ACOSH, ASINH and ATANH
compute the inverse hyperbolic cosine, sine or tangent respectively.
There is a single argument X, which may be of type Real or Complex; the
result of the function has the same type and kind.
When the argument is Complex, the imaginary part is expressed in radians and
lies in the range 0≤im≤π for the ACOSH function, and
−π/2≤im≤π/2 for the ASINH and ATANH functions.
For example, ACOSH(1.543081), ASINH(1.175201) and
ATANH(0.7615942) are all approximately equal to 1.0.
BESSEL_J0, BESSEL_Y0,
BESSEL_J1 and BESSEL_Y1 compute the Bessel functions
J0, Y0, J1 and Y1 respectively.
These functions are solutions to Bessel's differential equation.
The J functions are of the 1st kind and the Y
functions are of the 2nd kind; the following subscript indicates the
order (0 or 1).
There is a single argument X, which must be of type Real; the
result of the function has the same type and kind.
For functions of the 2nd kind (BESSEL_Y0 and BESSEL_Y1),
the argument X must be positive.
For example,
BESSEL_J0(1.5) is approximately 0.5118276,
BESSEL_Y0(1.5) is approximately 0.3824489,
BESSEL_J1(1.5) is approximately 0.5579365 and
BESSEL_Y1(1.5) is approximately -0.4123086.
BESSEL_JN and BESSEL_YN compute the
Bessel functions Jn and Yn respectively.
These functions come in two forms: an elemental form and a transformational
form.
The elemental form has two arguments: N, the order of the function to
compute, and X, the argument of the Bessel function.
BESSEL_JN(0,X) is identical to BESSEL_J0(X), etc..
The transformational form has three scalar arguments: N1, N2 and
X.
The result is a vector of size MAX(N2-N1+1,0), containing
approximations to the Bessel functions of orders N1 to N2 applied
to X.
For example,
BESSEL_JN(5,7.5) is approximately 0.283474,
BESSEL_YN(5,7.5) is approximately 0.175418,
BESSEL_JN(3,5,7.5) is approximately [ -0.258061, 0.023825, 0.283474 ] and
BESSEL_YN(3,5,7.5) is approximately [ 0.159708, 0.314180, 0.175418 ].
ERF, ERFC and ERFC_SCALED
compute the error function, the complementary error function and the scaled
complementary error function, respectively.
The single argument X must be of type real.
The error function is the integral of
−t2
from 0 to X, times
2/SQRT(π); this rapidly converges to 1.
The complementary error function is 1 minus the error function, and fairly
quickly converges to zero.
The scaled complementary error function scales the value (of 1 minus the error
function) by EXP(X**2); this also converges to zero but only very
slowly.
GAMMA and LOG_GAMMA
compute the gamma function and the natural logarithm of the absolute value of
the gamma function respectively.
The single argument X must be of type real, and must not be zero or a
negative integer.
The gamma function is the extension of factorial from the integers to the
reals; for positive integers, GAMMA(X) is equal to (X−1)!,
i.e. factorial of X−1.
This grows very rapidly and thus overflows for quite small X;
LOG_GAMMA also diverges but much more slowly.
HYPOT computes the
“Euclidean distance function” (square root of the sum of squares) of its
arguments X and Y without overflow or underflow for very large or
small X or Y (unless the result itself overflows or underflows).
The arguments must be of type Real with the same kind, and the result is of
type Real with that kind.
Note that HYPOT(X,Y) is semantically and numerically equal to
ABS(CMPLX(X,Y,KIND(X))).
For example, HYPOT(3e30,4e30) is approximately equal to 5e30.
NORM2(X,DIM) reduces Real arrays
using the L2-norm operation.
This operates exactly the same as SUM and PRODUCT, except for
the operation involved.
The L2 norm of an array is the square root of the sum of the squares
of the elements.
Note that unlike most of the other reduction functions, NORM2 does not
have a MASK argument.
The DIM argument is optional; an actual argument for DIM is not
itself permitted to be an optional dummy argument.
The calculation of the result value is done in such a way as to avoid
intermediate overflow and underflow, except when the result itself is outside
the maximum range.
For example, NORM2([X,Y]) is approximately the same as
HYPOT(X,Y).
BGE, BGT, BLE and
BLT perform bitwise (i.e. unsigned) comparisons.
They each have two arguments, I and J, which must be of type
Integer but may be of different kind.
The result is default Logical.
For example, BGE(INT(Z'FF',INT8),128) is true, while
INT(Z'FF',INT8)>=128 is false.
DSHIFTL and DSHIFTR perform
double-width shifting.
They each have three arguments, I, J and SHIFT which must
be of type Integer, except that one of I or J may be a BOZ literal
constant – it will be converted to the type and kind of the other I or
J argument.
I and J must have the same kind if they are both of type Integer.
The result is of type Integer, with the same kind as I and J.
