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diff --git a/doc/man/built-in.3 b/doc/man/built-in.3 new file mode 100644 index 00000000000..48af4cbe316 --- /dev/null +++ b/doc/man/built-in.3 @@ -0,0 +1,700 @@ +.\" This is -*-nroff-*- +.\" XXX standard disclaimer belongs here.... +.\" $Header: /cvsroot/pgsql/doc/man/Attic/built-in.3,v 1.1.1.1 1996/08/18 22:14:20 scrappy Exp $ +.TH BUILT-INS INTRO 11/05/95 Postgres95 Postgres95 +.SH "DESCRIPTION" +This section describes the data types, functions and operators +available to users in Postgres as it is distributed. +.SH "Built-in and System Types" +.SH "BUILT-IN TYPES" +This section describes both +.BR built-in +data types. +These Built-in types are +are installed in every database. +.PP +Users may add new types to Postgres using the +.IR "define type" +command described in this manual. User-defined types are not +described in this section. +.SH "List of built-in types" +.PP +.if n .ta 5 +15 +40 +.if t .ta 0.5i +1.5i +3.0i +.in 0 +.nf + \fBPOSTGRES Type\fP \fBMeaning\fP + abstime absolute date and time + aclitem access control list item + bool boolean + box 2-dimensional rectangle + bpchar blank-padded characters + bytea variable length array of bytes + char character + char2 array of 2 characters + char4 array of 4 characters + char8 array of 8 characters + char16 array of 16 characters + cid command identifier type + date ANSI SQL date type + filename large object filename + int alias for int4 + integer alias for int4 + int2 two-byte signed integer + int28 array of 8 int2 + int4 four-byte signed integer + float alias for float4 + float4 single-precision floating-point number + float8 double-precision floating-point number + lseg 2-dimensional line segment + name a multi-character type for storing system identifiers + oid object identifier type + oid8 array of 8 oid + oidchar16 oid and char16 composed + oidint2 oid and int2 composed + oidint4 oid and int4 composed + path variable-length array of lseg + point 2-dimensional geometric point + polygon 2-dimensional polygon + real alias for float4 + regproc registered procedure + reltime relative date and time + smgr storage manager + smallint alias for int2 + text variable length array of characters + tid tuple identifier type + time ANSI SQL time type + tinterval time interval + varchar variable-length characters + xid transaction identifier type + +.fi +.in +.PP +As a rule, the built-in types are all either (1) internal types, in +which case the user should not worry about their external format, or +(2) have obvious formats. The exceptions to this rule are the three +time types. +.SH "Syntax of date and time types" +.SH "ABSOLUTE TIME" +Absolute time is specified using the following syntax: +.nf +Month Day [ Hour : Minute : Second ] Year [ Timezone ] +.sp +where + Month is Jan, Feb, ..., Dec + Day is 1, 2, ..., 31 + Hour is 01, 02, ..., 24 + Minute is 00, 01, ..., 59 + Second is 00, 01, ..., 59 + Year is 1901, 1902, ..., 2038 +.fi +Valid dates are from Dec 13 20:45:53 1901 GMT to Jan 19 03:14:04 +2038 GMT. As of Version 3.0, times are no longer read and written +using Greenwich Mean Time; the input and output routines default to +the local time zone. +.PP +The special absolute time values \*(lqcurrent\*(rq, +\*(lqinfinity\*(rq and \*(lq-infinity\*(rq are also provided. +\*(lqinfinity\*(rq specifies a time later than any valid time, and +\*(lq-infinity\*(rq specifies a time earlier than any valid time. +\*(lqcurrent\*(rq indicates that the current time should be +substituted whenever this value appears in a computation. +.PP +The strings \*(lqnow\*(rq and \*(lqepoch\*(rq can be used to specify +time values. \*(lqnow\*(rq means the current time, and differs from +\*(lqcurrent\*(rq in that the current time is immediately substituted +for it. \*(lqepoch\*(rq means Jan 1 00:00:00 1970 GMT. +.SH "RELATIVE TIME" +Relative time is specified with the following syntax: +.nf +@ Quantity Unit [Direction] +.sp +where + Quantity is `1', `2', ... + Unit is ``second'', ``minute'', ``hour'', ``day'', ``week'', + ``month'' (30-days), or ``year'' (365-days), + or PLURAL of these units. + Direction is ``ago'' +.fi +.PP +.RB ( Note : +Valid relative times are less than or equal to 68 years.) +In addition, the special relative time \*(lqUndefined RelTime\*(rq is +provided. +.SH "TIME RANGES" +Time ranges are specified as: +.nf +[ 'abstime' 'abstime'] +.fi +where +.IR abstime +is a time in the absolute time format. Special abstime values such as +\*(lqcurrent\*(rq, \*(lqinfinity\*(rq and \*(lq-infinity\*(rq can be used. +.SH "Built-in operators and functions" +.SH OPERATORS +Postgres provides a large number of built-in operators on system types. +These operators are declared in the system catalog +\*(lqpg_operator\*(rq. Every entry in \*(lqpg_operator\*(rq includes +the object ID of the procedure that implements the operator. +.PP +Users may invoke operators using the operator name, as in +.nf +select * from emp where salary < 40000; +.fi +Alternatively, users may call the functions that implement the +operators directly. In this case, the query above would be expressed +as +.nf +select * from emp where int4lt(salary, 40000); +.fi +The rest of this section provides a list of the built-in operators and +the functions that implement them. Binary operators are listed first, +followed by unary operators. +.SH "BINARY OPERATORS" +This list was generated from the Postgres system catalogs with the +query: + +.nf +SELECT + t0.typname AS result, + t1.typname AS left_type, + t2.typname AS right_type, + o.oprname AS operatr, + p.proname AS func_name +FROM pg_proc p, pg_type t0, + pg_type t1, pg_type t2, + pg_operator o +WHERE p.prorettype = t0.oid AND + RegprocToOid(o.oprcode) = p.oid AND + p.pronargs = 2 AND + o.oprleft = t1.oid AND + o.oprright = t2.oid +ORDER BY result, left_type, right_type, operatr; +.fi + +These operations are cast in terms of SQL types and so are +.BR not +directly usable as C function prototypes. + +.nf +Operators: + +general + <\(eq less or equal + <> inequality + < less than + <\(eq greater or equal + >\(eq greater or equal + > greater than + \(eq equality + ~ A matches regular expression B, case-sensitive + !~ A does not match regular expression B, case-sensitive + ~* A matches regular expression B, case-insensitive. + !~* A does not match regular expression B, case-insensitive + ~~ A matches LIKE expression B, case-sensitive + !~~ A does not match LIKE expression B, case-sensitive + + + addition + \(mi subtraction + * multiplication + / division + % modulus + @ absolute value + +float8 + ^ exponentiation + % truncate to integer + |/ square root + ||/ cube root + : exponential function + ; natural logarithm + +point + !< A is left of B + !> A is right of B + !^ A is above B + !