NAME

exp, expm1, exp2, exp10, log, log1p, log2, log10, pow, compound, annuity − exponential, logarithm, power

SYNOPSIS

#include <math.h>

double exp(double x);

double expm1(double x);

double exp2(double x);

double exp10(double x);

double log(double x);

double log1p(double x);

double log2(double x);

double log10(double x);

double pow(double x, double y);

double compound(double r, double n);

double annuity(double r, double n);

DESCRIPTION

exp() returns the exponential function e∗∗x.

expm1() returns (e∗∗x)−1 accurately even for tiny x.

exp2() and exp10() return 2∗∗x and 10∗∗x respectively. 

log() returns the natural logarithm of x.

log1p() returns log(1+x) accurately even for tiny x.

log2() and log10() return the logarithm to base 2 and 10 respectively. 

pow() returns x∗∗y. pow(0.0,0.0) is 0.0 in conformance with SVID. 

compound() and annuity() are functions important in financial computations of the effect of interest at periodic rate r over n periods.  compound(r,n) computes (1+r)∗∗n, the compound interest factor. Given an initial principal P0, its value after n periods is just Pn = P0 ∗compound(r,n). annuity(r,n) computes (1 − (1+r)∗∗−n)/r, the present value of annuity factor.  Given an initial principal P0, the equivalent periodic payment is just p = P0 / annuity(r,n). compound() and annuity() are computed using log1p() and expm1() to avoid gratuitous inaccuracy for small-magnitude r. compound() and annuity() are not defined for r <= −1. 

Thus a principal amount P0 placed at 5% annual interest compounded quarterly for 30 years would yield

 P30 = P0 ∗ compound(.05/4, 30.0 ∗ 4)
 

while a conventional fixed-rate 30-year home loan of amount P0 at 10% annual interest would be amortized by monthly payments in the amount

 p = P0 / annuity(.10/12, 30.0 ∗ 12).
 

SEE ALSO

matherr(3M)

DIAGNOSTICS

All these functions handle exceptional arguments in conformance with SVID.  Thus for x == ±0, log(x) is −HUGE (HUGE = ∞) with a division by zero exception; for x < 0, log(x) is −HUGE with an invalid operation exception; for x == +∞ or a quiet NaN, log(x) is x without exception; for x a signaling NaN, log(x) is a quiet NaN with an invalid operation exception; for x == 1, log(x) is 0 without exception; for any other positive x, log(x) is a normalized number with an inexact exception. 

In addition, exp(), exp2(), exp10(), log(), log2(), log10() and pow() may also set errno and call matherr(3M). 

Sun Release 4.1  —  Last change: 24 October 1991