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Updated:
11 December 1998
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OpenVMS RTL General Purpose (OTS$) Manual
OTS$DIVCx
The Complex Division routines return a complex result of a division on
complex numbers.
Format
OTS$DIVC complex-dividend ,complex-divisor
OTS$DIVCD_R3 complex-dividend ,complex-divisor (VAX only)
OTS$DIVCG_R3 complex-dividend ,complex-divisor
Each of these three formats corresponds to one of the three
floating-point complex types.
RETURNS
OpenVMS usage: |
complex_number |
type: |
F_floating complex, D_floating complex, G_floating
complex |
access: |
write only |
mechanism: |
by value |
Complex result of complex division. OTS$DIVC returns an F-floating
complex number. OTS$DIVCD_R3 returns a D-floating complex number.
OTS$DIVCG_R3 returns a G-floating complex number.
Arguments
complex-dividend
OpenVMS usage: |
complex_number |
type: |
F_floating complex, D_floating complex, G_floating
complex |
access: |
read only |
mechanism: |
by value |
Complex dividend. The complex-dividend argument
contains a floating-point complex value. For OTS$DIVC,
complex-dividend is an F-floating complex number. For
OTS$DIVCD_R3, complex-dividend is a D-floating complex
number. For OTS$DIVCG_R3, complex-dividend is a
G-floating complex number.
complex-divisor
OpenVMS usage: |
complex_number |
type: |
F_floating complex, D_floating complex, G_floating
complex |
access: |
read only |
mechanism: |
by value |
Complex divisor. The complex-divisor argument contains
the value of the divisor. For OTS$DIVC,
complex-divisor is an F-floating complex number. For
OTS$DIVCD_R3, complex-divisor is a D-floating complex
number. For OTS$DIVCG_R3, complex-divisor is a
G-floating complex number.
Description
These routines return a complex result of a division on complex numbers.
The complex result is computed as follows:
- Let (a,b) represent the complex dividend.
- Let (c,d) represent the complex divisor.
- Let (r,i) represent the complex quotient.
The results of this computation are as follows:
r = (ac + bd)/(c2 + d2)
i = (bc - ad)/(c2 + d2)
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On Alpha systems, some restrictions apply when linking OTS$DIVC or
OTS$DIVCG_R3. See Chapter 1 for more information about these
restrictions.
Condition Values Signaled
SS$_FLTDIV_F
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Arithmetic fault. Floating-point division by zero.
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SS$_FLTOVF_F
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Arithmetic fault. Floating-point overflow.
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Examples
#1 |
C+
C This Fortran example forms the complex
C quotient of two complex numbers using
C OTS$DIVC and the Fortran random number
C generator RAN.
C
C Declare Z1, Z2, Z_Q, and OTS$DIVC as complex values.
C OTS$DIVC will return the complex quotient of Z1 divided
C by Z2: Z_Q = OTS$DIVC( %VAL(REAL(Z1)), %VAL(AIMAG(Z1),
C %VAL(REAL(Z2)), %VAL(AIMAG(Z2))
C-
COMPLEX Z1,Z2,Z_Q,OTS$DIVC
C+
C Generate a complex number.
C-
Z1 = (8.0,4.0)
C+
C Generate another complex number.
C-
Z2 = (1.0,1.0)
C+
C Compute the complex quotient of Z1/Z2.
C-
Z_Q = OTS$DIVC( %VAL(REAL(Z1)), %VAL(AIMAG(Z1)), %VAL(REAL(Z2)),
+ %VAL(AIMAG(Z2)))
TYPE *, ' The complex quotient of',Z1,' divided by ',Z2,' is'
TYPE *, ' ',Z_Q
END
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This Fortran program demonstrates how to call OTS$DIVC. The output
generated by this program is as follows:
The complex quotient of (8.000000,4.000000) divided by (1.000000,1.000000)
is (6.000000,-2.000000)
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#2 |
C+
C This Fortran example forms the complex
C quotient of two complex numbers by using
C OTS$DIVCG_R3 and the Fortran random number
C generator RAN.
C
C Declare Z1, Z2, and Z_Q as complex values. OTS$DIVCG_R3
C will return the complex quotient of Z1 divided by Z2:
C Z_Q = Z1/Z2
C-
COMPLEX*16 Z1,Z2,Z_Q
C+
C Generate a complex number.
