3.2.2 boolean
[Definition:] boolean has the
·value space· required to support the mathematical
concept of binary-valued logic: {true, false}.
3.2.2.1 Lexical representation
An instance of a datatype that is defined as ·boolean·
can have the following legal literals {true, false, 1, 0}.
3.2.2.2 Canonical representation
The canonical representation for boolean is the set of
literals {true, false}.
3.2.3 decimal
[Definition:] decimal
represents ↑a subset of the real numbers, which can be represented by decimal numerals↑↓arbitrary precision decimal numbers↓.
The ·value space· of decimal
is the set of ↑
numbers that can be obtained by multiplying an integer by a non-positive
power of ten, i.e., expressible as i × 10^-n
where i and n are integers
and n >= 0↑↓the values
i × 10^-n, where i
and n are integers such that
n >= 0↓.
↑Precision is not reflected in this value space;
the number 2.0 is not distinct from the number 2.00.↑
The ·order-relation· on decimal
is ↑the order relation on real numbers, restricted
to this subset↑↓: x < y
iff y - x is positive↓.
↓
[Definition:]
The ·value space· of types derived from decimal
with a value for ·totalDigits· of p
is the set of values i × 10^-n, where
n and i are integers such that
p >= n >= 0 and the number of significant decimal digits
in i is less than or equal to p.
↓
↓
[Definition:]
The ·value space· of types derived from decimal
with a value for ·fractionDigits· of s
is the set of values i × 10^-n, where
i and n are integers such
that 0 <= n <= s.
↓
Note:
All
·minimally conforming· processors
·must·
support decimal numbers with a minimum of 18 decimal digits (i.e., with a
·totalDigits· of 18). However,
·minimally conforming· processors
·may·
set an application-defined limit on the maximum number of decimal digits
they are prepared to support, in which case that application-defined
maximum number
·must· be clearly documented.
3.2.3.1 Lexical representation
decimal has a lexical representation
consisting of a finite-length sequence of decimal digits (#x30-#x39) separated
by a period as a decimal indicator.
↓
If ·totalDigits· is
specified, the number of digits must be less than or equal to
·totalDigits·.
If ·fractionDigits· is specified, the
number of digits following the decimal point must be less than or equal to
the ·fractionDigits·.
↓
An optional leading sign is allowed.
If the sign is omitted, "+" is assumed. Leading and trailing zeroes are optional.
If the fractional part is zero, the period and following zero(es) can
be omitted.
For example: -1.23, 12678967.543233, +100000.00, 210.
3.2.3.2 Canonical representation
The canonical representation for decimal is defined by
prohibiting certain options from the
Lexical representation (§3.2.3.1). Specifically, the preceding
optional "+" sign is prohibited. The decimal point is required. Leading and
trailing zeroes are prohibited subject to the following: there must be at least
one digit to the right and to the left of the decimal point which may be a zero.
3.2.4 float
[Definition:] float
↑is patterned after↑↓corresponds to↓ the IEEE single-precision 32-bit floating point type
[IEEE 754-1985]. The basic ·value space· of
float consists of the values
m × 2^e, where m
is an integer whose absolute value is less than
2^24, and e is an integer
between -149 and 104, inclusive. In addition to the basic
·value space· described above, the
·value space· of float also contains the
following
↑three↑
special values:
↓positive and negative zero,↓
positive and negative infinity and not-a-number
↑(NaN)↑.
The ·order-relation· on float
is: x < y iff y - x is positive
↑for x and y in the value space↑.
↑Positive infinity is greater than all other non-NaN values.
NaN equals itself but is ·incomparable· with (neither greater than nor less than)
any other value in the ·value space·.↑
↓
Positive zero is greater than negative zero. Not-a-number equals itself and is
greater than all float values including positive infinity.↓
Note:
↑
"Equality" in this Recommendation is defined to be "identity" (i.e., values that
are identical in the ·value space· are equal and vice versa).
Identity must be used for the few operations that are defined in this Recommendation.