| A is below B + \(eq|\(eq equality + ===> point inside box + ===` point on path + <===> distance between points + +box + && boxes overlap + &< box A overlaps box B, but does not extend to right of box B + &> box A overlaps box B, but does not extend to left of box B + << A is left of B + \(eq area equal + < area less than + <\(eq area less or equal + >\(eq area greater or equal + > area greater than + >> A is right of B + @ A is contained in B + ~\(eq box equality + ~= A same as B + ~ A contains B + @@ center of box + +polygon + && polygons overlap + &< A overlaps B but does not extend to right of B + &> A overlaps B but does not extend to left of B + << A is left of B + >> A is right of B + @ A is contained by B + ~\(eq equality + ~= A same as B + ~ A contains B + +tinterval + #<\(eq interval length less or equal reltime + #<> interval length not equal to reltime. + #< interval length less than reltime + #\(eq interval length equal to reltime + #>\(eq interval length greater or equal reltime + #> interval length greater than reltime + && intervals overlap + << A contains B + \(eq equality + <> interval bounded by two abstimes + <?> abstime in tinterval + | start of interval + <#> convert to interval + +result |left_type |right_type|operatr|func_name +---------+----------+----------+-------+--------------- +_aclitem |_aclitem |aclitem |+ |aclinsert +_aclitem |_aclitem |aclitem |- |aclremove +abstime |abstime |reltime |+ |timepl +abstime |abstime |reltime |- |timemi +bool |_abstime |_abstime |= |array_eq +bool |_aclitem |_aclitem |= |array_eq +bool |_aclitem |aclitem |~ |aclcontains +bool |_bool |_bool |= |array_eq +bool |_box |_box |= |array_eq +bool |_bytea |_bytea |= |array_eq +bool |_char |_char |= |array_eq +bool |_char16 |_char16 |= |array_eq +bool |_cid |_cid |= |array_eq +bool |_filename |_filename |= |array_eq +bool |_float4 |_float4 |= |array_eq +bool |_float8 |_float8 |= |array_eq +bool |_int2 |_int2 |= |array_eq +bool |_int28 |_int28 |= |array_eq +bool |_int4 |_int4 |= |array_eq +bool |_lseg |_lseg |= |array_eq +bool |_name |_name |= |array_eq +bool |_oid |_oid |= |array_eq +bool |_oid8 |_oid8 |= |array_eq +bool |_path |_path |= |array_eq +bool |_point |_point |= |array_eq +bool |_polygon |_polygon |= |array_eq +bool |_ref |_ref |= |array_eq +bool |_regproc |_regproc |= |array_eq +bool |_reltime |_reltime |= |array_eq +bool |_stub |_stub |= |array_eq +bool |_text |_text |= |array_eq +bool |_tid |_tid |= |array_eq +bool |_tinterval|_tinterval|= |array_eq +bool |_xid |_xid |= |array_eq +bool |abstime |abstime |< |abstimelt +bool |abstime |abstime |<= |abstimele +bool |abstime |abstime |<> |abstimene +bool |abstime |abstime |= |abstimeeq +bool |abstime |abstime |> |abstimegt +bool |abstime |abstime |>= |abstimege +bool |abstime |tinterval |<?> |ininterval +bool |bool |bool |<> |boolne +bool |bool |bool |= |booleq +bool |box |box |&& |box_overlap +bool |box |box |&< |box_overleft +bool |box |box |&> |box_overright +bool |box |box |< |box_lt +bool |box |box |<< |box_left +bool |box |box |<= |box_le +bool |box |box |= |box_eq +bool |box |box |> |box_gt +bool |box |box |>= |box_ge +bool |box |box |>> |box_right +bool |box |box |@ |box_contained +bool |box |box |~ |box_contain +bool |box |box |~= |box_same +bool |bpchar |bpchar |< |bpcharlt +bool |bpchar |bpchar |<= |bpcharle +bool |bpchar |bpchar |<> |bpcharne +bool |bpchar |bpchar |= |bpchareq +bool |bpchar |bpchar |> |bpchargt +bool |bpchar |bpchar |>= |bpcharge +bool |bpchar |text |!~ |textregexne +bool |bpchar |text |!~* |texticregexne +bool |bpchar |text |!~~ |textnlike +bool |bpchar |text |~ |textregexeq +bool |bpchar |text |~* |texticregexeq +bool |bpchar |text |~~ |textlike +bool |char |char |< |charlt +bool |char |char |<= |charle +bool |char |char |<> |charne +bool |char |char |= |chareq +bool |char |char |> |chargt +bool |char |char |>= |charge +bool |char16 |char16 |< |char16lt +bool |char16 |char16 |<= |char16le +bool |char16 |char16 |<> |char16ne +bool |char16 |char16 |= |char16eq +bool |char16 |char16 |> |char16gt +bool |char16 |char16 |>= |char16ge +bool |char16 |text |!~ |char16regexne +bool |char16 |text |!~* |char16icregexne +bool |char16 |text |!