HP OpenVMS RTL General Purpose (OTS$) Manual

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OTS$POWDD

The Raise a D-Floating Base to a D-Floating Exponent routine raises a D-floating base to a D-floating exponent.

Format

OTS$POWDD D-floating-point-base ,D-floating-point-exponent

RETURNS

OpenVMS usage: floating_point

type: D_floating

access: write only

mechanism: by value

Result of raising a D-floating base to a D-floating exponent.

Arguments

D-floating-point-base

OpenVMS usage: floating_point

type: D_floating

access: read only

mechanism: by value

Base. The D-floating-point-base argument is a D-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$POWDD raises a D-floating base to a D-floating exponent.
The internal calculations and the floating-point result have the same precision as the base value.
The D-floating result for OTS$POWDD is given by the following:

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

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 D-floating-point-base is zero and D-floating-point-exponent is zero or negative, or if the D-floating-point-base is negative.

OTS$POWDJ

The Raise a D-Floating Base to a Longword Exponent routine raises a D-floating base to a longword exponent.

Format

OTS$POWDJ D-floating-point-base ,longword-integer-exponent

RETURNS

OpenVMS usage: floating_point

type: D_floating

access: write only

mechanism: by value

Result of raising a D-floating base to a longword exponent.

Arguments

D-floating-point-base

OpenVMS usage: floating_point

type: D_floating

access: read only

mechanism: by value

Base. The D-floating-point-base argument is a D-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 integer exponent.

Description

OTS$POWDJ raises a D-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 D-floating-point-base is zero and longword-integer-exponent is zero or negative, or if the D-floating-point-base is negative.

OTS$POWDR

The Raise a D-Floating Base to an F-Floating Exponent routine raises a D-floating base to an F-floating exponent.

Format

OTS$POWDR D-floating-point-base ,F-floating-point-exponent

RETURNS

OpenVMS usage: floating_point

type: D_floating

access: write only

mechanism: by value

Result of raising a D-floating base to an F-floating exponent.

Arguments

D-floating-point-base

OpenVMS usage: floating_point

type: D_floating

access: read only

mechanism: by value

Base. The D-floating-point-base argument is a D-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$POWDR raises a D-floating base to an F-floating exponent.
The internal calculations and the floating-point result have the same precision as the base value.
OTS$POWDR converts the F-floating exponent to a D-floating number. The D-floating result for OTS$POWDR is given by the following:

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 D-floating-point-base is zero and F-floating-point-exponent is zero or negative, or if the D-floating-point-base is negative.

OTS$POWGG

The Raise a G-Floating Base to a G-Floating Exponent routine raises a G-floating base to a G-floating exponent.

Format

OTS$POWGG G-floating-point-base ,G-floating-point-exponent

RETURNS

OpenVMS usage: floating_point

type: G_floating

access: write only

mechanism: by value

Result of raising a G-floating base to a G-floating exponent.

Arguments

G-floating-point-base

OpenVMS usage: floating_point

type: G_floating

access: read only

mechanism: by value

Base that OTS$POWGG raises to a G-floating exponent. The G-floating-point-base argument is a G-floating number containing the base.
G-floating-point-exponent

OpenVMS usage: floating_point

type: G_floating

access: read only

mechanism: by value

Exponent to which OTS$POWGG raises the base. The G-floating-point-exponent argument is a G-floating number containing the exponent.

Description

OTS$POWGG raises a G-floating base to a G-floating exponent.
The internal calculations and the floating-point result have the same precision as the base value.
The G-floating result for OTS$POWGG 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$POWGG. 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 exponent. This error is signaled if G-floating-point-base is zero and G-floating-point-exponent is zero or negative, or if G-floating-point-base is negative.

Example


C+ C This example demonstrates the use of OTS$POWGG, C which raises a G-floating point base C to a G-floating point power. C- REAL8 X,Y,RESULT,OTS$POWGG C+ C The arguments of OTS$POWGG are passed by value. Fortran can C only pass INTEGER and REAL4 expressions as VALUE. Since C INTEGER and REAL4 values are one longword long, while REAL8 C values are two longwords long, equate the base (and power) to C two-dimensional INTEGER vectors. These vectors will be passed C by VALUE. C- INTEGER N(2),M(2) EQUIVALENCE (N(1),X), (M(1),Y) X = 8.0 Y = 2.0 C+ C To pass X by value, pass N(1) and N(2) by value. Similarly for Y. C- RESULT = OTS$POWGG(%VAL(N(1)),%VAL(N(2)),%VAL(M(1)),%VAL(M(2))) TYPE ,' 8.02.0 IS ',RESULT X = 9.0 Y = -0.5 C+ C In Fortran, OTS$POWWGG is indirectly called by simply using the C exponentiation operator. C- RESULT = XY TYPE ,' 9.0**-0.5 IS ',RESULT END

