Sisyphus

NAME

Data::Float::DoubleDouble - human-readable representation of the "double-double" long double

AIM

  Mostly, one would use Data::Float to do what this module does.
  But that module doesn't work with the 'double-double' type of
  long double ... hence, this module.

  Given a double-double value, we aim to be able to:
   1) Convert that NV to its internal packed hex form;
   2) Convert the packed hex form of 1) back to the original value;
   3) Convert that NV to a more human-readable packed hex form,
      similar to what Data::Float's float_hex function achieves;
   4) Convert the packed hex form of 3) back to the original value;

   For 1) we use NV2H().
   For 2) we use H2NV().
   For 3) we use float_H().
   For 4) we use H_float().

   We also have float_B and B_float which are the base 2
   equivalents of float_H and H_float.

FUNCTIONS

  #############################################

  $hex = NV2H($nv);

   Unpacks the NV to a string of 32 hex characters.
   The first 16 characters relate to the value of the most significant
   double:
    Characters 1 to 3 (incl) embody the sign of the mantissa, the value
    of the exponent, and the value (0 or 1) of the implied leading bit.
    Characters 4 to 16 (incl) embody the value of the 52-bit mantissa.

   The second 16 characters (17 to 32) relate to the value of the least
   siginificant double:
    Characters 17 to 19 (incl) embody the sign of the mantissa, the
    value of the exponent, and the value (0 or 1) of the implied
    leading bit.
    Characters 20 to 32 (incl) embody the value of the 52-bit mantissa.

   For a more human-readable hex representation, use float_H().

  #############################################

  $nv = H2NV($hex);

   For $hex written in the format returned by NV2H, H2NV($hex)
   returns the NV.

  #############################################

  $hex = D2H($nv);

   Treats the NV as a double and returns a string of 16 hex characters.
   Characters 1 to 3 (incl) embody the sign of the mantissa, the value
   (0 or 1) of the implied leading bit and the value of the exponent.
   Characters 4 to 16 (incl) embody the value of the 52-bit mantissa
   of the first double.

  #############################################

  $nv = H2D($hex, $opt); # Second arg is optional

   For $hex written in the format returned by D2H, H2D($hex) returns
   the NV.

  #############################################

  $readable_hex = float_H($nv, $opt); # Aliased to float_hex
                                           # $opt is optional

   For *most* NVs, returns a 106-bit hex representation of the NV
   (long double) $nv in the format
   s0xd.hhhhhhhhhhhhhhhhhhhhhhhhhhhpe where:
    s is the sign (either '-' or '+')
    0x is literally "0x"
    d is the leading (first) bit of the number (either '1' or '0')
    . is literally "." (the decimal point)
    hhhhhhhhhhhhhhhhhhhhhhhhhhh is a string of 27 hex digits
                                representing the remaining 105 bits
                                of the mantissa.
    p is a literal "p" that separates mantissa from exponent
    e is the (signed) exponent

   The keen mind will have realised that 27 hex digits encode 108
   (not 105) bits. However, the last 3 bits are to be ignored and
   will always be zero for a 106-bit float. Thus the 27th hex
   character for a 106-bit float will either be "8" (representing
   a "1") or "0" (representing a "0") for the 106th bit.

   BUT: Some NV values encapsulate a value that require more than
        106 bits in order to be correctly represented.
        If the string that float_H returns is larger than as
        described above, then it will, however,  have returned a
        string that contains the *minimum* number of characters
        needed to accurately represent the given value.
        As an extreme example: the double-double arrangement can
        represent the value 2**1023 + 2**-1074, but to express
        that value as a stream of bits requires 2098 bits, and to
        express that value in the format that float_H returns
        requires 526 hex characters (all of which are zero, except
        for the first and the last). When you add the sign, radix
        point, exponent, etc., the float_H representation of that
        value consists of 535 characters.

   If a second arg is provided, it must be the string 'raw' - in
   which case infs/nans will be returned in hex format instead of
   as "inf"/"nan" strings.

  #############################################

  $readable_hex = DD2HEX($nv, $fmt);

   As for float_H, but uses C's sprintf() function to do the
   conversion to the hex string. The second arg ($fmt) can be either
   "%La" (in which case the alphabetic characters will be lower
   case) or "%LA" (in which case the alphabetic characters will be
   upper case).
   Unlike float_H, this function cannot take the 'raw' argument.
   And, unlike float_H, this function will not return values that
   require more than 106 bits to be expressed.

  #############################################

  $standardised_readable_hex = std_float_H($nv, $fmt);

   As for float_H, but standardises the format to be the same as I
   get for DD2HEX. That is, there's no leading + for positive
   values, positive and zero exponents are prefixed with a +,
   trailing zeroes in the mantissa are removed, and zeroes are
   presented as (-)0x0p+0 or (-)0X0P+0. As for DD2HEX, the second
   arg ($fmt) can be either "%La" or "%LA" (nothing else) and that
   determines whether the alphabetic characters are lower case or
   upper case.
   Unlike float_H, this function cannot take the 'raw' argument.
   Like float_H it will, however, accurately express the value
   that's encapsulated in the double-double (even though that
   minimum may exceed the usual 27 hex digits).

  #############################################

  $readable = express($nv, $opt); # $opt is an optional arg.

   An alternative way of assessing the value of the double-double.
   Express the double as msd + lsd, where the 2 doubles (msd and lsd)
   are written in scientic notation. The doubles will be written in
   decimal format unless a second arg of 'h' or 'H' is provided - in
   which case they will be written in hex (respectively capitalised
   hex) format.
   The second arg ($opt), if provided, must be either 'h' or 'H'.

