Updated: 12 December 1998 |
Order Number: AA--PVXJB--TE
This manual documents the mathematics routines contained in the MTH$ facility of the OpenVMS Run-Time Library.
Revision/Update Information: This manual supersedes the OpenVMS VAX RTL Mathematics (MTH$) Manual, Version 5.5.
Software Version: OpenVMS VAX Version 7.1
Digital Equipment Corporation
Maynard, Massachusetts
Digital Equipment Corporation makes no representations that the use of its products in the manner described in this publication will not infringe on existing or future patent rights, nor do the descriptions contained in this publication imply the granting of licenses to make, use, or sell equipment or software in accordance with the description.
Possession, use, or copying of the software described in this publication is authorized only pursuant to a valid written license from Digital or an authorized sublicensor.
Digital conducts its business in a manner that conserves the environment and protects the safety and health of its employees, customers, and the community.
© Digital Equipment Corporation 1996. All rights reserved.
The following are trademarks of Digital Equipment Corporation: Bookreader, DECdirect, DECwindows, Digital, Digital FORTRAN, OpenVMS, OpenVMS Cluster, VAX, VAX Ada, VAX BASIC, VAX BLISS-32, VAX C, VAX COBOL, VAX CORAL, VAX DATATRIEVE, VAX DIBOL, VAX DOCUMENT, VAX DSM, VAX MACRO, VAX Pascal, VAX SCAN, VMS, and the DIGITAL logo.
The following are third-party trademarks:
BASIC is a registered trademark of the Trustees of Dartmouth College, D.B.A. Dartmouth College.
All other trademarks and registered trademarks are the property of their respective holders.
ZK6117
The OpenVMS documentation set is available on CD-ROM.
This document was prepared using VAX DOCUMENT, Version V3.2n.
Contents | Index |
This manual provides users of the OpenVMS operating system with detailed usage and reference information on mathematics routines supplied in the MTH$ facility of the Run-Time Library.
Run-Time Library routines can be used only in programs written in languages that produce native code for the VAX hardware. At present, these languages include VAX MACRO and the following compiled high-level languages:
Interpreted languages that can also access Run-Time Library routines include VAX DSM and VAX DATATRIEVE.
This manual is intended for system and application programmers who write programs that call MTH$ Run-Time Library routines.
This manual contains two tutorial chapters, two reference sections, and two appendixes:
The Run-Time Library routines are documented in a series of reference manuals. A description of how the Run-Time Library routines are accessed is presented in OpenVMS Programming Interfaces: Calling a System Routine. A description of OpenVMS features and functionality available through calls to the MTH$ Run-Time Library appears in OpenVMS Programming Concepts Manual. Descriptions of the other RTL facilities and their corresponding routines are presented in the following books:
Application programmers using any language can refer to the Guide to Creating OpenVMS Modular Procedures for writing modular and reentrant code.
High-level language programmers will find additional information on calling Run-Time Library routines in their language reference manuals. Additional information may also be found in the language user's guide provided with your OpenVMS language software.
For a complete list and description of the manuals in the OpenVMS documentation set, see the Overview of OpenVMS Documentation.
For additional information on the Open Systems Software Group (OSSG) products and services, access the Digital OpenVMS World Wide Web site. Use the following URL:
http://www.openvms.digital.com |
Digital welcomes your comments on this manual.
Print or edit the online form SYS$HELP:OPENVMSDOC_COMMENTS.TXT and send us your comments by:
Internet | openvmsdoc@zko.mts.dec.com |
Fax | 603 881-0120, Attention: OSSG Documentation, ZKO3-4/U08 |
OSSG Documentation Group, ZKO3-4/U08
110 Spit Brook Rd. Nashua, NH 03062-2698 |
Use the following table to order additional documentation or information. If you need help deciding which documentation best meets your needs, call 800-DIGITAL (800-344-4825).
The name of the OpenVMS AXP operating system has been changed to the OpenVMS Alpha operating system. Any references to OpenVMS AXP or AXP are synonymous with OpenVMS Alpha or Alpha.
