Data::Float(3pm) User Contributed Perl Documentation Data::Float(3pm)
NAME
Data::Float - details of the floating point data type
SYNOPSIS
use Data::Float qw(have_signed_zero);
if(have_signed_zero) { ...
# and many other constants; see text
use Data::Float qw(
float_class float_is_normal float_is_subnormal
float_is_nzfinite float_is_zero float_is_finite
float_is_infinite float_is_nan);
$class = float_class($value);
if(float_is_normal($value)) { ...
if(float_is_subnormal($value)) { ...
if(float_is_nzfinite($value)) { ...
if(float_is_zero($value)) { ...
if(float_is_finite($value)) { ...
if(float_is_infinite($value)) { ...
if(float_is_nan($value)) { ...
use Data::Float qw(float_sign signbit float_parts);
$sign = float_sign($value);
$sign_bit = signbit($value);
($sign, $exponent, $significand) = float_parts($value);
use Data::Float qw(float_hex hex_float);
print float_hex($value);
$value = hex_float($string);
use Data::Float qw(float_id_cmp totalorder);
@sorted_floats = sort { float_id_cmp($a, $b) } @floats;
if(totalorder($a, $b)) { ...
use Data::Float qw(
pow2 mult_pow2 copysign nextup nextdown nextafter);
$x = pow2($exp);
$x = mult_pow2($value, $exp);
$x = copysign($magnitude, $sign_from);
$x = nextup($x);
$x = nextdown($x);
$x = nextafter($x, $direction);
DESCRIPTION
This module is about the native floating point numerical data type. A
floating point number is one of the types of datum that can appear in
the numeric part of a Perl scalar. This module supplies constants
describing the native floating point type, classification functions,
and functions to manipulate floating point values at a low level.
FLOATING POINT
Classification
Floating point values are divided into five subtypes:
normalised
The value is made up of a sign bit (making the value positive or
negative), a significand, and exponent. The significand is a
number in the range [1, 2), expressed as a binary fraction of a
certain fixed length. (Significands requiring a longer binary
fraction, or lacking a terminating binary representation, cannot be
obtained.) The exponent is an integer in a certain fixed range.
The magnitude of the value represented is the product of the
significand and two to the power of the exponent.
subnormal
The value is made up of a sign bit, significand, and exponent, as
for normalised values. However, the exponent is fixed at the
minimum possible for a normalised value, and the significand is in
the range (0, 1). The length of the significand is the same as for
normalised values. This is essentially a fixed-point format, used
to provide gradual underflow. Not all floating point formats
support this subtype. Where it is not supported, underflow is
sudden, and the difference between two minimum-exponent normalised
values cannot be exactly represented.
zero
Depending on the floating point type, there may be either one or
two zero values: zeroes may carry a sign bit. Where zeroes are
signed, it is primarily in order to indicate the direction from
which a value underflowed (was rounded) to zero. Positive and
negative zero compare as numerically equal, and they give identical
results in most arithmetic operations. They are on opposite sides
of some branch cuts in complex arithmetic.
infinite
Some floating point formats include special infinite values. These
are generated by overflow, and by some arithmetic cases that
mathematically generate infinities. There are two infinite values:
positive infinity and negative infinity.
Perl does not always generate infinite values when normal floating
point behaviour calls for it. For example, the division "1.0/0.0"
causes an exception rather than returning an infinity.
not-a-number (NaN)
This type of value exists in some floating point formats to
indicate error conditions. Mathematically undefined operations may
generate NaNs, and NaNs propagate through all arithmetic
operations. A NaN has the distinctive property of comparing
numerically unequal to all floating point values, including itself.
Perl does not always generate NaNs when normal floating point
behaviour calls for it. For example, the division "0.0/0.0" causes
an exception rather than returning a NaN.
Perl has only (at most) one NaN value, even if the underlying
system supports different NaNs. (IEEE 754 arithmetic has NaNs
which carry a quiet/signal bit, a sign bit (yes, a sign on a not-
number), and many bits of implementation-defined data.)
Mixing floating point and integer values
Perl does not draw a strong type distinction between native integer
(see Data::Integer) and native floating point values. Both types of
value can be stored in the numeric part of a plain (string) scalar. No
distinction is made between the integer representation and the floating
point representation where they encode identical values. Thus, for
floating point arithmetic, native integer values that can be
represented exactly in floating point may be freely used as floating
point values.
