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#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;
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 [a manual with the abbreviation FPOINT].
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)
In addition, exp(), exp2(), exp10(), log(), log2(), log10() and pow() may also set errno and call matherr.3m
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