  #############################################

  $nv = H_float($hex);

   For $hex written in the format returned by float_H(), returns
   the NV that corresponds to $hex.

  #############################################

  @bin = float_B($nv, $opt); # Second arg isoptional

   Returns the sign, the mantissa (as a base 2 string), and the
   exponent of $nv. (There's an implied radix point between the
   first and second digits of the mantissa).
   For nan/inf, the mantissa is 'nan' or 'inf' respectively unless
   2nd arg is literally 'raw' - in which case it will be a base 2
   version of the nan/inf encoding.

  #############################################

  @bin = float_H2B($hex, $opt); # Second arg is optional

   As for the above float_B() function - but takes the hex
   string of the NV (as returned by float_H) as its argument,
   instead of the actual NV.
   For a more direct way of obtaining the array, use float_B
   instead.
   If a second arg is provided, it must be the string 'raw' - in
   which case inf/nan mantissas will be returned in hex format
   instead of as "inf"/"nan" strings.

  #############################################

  @bin = NV2binary($nv);

   Another way of arriving at (almost) the same binary representation
   of the NV -ie as an array consisting of (sign, mantissa, exponent).
   The mantissa if Infs and NaNs will be returned as 'inf' or 'nan'
   respectively and the sign associated with the nan will always
   be '+'.
   With this function, trailing zeroes are stripped from the mantissa
   and exponents for 0, inf and nan might not match the other binary
   representations.
   This function is based on code from the mpfr library's
   tests/tset_ld.c file.

  #############################################

  $hex = B2float_H(@bin, $opt); # $opt is an optional arg

   The reverse of float_H2B. It takes the array returned by
   either float_B or float_H2B as its arguments, and returns
   the corresponding hex form.
   If $opt is provided and is the string 'raw', the actual
   hex encoding of any nan/inf will be returned - instead of
   the string "inf" or "nan" respectively.

  #############################################

  ($sign1, $sign2) = get_sign($nv);

   Returns the signs of the two doubles contained in $nv.

  #############################################

  ($exp1, $exp2) = get_exp($nv);

   Returns the exponents of the two doubles contained in $nv.

  #############################################

  ($mantissa1, $mantissa2) = get_mant_H(NV2H($nv));

   Returns an array of the two 52-bit mantissa components of
   the two doubles in their hex form. The values of the
   implied leading (most significant) bits are not provided,
   nor are the values of the two exponents.

  #############################################

  $intermediate_zeroes = inter_zero(get_exp($nv));

   Returns the number of zeroes that need to come between the
   mantissas of the 2 doubles when $nv is translated to the
   representation that float_H() returns.

  #############################################

  $bool = are_inf(@nv); # Aliased to float_is_infinite.

   Returns true if and only if all of the (NV) arguments are
   infinities.
   Else returns false.

  #############################################

  $bool = are_nan(@nv); # Aliased to float_is_nan.

   Returns true if and only if all of the (NV) arguments are
   NaNs. Else returns false.

  #############################################

  $hex = dd_bytes($nv);

   Returns same as NV2H($nv).

  #############################################

  For Compatibility with Data::Float:

  #############################################

  $class = float_class($nv);

   Returns one of either "NAN", "INFINITE", "ZERO", "NORMAL"
   or "SUBNORMAL" - whichever is appropriate. (The NV must
   belong to one (and only one) class.

  #############################################

  $bool = float_is_nan($nv); # Alias for are_nan()

   Returns true if $nv is a NaN.
   Else returns false.

  #############################################

  $bool = float_is_infinite($nv); # Alias for are_inf()

   Returns true if $nv is infinite.
   Else returns false.

  #############################################

  $bool = float_is_finite($nv);

   Returns true if NV is neither infinite nor a NaN.
   Else returns false.

  #############################################

  $bool = float_is_nzfinite($nv);

   Returns true if NV is neither infinite, nor a NaN, nor zero.
   Else returns false.

  #############################################

  $bool = float_is_zero($nv);

   Returns true if NV is zero.
   Else returns false.

  #############################################

  $bool = float_is_normal($nv);

   Returns true if NV is finite && non-zero && the implied
   leading digit in its internal representation is '1'.
   Else returns false.

  #############################################

  $bool = float_is_subnormal($nv);

   Returns true if NV is finite && non-zero && the implied
   leading digit in its internal representation is '0'.

  #############################################

  $nv = nextafter($nv1, $nv2);

   $nv1 and $nv2 must both be floating point values. Returns the
   next representable floating point value adjacent to $nv1 in the
   direction of $nv2, or returns $nv2 if it is numerically
   equal to $nv1. 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
   then it has the same sign as $nv1. Returns
   NaN if either argument is a NaN.

  #############################################

  $nv = nextup($nv1);

   $nv1 must be a floating point value. Returns the next representable
   floating point value adjacent to $nv1 with a numerical value that
   is strictly greater than $nv1, or returns $nv1 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 $nv1 is the smallest representable negative
   value, and zeroes are signed, it is a negative zero that is
   returned. Returns NaN if $nv1 is a NaN.

  #############################################

  $nv = nextdown($nv1);

   $nv1 must be a floating point value. Returns the next representable
   floating point value adjacent to $nv1 with a numerical value that
   is strictly less than $nv1, or returns $nv1 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
   $nv 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.

  #############################################
  #############################################

TODO

   Over time, introduce the features of (and functions provided by)
   Data::Float

LICENSE

   This program is free software; you may redistribute it and/or
   modify it under the same terms as Perl itself.
   Copyright 2014 Sisyphus

AUTHOR

   Sisyphus <sisyphus at(@) cpan dot (.) org>