OpenVMS RTL General Purpose (OTS$) Manual

Document revision date: 19 July 1999

OpenVMS RTL General Purpose (OTS$) Manual

Contents

Index

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.

Base	Exponent	Result
Any	> 0	Product of ( base2 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/( base2 ⁱ ), where i is each nonzero bit position in longword-integer-exponent**.
= 0	< 0	Undefined exponentiation.
< 0	< 0	1.0/( base2 ⁱ ), where i is each nonzero bit position in longword-integer-exponent**.

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$POWII routine raises a word base to a word exponent.
On Alpha systems, some restrictions apply when linking OTS$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$POWJJ routine raises a signed longword base to a signed longword exponent.
On Alpha systems, some restrictions apply when linking OTS$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$POWLULU returns the unsigned longword integer result of raising an unsigned longword integer base to an unsigned longword integer exponent. Note that overflow cannot occur in this routine. If the result or intermediate result is greater than 32 bits, the low-order 32 bits are used.
On Alpha systems, some restrictions apply when linking OTS$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.

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)]}

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$POWRD, to raise an F-floating point C base to a D-floating point exponent. The result is a D-floating value. C- REAL4 X REAL8 Y,RESULT,OTS$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 ,' 9768.09.0 IS ',RESULT X = 7689.0 Y = -0.587436654545 C+ C In Fortran, OTS$POWRD is indirectly called by the exponentiation operator. C- RESULT = XY TYPE ,' 7689.0**-0.587436654545 IS ',RESULT END

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 systems, some restrictions apply when linking OTS$POWRJ. See Chapter 1 for more information about these restrictions.

Base	Exponent	Result
Any	> 0	Product of ( base2 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/( base2 ⁱ ), where i is each nonzero bit position in longword-integer-exponent**.
= 0	< 0	Undefined exponentiation.
< 0	< 0	1.0/( base2 ⁱ ), where i is each nonzero bit position in longword-integer-exponent**.

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 systems, some restrictions apply when linking OTS$POWRR. See Chapter 1 for more information about these restrictions.

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)]}

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$POWRR, which raises an F-floating C point base to an F-floating point power. C- REAL4 X,Y,RESULT,OTS$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 ,' 8.02.0 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 = XY TYPE ,' 9.0*-0.5 IS ',RESULT END

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

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OpenVMS usage:	floating_point
type:	H_floating
access:	write only
mechanism:	by value

OpenVMS usage:	longword_signed
type:	longword (signed)
access:	read only
mechanism:	by value

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.

OpenVMS usage:	word_signed
type:	word (signed)
access:	write only
mechanism:	by value

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.

OpenVMS usage:	longword_unsigned
type:	longword (unsigned)
access:	write only
mechanism:	by value