Applications using any of the datatypes defined in this Recommendation may use different
definitions of equality for computational purposes; [IEEE 754-1985]-based computation systems
are examples. Nothing in this Recommendation should be construed as requiring that
such applications use identity as their equality relationship when computing.
↑
↑
Any value ·incomparable· with the value used for the four bounding facets
(·minInclusive·, ·maxInclusive·,
·minExclusive·, and ·maxExclusive·) will be
excluded from the resulting restricted ·value space·. In particular,
when "NaN" is used as a facet value for a bounding facet, since no other
float values are ·comparable· with it, the result is a ·value space·
either having NaN as its only member (the inclusive cases) or that is empty
(the exclusive cases). If any other value is used for a bounding facet,
NaN will be excluded from the resulting restricted ·value space·;
to add NaN back in requires union with the NaN-only space.
↑
↑
This datatype differs from that of [IEEE 754-1985] in that there is only one
NaN and only one zero. This makes the equality and ordering of values in the data
space differ from that of [IEEE 754-1985] only in that for schema purposes NaN = NaN.
↑
A literal in the ·lexical space· representing a
decimal number d maps to the normalized value
in the ·value space· of float that is
closest to d in the sense defined by
[Clinger, WD (1990)]; if d is
exactly halfway between two such values then the even value is chosen.
3.2.4.1 Lexical representation
float values have a lexical representation
consisting of a mantissa followed, optionally, by the character
"E" or "e", followed by an exponent. The exponent ·must·
be an integer. The mantissa must be a decimal number. The representations
for exponent and mantissa must follow the lexical rules for
integer and decimal. If the "E" or "e" and
the following exponent are omitted, an exponent value of 0 is assumed.
The special values
↓positive and negative zero,↓
positive
and negative infinity and not-a-number have lexical representations
↓0, -0,↓
INF, -INF and
NaN, respectively.
↑
Lexical representations for zero may take a positive or negative sign.
↑
For example, -1E4, 1267.43233E12, 12.78e-2, 12
↑, -0, 0↑
and INF are all legal literals for float.
3.2.4.2 Canonical representation
The canonical representation for float is defined by
prohibiting certain options from the
Lexical representation (§3.2.4.1). Specifically, the exponent
must be indicated by "E". Leading zeroes and the preceding optional "+" sign
are prohibited in the exponent.
↑
If the exponent is zero, it must be indicated by "E0".
↑
For the mantissa, the preceding optional "+" sign is prohibited
and the decimal point is required.
↓
For the exponent, the preceding optional "+" sign is prohibited.
↓
Leading and trailing zeroes are prohibited subject to the following:
number representations must
be normalized such that there is a single digit
↑which is non-zero↑
to the left of the decimal point and at least a single digit to the
right of the decimal point
↑
unless the value being represented is zero. The canonical
representation for zero is 0.0E0↑.
3.2.5 double
[Definition:] The double
datatype
↑is patterned after the↑
↓corresponds to↓
IEEE double-precision 64-bit floating point
type [IEEE 754-1985]. The basic ·value space·
of double consists of the values
m × 2^e, where m
is an integer whose absolute value is less than
2^53, and e is an
integer between -1075 and 970, inclusive. In addition to the basic
·value space· described above, the
·value space· of double also contains
the following
↑three↑
special values:
↓positive and negative zero,↓
positive and negative infinity and not-a-number
↑(NaN)↑.
The ·order-relation· on double
is: x < y iff y - x is positive
↑for x and y in the value space↑.
↑Positive infinity is greater than all other non-NaN values.
NaN equals itself but is ·incomparable· with (neither greater than nor less than)
any other value in the ·value space·.↑
↓
Positive zero is greater than negative zero. Not-a-number equals itself and is
greater than all float values including positive infinity.↓
Note:
↑
"Equality" in this Recommendation is defined to be "identity" (i.e., values that
are identical in the ·value space· are equal and vice versa).
Identity must be used for the few operations that are defined in this Recommendation.