Native integer arithmetic has exactly one zero value, which has no
sign. If the floating point type does not have signed zeroes then the
floating point and integer zeroes are exactly equivalent. If the
floating point type does have signed zeroes then the integer zero can
still be used in floating point arithmetic, and it behaves as an
unsigned floating point zero. On such systems there are therefore
three types of zero available. There is a bug in Perl which sometimes
causes floating point zeroes to change into integer zeroes; see "BUGS"
for details.
Where a native integer value is used that is too large to exactly
represent in floating point, it will be rounded as necessary to a
floating point value. This rounding will occur whenever an operation
has to be performed in floating point because the result could not be
exactly represented as an integer. This may be confusing to functions
that expect a floating point argument.
Similarly, some operations on floating point numbers will actually be
performed in integer arithmetic, and may result in values that cannot
be exactly represented in floating point. This happens whenever the
arguments have integer values that fit into the native integer type and
the mathematical result can be exactly represented as a native integer.
This may be confusing in cases where floating point semantics are
expected.
See perlnumber(1) for discussion of Perl's numeric semantics.
CONSTANTS
Features
have_signed_zero
Truth value indicating whether floating point zeroes carry a sign.
If yes, then there are two floating point zero values: +0.0 and
-0.0. (Perl scalars can nevertheless also hold an integer zero,
which is unsigned.) If no, then there is only one zero value,
which is unsigned.
have_subnormal
Truth value indicating whether there are subnormal floating point
values.
have_infinite
Truth value indicating whether there are infinite floating point
values.
have_nan
Truth value indicating whether there are NaN floating point values.
It is difficult to reliably generate a NaN in Perl, so in some
unlikely circumstances it is possible that there might be NaNs that
this module failed to detect. In that case this constant would be
false but a NaN might still turn up somewhere. What this constant
reliably indicates is the availability of the "nan" constant below.
Extrema
significand_bits
The number of fractional bits in the significand of finite floating
point values. The significand also has an implicit integer bit,
not counted in this constant; the integer bit is always 1 for
normalised values and always 0 for subnormal values.
significand_step
The difference between adjacent representable values in the range
[1, 2] (where the exponent is zero). This is equal to
2^-significand_bits.
max_finite_exp
The maximum exponent permitted for finite floating point values.
max_finite_pow2
The maximum representable power of two. This is 2^max_finite_exp.
max_finite
The maximum representable finite value. This is
2^(max_finite_exp+1) - 2^(max_finite_exp-significand_bits).
max_number
The maximum representable number. This is positive infinity if
there are infinite values, or max_finite if there are not.
max_integer
The maximum integral value for which all integers from zero to that
value inclusive are representable. Equivalently: the minimum
positive integral value N for which the value N+1 is not
representable. This is 2^(significand_bits+1). The name is
somewhat misleading.
min_normal_exp
The minimum exponent permitted for normalised floating point
values.
min_normal
The minimum positive value representable as a normalised floating
point value. This is 2^min_normal_exp.
min_finite_exp
The base two logarithm of the minimum representable positive finite
value. If there are subnormals then this is min_normal_exp -
significand_bits. If there are no subnormals then this is
min_normal_exp.
min_finite
The minimum representable positive finite value. This is
2^min_finite_exp.
Special Values
pos_zero
The positive zero value. (Exists only if zeroes are signed, as
indicated by the "have_signed_zero" constant.)
If Perl is at risk of transforming floating point zeroes into
integer zeroes (see "BUGS"), then this is actually a non-constant
function that always returns a fresh floating point zero. Thus the
return value is always a true floating point zero, regardless of
what happened to zeroes previously returned.
neg_zero
The negative zero value. (Exists only if zeroes are signed, as
indicated by the "have_signed_zero" constant.)
If Perl is at risk of transforming floating point zeroes into
integer zeroes (see "BUGS"), then this is actually a non-constant
function that always returns a fresh floating point zero. Thus the
return value is always a true floating point zero, regardless of
what happened to zeroes previously returned.
pos_infinity
The positive infinite value. (Exists only if there are infinite
values, as indicated by the "have_infinite" constant.)
neg_infinity
The negative infinite value. (Exists only if there are infinite
values, as indicated by the "have_infinite" constant.)
nan Not-a-number. (Exists only if NaN values were detected, as
indicated by the "have_nan" constant.)
