siemens · the function blocks fb 36 and fb 37 use the system transfer data word ri 229 as a buffer...

SIEMENS

Mathematical Functions Standard Function Blocks CPU 922, 928, 9461947

Description C79000-B8576-C667-01

Mathematical Functions Contents

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1

2 Function Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1

3 Interrupt Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1

4 Technical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1

5 Description of Individual Function Blocks . . . . . . . . . . . . . . . . . . . . . . 5.1 5.1 Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 5.2 Arc Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 5.3 Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10 5.4 Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-13

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List of Tables Mathematical Functions

List of Tables

Table 1 . 1 Summary of function blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Table 1.2 File designations and library numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2.1 Flag modifications 2.2 Table 4.1 Technical data for CPU 922 and CPU 928 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Table 4.2 Technical data for CPU 9461947 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2

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Mathematical Functions Introduction

1 Introduction

These Programming Instructions describe the function blocks "Mathematical functions" for the S5-135U and S5-155U programmable controllers. The function blocks of the mathematical functions are divided into:

Table 1 . l Summary of function blocks

The function blocks of the mathematical functions are available in two versions: one version can be executed on the CPU 922 and CPU 928 (S5-135U), the other on the CPU 9461947 (S5-155U).

Table 1.2 File designations and library numbers

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Mathematical Functions Function Description

2 Function Description

General

The standard function blocks for the mathematical functions are handled like a corresponding STEP 5 statement. When these blocks are called: - the contents of accumulator 1 are modified according to the

executed function (without changing the contents of the other accumulators or the base address register BR) or the contents of accumulators 1 and 2 are linked together according to the executed function where the contents of accumulator 3 are shifted into accumulator 2 and the contents of accumulator 4 shifted into accumulator 3 (as with a STEP 5 calculation function). The contents of the BR register remain unchanged.

Example of conversion of the accumulator contents:

:L DD 120 Load floating-point number Z1 into accumulator

:L DD 142 Load floating-point number Z2 into accumulator

:JU FB 101 and generate the sine from these NAME :SINUS

xG Multiply Z1 by sine (22) :T DD 122 and store in the data double word DD 122

Example of linking of accumulators 1 and 2:

:L DD 150 Load number Z1 into accumulator :L DD 160 Load base (a) :ENT Load Z1 into accumulator 3 :L DD 162 Load power (n) :JU FB 114 Generate power (a to power n)

NAME :A2 "A1 :+G Divide Z1 by (a to power n) :T DD 170 and store in the data double word DD 170

All standard function blocks for mathematical functions process 32-bit floating-point numbers.

Function Description Mathematical Functions

The standard function blocks use certain data words in the system transfer data area RI (from RI 230 to RI 255) as an intermediate memory, partly for the scratchpad flags used in the remaining program. A function block of the mathematical functions operates with its "own" scratchpad flags. Before the function block is left, the "user- specific" assignment of the scratchpad flags is reestablished. In this manner the assignment of the scratchpad flags appears to the user to be unchanged during processing of a mathematical function.

Error handling

If the calculation in the function block is terminated correctly, the result of the logic operation is set to a signal status "0".

The calculation is aborted (without changing the accumulator contents) and the result of the logic operation is set to "1" if the input value for the function is not within the permissible limits or if the permissible number range is violated during the calculation in the function block.

The function blocks of the mathematical functions change the flags as follows:

Table 2.1 Flag modifications

1) The latching overflow bit is reset when a block is changed.

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Mathematical Functions Function Description

The flags are evaluated using jump functions. Example:

:L FD 160 Load input value :JU FB 101 Execute mathematical function

NAME :SINUS :T FD 180 Store result

:JO =OVER Jumpwith error message (can also be a conditional jump JC)

:JZ =NULL Jump if the result is zero :JP =POS Jump if the result is positive :JM =NEG Jump if the result is negative

l &bit mantissa with floating-point calculation

The CPU 922 always uses a 16-bit mantissa for calculations where (if the output values have a 24-bit mantissa) the bits 0 to 7 are set to zero. With the CPU 928, it is possible to adjust in data block DXO whether the processor is to calculate with a 16-bit or 24-bit rnantissa.

The standard function blocks are matched to the calculation with a 16-bit mantissa.