C-
Z1 = (8.0,4.0)
C+
C Generate another complex number.
C-
Z2 = (1.0,1.0)
C+
C Compute the complex quotient of Z1/Z2.
C-
Z_Q = Z1/Z2
TYPE *, ' The complex quotient of',Z1,' divided by ',Z2,' is'
TYPE *, ' ',Z_Q
END
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This Fortran example uses the OTS$DIVCG_R3 entry point instead. Notice
the difference in the precision of the output generated:
The complex quotient of (8.000000000000000,4.000000000000000) divided by
(1.000000000000000,1.000000000000000) is
(6.000000000000000,-2.000000000000000)
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OTS$DIV_PK_LONG
The Packed Decimal Division with Long Divisor routine divides
fixed-point decimal data, which is stored in packed decimal form, when
precision and scale requirements for the quotient call for multiple
precision division. The divisor must have a precision of 30 or 31
digits.
Format
OTS$DIV_PK_LONG packed-decimal-dividend ,packed-decimal-divisor
,divisor-precision ,packed-decimal-quotient ,quotient-precision
,precision-data ,scale-data
RETURNS
OpenVMS usage: |
cond_value |
type: |
longword (unsigned) |
access: |
write only |
mechanism: |
by value |
Arguments
packed-decimal-dividend
OpenVMS usage: |
varying_arg |
type: |
packed decimal string |
access: |
read only |
mechanism: |
by reference |
Dividend. The packed-decimal-dividend argument is the
address of a packed decimal string that contains the shifted dividend.
Before being passed as input, the
packed-decimal-dividend argument is always multiplied
by 10c, where c is defined as follows:
c = 31 - prec(packed-decimal-dividend)
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Multiplying packed-decimal-dividend by
10c makes packed-decimal-dividend
a 31-digit number.
packed-decimal-divisor
OpenVMS usage: |
varying_arg |
type: |
packed decimal string |
access: |
read only |
mechanism: |
by reference |
Divisor. The packed-decimal-divisor argument is the
address of a packed decimal string that contains the divisor.
divisor-precision
OpenVMS usage: |
word_signed |
type: |
word (signed) |
access: |
read only |
mechanism: |
by value |
Precision of the divisor. The divisor-precision
argument is a signed word that contains the precision of the divisor.
The high-order bits are filled with zeros.
packed-decimal-quotient
OpenVMS usage: |
varying_arg |
type: |
packed decimal string |
access: |
write only |
mechanism: |
by reference |
Quotient. The packed-decimal-quotient argument is the
address of the packed decimal string into which OTS$DIV_PK_LONG writes
the quotient.
quotient-precision
OpenVMS usage: |
word_signed |
type: |
word (signed) |
access: |
read only |
mechanism: |
by value |
Precision of the quotient. The quotient-precision
argument is a signed word that contains the precision of the quotient.
The high-order bits are filled with zeros.
precision-data
OpenVMS usage: |
word_signed |
type: |
word (signed) |
access: |
read only |
mechanism: |
by value |
Additional digits of precision required. The
precision-data argument is a signed word that contains
the value of the additional digits of precision required.
OTS$DIV_PK_LONG computes the precision-data argument
as follows:
precision-data = scale(packed-decimal-quotient)
+ scale(packed-decimal-divisor)
- scale(packed-decimal-dividend)
- 31 + prec(packed-decimal-dividend)
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scale-data
OpenVMS usage: |
word_signed |
type: |
word (signed) |
access: |
read only |
mechanism: |
by value |
Scale factor of the decimal point. The scale-data
argument is a signed word that contains the scale data.
OTS$DIV_PK_LONG defines the scale-data argument as
follows:
scale-data = 31 - prec(packed-decimal-divisor)
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Description
On VAX systems, before using this routine, you should determine whether
it is best to use OTS$DIV_PK_LONG, OTS$DIV_PK_SHORT, or the VAX
instruction DIVP. To determine this, you must first calculate
b, where b is defined as follows:
b = scale(packed-decimal-quotient)
+ scale(packed-decimal-divisor)
- scale(packed-decimal-dividend)
+ prec(packed-decimal-dividend)
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If b is greater than 31, then OTS$DIV_PK_LONG can be used to
perform the division. If b is less than 31, you could use the
instruction DIVP instead.
