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OpenVMS VAX RTL Mathematics (MTH$) Manual
MTH$HLOG2
The Base 2 Logarithm (H-Floating Value) routine returns the base 2
logarithm of the input value specified by
floating-point-input-value as an H-floating value.
Format
MTH$HLOG2 h-log2 ,floating-point-input-value
RETURNS
None.
Arguments
h-log2
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by reference |
Base 2 logarithm of floating-point-input-value. The
h-log2 argument is the address of an H-floating number
that is this base 2 logarithm. MTH$HLOG2 writes the address of this
logarithm into h-log2.
floating-point-input-value
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by reference |
The input value. The floating-point-input-value
argument is the address of a floating-point number that is this input
value. For MTH$HLOG2, floating-point-input-value
specifies an H-floating number.
Description
The base 2 logarithm function is computed as follows:
zLOG2(X) =
zLOG2(E) * zLOG(X)
Condition Values Signaled
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SS$_ROPRAND
|
Reserved operand. The MTH$HLOG2 routine encountered a floating-point
reserved operand due to incorrect user input. A floating-point reserved
operand is a floating-point datum with a sign bit of 1 and a biased
exponent of 0. Floating-point reserved operands are reserved for future
use by Compaq.
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MTH$_LOGZERNEG
|
Logarithm of zero or negative value. Argument
floating-point-input-value is less than or equal to
0.0. LIB$SIGNAL copies the floating-point reserved operand to the
mechanism argument vector CHF$L_MCH_SAVR0/R1. The result is the
floating-point reserved operand unless you have written a condition
handler to change CHF$L_MCH_SAVR0/R1.
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MTH$HLOG10
The Common Logarithm (H-Floating Value) routine returns the common
(base 10) logarithm of the input argument as an H-floating value.
Format
MTH$HLOG10 h-log10 ,floating-point-input-value
Corresponding JSB Entry Point
MTH$HLOG10_R8
RETURNS
None.
Arguments
h-log10
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by reference |
Common logarithm of the input value specified by
floating-point-input-value. The
h-log10 argument is the address of an H-floating
number that is this common logarithm. MTH$HLOG10 writes the address of
the common logarithm into h-log10.
floating-point-input-value
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by reference |
The input value. The floating-point-input-value
argument is the address of a floating-point number. For MTH$HLOG10,
floating-point-input-value specifies an H-floating
number.
Description
The common logarithm function is computed as follows:
zLOG10(X) =
zLOG10(E) * zLOG(X)
Condition Values Signaled
|
SS$_ROPRAND
|
Reserved operand. The MTH$HLOG10 routine encountered a floating-point
reserved operand due to incorrect user input. A floating-point reserved
operand is a floating-point datum with a sign bit of 1 and a biased
exponent of 0. Floating-point reserved operands are reserved for future
use by Compaq.
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MTH$_LOGZERNEG
|
Logarithm of zero or negative value. Argument
floating-point-input-value is less than or equal to
0.0. LIB$SIGNAL copies the floating-point reserved operand to the
mechanism argument vector CHF$L_MCH_SAVR0/R1. The result is the
floating-point reserved operand unless you have written a condition
handler to change CHF$L_MCH_SAVR0/R1.
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MTH$HSIN
The Sine of Angle Expressed in Radians (H-Floating Value) routine
returns the sine of a given angle (in radians) as an H-floating value.
Format
MTH$HSIN h-sine ,angle-in-radians
Corresponding JSB Entry Point
MTH$HSIN_R5
RETURNS
None.
Arguments
h-sine
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by reference |
The sine of the angle specified by angle-in-radians.
The h-sine argument is the address of an H-floating
number that is this sine. MTH$HSIN writes the address of the sine into
h-sine.
angle-in-radians
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by reference |
Angle (in radians). The angle-in-radians argument is
the address of a floating-point number that is this angle. For
MTH$HSIN, angle-in-radians specifies an H-floating
number.
Description
See MTH$xSINCOS for the algorithm used to compute this sine.
Condition Value Signaled
|
SS$_ROPRAND
|
Reserved operand. The MTH$HSIN routine encountered a floating-point
reserved operand due to incorrect user input. A floating-point reserved
operand is a floating-point datum with a sign bit of 1 and a biased
exponent of 0. Floating-point reserved operands are reserved for future
use by Compaq.
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MTH$HSIND
The Sine of Angle Expressed in Degrees (H-Floating Value) routine
returns the sine of a given angle (in degrees) as an H-floating value.
Format
MTH$HSIND h-sine ,angle-in-degrees
Corresponding JSB Entry Point
MTH$HSIND_R5
RETURNS
None.
Arguments
h-sine
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by reference |
Sine of the angle specified by angle-in-degrees.