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Mathematical Functions Interrupt Response

3 lnterrupt Response

The function blocks of the mathematical functions do not have an interrupt disable function. They can be interrupted by an interrupt event following each statement so that a fast reaction is possible to an interrupt (alarm or time interrupt). Since they have an own buffer area (the system transfer data RI), these blocks cannot be interrupted by themselves (and also not by other blocks of the mathematical functions).

If function blocks of the mathematical functions are called in the cyclic program as well as in the interrupt-controlled program, appropriate preparations must be made to enable fault-free processing of the function blocks. There are two possibilities: interrupt disable in the cyclic program or save buffer area in interrupt-controlled program.

With an interrupt disable in the cyclic program all interrupts are disabled prior to calling a function block of the mathematical functions and enabled again after this is called. Program example (cyclic program):

Program for CPU 922 and CPU 928:

:L KB2 :L KB5 AU OB 120 Disable interrupts

dU FB 101 Call mathematical functions NAME :SINUS

:L KB3 :L KB5 U OB 120 Enable interrupts

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Interrupt Response Mathematical Functions

Program for CPU 9461947:

:L KB1 ;IU OB 122 Disable intermpts

;IU FB 101 Call mathematical functions NAME :SINUS

:L KB2 :JU OB 122 Enable interrupts

When saving the buffer area, the system data used are saved at the beginning of the interrupt-controlled program into a data block (similar to the scratchpad flags) and loaded again at the end of the interrupt-controlled program.

Program example (in interrupt-controlled program):

:C DB n Data block as buffer memory ;IU FB 36 Save system data area

NAME :RI +DB

U FB 101 Mathematical functions NAME :SINUS

:C DB n Callbuffermemory ;IU FB 37 Load system data area

NAME :DB +RI

The data block used as a buffer memory must be called before calling the respective function block for saving or loading. It must be sufficiently long (initialized up to and including data word DW 25).

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Mathematical Functions Interrupt Response

Program example for CPU 922 and CPU 928:

Program example for CPU 9461947:

FB 36

NAME :RI+ DB :L KH E8E5 :TI R 6 ADD BN +26 :L RI 229 ADD BN +25 :TNW 26 :BE

FB 37

NAME :DB+ RI :L KH E8E5 :TI R 6 ADD BN +26 :L RI 229 ADD BN +25 :TAK :TN W 26 :BE

The function blocks FB 36 and FB 37 use the system transfer data word RI 229 as a buffer memory for the initial address of the data block. These function blocks are supplied together with the standard function blocks of the mathematical functions.

FB 36

NAME :RI + DB :L DH OOOE F4E5

:TI R 6 ADD BN +26 :L RI 229 :SLD 4 ADD DH 0000 0019

:TNW 26 :BE

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FB 37

NAME :DB+ RI :L DH OOOE F4E5

:TI R 6 ADD BN +26 :L RI 229 :SLD 4 ADD DH 0000 0019

:TAK :lNW 26 :BE

Mathematical Functions Technical Data

4 Technical Data

CPU 922 and CPU 928

Table 4.1 Technical data for CPU 922 and CPU 928

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Lib. No. (L1 MT23 ST.S5D)

906 906 906 906

907 91 0 913 913

906 906 906

913 906 906

Block No.

FB 101 FB 102 FB 103 FB 104

FB 105 FB 106 FB 107 FB 108

FB 109 FBI10 FB 11 1

FBI12 FB 113 FB 114

Lib. No.: P71 200-S..

