COBOL 2014 lists the following standard Intrinsic Functions:

======================================== ==========
Intrinsic Function                       Parameters
======================================== ==========
FUNCTION ABS                             1
FUNCTION ACOS                            1
FUNCTION ANNUITY                         2
FUNCTION ASIN                            1
FUNCTION ATAN                            1
FUNCTION BOOLEAN-OF-INTEGER              2
FUNCTION BYTE-LENGTH                     1
FUNCTION CHAR                            1
FUNCTION CHAR-NATIONAL                   1
FUNCTION COMBINED-DATETIME               2
FUNCTION COS                             1
FUNCTION CURRENCY-SYMBOL                 0
FUNCTION CURRENT-DATE                    0
FUNCTION DATE-OF-INTEGER                 1
FUNCTION DATE-TO-YYYYMMDD                Variable
FUNCTION DAY-OF-INTEGER                  1
FUNCTION DAY-TO-YYYYDDD                  Variable
FUNCTION DISPLAY-OF                      Variable
FUNCTION E                               0
FUNCTION EXCEPTION-FILE                  0
FUNCTION EXCEPTION-FILE-N                0
FUNCTION EXCEPTION-LOCATION              0
FUNCTION EXCEPTION-LOCATION-N            0
FUNCTION EXCEPTION-STATEMENT             0
FUNCTION EXCEPTION-STATUS                0
FUNCTION EXP                             1
FUNCTION EXP10                           1
FUNCTION FACTORIAL                       1
FUNCTION FORMATTED-CURRENT-DATE          1
FUNCTION FORMATTED-DATE                  2
FUNCTION FORMATTED-DATETIME              Variable
FUNCTION FORMATTED-TIME                  Variable
FUNCTION FRACTION-PART                   1
FUNCTION HIGHEST-ALGEBRAIC               1
FUNCTION INTEGER                         1
FUNCTION INTEGER-OF-BOOLEAN              1
FUNCTION INTEGER-OF-DATE                 1
FUNCTION INTEGER-OF-DAY                  1
FUNCTION INTEGER-OF-FORMATTED-DATE       2
FUNCTION INTEGER-PART                    1
FUNCTION LENGTH                          1
FUNCTION LENGTH-AN                       1
FUNCTION LOCALE-COMPARE                  Variable
FUNCTION LOCALE-DATE                     2
FUNCTION LOCALE-TIME                     2
FUNCTION LOCALE-TIME-FROM-SECONDS        2
FUNCTION LOG                             1
FUNCTION LOG10                           1
FUNCTION LOWER-CASE                      1
FUNCTION LOWEST-ALGEBRAIC                1
FUNCTION MAX                             Variable
FUNCTION MEAN                            Variable
FUNCTION MEDIAN                          Variable
FUNCTION MIDRANGE                        Variable
FUNCTION MIN                             Variable
FUNCTION MOD                             2
FUNCTION MODULE-CALLER-ID                0
FUNCTION MODULE-DATE                     0
FUNCTION MODULE-FORMATTED-DATE           0
FUNCTION MODULE-ID                       0
FUNCTION MODULE-PATH                     0
FUNCTION MODULE-SOURCE                   0
FUNCTION MODULE-TIME                     0
FUNCTION MONETARY-DECIMAL-POINT          0
FUNCTION MONETARY-THOUSANDS-SEPARATOR    0
FUNCTION NATIONAL-OF                     Variable
FUNCTION NUMERIC-DECIMAL-POINT           0
FUNCTION NUMERIC-THOUSANDS-SEPARATOR     0
FUNCTION NUMVAL                          1
FUNCTION NUMVAL-C                        2
FUNCTION NUMVAL-F                        1
FUNCTION ORD                             1
FUNCTION ORD-MAX                         Variable
FUNCTION ORD-MIN                         Variable
FUNCTION PI                              0
FUNCTION PRESENT-VALUE                   Variable
FUNCTION RANDOM                          Variable
FUNCTION RANGE                           Variable
FUNCTION REM                             2
FUNCTION REVERSE                         1
FUNCTION SECONDS-FROM-FORMATTED-TIME     2
FUNCTION SECONDS-PAST-MIDNIGHT           0
FUNCTION SIGN                            1
FUNCTION SIN                             1
FUNCTION SQRT                            1
FUNCTION STANDARD-COMPARE                Variable
FUNCTION STANDARD-DEVIATION              Variable
FUNCTION STORED-CHAR-LENGTH              1
FUNCTION SUM                             Variable
FUNCTION TAN                             1
FUNCTION TEST-DATE-YYYYMMDD              1
FUNCTION TEST-DAY-YYYYDDD                1
FUNCTION TEST-FORMATTED-DATETIME         2
FUNCTION TEST-NUMVAL                     1
FUNCTION TEST-NUMVAL-C                   2
FUNCTION TEST-NUMVAL-F                   1
FUNCTION TRIM                            2
FUNCTION UPPER-CASE                      1
FUNCTION VARIANCE                        Variable
FUNCTION WHEN-COMPILED                   0
FUNCTION YEAR-TO-YYYY                    Variable
======================================== ==========

GnuCOBOL adds

======================================== ==========
FUNCTION CONCATENATE                     Variable
FUNCTION SUBSTITUTE                      Variable
FUNCTION SUBSTITUTE-CASE                 Variable
======================================== ==========

The keyword FUNCTION is required unless source (or compile time option) includes

ENVIRONMENT DIVISION.
CONFIGURATION SECTION.
REPOSITORY.
    FUNCTION ALL INTRINSIC.

Where ALL INTRINSIC can be a list of functions to be used without the FUNCTION prefix in PROCEDURE DIVISION statements.

The LENGTH function has a sorted history. Some compilers include a LENGTH reserved word. For GnuCOBOL, this reserved word is only recognized when used in the phrase LENGTH OF, the OF token is required to disambiguate the function from the older reserved word extension.