MTH$HSIND writes into h-sine the address of an
H-floating number that is this sine.
angle-in-degrees
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by reference |
Angle (in degrees). The angle-in-degrees argument is
the address of an H-floating number that is this angle.
Description
See MTH$xSINCOSD for the algorithm used to compute the sine.
Condition Values Signaled
|
SS$_ROPRAND
|
Reserved operand. The MTH$HSIND routine encountered a floating-point
reserved operand due to incorrect user input. A floating-point reserved
operand is a floating-point datum with a sign bit of 1 and a biased
exponent of 0. Floating-point reserved operands are reserved for future
use by Compaq.
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MTH$_FLOUNDMAT
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Floating-point underflow in Math Library. The absolute value of the
input angle is less than 180/Pi sign*2
-m (where m = 16,384 for H-floating).
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MTH$HSINH
The Hyperbolic Sine (H-Floating Value) routine returns the hyperbolic
sine of the input value specified by
floating-point-input-value as an H-floating value.
Format
MTH$HSINH h-sinh ,floating-point-input-value
RETURNS
None.
Arguments
h-sinh
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by reference |
Hyperbolic sine of the input value specified by
floating-point-input-value. The
h-sinh argument is the address of an H-floating number
that is this hyperbolic sine. MTH$HSINH writes the address of the
hyperbolic sine into h-sinh.
floating-point-input-value
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by reference |
The input value. The floating-point-input-value
argument is the address of a floating-point number that is this value.
For MTH$HSINH, floating-point-input-value specifies an
H-floating number.
Description
Computation of the hyperbolic sine function depends on the magnitude of
the input argument. The range of the function is partitioned using
three data type dependent constants: a(z), b(z), and c(z). The
subscript z indicates the data type. The constants depend on
the number of exponent bits (e) and the number of fraction
bits (f) associated with the data type (z).
The values of e and f are as follows:
e = 15
f = 113
The values of the constants in terms of e and f are:
| Variable |
Value |
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a(z)
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2
(-f/2)
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b(z)
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(f+1)/2*ln(2)
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c(z)
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2
e-1*ln(2)
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Based on the above definitions, zSINH(X) is computed as follows:
| Value of X |
Value Returned |
|
|X|
< a(z)
|
X
|
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a(z)
<= |X|
< 1.0
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zSINH(X) is computed using a power series expansion in |X|
2
|
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1.0
<= |X|
< b(z)
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(zEXP(X) - zEXP(-X))/2
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b(z)
<= |X|
< c(z)
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SIGN(X)*zEXP(|X|)/2
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c(z)
<= |X|
|
Overflow occurs
|
Condition Values Signaled
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SS$_ROPRAND
|
Reserved operand. The MTH$HSINH routine encountered a floating-point
reserved operand due to incorrect user input. A floating-point reserved
operand is a floating-point datum with a sign bit of 1 and a biased
exponent of 0. Floating-point reserved operands are reserved for future
use by Compaq.
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MTH$_FLOOVEMAT
|
Floating-point overflow in Math Library: the absolute value of
floating-point-input-value is greater than
yyy. LIB$SIGNAL copies the floating-point reserved operand to
the mechanism argument vector CHF$L_MCH_SAVR0/R1. The result is the
floating-point reserved operand unless you have written a condition
handler to change CHF$L_MCH_SAVR0/R1. The value of
yyy is approximately 11356.523.
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MTH$HSQRT
The Square Root (H-Floating Value) routine returns the square root of
the input value floating-point-input-value as an
H-floating value.
Format
MTH$HSQRT h-sqrt ,floating-point-input-value
Corresponding JSB Entry Point
MTH$HSQRT_R8
RETURNS
None.
Arguments
h-sqrt
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by reference |
Square root of the input value specified by
floating-point-input-value. The
h-sqrt argument is the address of an H-floating number
that is this square root. MTH$HSQRT writes the address of the square
root into h-sqrt.
floating-point-input-value
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by reference |
Input value. The floating-point-input-value argument
is the address of a floating-point number that contains this input
value. For MTH$HSQRT, floating-point-input-value
specifies an H-floating number.
Description
The square root of X is computed as follows:
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If X
< 0 , an error is signaled.
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Let X = 2
K * F
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where:
|
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K is the exponential part of the floating-point data
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F is the fractional part of the floating-point data
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If K is even:
X = 2
(2*P) * F,
zSQRT(X) = 2
P * zSQRT(F),
1/2
<= F
< 1 , where P = K/2
|
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If K is odd:
X = 2
(2*P+1) * F = 2
(2*P+2) * (F/2) ,
zSQRT(X) = 2
(P+1) * zSQRT(F/2),
1/4
<= F/2
< 1/2 , where p = (K-1)/2
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Let F' = A*F + B, when K is even:
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A = 0.95F6198 (hex)
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B = 0.6BA5918 (hex)
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Let F' = A* (F/2) + B, when K is odd:
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A = 0.D413CCC (hex)
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B = 0.4C1E248 (hex)
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Let K' = P, when K is even
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Let K' = P+1, when K is odd
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Let Y[0] = 2K' * F' be a straight line approximation within
the given interval using coefficients A and B, which minimize the
absolute error at the midpoint and endpoint.