Applications using any of the datatypes defined in this Recommendation may use different
definitions of equality for computational purposes; [IEEE 754-1985]-based computation systems
are examples. Nothing in this Recommendation should be construed as requiring that
such applications use identity as their equality relationship when computing.
↑
↑
Any value ·incomparable· with the value used for the four bounding facets
(·minInclusive·, ·maxInclusive·,
·minExclusive·, and ·maxExclusive·) will be
excluded from the resulting restricted ·value space·. In particular,
when "NaN" is used as a facet value for a bounding facet, since no other
double values are ·comparable· with it, the result is a ·value space·
either having NaN as its only member (the inclusive cases) or that is empty
(the exclusive cases). If any other value is used for a bounding facet,
NaN will be excluded from the resulting restricted ·value space·;
to add NaN back in requires union with the NaN-only space.
↑
↑
This datatype differs from that of [IEEE 754-1985] in that there is only one
NaN and only one zero. This makes the equality and ordering of values in the data
space differ from that of [IEEE 754-1985] only in that for schema purposes NaN = NaN.
↑
A literal in the ·lexical space· representing a
decimal number d maps to the normalized value
in the ·value space· of double that is
closest to d; if d is
exactly halfway between two such values then the even value is chosen.
This is the best approximation of d
([Clinger, WD (1990)], [Gay, DM (1990)]), which is more
accurate than the mapping required by [IEEE 754-1985].
3.2.5.1 Lexical representation
double values have a lexical representation
consisting of a mantissa followed, optionally, by the character "E" or
"e", followed by an exponent. The exponent ·must· be
an integer. The mantissa must be a decimal number. The representations
for exponent and mantissa must follow the lexical rules for
integer and decimal. If the "E" or "e"
and the following exponent are omitted, an exponent value of 0 is assumed.
The special values
↓positive and negative zero,↓
positive
and negative infinity and not-a-number have lexical representations
↓0, -0,↓
INF, -INF and
NaN, respectively.
↑
Lexical representations for zero may take a positive or negative sign.
↑
For example, -1E4, 1267.43233E12, 12.78e-2, 12
↑, -0, 0↑
and INF
are all legal literals for double.
3.2.5.2 Canonical representation
The canonical representation for double is defined by
prohibiting certain options from the
Lexical representation (§3.2.5.1). Specifically, the exponent
must be indicated by "E". Leading zeroes and the preceding optional "+" sign
are prohibited in the exponent.
↑
If the exponent is zero, it must be indicated by "E0".
↑
For the mantissa, the preceding optional "+" sign is prohibited
and the decimal point is required.
↓
For the exponent, the preceding optional "+" sign is prohibited.
↓
Leading and trailing zeroes are prohibited subject to the following:
number representations must
be normalized such that there is a single digit
↑which is non-zero↑
to the left of the decimal point and at least a single digit to the
right of the decimal point
↑
unless the value being represented is zero. The canonical
representation for zero is 0.0E0↑.
3.2.6 duration
[Definition:]
duration represents a duration of time.
The ·value space· of duration is
a six-dimensional space where the coordinates
designate the Gregorian year, month, day, hour, minute, and second components defined in
§ 5.5.3.2 of [ISO 8601],
respectively. These components are ordered
in their significance by their order of appearance i.e. as year, month, day,
hour, minute, and second.
↑
Note:
All
·minimally conforming· processors
·must·
support year values with a minimum of 4 digits (i.e.,
YYYY) and a minimum fractional second precision of milliseconds or three decimal digits (i.e.
s.sss). However,
·minimally conforming· processors
·may·
set an application-defined limit on the maximum number of digits
they are prepared to support in these two cases, in which case that application-defined
maximum number
·must· be clearly documented.
↑
3.2.6.1 Lexical representation
The lexical representation for duration is the
[ISO 8601] extended format PnYn
MnDTnH nMnS, where
nY represents the number of years, nM the
number of months, nD the number of days, 'T' is the
date/time separator, nH the number of hours,
nM the number of minutes and nS the
number of seconds. The number of seconds can include decimal digits
to arbitrary precision.
