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HP OpenVMS RTL General Purpose (OTS$) Manual
OTS$POWHJ_R3 (VAX Only)
On VAX systems, the Raise an H-Floating Base to a Longword Exponent
routine raises an H-floating base to a longword exponent.
Format
OTS$POWHJ_R3 H-floating-point-base ,longword-integer-exponent
RETURNS
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by value |
Result of raising an H-floating base to a longword exponent.
Arguments
H-floating-point-base
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by value |
Base. The H-floating-point-base argument is an
H-floating number containing the base.
longword-integer-exponent
| OpenVMS usage: |
longword_signed |
| type: |
longword (signed) |
| access: |
read only |
| mechanism: |
by value |
Exponent. The longword-integer-exponent argument is a
signed longword that contains the signed longword exponent.
Description
OTS$POWHJ_R3 raises an H-floating base to a longword exponent.
The internal calculations and the floating-point result have the same
precision as the base value.
The floating-point result is as follows:
| Base |
Exponent |
Result |
|
Any
|
> 0
|
Product of (
base**2
i
), where
i is each nonzero bit position in
longword-integer-exponent.
|
|
> 0
|
= 0
|
1.0
|
|
= 0
|
= 0
|
Undefined exponentiation.
|
|
< 0
|
= 0
|
1.0
|
|
> 0
|
< 0
|
1.0/(
base**2
i
), where
i is each nonzero bit position in
longword-integer-exponent.
|
|
= 0
|
< 0
|
Undefined exponentiation.
|
|
< 0
|
< 0
|
1.0/(
base**2
i
), where
i is each nonzero bit position in
longword-integer-exponent.
|
Floating-point overflow can occur.
Undefined exponentiation occurs if the base is zero and the exponent is
zero or negative.
Condition Values Signaled
|
SS$_FLTOVF
|
Arithmetic trap. This error is signaled by the hardware if a
floating-point overflow occurs.
|
|
MTH$_FLOOVEMAT
|
Floating-point overflow in math library.
|
|
MTH$_FLOUNDMAT
|
Floating-point underflow in math library.
|
|
MTH$_UNDEXP
|
Undefined exponentiation. This error is signaled if
H-floating-point-base is zero and
longword-integer-exponent is zero or negative, or if
the
H-floating-point-base is negative.
|
OTS$POWII
The Raise a Word Base to a Word Exponent routine raises a word base to
a word exponent.
Format
OTS$POWII word-integer-base ,word-integer-exponent
RETURNS
| OpenVMS usage: |
word_signed |
| type: |
word (signed) |
| access: |
write only |
| mechanism: |
by value |
Result of raising a word base to a word exponent.
Arguments
word-integer-base
| OpenVMS usage: |
word_signed |
| type: |
word (signed) |
| access: |
read only |
| mechanism: |
by value |
Base. The word-integer-base argument is a signed word
containing the base.
word-integer-exponent
| OpenVMS usage: |
word_signed |
| type: |
word (signed) |
| access: |
read only |
| mechanism: |
by value |
Exponent. The word-integer-exponent argument is a
signed word containing the exponent.
Description
The OTS$POWII routine raises a word base to a word exponent.
On Alpha and I64 systems, some restrictions apply when linking
OTS$POWII. See Chapter 1 for more information about these
restrictions.
Condition Values Signaled
|
SS$_FLTDIV
|
Arithmetic trap. This error is signaled by the hardware if a
floating-point division by zero occurs.
|
|
SS$_FLTOVF
|
Arithmetic trap. This error is signaled by the hardware if a
floating-point overflow occurs.
|
|
MTH$_UNDEXP
|
Undefined exponentiation. This error is signaled if
word-integer-base is zero and
word-integer-exponent is zero or negative, or if
word-integer-base is negative.
|
OTS$POWJJ
The Raise a Longword Base to a Longword Exponent routine raises a
signed longword base to a signed longword exponent.
Format
OTS$POWJJ longword-integer-base ,longword-integer-exponent
RETURNS
| OpenVMS usage: |
longword_signed |
| type: |
longword (signed) |
| access: |
write only |
| mechanism: |
by value |
Result of raising a signed longword base to a signed longword exponent.
