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The `x1f4_e4_defaults`

function set implements a few common mathematical
and text generalities.

The `x1f4_e4_defaults`

object is an `x1f4_function_type`

array in
which the last element has the `name`

set to `NULL`

.

See x1f4_e4_defaults.

See x1f4_e4_computables.

Among the include functions:

- -
`real`‘`Gacos`’(`real``x`);is the in degrees specified arc cosine of

`x` - -
`real`‘`Gadiff`’(`real``x`,`real``y`);is the in degrees specified smallest angle between degrees

`x`and degrees`y`(or something) - -
`real`‘`Garccos`’(`real``x`);is same as ‘

`Gacos`’(`x`) - -
`real`‘`Garcctg2`’(`real``x`,`real``y`);is the in degrees specified arc tangent of

`y`/`x`, signs of both`x`and`y`being used to determine the quadrant of the result (same as ‘`Gatan2`’(`y`,`x`)) - -
`real`‘`Garcdiff`’(`real``x`,`real``y`);is same as ‘

`Gadiff`’(`x`,`y`) - -
`real`‘`Garcsin`’(`real``x`);is same as ‘

`Gasin`’(`x`) - -
`real`‘`Garctg`’(`real``x`);is same as ‘

`Gatan`’(`x`) - -
`real`‘`Garctg2`’(`real``y`,`real``x`);is same as ‘

`Gatan2`’(`y`,`x`) - -
`real`‘`Gasin`’(`real``x`);is the in degrees specified arc sine of

`x` - -
`real`‘`Gatan`’(`real``x`);is the in degrees specified arc tangent of

`x` - -
`real`‘`Gatan2`’(`real``y`,`real``x`);is the in degrees specified arc tangent of

`y`/`x`, signs of both`x`and`y`being used to determine the quadrant of the result - -
`real`‘`Gcos`’(`real``x`);is the cosine of degrees

`x` - -
`real`‘`Gparcctg2`’(`real``x`,`real``y`);is the positively defined, in radians specified arc tangent of

`y`/`x`, signs of both`x`and`y`being used to determine the quadrant of the result (same as ‘`Gpatan2`’(`y`,`x`)) - -
`real`‘`Gparctg2`’(`real``y`,`real``x`);is same as ‘

`Gpatan2`’(`y`,`x`) - -
`real`‘`Gpatan2`’(`real``y`,`real``x`);is the positively defined, in degrees specified arc tangent of

`y`/`x`, signs of both`x`and`y`being used to determine the quadrant of the result - -
`real`‘`Gsin`’(`real``x`);is the sine of degrees

`x` - -
`real`‘`Gtan`’(`real``x`);is the tangent of degrees

`x` - -
`real`‘`Gtg`’(`real``x`);is same as ‘

`Gtan`’(`x`) - -
`integer`‘`abs`’(`integer``m`);is the absolute value of

`m` - -
`real`‘`acos`’(`real``x`);is the in radians specified arc cosine of

`x` - -
`real`‘`adiff`’(`real``x`,`real``y`);is the in radians specified smallest angle between radians

`x`and radians`y`(or something) - -
`real`‘`arccos`’(`real``x`);is same as ‘

`acos`’(`x`) - -
`real`‘`arcctg2`’(`real``x`,`real``y`);is the in radians specified arc tangent of

`y`/`x`, signs of both`x`and`y`being used to determine the quadrant of the result (same as ‘`atan2`’(`y`,`x`)) - -
`real`‘`arcdiff`’(`real``x`,`real``y`);is same as ‘

`adiff`’(`x`,`y`) - -
`real`‘`arcsin`’(`real``x`);is same as ‘

`asin`’(`x`) - -
`real`‘`arctg`’(`real``x`);is same as ‘

`atan`’(`x`) - -
`real`‘`arctg2`’(`real``y`,`real``x`);is same as ‘

`atan2`’(`y`,`x`) - -
`real`‘`asin`’(`real``x`);is the in radians specified arc sine of

`x` - -
`real`‘`atan`’(`real``x`);is the in radians specified arc tangent of

`x` - -
`real`‘`atan2`’(`real``y`,`real``x`);is the in radians specified arc tangent of

