to EDOM and the reserved operand is returned by log unless x > 0, by log1p() unless x > -1. NOTES The functions exp(x)-1 and log(1+x) are called expm1 and logp1 in BASIC on the Hewlett-Packard HP-71B and APPLE Macintosh, EXP1 and LN1 in Pas- cal, exp1 and log1 in C on APPLE Macintoshes, where they have been pro- vided to make sure financial calculations of ((1+x)**n-1)/x, namely expm1(n*log1p(x))/x, will be accurate when x is tiny. They also provide accurate inverse hyperbolic functions. The function pow(x, 0) returns x**0 = 1 for all x including x = 0, Infin- ity (not found on a VAX), and NaN (the reserved operand on a VAX). Previous implementations of pow may have defined x**0 to be undefined in some or all of these cases. Here are reasons for returning x**0 = 1 al- ways: 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, in- cluding x = 0. This is compatible with the convention that ac- cepts a as the value of polynomial p(x) = a*x**0 + a*x**1 + a*x**2 +...+ a[n]*x**n at x = 0 rather than reject a*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 infinity**0 = 1/0**0 = 1 too; and then NaN**0 = 1 too because x**0 = 1 for all finite and infinite x, i.e., inde- pendently of x. SEE ALSO infnan(3), math(3) HISTORY A exp(), log() and pow() functions appeared in Version 6 AT&T UNIX. A log10() function appeared in Version 7 AT&T UNIX. The log1p() and expm1() functions appeared in 4.3BSD. OpenBSD 2.6 July 31, 1991 3 ``` Source: OpenBSD 2.6 man pages. Copyright: Portions are copyrighted by BERKELEY SOFTWARE DESIGN, INC., The Regents of the University of California, Massachusetts Institute of Technology, Free Software Foundation, FreeBSD Inc., and others. (Corrections, notes, and links courtesy of RocketAware.com) FreeBSD Sources for exp(3) functions
FreeBSD Sources for exp(3) functions
OpenBSD sources for exp(3) Up to: Floating point math - Floating point math (including complex numbers)

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