NAME

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

SYNOPSIS

#include <math.h>

double exp(x)
double x;

double expm1(x)
double x;

double exp2(x)
double x;

double exp10(x)
double x;

double log(x)
double x;

double log1p(x)
double x;

double log2(x)
double x;

double log10(x)
double x;

double pow(x, y)
double x, y;

double compound(r, n)
double r, n;

double annuity(r, n)
double r, 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(x,0.0) is 1 for all x, in conformance with 4.3BSD, as discussed in the Floating Point Programmers Guide. 

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 the spirit of ANSI/IEEE Std 754-1985.  Thus for x == ±0, log(x) is −∞ with a division by zero exception; for x < 0, including −∞, log(x) is a quiet NaN 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 4.0  —  Last change: 24 March 1988