Starting with Y[0], n Newton-Raphson iterations are performed:
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Y[n+1] = 1/2 * (Y[n] + X/Y[n])
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where n = 5 for H-floating.
Condition Values Signaled
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SS$_ROPRAND
|
Reserved operand. The MTH$HSQRT routine encountered a floating-point
reserved operand due to incorrect user input. A floating-point reserved
operand is a floating-point datum with a sign bit of 1 and a biased
exponent of 0. Floating-point reserved operands are reserved for future
use by Compaq.
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MTH$_SQUROONEG
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Square root of negative number. Argument
floating-point-input-value is less than 0.0.
LIB$SIGNAL copies the floating-point reserved operand to the mechanism
argument vector CHF$L_MCH_SAVR0/R1. The result is the floating-point
reserved operand unless you have written a condition handler to change
CHF$L_MCH_SAVR0/R1.
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MTH$HTAN
The Tangent of Angle Expressed in Radians (H-Floating Value) routine
returns the tangent of a given angle (in radians) as an H-floating
value.
Format
MTH$HTAN h-tan ,angle-in-radians
Corresponding JSB Entry Point
MTH$HTAN_R5
RETURNS
None.
Arguments
h-tan
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by reference |
Tangent of the angle specified by angle-in-radians.
The h-tan argument is the address of an H-floating
number that is this tangent. MTH$HTAN writes the address of the tangent
into h-tan.
angle-in-radians
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by reference |
The input angle (in radians). The angle-in-radians
argument is the address of a floating-point number that is this angle.
For MTH$HTAN, angle-in-radians specifies an H-floating
number.
Description
When the input argument is expressed in radians, the tangent function
is computed as follows:
- If |X| < 2(-f/2) , then zTAN(X) = X (see the section on
MTH$zCOSH for the definition of f)
- Otherwise, call MTH$zSINCOS to obtain zSIN(X) and zCOS(X); then
- If zCOS(X) = 0 , signal overflow
- Otherwise, zTAN(X) = zSIN(X)/zCOS(X)
Condition Values Signaled
|
SS$_ROPRAND
|
Reserved operand. The MTH$HTAN routine encountered a floating-point
reserved operand due to incorrect user input. A floating-point reserved
operand is a floating-point datum with a sign bit of 1 and a biased
exponent of 0. Floating-point reserved operands are reserved for future
use by Compaq.
|
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MTH$_FLOOVEMAT
|
Floating-point overflow in Math Library.
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MTH$HTAND
The Tangent of Angle Expressed in Degrees (H-Floating Value) routine
returns the tangent of a given angle (in degrees) as an H-floating
value.
Format
MTH$HTAND h-tan ,angle-in-degrees
Corresponding JSB Entry Point
MTH$HTAND_R5
RETURNS
None.
Arguments
h-tan
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
write only |
| mechanism: |
by reference |
Tangent of the angle specified by angle-in-degrees.
The h-tan argument is the address of an H-floating
number that is this tangent. MTH$HTAND writes the address of the
tangent into h-tan.
angle-in-degrees
| OpenVMS usage: |
floating_point |
| type: |
H_floating |
| access: |
read only |
| mechanism: |
by reference |
The input angle (in degrees). The angle-in-degrees
argument is the address of a floating-point number that is this angle.
For MTH$HTAND, angle-in-degrees specifies an
H-floating number.
Description
When the input argument is expressed in degrees, the tangent function
is computed as follows:
- If |X| < (180/Pi sign)*2(-2/(e-1)) and underflow
signaling is enabled, underflow is signaled (see the section on
MTH$zCOSH for the definition of e).
- Otherwise, if |X| < (180/Pi sign)*2(-f/2) , then
zTAND(X) = (Pi sign/180)*X . See the description of MTH$zCOSH for the
definition of f.
- Otherwise, call MTH$zSINCOSD to obtain zSIND(X) and zCOSD(X).
- Then, if zCOSD(X) = 0 , signal overflow
- Else, zTAND(X) = zSIND(X)/zCOSD(X)
Condition Values Signaled
|
SS$_ROPRAND
|
Reserved operand. The MTH$HTAND routine encountered a floating-point
reserved operand due to incorrect user input. A floating-point reserved
operand is a floating-point datum with a sign bit of 1 and a biased
exponent of 0. Floating-point reserved operands are reserved for future
use by Compaq.
|
|
MTH$_FLOOVEMAT
|
Floating-point overflow in Math Library.
|
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