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3.5 Mathematical And Text Generalities Functions

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) mth 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.