-9101 -D-01 -91 02-D-01 -91 03-D-01 -91 04-D-01

-91 05-D-01 -91 06-D-01 -91 07-D-01 -9108-D-01

-91 09-D-01 -91 10-D-01 -91 11-D-01

-91 12-D-01 -91 13-D-01 -91 14-D-01

Name

SINUS COSINUS TAN- GENS- COTANG

ASCSIN ARCCOS ARCTAN ARCCOT

LNX LGX B LOG X

EAX ZEHNAX A2"Al

Block lengtt

242 238 31 8 321

218 253 268 269

222 222 274

253 260 418

Runtime CPU 922

3.8 3.8 4.0 4.0

3.5 3.7 4.2 4.3

4.3 4.3 7.6

4.5 4.6 7.4

Scratchpad flag assignment

FY 246 - FY 255 FY 246 - P/ 255 FY 246 - FY 255 FY 246- FY 255

P/ 246- P/ 255 FY 246- FY 255 FY 246- FY 255 FY 246 - FY255

FY 244 - FY 255 FY244- W255 FY 236 - FY 255

FY 246 - FY 255 FY 246 - FY 255 FY 244 - FY 255

(ms) CPU 928

2.4 2.4 2.5 2.5

2.2 2.3 2.6 2.7

2.9 2.9 5.1

3.0 3.1 4.9

System data assignment

R1 243 - R1 255 R1 243 - R1 255 R1 243 - R1 255 R1 243- R1 255

R1 243 - R1 255 R1 243 - R1 255 R1 243 - R1 255 R1 243 - R1 255

R1 242 - R1 255 R1 242- R1 255 R1 236 - R1 255

R1 243 - R1 255 R1 243 - R1 255 R1 242 - R1 255

Technical Data Mathematical Functions

CPU 9461947

Table 4.2 Technical data for CPU 9461947

FB 105 FB 106 FB 107 FB 108

FBI09 FBI10 FB 11 1

FBI12 FB 113 FB 11 4

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ASCSIN ARCCOS ARCTAN ARCCOT

LNX LGX B LOG X

EAX ZEHNAX A2"Al

-61 05-D-01 -61 06-D-01 -6107-D-01 -61 08-D-01

-6109-D-01 -61 10-D-01 -61 1 1-D-01

-6112-D-01 -61 13-D-01 -6114-D-01

203 238 260 265

206 210 254

236 243 391

0.35 0.35 0.45 0.45

0.50 0.50 0.95

0.50 0.50 0.90

FY 246 - FY 255 FY 246 - FY 255 FY246-FY255 FY 246 - FY 255

FY 244 - FY 255 FY 244 - FY 255 FY 236 - FY 255

FY 246 - FY 255 FY 246 - FY 255 FY 244 - FY 255

RI 243 - R1 255 R1 243 - R1 255 R1243-R1255 R1 243 - R1 255

R1 242 - R1 255 R1 242 - R1 255 R1 236 - R1 255

R1 243 - R1 255 R1 243 - R1 255 R1 242 - R1 255

91 0 91 0 913 91 3

829 829 906

91 3 830 906

Mathematical Functions Description of Individual Function Blocks

5 Description of Individual Function Blocks

5.1 Trigonometric Functions

Calling of function block FB 101 (SINUS)

:L KG (X) Input value :JU FB 101 Sine (X)

NAME :SINUS := Fx.y Errorflag l )

:T xx Result present in accumulator 1

Accumulator assignments

The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The input value must be within the range from zero (KG = +0000000 +00) to 2 sc (KG = +6283185 +01). The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.

The input value OH = 0000 0000 is handled like a floating-point value of zero (KG = +0000000 +00 corresponding to DH = 8000 0000).

If the calculation is carried out correctly, the result of the logic operation following calling of the function block is "0".

In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is not within the range from 0 to 2 X ) . The contents of accumulator 1 then remain unchanged.

The assignments of the other registers and of the scratchpad flags are not changed.

The flags are set in the same manner as in the general function description (see above).

1) Error analysis is also possible using the result of the logic operation with a conditional jump JC or using the overflow bit Ov with a jump with overflow JO.

Sine (X)

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Description of Individual Function Blocks Mathematical Functions

Calling of function block FB 102 (COSINUS)

Cosine (X)

:L KG (X) Input value :JU FB 102 Cosine (X)

NAME :COSINUS

:= Fx.y Error flag l )

:T xx Resutt present in accumulator 1


The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The input value must be within the range from zero (KG = +0000000 +00) to 2 . K (KG = +6283185 +01). The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.

The input value DH = 0000 0000 is handled like a floating-point value of zero (KG = +0000000 +00 corresponding to DH = 8000 0000).


In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is not within the range from 0 to 2 K). The contents of accumulator 1 then remain unchanged.