`y`/`x`, signs of both`x`and`y`being used to determine the quadrant of the result - -
`integer`‘`base2`’(`integer``m`);is the greatest power of 2 less than or equal to

`m`if`m`is not less than zero, some undefined value otherwise - -
`integer`‘`bcount`’(`integer``m`);is the

`m`bitcount (i.e. the number of bits set in`m`) - -
`cardinal`‘`cardinal`’(`cardinal``z`);is

`z` - -
`real`‘`ceil`’(`real``x`);is the up rounded value of

`x` - -
`integer`‘`character`’(`text``s`,`integer``m`);is the (positively defined value of the)

`m`th character of`s`, if such character exists, 0 otherwise (negative position indications are interpreted with respect to the end of string)See Negative Indices.

- -
`integer`‘`compare`’(`text``s`,`text``t`);is 0 if

`s`is (case sensitive) same as`t`, less than 0 if`s`is less than`t`and greater than 0 if`s`is greater than`t` - -
`real`‘`cos`’(`real``x`);is the cosine of radians

`x` - -
`integer`‘`deck2`’(`integer``m`);is the lesser power of 2 greater than or equal to

`m`if`m`is not less than zero, some undefined value otherwise - -
`integer`‘`drand`’(`integer``m`);is a pseudo-random integer between inclusive 0 and

`m` - -
`text`‘`echo`’(`text``s`);is

`s` - -
`real`‘`exp`’(`real``x`);is the value of e (the base of natural logarithms) raised to the power of

`x` - -
`real`‘`exp2`’(`real``x`);is the value of 2 raised to the power of

`x` - -
`real`‘`fabs`’(`real``x`);is the absolute value of

`x` - -
`real`‘`fclip`’(`real``min`,`real``x`,`real``max`);is the minimum between

`max`and the maximum between`x`and`min` - -
`integer`‘`ffs`’(`integer``m`);is the 1 based position of the first (least significant) bit set in

`m`if any, 0 otherwise - -
`real`‘`floor`’(`real``x`);is the down rounded value of

`x` - -
`integer`‘`fls`’(`integer``m`);is the 1 based position of the last (most significant) bit set in

`m`if any, 0 otherwise - -
`real`‘`fmax`’(`real``x`,`real``y`);is the maximum of

`x`and`y` - -
`real`‘`fmin`’(`real``x`,`real``y`);is the minimum of

`x`and`y` - -
`real`‘`fmod`’(`real``x`,`real``y`);is the remainder of dividing

`x`by`y`, more specifically`x`-`n`*`y`, where`n`is the quotient of`x`/`y`, rounded toward zero to an integer - -
`real`‘`fmodf`’(`real``x`);is the same sign as

`x`fractional part of`x` - -
`integer`‘`frame`’(`text``s`,`integer``c`);is the position of the last occurrence of the

`c`non zero character in the`s`string if any, -1 otherwise - -
`real`‘`frand`’(`void`);is a pseudo-random real between 0 and 1

- -
`real`‘`fsign`’(`real``x`);is -1 if

`x`is negative, 0 of`x`is zero, 1 otherwise - -
`integer`‘`gcd`’(`integer``m`,`integer``n`);is the greatest common denominator of

`m`and`n` - -
`integer`‘`iclip`’(`integer``min`,`integer``m`,`integer``max`);is the minimum between

`max`and the maximum between`m`and`min` - -
`integer`‘`icompare`’(`text``s`,`text``t`);is 0 if

`s`is (case insensitive) same as`t`, non 0 otherwise - -
`integer`‘`imatch`’(`text``s`,`text``t`);is 0 if

`t`wild card (case insensitive) matches the`s`pattern (the`*`and`?`literal sign are interpreted as for their shell pattern equivalents), non 0 otherwise - -
`real`‘`imodf`’(`real``x`);is the same sign as

`x`integral part of`x` - -
`integer`‘`index`’(`text``s`,`integer``c`);is the position of the first occurrence of the

`c`non zero character in the`s`string if any, -1 otherwise - -
`integer`‘`initial`’(`text``s`);is the first character of