When using this routine on an OpenVMS Alpha system or on an OpenVMS VAX
system and you have determined that you cannot use DIVP, you need to
determine whether you should use OTS$DIV_PK_LONG or OTS$DIV_PK_SHORT.
To determine this, you must examine the value of
scale-data. If scale-data is less
than or equal to 1, then you should use OTS$DIV_PK_LONG. If
scale-data is greater than 1, you should use
OTS$DIV_PK_SHORT instead.
Condition Value Signaled
SS$_FLTDIV
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Fatal error. Division by zero.
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Example
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1
OPTION &
TYPE = EXPLICIT
!+
! This program uses OTS$DIV_PK_LONG to perform packed decimal
! division.
!-
!+
! DECLARATIONS
!-
DECLARE DECIMAL (31, 2) NATIONAL_DEBT
DECLARE DECIMAL (30, 3) POPULATION
DECLARE DECIMAL (10, 5) PER_CAPITA_DEBT
EXTERNAL SUB OTS$DIV_PK_LONG (DECIMAL(31,2), DECIMAL (30, 3), &
WORD BY VALUE, DECIMAL(10, 5), WORD BY VALUE, WORD BY VALUE, &
WORD BY VALUE)
!+
! Prompt the user for the required input.
!-
INPUT "Enter national debt: ";NATIONAL_DEBT
INPUT "Enter current population: ";POPULATION
!+
! Perform the division and print the result.
!
! scale(divd) = 2
! scale(divr) = 3
! scale(quot) = 5
!
! prec(divd) = 31
! prec(divr) = 30
! prec(quot) = 10
!
! prec-data = scale(quot) + scale(divr) - scale(divd) - 31 +
! prec(divd)
! prec-data = 5 + 3 - 2 - 31 + 31
! prec-data = 6
!
! b = scale(quot) + scale(divr) - scale(divd) + prec(divd)
! b = 5 + 3 - 2 + 31
! b = 37
!
! c = 31 - prec(divd)
! c = 31 - 31
! c = 0
!
! scale-data = 31 - prec(divr)
! scale-data = 31 - 30
! scale-data = 1
!
! b is greater than 31, so either OTS$DIV_PK_LONG or
! OTS$DIV_PK_SHORT may be used to perform the division.
! If b is less than or equal to 31, then the DIVP
! instruction may be used.
!
! scale-data is less than or equal to 1, so OTS$DIV_PK_LONG
! should be used instead of OTS$DIV_PK_SHORT.
!
!-
CALL OTS$DIV_PK_LONG( NATIONAL_DEBT, POPULATION, '30'W, PER_CAPITA_DEBT, &
'10'W, '6'W, '1'W)
PRINT "The per capita debt is ";PER_CAPITA_DEBT
END
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This BASIC example program uses OTS$DIV_PK_LONG to perform packed
decimal division. One example of the output generated by this program
is as follows:
$ RUN DEBT
Enter national debt: ? 12345678
Enter current population: ? 1212
The per capita debt is 10186.20297
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OTS$DIV_PK_SHORT
The Packed Decimal Division with Short Divisor routine divides
fixed-point decimal data when precision and scale requirements for the
quotient call for multiple-precision division.
Format
OTS$DIV_PK_SHORT packed-decimal-dividend ,packed-decimal-divisor
,divisor-precision ,packed-decimal-quotient ,quotient-precision
,precision-data
RETURNS
OpenVMS usage: |
cond_value |
type: |
longword (unsigned) |
access: |
write only |
mechanism: |
by value |
Arguments
packed-decimal-dividend
OpenVMS usage: |
varying_arg |
type: |
packed decimal string |
access: |
read only |
mechanism: |
by reference |
Dividend. The packed-decimal-dividend argument is the
address of a packed decimal string that contains the shifted dividend.