FUNCTIONS
Each "float_" function takes a floating point argument to operate on.
The argument must be a native floating point value, or a native integer
with a value that can be represented in floating point. Giving a non-
numeric argument will cause mayhem. See "is_number" in
Params::Classify for a way to check for numericness. Only the numeric
value of the scalar is used; the string value is completely ignored, so
dualvars are not a problem.
Classification
Each "float_is_" function returns a simple truth value result.
float_class(VALUE)
Determines which of the five classes described above VALUE falls
into. Returns "NORMAL", "SUBNORMAL", "ZERO", "INFINITE", or "NAN"
accordingly.
float_is_normal(VALUE)
Returns true iff VALUE is a normalised floating point value.
float_is_subnormal(VALUE)
Returns true iff VALUE is a subnormal floating point value.
float_is_nzfinite(VALUE)
Returns true iff VALUE is a non-zero finite value (either normal or
subnormal; not zero, infinite, or NaN).
float_is_zero(VALUE)
Returns true iff VALUE is a zero. If zeroes are signed then the
sign is irrelevant.
float_is_finite(VALUE)
Returns true iff VALUE is a finite value (either normal, subnormal,
or zero; not infinite or NaN).
float_is_infinite(VALUE)
Returns true iff VALUE is an infinity (either positive infinity or
negative infinity).
float_is_nan(VALUE)
Returns true iff VALUE is a NaN.
Examination
float_sign(VALUE)
Returns "+" or "-" to indicate the sign of VALUE. An unsigned zero
returns the sign "+". "die"s if VALUE is a NaN.
signbit(VALUE)
VALUE must be a floating point value. Returns the sign bit of
VALUE: 0 if VALUE is positive or a positive or unsigned zero, or 1
if VALUE is negative or a negative zero. Returns an unpredictable
value if VALUE is a NaN.
This is an IEEE 754 standard function. According to the standard
NaNs have a well-behaved sign bit, but Perl can't see that bit.
float_parts(VALUE)
Divides up a non-zero finite floating point value into sign,
exponent, and significand, returning these as a three-element list
in that order. The significand is returned as a floating point
value, in the range [1, 2) for normalised values, and in the range
(0, 1) for subnormals. "die"s if VALUE is not finite and non-zero.
String conversion
float_hex(VALUE[, OPTIONS])
Encodes the exact value of VALUE as a hexadecimal fraction,
returning the fraction as a string. Specifically, for finite
values the output is of the form "s0xm.mmmmmpeee", where "s" is the
sign, "m.mmmm" is the significand in hexadecimal, and "eee" is the
exponent in decimal with a sign.
The details of the output format are very configurable. If OPTIONS
is supplied, it must be a reference to a hash, in which these keys
may be present:
exp_digits
The number of digits of exponent to show, unless this is
modified by exp_digits_range_mod or more are required to show
the exponent exactly. (The exponent is always shown in full.)
Default 0, so the minimum possible number of digits is used.
exp_digits_range_mod
Modifies the number of exponent digits to show, based on the
number of digits required to show the full range of exponents
for normalised and subnormal values. If "IGNORE" then nothing
is done. If "ATLEAST" then at least this many digits are
shown. Default "IGNORE".
exp_neg_sign
The string that is prepended to a negative exponent. Default
"-".
exp_pos_sign
The string that is prepended to a non-negative exponent.
Default "+". Make it the empty string to suppress the positive
sign.
frac_digits
The number of fractional digits to show, unless this is
modified by frac_digits_bits_mod or frac_digits_value_mod.
Default 0, but by default this gets modified.
frac_digits_bits_mod
Modifies the number of fractional digits to show, based on the
length of the significand. There is a certain number of digits
that is the minimum required to explicitly state every bit that
is stored, and the number of digits to show might get set to
that number depending on this option. If "IGNORE" then nothing
is done. If "ATLEAST" then at least this many digits are
shown. If "ATMOST" then at most this many digits are shown.
If "EXACTLY" then exactly this many digits are shown. Default
"ATLEAST".
frac_digits_value_mod
Modifies the number of fractional digits to show, based on the
number of digits required to show the actual value exactly.
