2.5 Mathematical And Text Generalities Function Set

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.

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)

• mode `abs'(mode 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

• mode `base2'(mode m);

  is the greatest power of 2 less than or equal to m if m is not less than zero, some undefined value otherwise

• mode `bcount'(mode m);

  is the m bitcount (i.e. the number of bits set in m)

• real `ceil'(real x);

  is the up rounded value of x

• mode `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

• mode `deck2'(mode m);

  is the lesser power of 2 greater than or equal to m if m is not less than zero, some undefined value otherwise

• mode `drand'(mode 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

• mode `ffs'(mode 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

• mode `fls'(mode 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

• 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

• mode `gcd'(mode m, mode n);

  is the greatest common denominator of m and n

• mode `iclip'(mode min, mode m, mode max);

  is the minimum between max and the maximum between m and min

• real `imodf'(real x);

  is the same sign as x integral part of x

• mode `irand'(mode m, mode n);

  is a pseudo-random integer between inclusive m and n

• mode `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

• mode `lz'(mode m);

  is the m leading zero bits count, same as `xls'(m)

• mode `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

• mode `max'(mode m, mode n);

  is the maximum of m and n

• mode `min'(mode m, mode n);

  is the minimum of m and n

• mode `mode'(real x);

  is 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

• real `real'(mode m);

  is m

• real `round'(real x);

  is the towards nearest integer, half cases away from zero rounded value of x

• mode `sign'(mode m);

  is -1 if m is negative, 0 of m is zero, 1 otherwise

• 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

• mode `text'(text s, mode m);

  is the (positively defined value of the) mth character of s, if such character exists, 0 otherwise

• real `tg'(real x);

  is same as `tan'(x)

• real `track'(real x);

  is the towards zero rounded value of x

• mode `tz'(mode m);

  is the m trailing zero bits count, same as `xfs'(m)

• mode `xfs'(mode 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))

• mode `xls'(mode 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 mode, real, text and void designate the integer, real, string and void types, respectively.