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Calling of function block FB 103 (TANGENS)

Tangent (X)

:L KG (X) Input value :JU FB 103 Tangent (X)

NAME :TANGENS := Fx.y Error flag l )



The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The input value must be within the range from zero (KG = +0000000 +00) to 2 . n: (KG = +6283185 +01). The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.



In the event of an error, the function block sets the result of the logic operation to a signal state "1 ". The contents of accumulator 1 then remain unchanged. One of the following errors is present:

The input value is not within the range from 0 to 2 . 7 ~ . The number range was exceeded during calculation of the function. The input value is d 2 (KG = +l570796 +01) or 3 . x 12 (KG = +4712389 +01). The f~nction~value is then infinite and the function block signals an error. )




2) The numbers specified apply to a calculation with a 24-bit mantissa. With a 16-bit mantissa, an error is signalled in the ranges KG = +l570740 +01 to +l570801 +01 and KG = +4712158 +01 to +4712402 +01.

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Calling of function block FB 104 (COTANG)

Cotangent (X)

:L KG (X) Input value :JU FB 104 Cotangent (X)

NAME :COTANG := Fx.y Error flag l )



The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The input value must be within the range from KG = +2938734 -34 to (almost) 2 . x (KG = +6283184 +01). The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.



In the event of an error, the function block sets the result of the logic operation to a signal state "1 ". The contents of accumulator 1 then remain unchanged. One of the following errors is present:

The input value is not within the range from KG = +2938734 -34 to KG = +6283184 +01 .2) The number range was exceeded during calculation of the function. The input value is 0, .rc (KG = +3141593 +01) or 2 x (KG = +6283185 +01). The function value is then infinite and the function block signals an error.3)


2) All central processors calculate the function value within the defined limits. The range can be expanded slightly depending on the CPU used or on whether the calculation is carried out with a l b b i t or 24-bit mantissa.

3) The numbers specified apply to a calculation with a 24-bit mantissa. With a 16-bit mantissa, an error is signalled in the range KG = +3141479 +01 to +3141602 +01.

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5.2 Arc Functions

Calling of function block FB 105 (ARCSIN)

Arc sine (X)

:L KG(x) Inputvalue :JU FB 105 Arc sine (X)

NAME :ARCSIN

:= Fx.y Errorflag l )



The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The input value must be within the range from -1 (KG = -1 000000 +01) to +l (KG = +l000000 +01). The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.



In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is not within the range from -1 to +l). The contents of accumulator 1 then remain unchanged.




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Calling of function block FB 106 (ARCCOS)

Arc cosine (X)

:L KG (X) Input value :JU F B I 0 6 Arccosine(x)

NAME :ARCCOS := F x.y Error flag l) :T xx Result present in accumulator 1


The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The input value must be within the range from -1 (KG = -1000000 +01) to +l (KG = +l000000 +01). The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.



In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is not within the range from -1 to +l). The contents of accumulator 1 then remain unchanged.



1 ) Error analysis is also possible using the result of the logic operation with a conditional jump JC or using the overflow bit Ov with a jump with overflow JO.

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Calling of function block FB 107 (ARCTAN)

Arc tangent (X)

:L KG (X) Input value :JU FB 107 Arc tangent (X)

NAME :ARCTAN := F x.y Error flag l )



The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The function block also stores the result in accumulator 1 as a 24/32-bit floating-point number.


A result of +d2 (KG = +l570796 +01) is output with an input value greater than KG = +l209486 +07, a result of -IT 12 (KG = -1 570796 +01) is output with an input value less than KG = -5773456 +07.

The result of the logic operation is set to a signal state of "0"




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Calling of function block FB 108 (ARCCOT)

Arc cotangent (X)

:L KG (X) Input value :JU FB 108 Arc cotangent (X)

NAME :ARCCOT := Fx.y Errorflag l )



The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.


A result of 0 (KG = +0000000 +00) is output with an input value greater than KG = +l 209486 +07, a result of x (KG = +3141593 +O1) is output with an input value less than KG = -5773456 +07.

The result of the logic operation is set to a signal state of "0".




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5.3 Logarithmic Functions

Calling of function block FB 109 (LN X)

Napierian logarithm loge (X)

:L KG (X) Input value :JU FB 109 Napierian logarithm loge (X)

NAME :LN X := Fx.y Error flag l )

:T xx Resutt present in accumulator 1


The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The input value must be greater than zero. The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.