Works the same way as frac_digits_bits_mod. Default "ATLEAST".
hex_prefix_string
The string that is prefixed to hexadecimal digits. Default
"0x". Make it the empty string to suppress the prefix.
infinite_string
The string that is returned for an infinite magnitude. Default
"inf".
nan_string
The string that is returned for a NaN value. Default "nan".
neg_sign
The string that is prepended to a negative value (including
negative zero). Default "-".
pos_sign
The string that is prepended to a positive value (including
positive or unsigned zero). Default "+". Make it the empty
string to suppress the positive sign.
subnormal_strategy
The manner in which subnormal values are displayed. If
"SUBNORMAL", they are shown with the minimum exponent for
normalised values and a significand in the range (0, 1). This
matches how they are stored internally. If "NORMAL", they are
shown with a significand in the range [1, 2) and a lower
exponent, as if they were normalised. This gives a consistent
appearance for magnitudes regardless of normalisation. Default
"SUBNORMAL".
zero_strategy
The manner in which zero values are displayed. If
"STRING=str", the string str is used, preceded by a sign. If
"SUBNORMAL", it is shown with significand zero and the minimum
normalised exponent. If "EXPONENT=exp", it is shown with
significand zero and exponent exp. Default "STRING=0.0". An
unsigned zero is treated as having a positive sign.
hex_float(STRING)
Generates and returns a floating point value from a string encoding
it in hexadecimal. The standard input form is
"[s][0x]m[.mmmmm][peee]", where "s" is the sign, "m[.mmmm]" is a
(fractional) hexadecimal number, and "eee" an optionally-signed
exponent in decimal. If present, the exponent identifies a power
of two (not sixteen) by which the given fraction will be
multiplied.
If the value given in the string cannot be exactly represented in
the floating point type because it has too many fraction bits, the
nearest representable value is returned, with ties broken in favour
of the value with a zero low-order bit. If the value given is too
large to exactly represent then an infinity is returned, or the
largest finite value if there are no infinities.
Additional input formats are accepted for special values.
"[s]inf[inity]" returns an infinity, or "die"s if there are no
infinities. "[s][s]nan" returns a NaN, or "die"s if there are no
NaNs available.
All input formats are understood case insensitively. The function
correctly interprets all possible outputs from "float_hex" with
default settings.
Comparison
float_id_cmp(A, B)
This is a comparison function supplying a total ordering of
floating point values. A and B must both be floating point values.
Returns -1, 0, or +1, indicating whether A is to be sorted before,
the same as, or after B.
The ordering is of the identities of floating point values, not
their numerical values. If zeroes are signed, then the two types
are considered to be distinct. NaNs compare equal to each other,
but different from all numeric values. The exact ordering provided
is mostly numerical order: NaNs come first, followed by negative
infinity, then negative finite values, then negative zero, then
positive (or unsigned) zero, then positive finite values, then
positive infinity.
In addition to sorting, this function can be useful to check for a
zero of a particular sign.
totalorder(A, B)
This is a comparison function supplying a total ordering of
floating point values. A and B must both be floating point values.
Returns a truth value indicating whether A is to be sorted before-
or-the-same-as B. That is, it is a <= predicate on the total
ordering. The ordering is the same as that provided by
"float_id_cmp": NaNs come first, followed by negative infinity,
then negative finite values, then negative zero, then positive (or
unsigned) zero, then positive finite values, then positive
infinity.
This is an IEEE 754r standard function. According to the standard
it is meant to distinguish different kinds of NaNs, based on their
sign bit, quietness, and payload, but this function (like the rest
of Perl) perceives only one NaN.
Manipulation
pow2(EXP)
EXP must be an integer. Returns the value two the the power EXP.
"die"s if that value cannot be represented exactly as a floating
point value. The return value may be either normalised or
subnormal.
mult_pow2(VALUE, EXP)
EXP must be an integer, and VALUE a floating point value.
Multiplies VALUE by two to the power EXP. This gives exact
results, except in cases of underflow and overflow. The range of
EXP is not constrained. All normal floating point multiplication
behaviour applies.
copysign(VALUE, SIGN_FROM)
VALUE and SIGN_FROM must both be floating point values. Returns a
floating point value with the magnitude of VALUE and the sign of
SIGN_FROM. If SIGN_FROM is an unsigned zero then it is treated as
positive. If VALUE is an unsigned zero then it is returned
unchanged. If VALUE is a NaN then it is returned unchanged. If
SIGN_FROM is a NaN then the sign copied to VALUE is unpredictable.