VMScluster systems are now referred to as OpenVMS Cluster systems. Unless otherwise specified, references to OpenVMS Clusters or clusters in this document are synonymous with VMSclusters.
In this manual, every use of DECwindows and DECwindows Motif refers to DECwindows Motif for OpenVMS software.
The following conventions are also used in this manual:
Ctrl/ x | A sequence such as Ctrl/ x indicates that you must hold down the key labeled Ctrl while you press another key or a pointing device button. |
PF1
x or
GOLD x |
A sequence such as PF1
x or GOLD
x indicates that you must first press and release the key
labeled PF1 or GOLD and then press and release another key or a
pointing device button.
GOLD key sequences can also have a slash (/), dash (--), or underscore (_) as a delimiter in EVE commands. |
[Return] | In examples, a key name enclosed in a box indicates that you press a key on the keyboard. (In text, a key name is not enclosed in a box.) |
... |
Horizontal ellipsis points in examples indicate one of the following
possibilities:
|
.
. . |
Vertical ellipsis points indicate the omission of items from a code example or command format; the items are omitted because they are not important to the topic being discussed. |
( ) | In command format descriptions, parentheses indicate that, if you choose more than one option, you must enclose the choices in parentheses. |
[ ] | In command format descriptions, brackets indicate optional elements. You can choose one, none, or all of the options. (Brackets are not optional, however, in the syntax of a directory name in an OpenVMS file specification or in the syntax of a substring specification in an assignment statement.) |
{ } | In command format descriptions, braces indicate a required choice of options; you must choose one of the options listed. |
text style |
This text style represents the introduction of a new term or the name
of an argument, an attribute, or a reason.
This style is also used to show user input in Bookreader versions of the manual. |
italic text | Italic text indicates important information, complete titles of manuals, or variables. Variables include information that varies in system output (Internal error number), in command lines (/PRODUCER= name), and in command parameters in text (where device-name contains up to five alphanumeric characters). |
UPPERCASE TEXT | Uppercase text indicates a command, the name of a routine, the name of a file, or the abbreviation for a system privilege. |
Monospace type |
Monospace type indicates code examples and interactive screen displays.
In the C programming language, monospace type in text identifies the following elements: keywords, the names of independently compiled external functions and files, syntax summaries, and references to variables or identifiers introduced in an example. |
- | A hyphen at the end of a command format description, command line, or code line indicates that the command or statement continues on the following line. |
numbers | All numbers in text are assumed to be decimal unless otherwise noted. Nondecimal radixes---binary, octal, or hexadecimal---are explicitly indicated. |
The OpenVMS Run-Time Library Mathematics (MTH$) facility contains routines to perform a wide variety of computations including the following:
The OTS$ facility provides additional language-independent arithmetic support routines (see the OpenVMS RTL General Purpose (OTS$) Manual).
This chapter contains an introduction to the MTH$ facility and includes examples of how to call mathematics routines from BASIC, COBOL, Fortran, MACRO, Pascal, PL/I, and Ada.
Chapter 2 contains an overview of the vector routines available on VAX processors.
The Scalar MTH$ Reference Section describes the MTH$ scalar routines.
The Vector MTH$ Reference Section describes the MTH$ vector routines.
1.1 Entry Point Names
The names of the mathematics routines are formed by adding the MTH$ prefix to the function names.
When function arguments and returned values are of the same data type, the first letter of the name indicates this data type. When function arguments and returned values are of different data types, the first letter indicates the data type of the returned value, and the second letter indicates the data type of the arguments.
The letters used as data type prefixes are listed below.
Letter | Data Type |
---|---|
I | Word |
J | Longword |
D | D_floating |
G | G_floating |
H | H_floating |
C | F_floating complex |
CD | D_floating complex |
CG | G_floating complex |
Generally, F-floating data types have no letter designation. For
example, MTH$SIN returns an F-floating value of the sine of an
F-floating argument and MTH$DSIN returns a D-floating value of the sine
of a D-floating argument. However, in some of the miscellaneous
functions, F-floating data types are referenced by the letter
designation A.
