Provided by: libdata-float-perl_0.012-2_all 
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 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.