module Float_intf:sig
..end
module Binable: Binable0
module type S =sig
..end
max
and min
will return nan if either argument is nan.
The validate_*
functions always fail if class is Nan
or Infinite
.
The results of robust comparisons on nan
should be considered undefined.
validate_ordinary
fails if class is Nan
or Infinite
.
equal to infinity
equal to neg_infinity
See Robust_compare
The difference between 1.0 and the smallest exactly representable floating-point
number greater than 1.0. That is:
epsilon_float = (one_ulp `Up 1.0) -. 1.0
This gives the relative accuracy of type t
, in the sense that for numbers on the
order of x
, the roundoff error is on the order of x *. float_epsilon
.
See also: http://en.wikipedia.org/wiki/Machine_epsilon
min_positive_subnormal_value = 2 ** -1074
min_positive_normal_value = 2 ** -1022
An order-preserving bijection between all floats except for nans, and all int64s
with absolute value smaller than or equal to 2**63 - 2**52
.
Note both 0. and -0. map to 0L.
returns nan
if the absolute value of the argument is too large
The next or previous representable float. ULP stands for "unit of least precision",
and is the spacing between floating point numbers. Both one_ulp `Up infinity
and
one_ulp `Down neg_infinity
return a nan.
round
rounds a float to an integer float. iround{,_exn}
rounds a float to an
int. Both round according to a direction dir
, with default dir
being `Nearest
.
| `Down | rounds toward Float.neg_infinity | | `Up | rounds toward Float.infinity | | `Nearest | rounds to the nearest int ("round half-integers up") | | `Zero | rounds toward zero |
iround_exn
raises when trying to handle nan or trying to handle a float outside the
range [float min_int, float max_int).
Here are some examples for round
for each direction:
| `Down | [-2.,-1.) to -2. | [-1.,0.) to -1. | [0.,1.) to 0., [1.,2.) to 1. | | `Up | (-2.,-1.] to -1. | (-1.,0.] to -0. | (0.,1.] to 1., (1.,2.] to 2. | | `Zero | (-2.,-1.] to -1. | (-1.,1.) to 0. | [1.,2.) to 1. | | `Nearest | [-1.5,-0.5) to -1. | [-0.5,0.5) to 0. | [0.5,1.5) to 1. |
For convenience, versions of these functions with the dir
argument hard-coded are
provided. If you are writing performance-critical code you should use the
versions with the hard-coded arguments (e.g. iround_down_exn
). The _exn
ones
are the fastest.
The following properties hold:
of_int (iround_*_exn i) = i
for any float i
that is an integer with
min_int <= i <= max_int
.round_* i = i
for any float i
that is an integer.iround_*_exn (of_int i) = i
for any int i
with -2**52 <= i <= 2**52
.f <= iround_lbound || f >= iround_ubound
, then iround*
functions will refuse
to round f
, returning None
or raising as appropriate.nan
. Returns
nan
if both arguments are nan
.modf
(-3.14)
returns { fractional = -0.14; integral = -3.; }
!mod_float x y
returns a result with the same sign as x
. It returns nan
if y
is 0
. It is basically
let mod_float x y = x -. float(truncate(x/.y)) *. y
not
let mod_float x y = x -. floor(x/.y) *. y
and therefore resembles mod
on integers more than %
.
These are for modules that inherit from t, since the infix operators are more
convenient
A sub-module designed to be opened to make working with floats more convenient.
Like to_string
, but guaranteed to be round-trippable.
It usually yields as few significant digits as possible. That is, it won't print
3.14
as 3.1400000000000001243
. The only exception is that occasionally it will
output 17 significant digits when the number can be represented with just 16 (but
not 15 or less) of them.
Pretty print float, for example to_string_hum ~decimals:3 1234.1999 = "1_234.200"
to_string_hum ~decimals:3 ~strip_zero:true 1234.1999 = "1_234.2"
. No delimiters
are inserted to the right of the decimal.
defaults to '_'
defaults to 3
defaults to false
Produce a lossy compact string representation of the float. The float is scaled by
an appropriate power of 1000 and rendered with one digit after the decimal point,
except that the decimal point is written as '.', 'k', 'm', 'g', 't', or 'p' to
indicate the scale factor. (However, if the digit after the "decimal" point is 0,
it is suppressed.) The smallest scale factor that allows the number to be rendered
with at most 3 digits to the left of the decimal is used. If the number is too
large for this format (i.e., the absolute value is at least 999.95e15), scientific
notation is used instead. E.g.:
to_padded_compact_string (-0.01) = "-0 "
to_padded_compact_string 1.89 = "1.9"
to_padded_compact_string 999_949.99 = "999k9"
to_padded_compact_string 999_950. = "1m "
In the case where the digit after the "decimal", or the "decimal" itself are omitted, the numbers are padded on the right with spaces to ensure the last two columns of the string always correspond to the decimal and the digit afterward (except in the case of scientific notation, where the exponent is the right-most element in the string and could take up to four characters).
to_padded_compact_string 1. = "1 ";
to_padded_compact_string 1.e6 = "1m ";
to_padded_compact_string 1.e16 = "1.e+16";
to_padded_compact_string max_finite_value = "1.8e+308";
Numbers in the range -.05 < x < .05 are rendered as "0 " or "-0 ".
Other cases:
to_padded_compact_string nan = "nan "
to_padded_compact_string infinity = "inf "
to_padded_compact_string neg_infinity = "-inf "
Exact ties are resolved to even in the decimal:
to_padded_compact_string 3.25 = "3.2"
to_padded_compact_string 3.75 = "3.8"
to_padded_compact_string 33_250. = "33k2"
to_padded_compact_string 33_350. = "33k4"
ldexp x n
returns x *. 2 ** n
frexp f
returns the pair of the significant and the exponent of f. When f is zero,
the significant x and the exponent n of f are equal to zero. When f is non-zero,
they are defined by f = x *. 2 ** n
and 0.5 <= x < 1.0
.t Class.t example ^ neg_infinity Infinite neg_infinity | neg normals Normal -3.14 | neg subnormals Subnormal -.2. ** -1023. | (-/+) zero Zero 0. | pos subnormals Subnormal 2. ** -1023. | pos normals Normal 3.14 v infinity Infinite infinity
is_finite t
returns true
iff classify t
is in Normal; Subnormal; Zero;
.
In particular, if 1 <= exponent <= 2046, then:
create_ieee_exn ~negative:false ~exponent ~mantissa =
2 ** (exponent - 1023) * (1 + (2 ** -52) * mantissa)
S-expressions contain at most 8 significant digits.