1.2 Calling Conventions
For calling conventions specific to the MTH$ vector routines, refer to Chapter 2.
All calls to mathematics routines, as described in the Format section of each routine, accept arguments passed by reference. JSB entry points accept arguments passed by value.
All mathematics routines return values in R0 or R0/R1 except those routines for which the values cannot fit in 64 bits. D-floating complex, G-floating complex, and H-floating values are data structures which are larger than 64 bits. Routines returning values that cannot fit in registers R0/R1 return their function values into the first argument in the argument list.
The notation JSB MTH$NAME_Rn, where n is the highest register number referenced, indicates that an equivalent JSB entry point is available. Registers R0:Rn are not preserved.
Routines with JSB entry points accept a single argument in R0:Rm, where m, which is defined in the following table, is dependent on the data type.
Data Type | m |
---|---|
F_floating | 0 |
D_floating | 1 |
G_floating | 1 |
H_floating | 3 |
A routine returning one value returns it to registers R0:Rm.
When a routine returns two values (for example, MTH$SINCOS), the first value is returned in R0:Rm and the second value is returned in (R<m+1>:R<2*m+1>).
Note that for routines returning a single value, n>=m. For routines returning two values, n>=2*m + 1.
In general, CALL entry points for mathematics routines do the following:
JSB entry points execute in the context of the caller with the enable operations as set by the caller. Since the routines do not cause arithmetic traps or faults, their operation is not affected by the setting of the arithmetic trap enables, except as noted.
For more detailed information on CALL and JSB entry points, refer to
the OpenVMS Programming Interfaces: Calling a System Routine.
1.3 Algorithms
For those mathematics routines having corresponding algorithms, the
complete algorithm can be found in the Description section of the
routine description appearing in the Scalar MTH$ Reference Section of this manual.
1.4 Condition Handling
Error conditions are indicated by using the VAX signaling mechanism. The VAX signaling mechanism signals all conditions in mathematics routines as SEVERE by calling LIB$SIGNAL. When a SEVERE error is signaled, the default handler causes the image to exit after printing an error message. A user-established condition handler can be written to cause execution to continue at the point of the error by returning SS$_CONTINUE. A mathematics routine returns to its caller after the contents of R0/R1 have been restored from the mechanism argument vector CHF$L_MCH_SAVR0/R1. Thus, the user-established handler should correct CHF$L_MCH_SAVR0/R1 to the desired function value to be returned to the caller of the mathematics routine.
D-floating complex, G-floating complex, and H-floating values cannot be corrected with a user-established condition handler, because R2/R3 is not available in the mechanism argument vector.
Note that it is more reliable to correct R0 and R1 to resemble R0 and R1 of a double-precision floating-point value. A double-precision floating-point value correction works for both single- and double-precision values.
If the correction is not performed, the floating-point reserved operand --0.0 is returned. A floating-point reserved operand is a floating-point datum with a sign bit of 1 and a biased exponent of 0. Accessing the floating-point reserved operand will cause a reserved operand fault. See the OpenVMS RTL Library (LIB$) Manual for a complete description of how to write user condition handlers for SEVERE errors.
A few mathematics routines signal floating underflow if the calling program (JSB or CALL) has enabled floating underflow faults or traps.
All mathematics routines access input arguments and the real and
imaginary parts of complex numbers using floating-point instructions.
Therefore, a reserved operand fault can occur in any mathematics
routine.
1.5 Complex Numbers
A complex number y is defined as an ordered pair of real numbers r and i, where r is the real part and i is the imaginary part of the complex number.
y=(r,i) |
OpenVMS supports three floating-point complex types: F-floating complex, D-floating complex, and G-floating complex. There is no H-floating complex data type.
Run-Time Library mathematics routines that use complex arguments require a pointer to a structure containing two x-floating values to be passed by reference for each argument. The first x-floating value contains r, the real part of the complex number. The second x-floating value contains i, the imaginary part of the complex number. Similarly, Run-Time Library mathematics routines that return complex function values return two x-floating values. Some Language Independent Support (OTS$) routines also calculate complex functions.
Note that complex functions have no JSB entry points.