The I and J arguments are effectively concatenated to form a
single double-width value, which is shifted left or right by SHIFT
positions; for DSHIFTL the result is the top half of the combined shift,
and for DSHIFTR the result is the bottom half of the combined shift.
For example, DSHIFTL(INT(B'11000101',1),B'11001001',2) has the value
INT(B'00010111',1) (decimal value 23), whereas
DSHIFTR(INT(B'11000101',1),B'11001001',2) has the value
INT(B'01110010',1) (decimal value 114).
IALL, IANY and
IPARITY reduce arrays using bitwise operations.
These are exactly the same as SUM and PRODUCT, except that
instead of reducing the array by the + or * operation, they
reduce it by the IAND, IOR and IEOR intrinsic functions
respectively.
That it, each element of the result is the bitwise-and, bitwise-or, or
bitwise-exclusive-or of the reduced elements.
If the number of reduced elements is zero, the result is zero for IANY
and IPARITY, and NOT(zero) for IALL.
LEADZ and TRAILZ
return the number of leading (most significant) and trailing
(least significant) zero bits in the argument I, which must be of type
Integer (of any kind).
The result is default Integer.
MASKL and MASKR
generate simple left-justified and right-justified bitmasks.
The value of MASKL(I,KIND) is an integer with the specified kind that
has its leftmost I bits set to one and the rest set to zero; I
must be non-negative and less than or equal to the bitsize of the result.
If KIND is omitted, the result is default integer.
The value of MASKR is similar, but has its rightmost I bits set
to one instead.
MERGE_BITS(I,J,MASK) merges the bits
from Integer values I and J, taking the bit from I when
the corresponding bit in MASK is 1, and taking the bit from
J when it is zero.
All arguments must be BOZ literal constants or of type Integer, and all the
Integer arguments must have the same kind; at least one of I and
J must be of type Integer, and the result has the same type and kind.
Note that MERGE_BITS(I,J,MASK) is identical to
IOR(IAND(I,MASK),IAND(J,NOT(MASK))).
For example, MERGE_BITS(INT(B'00110011',1),B'11110000',B'10101010')
is equal to INT(B'01110010') (decimal value 114).
PARITY reduces Logical arrays.
It is exactly the same as ALL and ANY, except that instead of
reducing the array by the .AND. or .OR. operation, it reduces it
by the .NEQV. operation.
That is, each element of the result is .TRUE. if an odd number of
reduced elements is .TRUE..
POPCNT(I) returns the number of bits in
the Integer argument I that are set to 1.
The elemental intrinsic function POPPAR(I) returns zero if the number of
bits in I that are set to 1 are even, and one if it is odd.
The result is default Integer.
EXECUTE_COMMAND_LINE passes a command line to
the operating system's command processor for execution.
It has five arguments, in order these are:
CHARACTER(*),INTENT(IN) :: COMMAND — the command to be executed;
LOGICAL,INTENT(IN),OPTIONAL :: WAIT — whether to wait for command
completion (default true);
INTEGER,INTENT(INOUT),OPTIONAL :: EXITSTAT — the result value of the
command;
INTEGER,INTENT(OUT),OPTIONAL :: CMDSTAT — see below;
CHARACTER(*),INTENT(INOUT),OPTIONAL :: CMDMSG — the error message if
CMDSTAT is non-zero.
CMDSTAT values are zero for success, −1 if command line execution is
not supported, −2 if WAIT is present and false but asynchronous
execution is not supported, and a positive value to indicate some other error.
If CMDSTAT is not present but would have been set non-zero, the program
will be terminated.
Note that Release 5.3.1 supports command line execution on all systems, and
does not support asynchronous execution on any system.
For example, CALL EXECUTE_COMMAND_LINE('echo Hello') will probably
display ‘Hello’ in the console window.
STORAGE_SIZE(A,KIND) returns the size in bits of
a scalar object with the same dynamic type and type parameters as A,
when it is stored as an array element (i.e. including any padding).
The KIND argument is optional; the result is type Integer with kind
KIND if it is present, and default kind otherwise.
If A is allocatable or a pointer, it does not have to be allocated
unless it has a deferred type parameter (e.g. CHARACTER(:)) or is
CLASS(*).
If it is a polymorphic pointer, it must not have an undefined status.
For example, STORAGE_SIZE(13_1) is equal to 8 (bits).
IS_CONTIGUOUS has a single argument
ARRAY, which can be an array of any type.
The function returns true if ARRAY is stored contiguously, and false
otherwise.
Note that this question has no meaning for an array with no elements, or for
an array expression since that is a value and not a variable.
FINDLOC is similar to MAXLOC and MINLOC, but instead of finding the location of the
maximum or minimum value of an array, it finds a location that is equal to a specified value;
thus it is available for all intrinsic types including COMPLEX and LOGICAL.