In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is less than or equal to 0). The contents of accumulator 1 then remain unchanged.




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Calling of function block FB 110 (LG X)

Decimal logarithm log10 (X)

:L KG (X) Input value :JU FB 110 Decimal logarithm log10 (X)

NAME :LG X := Fx.y Errorflag



The function block expects the input value in accumulator 1 as a 24132-bit floating-point number. The input value must be greater than zero. The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.


In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is less than or equal to 0). The contents of accumulator 1 then remain unchanged.





Calling of function block FB 11 1 (B LOG X)

General logarithm log (X) to base b

:L KG (b) lnput value (base) :L KG (X) Input value (number) :JU FB 11 1 General logariihm log (X) to base b

NAME :B LOG X := F x.y Error flag l) :T xx Result present in accumulator 1


The function block expects the input value for the base (b) in accumulator 2 and the input value for the number (X) in accumulator 1, both as 24132-bit floating-point numbers. Both input values must be greater than zero; in addition, the base must not have a value of +l. The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.


In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is less than or equal to 0 or if the base has a value of +l). The contents of the accumulators then remain unchanged.

If the calculation is carried out correctly, the result is present in accumulator 1, the previous contents of accumulator 3 are present in accumulator 2, and the previous contents of accumulator 4 are present in accumulator 3. The contents of accumulator 4 are not changed.

The assignments of the scratchpad flags are not changed.


l) Error analysis is also possible using the result of the logic operation with a conditional jump JC or using the overflow bit Ov with a jump with overflow JO.

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5.4 Exponential Functions

Calling of function block FB 112 (E A N)

e to power n :L KG (X) Input value :JU FBI12 etopowern

NAME :EAN := Fx.y Errorflag l) :T xx Result present in accumulator 1





In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is not within the range from KG = -8802962 +02 to KG = +8802966 +02; the function value would then be outside the numeric range). The ntents of accumulator 1 then remain unchanged. f? The assignments of the other registers and of the scratchpad flags are not changed.


1 ) Error analysis is also possible using the result of the logic operation with a conditional jump JC or using the overflow bit Ov with a jump with overflow JO.

2) All central processors calculate the function value within the defined limits. The range can be expanded slightly depending on the CPU used or on whether the calculation is carried out with a 16-bit or 24-bit mantissa.

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Calling of function block FB 113 (ZEHN A N)

10 to power n :L KG (n) Input value :JU FBI13 10topowern

NAME :ZEHNAN := Fx.y Errorflag :T xx Resutt present in accumulator 1





In the event of an error, the function block sets the result of the logic operation to a signal state "1" (if the input value is not within the range from KG = -3823079 +02 to KG = +3823080 +02; the function value would then be outside the numeric range). The ontents of accumulator 1 then remain unchanged. 27




2) All central processors calculate the function value within the defined limits. The range can be expanded slightly depending on the CPU used or on whether the calculation is carried out with a 16-bit or 24-bit mantissa.

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Calling of function block FB 114 (A2 A AI )

Accumulator 2 to power accumulator l

:L KG (a2) Input value (base)

:L KG (al) Input value (exponent) :JU F6 114 Accumulator 2 to power accumulator 1

NAME :A2AA1 := Fx.y Errorflag l )



The function block expects the input value for the base in accumulator 2 and the input value for the exponent in accumulator 1, both as 24132-bit floating-point numbers. The input value for the base must be positive. The function block also stores the result in accumulator 1 as a 24132-bit floating-point number.


A result of zero is output for zero to power zero.

If the calculation is carried out correctly, the result of the logic operation following calling of the function block is "0". One of the following errors is present if the result of the logic operation is "1":

The input value for the base is less than zero. The number range was exceeded during calculation of the function.

The contents of accumulators 1 and 2 remain unchanged in the event of an error.

If the calculation is carried out correctly, the result is present in accumulator 1, the previous contents of accumulator 3 are present in accumulator 2, and the previous contents of accumulator 4 are present in accumulator 3. The contents of accumulator 4 are not changed.



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siemens · the function blocks fb 36 and fb 37 use the system transfer data word ri 229 as a buffer...

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