1.6 Mathematics Routines Not Documented in the MTH$ Reference Section
The mathematics routines in Table 1-1 are not found in the reference section of this manual. Instead, their entry points and argument information are listed in Appendix A of this manual.
A reserved operand fault can occur for any floating-point input argument in any mathematics routine. Other condition values signaled by each mathematics routine are indicated in the footnotes.
Entry Point | Function |
---|---|
Absolute Value Routines | |
MTH$ABS | F-floating absolute value |
MTH$DABS | D-floating absolute value |
MTH$GABS | G-floating absolute value |
MTH$HABS | H-floating absolute value 1 |
MTH$IIABS | Word absolute value 2 |
MTH$JIABS | Longword absolute value 2 |
Bitwise AND Operator Routines | |
MTH$IIAND | Bitwise AND of two word parameters |
MTH$JIAND | Bitwise AND of two longword parameters |
F-Floating Conversion Routines | |
MTH$DBLE | Convert F-floating to D-floating (exact) |
MTH$GDBLE | Convert F-floating to G-floating (exact) |
MTH$IIFIX | Convert F-floating to word (truncated) 2 |
MTH$JIFIX | Convert F-floating to longword (truncated) 2 |
Floating-Point Positive Difference Routines | |
MTH$DIM | Positive difference of two F-floating parameters 3 |
MTH$DDIM | Positive difference of two D-floating parameters 3 |
MTH$GDIM | Positive difference of two G-floating parameters 3 |
MTH$HDIM | Positive difference of two H-floating parameters 1,3 |
MTH$IIDIM | Positive difference of two word parameters 2 |
MTH$JIDIM | Positive difference of two longword parameters 2 |
Bitwise Exclusive OR Operator Routines | |
MTH$IIEOR | Bitwise exclusive OR of two word parameters |
MTH$JIEOR | Bitwise exclusive OR of two longword parameters |
Integer to Floating-Point Conversion Routines | |
MTH$FLOATI | Convert word to F-floating (exact) |
MTH$DFLOTI | Convert word to D-floating (exact) |
MTH$GFLOTI | Convert word to G-floating (exact) |
MTH$FLOATJ | Convert longword to F-floating (rounded) |
MTH$DFLOTJ | Convert longword to D-floating (exact) |
MTH$GFLOTJ | Convert longword to G-floating (exact) |
Conversion to Greatest Floating-Point Integer Routines | |
MTH$FLOOR | Convert F-floating to greatest F-floating integer |
MTH$DFLOOR | Convert D-floating to greatest D-floating integer |
MTH$GFLOOR | Convert G-floating to greatest G-floating integer |
MTH$HFLOOR | Convert H-floating to greatest H-floating integer 1 |
Floating-Point Truncation Routines | |
MTH$AINT | Convert F-floating to truncated F-floating |
MTH$IINT | Convert F-floating to truncated word 2 |
MTH$JINT | Convert F-floating to truncated longword 2 |
MTH$DINT | Convert D-floating to truncated D-floating |
MTH$IIDINT | Convert D-floating to truncated word 2 |
MTH$JIDINT | Convert D-floating to truncated longword 2 |
MTH$GINT | Convert G-floating to truncated G-floating |
MTH$IIGINT | Convert G-floating to truncated word 2 |
MTH$JIGINT | Convert G-floating to truncated longword 2 |
MTH$HINT | Convert H-floating to truncated H-floating 1 |
MTH$IIHINT | Convert H-floating to truncated word 2 |
MTH$JIHINT | Convert H-floating to truncated longword 2 |
Bitwise Inclusive OR Operator Routines | |
MTH$IIOR | Bitwise inclusive OR of two word parameters |
MTH$JIOR | Bitwise inclusive OR of two longword parameters |
Maximum Value Routines | |
MTH$AIMAX0 | F-floating maximum of n word parameters |
MTH$AJMAX0 | F-floating maximum of n longword parameters |
