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Re: #\a octothorpe syntax vs SRFI 10



 | Date: Mon, 27 Dec 2004 10:24:38 -0800 (PST)
 | From: bear <bear@xxxxxxxxx>
 | 
 | For what it's worth, I think that it may be time to look at
 | using the square bracket characters [] which R5RS reserves.
 | 
 | I realize that lots of people are using them for things that
 | aren't arrays and that this will break code which uses them
 | in that wise; but I think that arrays are the natural and
 | obvious use for these characters.

#2Au32[[0 1 2][3 4 5]] looks good.  #2A[[#f () #t][#f (a b c) #f]]
gives visual distinction between list elements and array structure.
This has no conflict with other syntax because the #2A... prefix would
be new.

 | I dislike srfi-58 (and several earlier srfi's) for being
 | incompletely specified w/r/t machines of architectures where
 | the given "hardware types" make no sense.
 | 
 | For example, if I'm running scheme on a PDP-11 which has

PDP-11 was 16-bit; PDP-10 was 36 bit.

 | 18-bit halfwords and 36-bit words, and which uses a float
 | representation that has no simple mapping to IEEE1178 32-bit
 | floats, how am I supposed to implement this?  Conversely, if
 | a new CPU becomes popular in 10 years that uses 56-bit floats
 | and integers in a tagged architecture with 8 bits of a 64-bit
 | word reserved for tags, how will this srfi be meaningful?

SRFI-47 specifies minimum precisions for uniform-array types.  It is
quite specific for exact integers:

Function: as64
    Returns an exact signed integer uniform-array prototype with at
    least 64 bits of precision.

Function: as32
    Returns an exact signed integer uniform-array prototype with at
    least 32 bits of precision.

Function: as16
    Returns an exact signed integer uniform-array prototype with at
    least 16 bits of precision.

Function: as8
    Returns an exact signed integer uniform-array prototype with at
    least 8 bits of precision.

Function: au64
    Returns an exact non-negative integer uniform-array prototype with
    at least 64 bits of precision.

Function: au32
    Returns an exact non-negative integer uniform-array prototype with
    at least 32 bits of precision.

Function: au16
    Returns an exact non-negative integer uniform-array prototype with
    at least 16 bits of precision.

Function: au8
    Returns an exact non-negative integer uniform-array prototype with
    at least 8 bits of precision.

The restriction to power-of-two number of bits could be lifted by
having two procedures, one for signed, one for unsigned, which take
the minimum number-of-bits as an argument.

 | Many recent RISC processors have no 8-bit operations.  Some
 | in the fairly near future will probably also lack 16-bit
 | operations.  It would be far more efficient for these
 | systems to allocate 16 bits where an 'au8' is requested;

No, it won't.  Modern CPUs are almost always (I/O-bound or) limited by
their memory bandwidth through the cache.  If you double or quadruple
the data movement necessary, you will execute at half or quarter the
speed.

 | is it legal for them to do so?  Was 'au8' a minimum number
 | of bits to be provided, or must it be *exactly* 8 for purposes
 | of this SRFI?

Function: au8
    Returns an exact non-negative integer uniform-array prototype with
    at least 8 bits of precision.

 | IOW, are we looking at these things for internal use (in which
 | case a minimum bit count is appropriate) or is this aiming at
 | FFI on 32-bit Intel processors (in which case an exact bit count
 | is appropriate and we may as well specify the endianness)?

For exact integers it is the minimum.  For inexact complexes and
reals, there is more to numerical quality than just a single length.
My intent was for these precisions to be minimums; as expressed by the
text of R5RS:

 ... the IEEE 32-bit and 64-bit floating point standards be followed
 by implementations that use flonum representations, and that
 implementations using other representations should match or exceed
 the precision achievable using these floating point standards.

 | Are we specifically giving scheme developers quasi-numeric
 | binary types in which they can *RELY* on getting round-off and
 | wraparaound phenomena of particular kinds at particular thresholds?
 | And if so do we require any scheme systems to simulate exactly
 | those roundoffs and those wraparounds regardless of the
 | underlying hardware architecture?

No.  And SRFI-47 specifically removes the possibility of exposing
wraparound:

  Conversions

    * All the elements of arrays of type au8, au16, au32, au64, as8,
      as16, as32, or as64 are exact.

    * The value retrieved from an exact array element will equal (=)
      the value stored in that element.

    * Assigning a non-integer to array-type au8, au16, au32, au64,
      as8, as16, as32, or as64 is an error.

    * Assigning a number larger than can be represented in array-type
      au8, au16, au32, au64, as8, as16, as32, or as64 is an error.

    * Assigning a negative number to array-type au8, au16, au32, or
      au64 is an error.

    * Assigning an inexact number to array-type au8, au16, au32, au64,
      as8, as16, as32, or as64 is an error.


    * All the elements of arrays of type ar32, ar64, ac32, or ac64 are
      inexact.

    * When assigning an exact number to array-type ar32, ar64, ac32,
      or ac64, the procedure may report a violation of an
      implementation restriction.

    * Assigning a non-real number (eg. real? returns #f) to an ar64 or
      ar32 array is an error.

    * An implementation may reduce the precision of a number assigned
      to an inexact array.

Code can be written which detects the precision of the elements of
inexact arrays; but code can also be written which detects the
precision of inexacts generally.  So not-screwing-yourself with flonum
precision requires some forethought, as it always has.

 | I think that would be a preposterous thing to do.

SRFI-47 does not do that.

 | Scheme, IMO, needs ways to handle array rank and multi-index
 | array reference; but the mapping of hardware types to scheme
 | types is best left for a declaration syntax that can be given
 | a syntax-rules definition that makes it simply "disappear" on
 | systems where the SRFI isn't implemented.

In procedures which operate in parallel on all the elements of arrays,
the time to dispatch on the array type is negligible compared to the
time spent on the operations.  Using uniform-arrays, APL interpreters
can apply highly optimized array primitives with great effect.  This
doesn't work if type dispatch must be done on each element of arrays.
Thus uniform-arrays provide more than just storage efficiency.