Arguments
longword-integer-base
| OpenVMS usage: |
longword_signed |
| type: |
longword (signed) |
| access: |
read only |
| mechanism: |
by value |
Base. The longword-integer-base argument is a signed
longword containing the base.
longword-integer-exponent
| OpenVMS usage: |
longword_signed |
| type: |
longword (signed) |
| access: |
read only |
| mechanism: |
by value |
Exponent. The longword-integer-exponent argument is a
signed longword containing the exponent.
Description
The OTS$POWJJ routine raises a signed longword base to a signed
longword exponent.
On Alpha and I64 systems, some restrictions apply when linking
OTS$POWJJ. See Chapter 1 for more information about these
restrictions.
Condition Values Signaled
|
SS$_FLTDIV
|
Arithmetic trap. This error is signaled by the hardware if a
floating-point division by zero occurs.
|
|
SS$_FLTOVF
|
Arithmetic trap. This error is signaled by the hardware if a
floating-point overflow occurs.
|
|
MTH$_UNDEXP
|
Undefined exponentiation. This error is signaled if
longword-integer-base is zero and
longword-integer-exponent is zero or negative, or if
longword-integer-base is negative.
|
OTS$POWLULU
The Raise an Unsigned Longword Base to an Unsigned Longword Exponent
routine raises an unsigned longword integer base to an unsigned
longword integer exponent.
Format
OTS$POWLULU unsigned-lword-int-base, unsigned-lword-int-exponent
RETURNS
| OpenVMS usage: |
longword_unsigned |
| type: |
longword (unsigned) |
| access: |
write only |
| mechanism: |
by value |
Result of raising an unsigned longword integer base to an unsigned
longword integer exponent.
Arguments
unsigned-lword-int-base
| OpenVMS usage: |
longword_unsigned |
| type: |
longword (unsigned) |
| access: |
read only |
| mechanism: |
by value |
Unsigned longword integer base. The
unsigned-lword-int-base argument contains the value of
the integer base.
unsigned-lword-int-exponent
| OpenVMS usage: |
longword_unsigned |
| type: |
longword (unsigned) |
| access: |
read only |
| mechanism: |
by value |
Unsigned longword integer exponent. The
unsigned-lword-int-exponent argument contains the
value of the integer exponent.
Description
OTS$POWLULU returns the unsigned longword integer result of raising an
unsigned longword integer base to an unsigned longword integer
exponent. Note that overflow cannot occur in this routine. If the
result or intermediate result is greater than 32 bits, the low-order 32
bits are used.
On Alpha and I64 systems, some restrictions apply when linking
OTS$POWLULU. See Chapter 1 for more information about these
restrictions.
Condition Values Signaled
|
MTH$_UNDEXP
|
Both the base and exponent values are zero.
|
OTS$POWRD
The Raise an F-Floating Base to a D-Floating Exponent routine raises an
F-floating base to a D-floating exponent.
Format
OTS$POWRD F-floating-point-base ,D-floating-point-exponent
RETURNS
| OpenVMS usage: |
floating_point |
| type: |
D_floating |
| access: |
write only |
| mechanism: |
by value |
Result of raising an F-floating base to a D-floating exponent.
Arguments
F-floating-point-base
| OpenVMS usage: |
floating_point |
| type: |
F_floating |
| access: |
read only |
| mechanism: |
by value |
Base. The F-floating-point-base argument is an
F-floating number containing the base.
D-floating-point-exponent
| OpenVMS usage: |
floating_point |
| type: |
D_floating |
| access: |
read only |
| mechanism: |
by value |
Exponent. The D-floating-point-exponent argument is a
D-floating number that contains the exponent.
Description
OTS$POWRD raises an F-floating base to a D-floating exponent.
The internal calculations and the floating-point result have the same
precision as the base value.