MTH$IMAX0 | Word maximum of n word parameters |
MTH$JMAX0 | Longword maximum of n longword parameters |
MTH$AMAX1 | F-floating maximum of n F-floating parameters |
MTH$DMAX1 | D-floating maximum of n D-floating parameters |
MTH$GMAX1 | G-floating maximum of n G-floating parameters |
MTH$HMAX1 | H-floating maximum of n H-floating parameters 1 |
MTH$IMAX1 | Word maximum of n F-floating parameters 2 |
MTH$JMAX1 | Longword maximum of n F-floating parameters 2 |
Minimum Value Routines | |
MTH$AIMIN0 | F-floating minimum of n word parameters |
MTH$AJMIN0 | F-floating minimum of n longword parameters |
MTH$IMIN0 | Word minimum of n word parameters |
MTH$JMIN0 | Longword minimum of n longword parameters |
MTH$AMIN1 | F-floating minimum of n F-floating parameters |
MTH$DMIN1 | D-floating minimum of n D-floating parameters |
MTH$GMIN1 | G-floating minimum of n G-floating parameters |
MTH$HMIN1 | H-floating minimum of n H-floating parameters 1 |
MTH$IMIN1 | Word minimum of n F-floating parameters 2 |
MTH$JMIN1 | Longword minimum of n F-floating parameters 2 |
Remainder Routines | |
MTH$AMOD | Remainder of two F-floating parameters, arg1/arg2 3,6 |
MTH$DMOD | Remainder of two D-floating parameters, arg1/arg2 3,6 |
MTH$GMOD | Remainder of two G-floating parameters, arg1/arg2 3 |
MTH$HMOD | Remainder of two H-floating parameters, arg1/arg2 1,3 |
MTH$IMOD | Remainder of two word parameters, arg1/arg2 5 |
MTH$JMOD | Remainder of two longword parameters, arg1/arg2 5 |
Floating-Point Conversion to Nearest Value Routines | |
MTH$ANINT | Convert F-floating to nearest F-floating integer |
MTH$ININT | Convert F-floating to nearest word integer 2 |
MTH$JNINT | Convert F-floating to nearest longword integer 2 |
MTH$DNINT | Convert D-floating to nearest D-floating integer |
MTH$IIDNNT | Convert D-floating to nearest word integer 2 |
MTH$JIDNNT | Convert D-floating to nearest longword integer 2 |
MTH$GNINT | Convert G-floating to nearest G-floating integer |
MTH$IIGNNT | Convert G-floating to nearest word integer 2 |
MTH$JIGNNT | Convert G-floating to nearest longword integer 2 |
MTH$HNINT | Convert H-floating to nearest H-floating integer 1 |
MTH$IIHNNT | Convert H-floating to nearest word integer 2 |
MTH$JIHNNT | Convert H-floating to nearest longword integer 2 |
Bitwise Complement Operator Routines | |
MTH$INOT | Bitwise complement of word parameter |
MTH$JNOT | Bitwise complement of longword parameter |
Floating-Point Multiplication Routines | |
MTH$DPROD | D-floating product of two F-floating parameters 3 |
MTH$GPROD | G-floating product of two F-floating parameters |
Bitwise Shift Operator Routines | |
MTH$IISHFT | Bitwise shift of word |
MTH$JISHFT | Bitwise shift of longword |
Floating-Point Sign Function Routines | |
MTH$SGN | F- or D-floating sign function |
MTH$SIGN | F-floating transfer of sign of y to sign of x |
MTH$DSIGN | D-floating transfer of sign of y to sign of x |
MTH$GSIGN | G-floating transfer of sign of y to sign of x |
MTH$HSIGN | H-floating transfer of sign of y to sign of x 1 |
MTH$IISIGN | Word transfer of sign of y to sign of x |
MTH$JISIGN | Longword transfer of sign of y to sign of x |
Conversion of Double to Single Floating-Point Routines | |
MTH$SNGL | Convert D-floating to F-floating (rounded) 3 |
MTH$SNGLG |
Convert G-floating to F-floating (rounded)
3,4
|
Next | Contents | Index |
Copyright © Compaq Computer Corporation 1998. All rights reserved. Legal |
6117PRO.HTML
|