This is an IEEE 754 standard function. According to the standard
NaNs have a well-behaved sign bit, which can be read and modified
by this function, but Perl only perceives one NaN and can't see its
sign bit, so behaviour on NaNs is not standard-conforming.
nextup(VALUE)
VALUE must be a floating point value. Returns the next
representable floating point value adjacent to VALUE with a
numerical value that is strictly greater than VALUE, or returns
VALUE unchanged if there is no such value. Infinite values are
regarded as being adjacent to the largest representable finite
values. Zero counts as one value, even if it is signed, and it is
adjacent to the smallest representable positive and negative finite
values. If a zero is returned, because VALUE is the smallest
representable negative value, and zeroes are signed, it is a
negative zero that is returned. Returns NaN if VALUE is a NaN.
This is an IEEE 754r standard function.
nextdown(VALUE)
VALUE must be a floating point value. Returns the next
representable floating point value adjacent to VALUE with a
numerical value that is strictly less than VALUE, or returns VALUE
unchanged if there is no such value. Infinite values are regarded
as being adjacent to the largest representable finite values. Zero
counts as one value, even if it is signed, and it is adjacent to
the smallest representable positive and negative finite values. If
a zero is returned, because VALUE is the smallest representable
positive value, and zeroes are signed, it is a positive zero that
is returned. Returns NaN if VALUE is a NaN.
This is an IEEE 754r standard function.
nextafter(VALUE, DIRECTION)
VALUE and DIRECTION must both be floating point values. Returns
the next representable floating point value adjacent to VALUE in
the direction of DIRECTION, or returns DIRECTION if it is
numerically equal to VALUE. Infinite values are regarded as being
adjacent to the largest representable finite values. Zero counts
as one value, even if it is signed, and it is adjacent to the
positive and negative smallest representable finite values. If a
zero is returned and zeroes are signed then it has the same sign as
VALUE. Returns NaN if either argument is a NaN.
This is an IEEE 754 standard function.
BUGS
As of Perl 5.8.7 floating point zeroes will be partially transformed
into integer zeroes if used in almost any arithmetic, including
numerical comparisons. Such a transformed zero appears as a floating
point zero (with its original sign) for some purposes, but behaves as
an integer zero for other purposes. Where this happens to a positive
zero the result is indistinguishable from a true integer zero. Where
it happens to a negative zero the result is a fourth type of zero, the
existence of which is a bug in Perl. This fourth type of zero will
give confusing results, and in particular will elicit inconsistent
behaviour from the functions in this module.
Because of this transforming behaviour, it is best to avoid relying on
the sign of zeroes. If you require signed-zero semantics then take
special care to maintain signedness. Avoid using a zero directly in
arithmetic and handle it as a special case. Any flavour of zero can be
accurately copied from one scalar to another without affecting the
original. The functions in this module all avoid modifying their
arguments, and where they are meant to return signed zeroes they always
return a pristine one.
As of Perl 5.8.7 stringification of a floating point zero does not
preserve its signedness. The number-to-string-to-number round trip
turns a positive floating point zero into an integer zero, but
accurately maintains negative and integer zeroes. If a negative zero
gets partially transformed into an integer zero, as described above,
the stringification that it gets is based on its state at the first
occasion on which the scalar was stringified.
NaN handling is generally not well defined in Perl. Arithmetic with a
mathematically undefined result may either "die" or generate a NaN.
Avoid relying on any particular behaviour for such operations, even if
your hardware's behaviour is known.
As of Perl 5.8.7 the % operator truncates its arguments to integers, if
the divisor is within the range of the native integer type. It
therefore operates correctly on non-integer values only when the
divisor is very large.
SEE ALSO
Data::Integer, Scalar::Number, perlnumber(1)
AUTHOR
Andrew Main (Zefram) <zefram@fysh.org>
COPYRIGHT
Copyright (C) 2006, 2007, 2008, 2010, 2012, 2017 Andrew Main (Zefram)
<zefram@fysh.org>
LICENSE
This module is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
perl v5.34.0 2022-10-13 Data::Float(3pm)
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