It has one of the following two forms:
FINDLOC (ARRAY, VALUE, DIM, MASK, KIND, BACK )
FINDLOC (ARRAY, VALUE, MASK, KIND, BACK )
where
ARRAY | is an array of intrinsic type, with rank N; |
VALUE | is a scalar of the same type (if LOGICAL) or which may be compared with ARRAY using the intrinsic |
operator == (or .EQ.); | |
DIM | is a scalar INTEGER in the range 1 to N; |
MASK | (optional) is an array of type LOGICAL with the same shape as ARRAY |
KIND | (optional) is a scalar INTEGER constant expression that is a valid Integer kind number; |
BACK | (optional) is a scalar LOGICAL value. |
The result of the function is type INTEGER, or INTEGER(KIND) if KIND is present.
In the form without DIM, the result is a vector of length N, and is the location of the element of
ARRAY that is equal to VALUE; if MASK is present, only elements for which the corresponding
element of MASK are .TRUE. are considered.
As in MAXLOC and MINLOC, the location is reported with 1 for the first element in each dimension;
if no element equal to VALUE is found, the result is zero.
If BACK is present with the value .TRUE., the element found is the last one (in array element order);
otherwise, it is the first one.
In the form with DIM, the result has rank N−1 (thus scalar if ARRAY is a vector), the shape being that of ARRAY with dimension DIM removed, and each element of the result is the location of the (masked) element
in the dimension DIM vector that is equal to VALUE.
For example, if ARRAY is an Integer vector with value [ 10,20,30,40,50 ],
FINDLOC(ARRAY,30) will return the vector [ 3 ] and FINDLOC(ARRAY,7)
will return the vector [ 0 ].
ACOS, ASIN, ATAN, COSH,
SINH, TAN and TANH now accept arguments of type Complex.
Note that the hyperbolic and non-hyperbolic versions of these functions and the
new ACOSH, ASINH and ATANH functions are all related by
simple algebraic identities, for example the new COSH(X) is identical to
the old COS((0,1)*X) and the new SINH(X) is identical to the old
(0,-1)*SIN((0,1)*X).
ATAN now has an extra form ATAN(Y,X), with
exactly the same semantics as ATAN2(Y,X).
MAXLOC and MINLOC now have an additional
optional argument BACK following the KIND argument.
It is scalar and of type Logical; if present with the value .True., if
there is more than one element that has the maximum value (for MAXLOC)
or minimum value (for MINLOC), the array element index returned is for
the last element with that value rather than the first.
For example, the value of
MAXLOC( [ 5,1,5 ], BACK=.TRUE.)
is the array [ 3 ], rather than [ 1 ].
SELECTED_REAL_KIND now has a third argument
RADIX; this specifies the desired radix of the Real kind requested.
Note that the function IEEE_SELECTED_REAL_KIND in the intrinsic module
IEEE_ARITHMETIC also has this new third argument, and will allow
requesting IEEE decimal floating-point kinds if they become available in the
future.
ISO_C_BINDING additions [6.2]ISO_C_BINDING contains an additional
procedure as follows.
INTERFACE c_sizeof
PURE INTEGER(c_size_t) FUNCTION c_sizeof...(x) ! Specific name not visible
TYPE(*) :: x(..)
END FUNCTION
END INTERFACE
The actual argument x must be interoperable.
The result is the same as the C sizeof operator applied to the
conceptually corresponding C entity; that is, the size of x in
bytes.
If x is an array, it is the size of the whole array,
not just one element.
Note that x cannot be an assumed-size array.
ISO_FORTRAN_ENV additionsISO_FORTRAN_ENV contains additional named
constants as follows.
INT8, INT16, INT32, INT64,
REAL32, REAL64 and REAL128 supply the kind type
parameter values for integer and real kinds with the indicated bit sizes.
CHARACTER_KINDS,
INTEGER_KINDS, LOGICAL_KINDS and REAL_KINDS list the
available kind type parameter values for each type (in no particular order).
[6.1]
The standard intrinsic module ISO_FORTRAN_ENV contains two new
functions as follows.
COMPILER_VERSION.
This function is pure, has no arguments, and returns a scalar default character
string that identifies the version of the compiler that was used to compile the
source file.
This function may be used in a constant expression, e.g. to initialise a
variable or named constant with this information.
For example,
Module version_info
Use Iso_Fortran_Env
Character(Len(Compiler_Version())) :: compiler = Compiler_Version()
End Module
Program show_version_info
Use version_info
Print *,compiler
End Program
With release 6.1 of the NAG Fortran Compiler, this program will print something
like
NAG Fortran Compiler Release 6.1(Tozai) Build 6105
COMPILER_OPTIONS.
This function is pure, has no arguments, and returns a scalar default character
string that identifies the options supplied to the compiler when the source
file was compiled.
This function may be used in a constant expression, e.g. to initialise a
variable or named constant with this information.
For example,
Module options_info
Use Iso_Fortran_Env
Character(Len(Compiler_Options())) :: compiler = Compiler_Options()
End Module
Program show_options_info
Use options_info
Print *,compiler
End Program
If compiled with the options -C=array
-C=pointer -O, this program will print
something like
-C=array -C=pointer -O