OTS$POWRD first converts the F-floating base to D-floating. The
D-floating result for OTS$POWRD is as follows:
| Base |
Exponent |
Result |
|
= 0
|
> 0
|
0.0
|
|
= 0
|
= 0
|
Undefined exponentiation
|
|
= 0
|
< 0
|
Undefined exponentiation
|
|
< 0
|
Any
|
Undefined exponentiation
|
|
> 0
|
> 0
|
2
[
exponent*LOG2(
base)]
|
|
> 0
|
= 0
|
1.0
|
|
> 0
|
< 0
|
2
[
exponent*LOG2(
base)]
|
Floating-point overflow can occur.
Undefined exponentiation occurs if the base is zero and the exponent is
zero or negative, or if the base is negative.
Condition Values Signaled
|
SS$_FLTOVF
|
Arithmetic trap. This error is signaled by the hardware if a
floating-point overflow occurs.
|
|
MTH$_FLOOVEMAT
|
Floating-point overflow in math library.
|
|
MTH$_FLOUNDMAT
|
Floating-point underflow in math library.
|
|
MTH$_UNDEXP
|
Undefined exponentiation. This error is signaled if
F-floating-point-base is zero and
D-floating-point-exponent is zero or negative, or if
F-floating-point-base is negative.
|
Example
|
C+
C This Fortran example uses OTS$POWRD, to raise an F-floating point
C base to a D-floating point exponent. The result is a D-floating value.
C-
REAL*4 X
REAL*8 Y,RESULT,OTS$POWRD
INTEGER M(2)
EQUIVALENCE (M(1),Y)
X = 9768.0
Y = 9.0
C+
C The arguments of OTS$POWRD are passed by value.
C-
RESULT = OTS$POWRD(%VAL(X),%VAL(M(1)),%VAL(M(2)))
TYPE *,' 9768.0**9.0 IS ',RESULT
X = 7689.0
Y = -0.587436654545
C+
C In Fortran, OTS$POWRD is indirectly called by the exponentiation operator.
C-
RESULT = X**Y
TYPE *,' 7689.0**-0.587436654545 IS ',RESULT
END
|
This Fortran example uses OTS$POWRD to raise an F-floating base to a
D-floating exponent. Notice the difference in the precision of the
result produced by this routine in comparison to the result produced by
OTS$POWRR. The output generated by this program is as follows:
9768.0**9.0 IS 8.0956338648832908E+35
7689.0**-0.587436654545 IS 5.2155199252836588E-03
|
OTS$POWRJ
The Raise an F-Floating Base to a Longword Exponent routine raises an
F-floating base to a longword exponent.
Format
OTS$POWRJ F-floating-point-base ,longword-integer-exponent
RETURNS
| OpenVMS usage: |
floating_point |
| type: |
F_floating |
| access: |
write only |
| mechanism: |
by value |
Result of raising an F-floating base to a longword exponent.
Arguments
F-floating-point-base
| OpenVMS usage: |
floating_point |
| type: |
F_floating |
| access: |
read only |
| mechanism: |
by value |
Base. The F-floating-point-base argument is an
F-floating number containing the base.
longword-integer-exponent
| OpenVMS usage: |
longword_signed |
| type: |
longword (signed) |
| access: |
read only |
| mechanism: |
by value |
Exponent. The longword-integer-exponent argument is a
signed longword that contains the longword exponent.
Description
OTS$POWRJ raises an F-floating base to a longword exponent.
The internal calculations and the floating-point result have the same
precision as the base value.
The floating-point result is as follows:
| Base |
Exponent |
Result |
|
Any
|
> 0
|
Product of (
base**2
i
), where
i is each nonzero bit position in
longword-integer-exponent.
|
|
> 0
|
= 0
|
1.0
|
|
= 0
|
= 0
|
Undefined exponentiation.
|
|
< 0
|
= 0
|
1.0
|
|
> 0
|
< 0
|
1.0/(
base**2
i
), where
i is each nonzero bit position in
longword-integer-exponent.
|
|
= 0
|
< 0
|
Undefined exponentiation.
|
|
< 0
|
< 0
|
1.0/(
base**2
i
), where
i is each nonzero bit position in
longword-integer-exponent.
|
Floating-point overflow can occur.
