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Math Instructions

Math instructions perform mathematical operations on registers and constants, and output the results to registers.

Instr.	Desc.	# Param	One Shot	SC40	SC43	SC46
MATHDEC	Decimal math	3	X	X	X	X
MATHHEX	Hexa- decimal math	3	X	X	X	X
SUM	Sum a range of registers	3 or 4	X		X

There are only three math instructions. However, they accept complete equations as input parameters allowing them to perform many different operations.

The decimal and hexadecimal math instructions are similar except for the functions and operators they offer, and for the type of registers they operate on. The general operation of both is desribed here with the details of the functions and operators listed separately below.

The MATHDEC and MATHHEX instruction expects the following parameters:

Destination - The the destination register. Register types may be DS, DD, DF, DH. The destination register must be compatible with the source registers. DH registers may not be mixed with the other register types.
A mandatory one shot parameter of 0 or 1. If the paramter is set to "1", the one-shot option is enabled and the instruction executes only when the logic stack transitions from false to true. If the paramter is set to "0", the one-shot option is disabled and the instruction executes whenever the logic stack is true. The one shot parameter must always be specified for these instructions as the variable number of equation elements would otherwise make it impossible to distinguish from from the equations.
Math equation - All elements following are treated as part of the math equation and must form a legal mathematical equation.

MATHDEC destination one-shot equationparameters

MATHHEX destination one-shot equationparameters

The error flags are set under the following conditions:

SC40 - A division by zero was attempted.
SC43 - The data could not be converted to the correct type, or the data value is out of range for the destination register.
SC46 - An unspecified math error has occurred. This includes all math errors not covered by the other math error flags.

Example:


	// Decimal math. Will resolve to 10.77245
	NETWORK 1
	STR X1
	COPY 2 DS1
	MATHDEC DF1 0 (1 + DS1) ^ 2 + SQRT(PI)
	
	// Hexadecimal math. Will resolve to 22h (in hexadecimal)
	NETWORK 2
	STR X2
	COPY 4 DH2
	MATHHEX DH1 0 (LSH(DH2, 2h) + 1h) * 2h

Decimal Math Operations

Decimal math operations are conducted by functions and operators. The input values may be DS, DD, or DF registers, or decimal constants. The destination may be a DS, DD, or DF register.

Angles for transcendental functions (SIN, COS, etc.) are in radians.

Using a function that operates in floating point (transcendental, logmarithic, square root), or using any floating point number (including the PI constant) will cause the entire equation to be conducted in floating point. The result will then be converted to a type that is compatible with the destination register. If a floating point number is copied to an integer register, the decimal part of the result is truncated, not rounded.

Operation	Description	Example
SIN	Sine	SIN(DF1)
COS	Cosine	COS(DF2)
TAN	Tangent	TAN(DF3)
ASIN	Arcsine	ASIN(DF4)
ACOS	Arccosine	ACOS(DF5)
ATAN	Arctagent	ATAN(DF6)
LOG	Log (base 10)	LOG(DF7)
LN	Natural log	LN(DF8)
SQRT	Square root	SQRT(DD3)
RAD	Convert degrees to radians	RAD(DF21)
DEG	Convert radians to degrees	DEG(DF22)
+	Add	DS1 + 7
-	Subtract	DS3 - DS4
*	Multiply	DS5 * 10
/	Divide	DF7 / DS1
MOD	Modulus (remainder)	DS22 MOD DS21
^	Exponentiate	DF52 ^ 3
PI	The constant PI	PI * DF102
()	Parentheses (group operations)	(DS2 + 71) * DF9

Hexadecimal Math Operations

Hexadecimal math operations are conducted by functions and operators. The input values may be DH registers, or hexadecimal constants. The destination must be a DH register.

Shifts and rotates take place within a 16 bit register size.

Operation	Description	Example
LSH	Shift left a specified amount	LSH(DH1, 2h)
RSH	Shift right a specified amount	RSH(DH2, 2h)
LRO	Rotate left a specified amount	LRO(DH3, 10h)
RRO	Rotate right a specified amount	RRO(DH4, 10h)
AND	AND words	DH5 AND Fh
OR	OR words	DH6 OR 7Fh
XOR	XOR words	DH7 XOR 1Ah
+	Add	DH1 + 7h
-	Subtract	DH3 - DH4
*	Multiply	DH5 * 1fh
/	Divide	DH7 / DH1
MOD	Modulus (remainder)	DH22 MOD DH21
()	Parentheses (group operations)	(DH2 + a1h) * DH9

Sum

The SUM function is provided as a separate instruction instead of being called from within the other math instructions.

The Sum instruction expects the following parameters:

Source Start - The start of the register address range. Register types may be DS, DD, DF, DH.
Source End - The end of the register address range. This must be a higher address of the same type as the source start.
Destination - The the destination register. Register types may be DS, DD, DF, DH. The destination register must be compatible with the source registers.
An optional one shot parameter of 0 or 1. If the paramter is set to "1", the one-shot option is enabled and the instruction executes only when the logic stack transitions from false to true. If the paramter is set to "0", the one-shot option is disabled and the instruction executes whenever the logic stack is true. If the parameter is missing, it has the same effect as setting it to "0".

SUM sourcestart sourceend destination (one-shot)

The error flags are set under the following conditions:

SC43 - The data could not be converted to the correct type, or the data value is out of range for the destination register.

Example:


	// Sum a series of registers.
	NETWORK 1
	STR X1
	SUM DS10 DS19 DF20
	
	// Sum with a one shot.
	NETWORK 2
	STR X2
	SUM DH10 DH19 DH20 1

Ladder Examples

The following shows examples in ladder format.

match example 1