The values of the
Year, Month, Day, Hour and Minutes components are not restricted but
allow an arbitrary
↑unsigned↑ integer↑, i.e., an integer that
conforms to the pattern [0-9]+.↑.
Similarly, the value of the Seconds component
allows an arbitrary ↑unsigned↑ decimal.
↑Following [ISO 8601], at least one digit must
follow the decimal point if it appears. That is, the value of the Seconds component
must conform to the pattern [0-9]+(\.[0-9]+)?.↑
Thus, the lexical representation of
duration does not follow the alternative
format of § 5.5.3.2.1 of [ISO 8601].
An optional preceding minus sign ('-') is
allowed, to indicate a negative duration. If the sign is omitted a
positive duration is indicated. See also ISO 8601 Date and Time Formats (§D).
For example, to indicate a duration of 1 year, 2 months, 3 days, 10
hours, and 30 minutes, one would write: P1Y2M3DT10H30M.
One could also indicate a duration of minus 120 days as:
-P120D.
Reduced precision and truncated representations of this format are allowed
provided they conform to the following:
-
If the number of years, months, days, hours, minutes, or seconds in any
expression equals zero, the number and its corresponding designator ·may·
be omitted. However, at least one number and its designator ·must·
be present.
-
The seconds part ·may· have a decimal fraction.
-
The designator 'T' ↑must↑↓shall↓
be absent if ↑and only if↑ all of the time items are absent.
The designator 'P' must always be present.
For example, P1347Y, P1347M and P1Y2MT2H are all allowed;
P0Y1347M and P0Y1347M0D are allowed. P-1347M is not allowed although
-P1347M is allowed. P1Y2MT is not allowed.
3.2.6.2 Order relation on duration
In general, the ·order-relation· on duration
is a partial order since there is no determinate relationship between certain
durations such as one month (P1M) and 30 days (P30D).
The ·order-relation·
of two duration values x and
y is x < y iff s+x < s+y
for each qualified dateTime s
in the list below. These values for s cause the greatest deviations in the addition of
dateTimes and durations. Addition of durations to time instants is defined
in Adding durations to dateTimes (§E).
- 1696-09-01T00:00:00Z
- 1697-02-01T00:00:00Z
- 1903-03-01T00:00:00Z
- 1903-07-01T00:00:00Z
The following table shows the strongest relationship that can be determined
between example durations. The symbol <> means that the order relation is
indeterminate. Note that because of leap-seconds, a seconds field can vary
from 59 to 60. However, because of the way that addition is defined in
Adding durations to dateTimes (§E), they are still totally ordered.
| | Relation |
|---|
| P1Y | > P364D | <> P365D | | <> P366D | < P367D |
| P1M | > P27D | <> P28D | <> P29D | <> P30D | <> P31D | < P32D |
| P5M | > P149D | <> P150D | <> P151D | <> P152D | <> P153D | < P154D |
Implementations are free to optimize the computation of the ordering relationship. For example, the following table can be used to
compare durations of a small number of months against days.
| | Months | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ... |
|---|
| Days | Minimum | 28 | 59 | 89 | 120 | 150 | 181 | 212 | 242 | 273 | 303 | 334 | 365 | 393 | ... |
|---|
| Maximum | 31 | 62 | 92 | 123 | 153 | 184 | 215 | 245 | 276 | 306 | 337 | 366 | 397 | ... |
|---|
3.2.6.4 Totally ordered durations
Certain derived datatypes of durations can be guaranteed have a total order. For
this, they must have fields from only one row in the list below and the time zone
must either be required or prohibited.
- year, month
- day, hour, minute, second
For example, a datatype could be defined to correspond to the
[SQL] datatype Year-Month interval that required a four digit
year field and a two digit month field but required all other fields to be unspecified. This datatype could be defined as below and would have a total order.
<simpleType name='SQL-Year-Month-Interval'>
<restriction base='duration'>
<pattern value='P\p{Nd}{4}Y\p{Nd}{2}M'/>
</restriction>
</simpleType>
3.2.6.5 Constraining facets
