Re: list of operations for test suite. suggested format

[Ulrich Kulisch <ulrich.kulisch@xxxxxxx>]

I wonder whether the operations for 'complete arithmetic' should also be listed here. See my mail of April 17, 2013.

Ulrich Kulisch



Am 28.04.2013 02:11, schrieb Richard Fateman:

By my count there are 113 operators, assuming that inv and recip are the 
same. I use the name recip below.
They are listed in the order they appear in the proposed standard except 
that I put divpair in at location 55.
There are other possible orderings, including alphabetical, and it 
doesn't matter much to me.  I am just
suggesting this one to be definite.  I hope I've included everything, 
and spelled right.

neg add sub mul div recip sqrt fma case sqr pown pow exp exp2 exp10 log 
log2 log10 sin cos tan asin acos
  atan atan2 sinh cosh tanh asinh acosh atanh sign ceil floor trunc 
roundTiesToEven roundTiesToAway abs min
  max sqRev recipRev absRev sinRev cosRev tanRev coshRev mulRev divRev1 
divRev2 powRev1 powRev2 atanRev1
  atan2Rev2 divpair inf sup mid wid rad mag mig intersection convexHull 
isEqual containedIn less precedes
  isInterior strictlyLess strictlyPrecedes aredisjoint rootn expm1 
exp2m1 exp10m1 logp1 log10p1 compoundm1
  hypot rSqrt sinPi cosPi tanPi asinPi acosPi atanPi atan2Pi bothEmpty 
firstEmptysecondEmpty before meets
  overlaps starts containedBy finishes equal finishedBy contains 
startedBy overlappedBy metBy after
  expSlope1 expSlope2 logSlope1 logSlope2 cosSlope2 sinSlppe3 asinSlope3 
atanSlope3 coshSlope2 sinhSlope3

If we attach numbers to them, the encoding could be this.

  (1 . neg) (2 . add) (3 . sub) (4 . mul) (5 . div) (6 . recip) (7 . 
sqrt) (8 . fma) (9 . case) (10 . sqr)
  (11 . pown) (12 . pow) (13 . exp) (14 . exp2) (15 . exp10) (16 . log) 
(17 . log2) (18 . log10) (19 . sin)
  (20 . cos) (21 . tan) (22 . asin) (23 . acos) (24 . atan) (25 . atan2) 
(26 . sinh) (27 . cosh) (28 . tanh)
  (29 . asinh) (30 . acosh) (31 . atanh) (32 . sign) (33 . ceil) (34 . 
floor) (35 . trunc)
  (36 . roundTiesToEven) (37 . roundTiesToAway) (38 . abs) (39 . min) 
(40 . max) (41 . sqRev)
  (42 . recipRev) (43 . absRev) (44 . sinRev) (45 . cosRev) (46 . 
tanRev) (47 . coshRev) (48 . mulRev)
  (49 . divRev1) (50 . divRev2) (51 . powRev1) (52 . powRev2) (53 . 
atanRev1) (54 . atan2Rev2)
  (55 . divpair) (56 . inf) (57 . sup) (58 . md) (59 . wid) (60 . rad) 
(61 . mag) (62 . mig)
  (63 . intersection) (64 . convexHull) (65 . isEqual) (66 . 
containedIn) (67 . less) (68 . precedes)
  (69 . isInterior) (70 . strictlyLess) (71 . strictlyPrecedes) (72 . 
aredisjoint) (73 . rootn) (74 . expm1)
  (75 . exp2m1) (76 . exp10m1) (77 . logp1) (78 . log10p1) (79 . 
compoundm1) (80 . hypot) (81 . rSqrt)
  (82 . sinPi) (83 . cosPi) (84 . tanPi) (85 . asinPi) (86 . acosPi) (87 
. atanPi) (88 . atan2Pi)
  (89 . bothEmpty) (90 . firstEmptysecondEmpty) (91 . before) (92 . 
meets) (93 . overlaps) (94 . starts)
  (95 . containedBy) (96 . finishes) (97 . equal) (98 . finishedBy) (99 
. contains) (100 . startedBy)
  (101 . overlappedBy) (102 . metBy) (103 . after) (104 . expSlope1) 
(105 . expSlope2) (106 . logSlope1)
  (107 . logSlope2) (108 . cosSlope2) (109 . sinSlope3) (110 . 
asinSlope3) (111 . atanSlope3)
  (112 . coshSlope2) (113 . sinhSlope3)

a typical line in the test file for IEEE-754 binary double looks like this

50001 1 1 1 (1 -52 0x10000000000000)(1 -51 0x10000000000000)(-1 -51 
0x10000000000000)(-1 -52 0x10000000000000)

meaning
test sequence number 50001
operation number 1  (that is, negation)
number of interval inputs 1
number of interval outputs 1
inf of input 1 (1 -52 0x10000000000000)  (that is (+1) * 2^(-52)* 
0x10000000000000,  i.e. 1.0
sup of input 1 (1 -51 0x10000000000000)  (that is (+1) * 2^(-51)* 
0x10000000000000,  i.e. 2.0
inf of output 1 (-1 -51 0x10000000000000)  (that is (-1) * 2^(-51)* 
0x10000000000000, i.e. -2.0
sup of output 1  ...etc i.e. -1.0

It is possible to use decimal instead of hexadecimal numbers throughout; 
I've used hex only for the fraction part.
An alternative to using triples inside parentheses could be any encoding 
that is bit-specific and covers
NaN, infinities, signed zero, denormalized numbers, and can be read into 
(or converted into) every language for which the
test suite might be of use in determining conformance to the standard.
If for some reason the parentheses cause problems, they can be replaced 
with white space, since each number
has exactly three components.

Some of these functions return integers or floats or logical values, any 
of which can be easily encoded as intervals.

Considering merely the number of edge cases needed, there seem to be a 
minimum of several thousand
cases, without even delving into questions of accuracy.

RJF

-- 
Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik
D-76128 Karlsruhe, Germany
Prof. Ulrich Kulisch

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