Undefined exponentiation occurs if the base is zero and the exponent is
zero or negative.
On Alpha and I64 systems, some restrictions apply when linking
OTS$POWRJ. See Chapter 1 for more information about these
restrictions.
Condition Values Signaled
|
SS$_FLTOVF
|
Arithmetic trap. This error is signaled by the hardware if a
floating-point overflow occurs.
|
|
MTH$_FLOOVEMAT
|
Floating-point overflow in math library.
|
|
MTH$_FLOUNDMAT
|
Floating-point underflow in math library.
|
|
MTH$_UNDEXP
|
Undefined exponentiation. This error is signaled if
F-floating-point-base is zero and
longword-integer-exponent is zero or negative, or if
F-floating-point-base is negative.
|
OTS$POWRR
The Raise an F-Floating Base to an F-Floating Exponent routine raises
an F-floating base to an F-floating exponent.
Format
OTS$POWRR F-floating-point-base ,F-floating-point-exponent
RETURNS
| OpenVMS usage: |
floating_point |
| type: |
F_floating |
| access: |
write only |
| mechanism: |
by value |
Result of raising an F-floating base to an F-floating exponent.
Arguments
F-floating-point-base
| OpenVMS usage: |
floating_point |
| type: |
F_floating |
| access: |
read only |
| mechanism: |
by value |
Base. The F-floating-point-base argument is an
F-floating number containing the base.
F-floating-point-exponent
| OpenVMS usage: |
floating_point |
| type: |
F_floating |
| access: |
read only |
| mechanism: |
by value |
Exponent. The F-floating-point-exponent argument is an
F-floating number that contains the exponent.
Description
OTS$POWRR raises an F-floating base to an F-floating exponent.
The internal calculations and the floating-point result have the same
precision as the base value.
The F-floating result for OTS$POWRR is as follows:
| Base |
Exponent |
Result |
|
= 0
|
> 0
|
0.0
|
|
= 0
|
= 0
|
Undefined exponentiation
|
|
= 0
|
< 0
|
Undefined exponentiation
|
|
< 0
|
Any
|
Undefined exponentiation
|
|
> 0
|
> 0
|
2
[
exponent*log2(
base)]
|
|
> 0
|
= 0
|
1.0
|
|
> 0
|
< 0
|
2
[
exponent*log2(
base)]
|
Floating-point overflow can occur.
Undefined exponentiation occurs if the base is zero and the exponent is
zero or negative, or if the base is negative.
On Alpha and i64 systems, some restrictions apply when linking
OTS$POWRR. See Chapter 1 for more information about these
restrictions.
Condition Values Signaled
|
SS$_FLTOVF
|
Arithmetic trap. This error is signaled by the hardware if a
floating-point overflow occurs.
|
|
MTH$_FLOOVEMAT
|
Floating-point overflow in math library.
|
|
MTH$_FLOUNDMAT
|
Floating-point underflow in math library.
|
|
MTH$_UNDEXP
|
Undefined exponentiation. This error is signaled if
F-floating-point-base is zero and
F-floating-point-exponent is zero or negative, or if
F-floating-point-base is negative.
|
Example
|
C+
C This Fortran example demonstrates the use
C of OTS$POWRR, which raises an F-floating
C point base to an F-floating point power.
C-
REAL*4 X,Y,RESULT,OTS$POWRR
X = 8.0
Y = 2.0
C+
C The arguments of OTS$POWRR are passed by value.
C-
RESULT = OTS$POWRR(%VAL(X),%VAL(Y))
TYPE *,' 8.0**2.0 IS ',RESULT
X = 9.0
Y = -0.5
C+
C In Fortran, OTS$POWRR is indirectly called by simply
C using the exponentiation operator.
C-
RESULT = X**Y
TYPE *,' 9.0**-0.5 IS ',RESULT
END
|
This Fortran example uses OTS$POWRR to raise an F-floating point base
to an F-floating point exponent. The output generated by this program
is as follows:
8.0**2.0 IS 64.00000
9.0**-0.5 IS 0.3333333
|
|