~~ |char16nlike +bool |char16 |text |!~~ |char16nlike +bool |char16 |text |~ |char16regexeq +bool |char16 |text |~* |char16icregexeq +bool |char16 |text |~~ |char16like +bool |char16 |text |~~ |char16like +bool |char2 |char2 |< |char2lt +bool |char2 |char2 |<= |char2le +bool |char2 |char2 |<> |char2ne +bool |char2 |char2 |= |char2eq +bool |char2 |char2 |> |char2gt +bool |char2 |char2 |>= |char2ge +bool |char2 |text |!~ |char2regexne +bool |char2 |text |!~* |char2icregexne +bool |char2 |text |!~~ |char2nlike +bool |char2 |text |~ |char2regexeq +bool |char2 |text |~* |char2icregexeq +bool |char2 |text |~~ |char2like +bool |char4 |char4 |< |char4lt +bool |char4 |char4 |<= |char4le +bool |char4 |char4 |<> |char4ne +bool |char4 |char4 |= |char4eq +bool |char4 |char4 |> |char4gt +bool |char4 |char4 |>= |char4ge +bool |char4 |text |!~ |char4regexne +bool |char4 |text |!~* |char4icregexne +bool |char4 |text |!~~ |char4nlike +bool |char4 |text |~ |char4regexeq +bool |char4 |text |~* |char4icregexeq +bool |char4 |text |~~ |char4like +bool |char8 |char8 |< |char8lt +bool |char8 |char8 |<= |char8le +bool |char8 |char8 |<> |char8ne +bool |char8 |char8 |= |char8eq +bool |char8 |char8 |> |char8gt +bool |char8 |char8 |>= |char8ge +bool |char8 |text |!~ |char8regexne +bool |char8 |text |!~* |char8icregexne +bool |char8 |text |!~~ |char8nlike +bool |char8 |text |~ |char8regexeq +bool |char8 |text |~* |char8icregexeq +bool |char8 |text |~~ |char8like +bool |date |date |< |date_lt +bool |date |date |<= |date_le +bool |date |date |<> |date_ne +bool |date |date |= |date_eq +bool |date |date |> |date_gt +bool |date |date |>= |date_ge +bool |float4 |float4 |< |float4lt +bool |float4 |float4 |<= |float4le +bool |float4 |float4 |<> |float4ne +bool |float4 |float4 |= |float4eq +bool |float4 |float4 |> |float4gt +bool |float4 |float4 |>= |float4ge +bool |float4 |float8 |< |float48lt +bool |float4 |float8 |<= |float48le +bool |float4 |float8 |<> |float48ne +bool |float4 |float8 |= |float48eq +bool |float4 |float8 |> |float48gt +bool |float4 |float8 |>= |float48ge +bool |float8 |float4 |< |float84lt +bool |float8 |float4 |<= |float84le +bool |float8 |float4 |<> |float84ne +bool |float8 |float4 |= |float84eq +bool |float8 |float4 |> |float84gt +bool |float8 |float4 |>= |float84ge +bool |float8 |float8 |< |float8lt +bool |float8 |float8 |<= |float8le +bool |float8 |float8 |<> |float8ne +bool |float8 |float8 |= |float8eq +bool |float8 |float8 |> |float8gt +bool |float8 |float8 |>= |float8ge +bool |int2 |int2 |< |int2lt +bool |int2 |int2 |<= |int2le +bool |int2 |int2 |<> |int2ne +bool |int2 |int2 |= |int2eq +bool |int2 |int2 |> |int2gt +bool |int2 |int2 |>= |int2ge +bool |int4 |int4 |< |int4lt +bool |int4 |int4 |<= |int4le +bool |int4 |int4 |<> |int4ne +bool |int4 |int4 |= |int4eq +bool |int4 |int4 |> |int4gt +bool |int4 |int4 |>= |int4ge +bool |int4 |name |!!= |int4notin +bool |int4 |oid |= |int4eqoid +bool |name |name |< |namelt +bool |name |name |<= |namele +bool |name |name |<> |namene +bool |name |name |= |nameeq +bool |name |name |> |namegt +bool |name |name |>= |namege +bool |name |text |!~ |nameregexne +bool |name |text |!~* |nameicregexne +bool |name |text |!~~ |namenlike +bool |name |text |~ |nameregexeq +bool |name |text |~* |nameicregexeq +bool |name |text |~~ |namelike +bool |oid |int4 |= |oideqint4 +bool |oid |name |!!