6.1
1 Constants and Elementary Functions
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For convenience, math/base re-exports racket/math
as well as providing the values document below.
In general, the functions provided by math/base are elementary
functions, or those functions that can be defined in terms of a finite number of
arithmetic operations, logarithms, exponentials, trigonometric functions, and constants.
For others, see math/special-functions and math/distributions.
1.1 Constants
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If you need more accurate approximations than the following flonums, see, for example,
phi.bf and bigfloat->rational.
| > euler.0 |
2.718281828459045 |
| > (exp 1) |
2.718281828459045 |
1.2 Functions
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Returns a new complex number with a flonum real part and a flonum imaginary part.
Analogous to
real->double-flonum.
Returns #t when x is an integer power of 2.
Like
(apply + xs), but incurs rounding error only once when adding inexact numbers.
(In fact, the inexact numbers in
xs are summed separately using
flsum.)
1.3 Random Number Generation
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Returns a random natural number less than
k, which must be positive.
Use
(random-natural k) instead of
(random k) when
k
could be larger than
4294967087.
Returns a random integer
n such that
(<= a n) and
(< n b).
Returns a random natural smaller than
(expt 2 num);
num must be positive.
For powers of two, this is faster than using
random-natural, which
is implemented in terms of
random-bits, using biased rejection sampling.
As an example of use, the significands of the numbers returned by bfrandom
are chosen by (random-bits (bf-precision)).
1.4 Measuring Error
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Usually computes
(abs (- x r)) using exact rationals, but handles non-rational
reals such as
+inf.0 specially.
Measures how close an approximation x is to the correct value r,
relative to the magnitude of r.
This function usually computes (abs (/ (- x r) r)) using exact rationals,
but handles non-rational reals such as +inf.0 specially, as well as
r = 0.
In the last two examples, relative error is high because the result is near zero. (Compare
the same examples with
absolute-error.) Because flonums are particularly dense
near zero, this makes relative error better than absolute error for measuring the error
in a flonum approximation. An even better one is error in
ulps; see
flulp-error.