Before being passed as input, the
packed-decimal-dividend argument is always multiplied
by 10c, where c is defined as follows:
c = 31 - prec(packed-decimal-dividend)
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Multiplying packed-decimal-dividend by
10c makes packed-decimal-dividend
a 31-digit number.
packed-decimal-divisor
OpenVMS usage: |
varying_arg |
type: |
packed decimal string |
access: |
read only |
mechanism: |
by reference |
Divisor. The packed-decimal-divisor argument is the
address of a packed decimal string that contains the divisor.
divisor-precision
OpenVMS usage: |
word_signed |
type: |
word (signed) |
access: |
read only |
mechanism: |
by value |
Precision of the divisor. The divisor-precision
argument is a signed word integer that contains the precision of the
divisor; high-order bits are filled with zeros.
packed-decimal-quotient
OpenVMS usage: |
varying_arg |
type: |
packed decimal string |
access: |
write only |
mechanism: |
by reference |
Quotient. The packed-decimal-quotient argument is the
address of a packed decimal string into which OTS$DIV_PK_SHORT writes
the quotient.
quotient-precision
OpenVMS usage: |
word_signed |
type: |
word (signed) |
access: |
read only |
mechanism: |
by value |
Precision of the quotient. The quotient-precision
argument is a signed word that contains the precision of the quotient;
high-order bits are filled with zeros.
precision-data
OpenVMS usage: |
word_signed |
type: |
word (signed) |
access: |
read only |
mechanism: |
by value |
Additional digits of precision required. The
precision-data argument is a signed word that contains
the value of the additional digits of precision required.
OTS$DIV_PK_SHORT computes the precision-data argument
as follows:
precision-data = scale(packed-decimal-quotient)
+ scale(packed-decimal-divisor)
- scale(packed-decimal-dividend)
- 31 + prec(packed-decimal-dividend)
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Description
On VAX systems, before using this routine, you should determine whether
it is best to use OTS$DIV_PK_LONG, OTS$DIV_PK_SHORT, or the VAX
instruction DIVP. To determine this, you must first calculate
b, where b is defined as follows:
b = scale(packed-decimal-quotient) + scale(packed-decimal-divisor) -
scale(packed-decimal-dividend) + prec(packed-decimal-dividend)
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If b is greater than 31, then OTS$DIV_PK_SHORT can be used to
perform the division. If b is less than 31, you could use the
VAX instruction DIVP instead.
When using this routine on an OpenVMS Alpha system or on an OpenVMS VAX
system and you have determined that you cannot use DIVP, you need to
determine whether you should use OTS$DIV_PK_LONG or OTS$DIV_PK_SHORT.
To determine this, you must examine the value of
scale-data. If scale-data is less
than or equal to 1, then you should use OTS$DIV_PK_LONG. If
scale-data is greater than 1, you should use
OTS$DIV_PK_SHORT instead.
Condition Value Signaled
SS$_FLTDIV
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Fatal error. Division by zero.
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OTS$MOVE3
The Move Data Without Fill routine moves up to 232 - 1 bytes
(2,147,483,647 bytes) from a specified source address to a specified
destination address.
Format
OTS$MOVE3 length-value ,source-array ,destination-array
Corresponding JSB Entry Point
OTS$MOVE3_R5
RETURNS
None.
Arguments
length-value
OpenVMS usage: |
longword_signed |
type: |
longword (signed) |
access: |
read only |
mechanism: |
by value |
Number of bytes of data to move. The length-value
argument is a signed longword that contains the number of bytes to
move. The value of length-value may range from 0 to
2,147,483,647 bytes.
source-array
OpenVMS usage: |
vector_byte_unsigned |
type: |
byte (unsigned) |
access: |
read only |
mechanism: |
by reference, array reference |
Data to be moved by OTS$MOVE3. The source-array
argument contains the address of an unsigned byte array that contains
this data.
destination-array
OpenVMS usage: |
vector_byte_unsigned |
type: |
byte (unsigned) |
access: |
write only |
mechanism: |
by reference, array reference |
Address into which source-array will be moved. The
destination-array argument is the address of an
unsigned byte array into which OTS$MOVE3 writes the source data.
Description
OTS$MOVE3 performs the same function as the VAX MOVC3 instruction
except that the length-value is a longword integer
rather than a word integer. When called from the JSB entry point, the
register outputs of OTS$MOVE3_R5 follow the same pattern as those of
the MOVC3 instruction:
R0
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0
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R1
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Address of one byte beyond the source string
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R2
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0
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R3
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Address of one byte beyond the destination string
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R4
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0
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R5
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0
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For more information, see the description of the MOVC3 instruction in
the VAX Architecture Reference Manual. See also the routine LIB$MOVC3, which is a callable
version of the MOVC3 instruction.
Condition Values Returned
None.