`s`, if such character exists, 0 otherwise - -
`integer`‘`integer`’(`integer``m`);is

`m` - -
`integer`‘`irand`’(`integer``m`,`integer``n`);is a pseudo-random integer between inclusive

`m`and`n` - -
`integer`‘`length`’(`text``s`);is the length of

`s` - -
`real`‘`limit`’(`real``x`);is the away from zero rounded value of

`x` - -
`real`‘`ln`’(`real``x`);is same as ‘

`log`’(`x`) - -
`real`‘`log`’(`real``x`);is the natural logarithm of

`x` - -
`real`‘`log10`’(`real``x`);is the base 10 logarithm of

`x` - -
`real`‘`log2`’(`real``x`);is the base 2 logarithm of

`x` - -
`real`‘`lrand`’(`void`);is a pseudo-random real between -1 and 1

- -
`integer`‘`lz`’(`integer``m`);is the

`m`leading zero bits count, same as ‘`xls`’(`m`) - -
`integer`‘`match`’(`text``s`,`text``t`);is 0 if

`t`wild card (case sensitive) matches the`s`pattern (the`*`and`?`literal sign are interpreted as for their shell pattern equivalents), non 0 otherwise - -
`integer`‘`max`’(`integer``m`,`integer``n`);is the maximum of

`m`and`n` - -
`integer`‘`min`’(`integer``m`,`integer``n`);is the minimum of

`m`and`n` - -
`real`‘`modf`’(`real``x`,`real`&`y`);is the same sign as

`x`fractional part of`x`,`y`is the same sign as`x`integral part of`x` - -
`real`‘`parcctg2`’(`real``x`,`real``y`);is the positively defined, in radians specified arc tangent of

`y`/`x`, signs of both`x`and`y`being used to determine the quadrant of the result (same as ‘`patan2`’(`y`,`x`)) - -
`real`‘`parctg2`’(`real``y`,`real``y`);is same as ‘

`patan2`’(`y`,`x`) - -
`real`‘`patan2`’(`real``y`,`real``x`);is the positively defined, in radians specified arc tangent of

`y`/`x`, signs of both`x`and`y`being used to determine the quadrant of the result - -
`real`‘`pow`’(`real``x`,`real``y`);is the value of

`x`raised to the power of`y` - -
`text`‘`project`’(`text``s`,`integer``m`);is

`s`after position`m`(negative position indications are interpreted with respect to the end of string,`m`is clipped to fall inside`s`)See Negative Indices.

- -
`real`‘`real`’(`real``x`);is

`x` - -
`real`‘`round`’(`real``x`);is the towards nearest integer, half cases away from zero rounded value of

`x` - -
`integer`‘`sign`’(`integer``m`);is -1 if

`m`is negative, 0 of`m`is zero, 1 otherwise - -
`integer`‘`signed`’(`cardinal``z`);is

`z` - -
`real`‘`sin`’(`real``x`);is the sine of radians

`x` - -
`real`‘`sq`’(`real``x`);is the square of

`x` - -
`real`‘`sqrt`’(`real``x`);is the square root of

`x` - -
`real`‘`tan`’(`real``x`);is the tangent of radians

`x` - -
`real`‘`tg`’(`real``x`);is same as ‘

`tan`’(`x`) - -
`real`‘`track`’(`real``x`);is the towards zero rounded value of

`x` - -
`integer`‘`tz`’(`integer``m`);is the

`m`trailing zero bits count, same as ‘`xfs`’(`m`) - -
`cardinal`‘`unsigned`’(`integer``m`);is

`m` - -
`integer`‘`xfs`’(`integer``m`);is the 0 based position of the first (least significant) bit set in

`m`if any, the number of bits in`m`otherwise (same as ‘`tz`’(`m`)) - -
`integer`‘`xls`’(`integer``m`);is the 0 based position of the last (most significant) bit set in

`m`if any, the number of bits in`m`otherwise (same as ‘`lz`’(`m`))

The literals `cardinal`, `integer`, `real`, `text`
and `void` designate the *cardinal*, *integer*, *real*,
*string* and *void* types, respectively.

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