exp, expm1, exp2, exp10, log, log1p, log2, log10, pow, compound, annu-
ity - exponential, logarithm, power
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
compound() and annuity() are functions important in financial computa-
tions 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 annu-
ity() are computed using log1p() and expm1() to avoid gratuitous inac-
curacy 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)
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
In addition, exp(), exp2(), exp10(), log(), log2(), log10() and pow()
may also set errno and call matherr(3M).
24 March 1988 EXP(3M)