= |oidnotin +bool |oid |oid |< |int4lt +bool |oid |oid |<= |int4le +bool |oid |oid |<> |oidne +bool |oid |oid |= |oideq +bool |oid |oid |> |int4gt +bool |oid |oid |>= |int4ge +bool |oidint2 |oidint2 |< |oidint2lt +bool |oidint2 |oidint2 |<= |oidint2le +bool |oidint2 |oidint2 |<> |oidint2ne +bool |oidint2 |oidint2 |= |oidint2eq +bool |oidint2 |oidint2 |> |oidint2gt +bool |oidint2 |oidint2 |>= |oidint2ge +bool |oidint4 |oidint4 |< |oidint4lt +bool |oidint4 |oidint4 |<= |oidint4le +bool |oidint4 |oidint4 |<> |oidint4ne +bool |oidint4 |oidint4 |= |oidint4eq +bool |oidint4 |oidint4 |> |oidint4gt +bool |oidint4 |oidint4 |>= |oidint4ge +bool |oidname |oidname |< |oidnamelt +bool |oidname |oidname |<= |oidnamele +bool |oidname |oidname |<> |oidnamene +bool |oidname |oidname |= |oidnameeq +bool |oidname |oidname |> |oidnamegt +bool |oidname |oidname |>= |oidnamege +bool |point |box |===> |on_pb +bool |point |path |===` |on_ppath +bool |point |point |!< |point_left +bool |point |point |!> |point_right +bool |point |point |!^ |point_above +bool |point |point |!\| |point_below +bool |point |point |=\|= |point_eq +bool |polygon |polygon |&& |poly_overlap +bool |polygon |polygon |&< |poly_overleft +bool |polygon |polygon |&> |poly_overright +bool |polygon |polygon |<< |poly_left +bool |polygon |polygon |>> |poly_right +bool |polygon |polygon |@ |poly_contained +bool |polygon |polygon |~ |poly_contain +bool |polygon |polygon |~= |poly_same +bool |reltime |reltime |< |reltimelt +bool |reltime |reltime |<= |reltimele +bool |reltime |reltime |<> |reltimene +bool |reltime |reltime |= |reltimeeq +bool |reltime |reltime |> |reltimegt +bool |reltime |reltime |>= |reltimege +bool |text |text |!~ |textregexne +bool |text |text |!~* |texticregexne +bool |text |text |!~~ |textnlike +bool |text |text |< |text_lt +bool |text |text |<= |text_le +bool |text |text |<> |textne +bool |text |text |= |texteq +bool |text |text |> |text_gt +bool |text |text |>= |text_ge +bool |text |text |~ |textregexeq +bool |text |text |~* |texticregexeq +bool |text |text |~~ |textlike +bool |time |time |< |time_lt +bool |time |time |<= |time_le +bool |time |time |<> |time_ne +bool |time |time |= |time_eq +bool |time |time |> |time_gt +bool |time |time |>= |time_ge +bool |tinterval |reltime |#< |intervallenlt +bool |tinterval |reltime |#<= |intervallenle +bool |tinterval |reltime |#<> |intervallenne +bool |tinterval |reltime |#= |intervalleneq +bool |tinterval |reltime |#> |intervallengt +bool |tinterval |reltime |#>= |intervallenge +bool |tinterval |tinterval |&& |intervalov +bool |tinterval |tinterval |<< |intervalct +bool |tinterval |tinterval |= |intervaleq +bool |varchar |text |!~ |textregexne +bool |varchar |text |!~* |texticregexne +bool |varchar |text |!~~ |textnlike +bool |varchar |text |~ |textregexeq +bool |varchar |text |~* |texticregexeq +bool |varchar |text |~~ |textlike +bool |varchar |varchar |< |varcharlt +bool |varchar |varchar |<= |varcharle +bool |varchar |varchar |<> |varcharne +bool |varchar |varchar |= |varchareq +bool |varchar |varchar |> |varchargt +bool |varchar |varchar |>= |varcharge +char |char |char |* |charmul +char |char |char |+ |charpl +char |char |char |- |charmi +char |char |char |/ |chardiv +float4 |float4 |float4 |* |float4mul +float4 |float4 |float4 |+ |float4pl +float4 |float4 |float4 |- |float4mi +float4 |float4 |float4 |/ |float4div +float8 |float4 |float8 |* |float48mul +float8 |float4 |float8 |+ |float48pl +float8 |float4 |float8 |- |float48mi +float8 |float4 |float8 |/ |float48div +float8 |float8 |float4 |* |float84mul +float8 |float8 |float4 |+ |float84pl +float8 |float8 |float4 |- |float84mi +float8 |float8 |float4 |/ |float84div +float8 |float8 |float8 |* |float8mul +float8 |float8 |float8 |+ |float8pl +float8 |float8 |float8 |- |float8mi +float8 |float8 |float8 |/ |float8div +float8 |float8 |float8 |^ |dpow +int2 |int2 |int2 |% |int2mod +int2 |int2 |int2 |* |int2mul +int2 |int2 |int2 |+ |int2pl +int2 |int2 |int2 |- |int2mi +int2 |int2 |int2 |/ |int2div +int4 |int2 |int4 |% |int24mod +int4 |int2 |int4 |* |int24mul +int4 |int2 |int4 |+ |int24pl +int4 |int2 |int4 |- |int24mi +int4 |int2 |int4 |/ |int24div +int4 |int2 |int4 |< |int24lt +int4 |int2 |int4 |<= |int24le +int4 |int2 |int4 |<> |int24ne +int4 |int2 |int4 |= |int24eq +int4 |int2 |int4 |> |int24gt +int4 |int2 |int4 |>= |int24ge +int4 |int4 |int2 |% |int42mod +int4 |int4 |int2 |* |int42mul +int4 |int4 |int2 |+ |int42pl +int4 |int4 |int2 |- |int42mi +int4 |int4 |int2 |/ |int42div +int4 |int4 |int2 |< |int42lt +int4 |int4 |int2 |<= |int42le +int4 |int4 |int2 |<> |int42ne +int4 |int4 |int2 |= |int42eq +int4 |int4 |int2 |> |int42gt +int4 |int4 |int2 |>= |int42ge +int4 |int4 |int4 |% |int4mod +int4 |int4 |int4 |* |int4mul +int4 |int4 |int4 |+ |int4pl +int4 |int4 |int4 |- |int4mi +int4 |int4 |int4 |/ |int4div +int4 |point |point |<===> |pointdist +tinterval|abstime |abstime |<#> |mktinterval + + +.fi +.SH "LEFT UNARY OPERATORS" +The table below gives the left unary operators that are +registered in the system catalogs. + +This list was generated from the Postgres system catalogs with the query: + +.nf +SELECT o.oprname AS left_unary, + right.typname AS operand, + result.typname AS return_type +FROM pg_operator o, pg_type right, pg_type result +WHERE o.oprkind = 'l' AND -- left unary + o.oprright = right.oid AND + o.oprresult = result.oid +ORDER BY operand; + +left_unary|operand |return_type +----------+---------+----------- +@@ |box |point +@ |float4 |float4 +- |float4 |float4 +; |float8 |float8 +: |float8 |float8 +% |float8 |float8 +\|\|/ |float8 |float8 +\|/ |float8 |float8 +@ |float8 |float8 +- |float8 |float8 +- |int2 |int2 +- |int4 |int4 +!! |int4 |int4 +\| |tinterval|abstime + +.fi +.in +.SH "RIGHT UNARY OPERATORS" +The table below gives the right unary operators that are +registered in the system catalogs. + +This list was generated from the Postgres system catalogs with the query: + +.nf +SELECT o.oprname AS right_unary, + left.typname AS operand, + result.typname AS return_type +FROM pg_operator o, pg_type left, pg_type result +WHERE o.oprkind = 'r' AND -- right unary + o.oprleft = left.oid AND + o.oprresult = result.oid +ORDER BY operand; + +right_unary|operand|return_type +-----------+-------+----------- +% |float8 |float8 +! |int4 |int4 + +.fi +.in +.SH "AGGREGATE FUNCTIONS" +The table below gives the aggregate functions that are +registered in the system catalogs. + +This list was generated from the Postgres system catalogs with the query: + +.nf +SELECT a.aggname, t.typname +FROM pg_aggregate a, pg_type t +WHERE a.aggbasetype = t.oid +ORDER BY aggname, typname; + +aggname|typname +-------+------- +avg |float4 +avg |float8 +avg |int2 +avg |int4 +max |float4 +max |float8 +max |int2 +max |int4 +min |float4 +min |float8 +min |int2 +min |int4 +sum |float4 +sum |float8 +sum |int2 +sum |int4 + +\fBcount\fR is also available. + +.fi +.in +.SH "SEE ALSO" +For examples on specifying literals of built-in types, see +.IR SQL(l). +.SH BUGS +.PP +Although most of the input and output functions correponding to the +base types (e.g., integers and floating point numbers) do some +error-checking, none of them are particularly rigorous about it. More +importantly, almost none of the operators and functions (e.g., +addition and multiplication) perform any error-checking at all. +Consequently, many of the numeric operations will (for example) +silently underflow or overflow. +.PP +Some of the input and output functions are not invertible. That is, +the result of an output function may lose precision when compared to +the original input. |