C+ 
C   This example demonstrates the use of OTS$POWGG, 
C   which raises a G-floating point base 
C   to a G-floating point power. 
C- 
        REAL*8 X,Y,RESULT,OTS$POWGG 
C+ 
C   The arguments of OTS$POWGG are passed by value. Fortran can 
C   only pass INTEGER and REAL*4 expressions as VALUE. Since 
C   INTEGER and REAL*4 values are one longword long, while REAL*8 
C   values are two longwords long, equate the base (and power) to 
C   two-dimensional INTEGER vectors. These vectors will be passed 
C   by VALUE. 
C- 
        INTEGER N(2),M(2) 
        EQUIVALENCE (N(1),X), (M(1),Y) 
        X = 8.0 
        Y = 2.0 
C+ 
C  To pass X by value, pass N(1) and N(2) by value. Similarly for Y. 
C- 
        RESULT = OTS$POWGG(%VAL(N(1)),%VAL(N(2)),%VAL(M(1)),%VAL(M(2))) 
        TYPE *,' 8.0**2.0 IS ',RESULT 
        X = 9.0 
        Y = -0.5 
C+ 
C   In Fortran, OTS$POWWGG is indirectly called by simply using the 
C   exponentiation operator. 
C- 
        RESULT = X**Y 
        TYPE *,' 9.0**-0.5 IS ',RESULT 
        END

This Fortran example uses OTS$POWGG to raise a G-floating base to a G-floating exponent.
The output generated by this example is as follows:
8.0**2.0 IS 64.0000000000000 9.0**-0.5 IS 0.333333333333333

OTS$POWGJ

The Raise a G-Floating Base to a Longword Exponent routine raises a G-floating base to a longword exponent.

Format

OTS$POWGJ G-floating-point-base ,longword-integer-exponent

RETURNS

OpenVMS usage: floating_point

type: G_floating

access: write only

mechanism: by value

Result of raising a G-floating base to a longword exponent.

Arguments

G-floating-point-base

OpenVMS usage: floating_point

type: G_floating

access: read only

mechanism: by value

Base that OTS$POWGJ raises to a longword exponent. The G-floating-point-base argument is a G-floating number containing the base.
longword-integer-exponent

OpenVMS usage: longword_signed

type: longword (signed)

access: read only

mechanism: by value

Exponent to which OTS$POWGJ raises the base. The longword-integer-exponent argument is a signed longword containing the exponent.

Description

OTS$POWGJ raises a G-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$POWGJ. 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 exponent. This error is signaled if G-floating-point-base is zero and longword-integer-exponent is zero or negative, or if G-floating-point-base is negative.

OTS$POWHH_R3 (VAX Only)

On VAX systems, the Raise an H-Floating Base to an H-Floating Exponent routine raises an H-floating base to an H-floating exponent.

Format

OTS$POWHH_R3 H-floating-point-base ,H-floating-point-exponent

RETURNS

OpenVMS usage: floating_point

type: H_floating

access: write only

mechanism: by value

Result of raising an H-floating base to an H-floating 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.
H-floating-point-exponent

OpenVMS usage: floating_point

type: H_floating

access: read only

mechanism: by value

Exponent. The H-floating-point-exponent argument is an H-floating number that contains the H-floating exponent.

Description

OTS$POWHH_R3 raises an H-floating base to an H-floating exponent.
The internal calculations and the floating-point result have the same precision as the base value.
The H-floating result for OTS$POWHH_R3 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 H-floating-point-base is zero and H-floating-point-exponent is zero or negative, or if the H-floating-point-base is negative.

Example


C+ C Example of OTS$POWHH, which raises an H_floating C point base to an H_floating point power. In Fortran, C it is not directly called. C- REAL16 X,Y,RESULT X = 9877356535.0 Y = -0.5837653 C+ C In Fortran, OTS$POWWHH is indirectly called by simply using the C exponentiation operator. C- RESULT = XY TYPE ,' 9877356535.0**-0.5837653 IS ',RESULT END

C+ 
C Example of OTS$POWHH, which raises an H_floating 
C point base to an H_floating point power. In Fortran, 
C it is not directly called. 
C- 
        REAL*16 X,Y,RESULT 
        X = 9877356535.0 
        Y = -0.5837653 
C+ 
C In Fortran, OTS$POWWHH is indirectly called by simply using the 
C exponentiation operator. 
C- 
        RESULT = X**Y 
        TYPE *,' 9877356535.0**-0.5837653 IS ',RESULT 
        END

This Fortran example demonstrates how to call OTS$POWHH_R3 to raise an H-floating base to an H-floating power.
The output generated by this program is as follows:
9877356535.0**-0.5837653 IS 1.463779145994628357482343598205427E-0006

Contents

Index

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

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 D-floating-point-base is zero and D-floating-point-exponent is zero or negative, or if the D-floating-point-base is negative.

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 D-floating-point-base is zero and longword-integer-exponent is zero or negative, or if the D-floating-point-base is negative.