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Syntax Operators Constants Boolean-Logic

Introduction

WinHoldEm formulas are very similar to the C programming expression syntax. If you already know and understand C programming expressions then this tutorial may serve as a convenient reference. If you are a beginner to the C programming syntax then we hope you find this primer useful.

Everything described here is standard ANSI C except where specifically noted otherwise.

Syntax

The general syntax for WinHoldem formulas is same as that of the C programming language. For the C programmers out there, you should feel right at home. For the uninitiated it will seem cryptic at first, but you know you've always wanted to learn C. Here's your chance. Welcome to the club.

The formulas are strict R-VALUES (right side of an assignment expression). There is no assignment operator. All values are stored as (double) floating point values on the expression stack. For bitwise operations the values are first converted to (int) and then the operator is applied.

WinHoldem Formula Operators

Operator Precedence
category operator associativity

Exponentiation* ** ln Right to Left
Unary ! ~ - ` Right to Left
Multiplicative * / % Left to Right
Additive + - Left to Right
Bitwise Shift << >> Left to Right
Relational < > <= >= Left to Right
Equality == != Left to Right
Bitwise AND & Left to Right
Bitwise XOR ^ Left to Right
Bitwise OR | Left to Right
Logical AND && Left to Right
Logical XOR* ^^ Left to Right
Logical OR || Left to Right
Conditional ?: Right to Left
Group * () [] {} Left to Right
* not standard ANSI C

Operator Precedence
category	operator	associativity
Exponentiation*	** ln	Right to Left
Unary	! ~ - `	Right to Left
Multiplicative	* / %	Left to Right
Additive	+ -	Left to Right
Bitwise Shift	<< >>	Left to Right
Relational	< > <= >=	Left to Right
Equality	== !=	Left to Right
Bitwise AND	&	Left to Right
Bitwise XOR	^	Left to Right
Bitwise OR	\|	Left to Right
Logical AND	&&	Left to Right
Logical XOR*	^^	Left to Right
Logical OR	\|\|	Left to Right
Conditional	?:	Right to Left
Group *	() [] {}	Left to Right

Boolean Logic

A boolean expression is composed of LOGICAL OPERATORS and OPERANDS. All boolean operands have only two values - true false. Each LOGICAL OPERAND has a very well defined operation upon the OPERAND(S) in the expression, with a very well defined result.

True False

When any numeric value is used in conjunction with a LOGICAL operator
any zero values are considered to be false (0)
any non-zero values are considered to be true (1)

Put very simply, if the numeric value in question is not zero
then it is considered to be true for boolean purposes.

Numeric Boolean
Values

Numeric
Value Boolean
Value

0 false

1 true

other true

Logical Operators

Operator
Name Operator
Token

NOT !

AND &&

OR ||

XOR ^^

Numeric Boolean Values
Numeric Value	Boolean Value
0	false
1	true
other	true

Logical Operators
Operator Name	Operator Token
NOT	!
AND	&&
OR	\|\|
XOR	^^

Unary

A unary operator takes a single operand.
Natural Log ln
Logical NOT !
Bitwise NOT ~
Unary Minus -
Bit Count `

Unary Minus -

A good example is the minus sign when it is used to alter the sign of a value.
Example: a + b / -4
The minus sign in front of the 4 is a unary minus.

Bit Count ` (not ANSI-C)

BIT COUNT 32-bit example

a `a

0000000000000000000000000000000 0

0000000000000100000000000000000 1

0000010000000100000000000010000 3

1111111111111111111111111111111 32

BIT COUNT 32-bit example
a	`a
0000000000000000000000000000000	0
0000000000000100000000000000000	1
0000010000000100000000000010000	3
1111111111111111111111111111111	32

Eponentiation

Power ** (not ANSI-C)

a ** b
Standard algebraic exponentiation on a and b.
a is raised to the power of b.

Natural Log ln (not ANSI-C)

ln a
Standard algebraic natural log of a
a == e ** (ln a)

Natural Log Base e (not ANSI-C)

e == ln(1)
e == 2.71828182845905

Multiplicative

Multiply *

a * b
Standard algebraic multiplication on a and b.

Divide /

a / b
Standard algebraic division on a and b.

Modulo %

a % b
Standard algebraic modulo on a and b.

Additive

Add +

a + b
Standard algebraic addition on a and b.

Subtract -

a - b
Standard algebraic subtraction on a and b.

BITWISE

BITWISE NOT ~

a LOGICAL NOT operation on a bit by bit basis

BITWISE NOT 32-bit example

expression binary

a 11001001011101010110010101111010

~a 00110110100010101001101010000101

BITWISE NOT 32-bit example
expression	binary
a	11001001011101010110010101111010
~a	00110110100010101001101010000101

BITWISE AND &

a LOGICAL AND operation on a bit by bit basis

BITWISE AND 32-bit example

expression binary

a 11001001011101010110010101111010

b 01001010010100101110001010101111

a&b 01001000010100000110000000101010

BITWISE AND 32-bit example
expression	binary
a	11001001011101010110010101111010
b	01001010010100101110001010101111
a&b	01001000010100000110000000101010

BITWISE OR |

a LOGICAL OR operation on a bit by bit basis

BITWISE OR 32-bit example

expression binary

a 11001001011101010110010101111010

b 01001010010100101110001010101111

a|b 11001011011101111110011111111111

BITWISE OR 32-bit example
expression	binary
a	11001001011101010110010101111010
b	01001010010100101110001010101111
a\|b	11001011011101111110011111111111

BITWISE XOR ^

a LOGICAL XOR operation on a bit by bit basis

BITWISE XOR 32-bit example

expression binary

a 11001001011101010110010101111010

b 01001010010100101110001010101111

a^b 10000011001001111000011111010101

BITWISE XOR 32-bit example
expression	binary
a	11001001011101010110010101111010
b	01001010010100101110001010101111
a^b	10000011001001111000011111010101

BITWISE SHIFT

BITWISE SHIFTLEFT <<

Slide the entire bit pattern to the left by N

BITWISE SHIFTLEFT 32-bit example

expression binary

a 11001001011101010110010101111010

a<<1 10010010111010101100101011110100

a<<7 10111010101100101011110100000000

a<<31 00000000000000000000000000000000

a<<32 11001001011101010110010101111010

Note that the leftmost bits are simply dropped.
Note that the rightmost bits are filled with incoming 0's. Note that shift magnitude is used as modulo 32.

BITWISE SHIFTLEFT 32-bit example
expression	binary
a	11001001011101010110010101111010
a<<1	10010010111010101100101011110100
a<<7	10111010101100101011110100000000
a<<31	00000000000000000000000000000000
a<<32	11001001011101010110010101111010

BITWISE SHIFTRIGHT >>

Slide the entire bit pattern to the right by N

BITWISE SHIFTRIGHT 32-bit example

expression binary

a 11001001011101010110010101111010

a>>1 11100100101110101011001010111101

a>>7 11111111100100101110101011001010

a>>31 11111111111111111111111111111111

a>>32 11001001011101010110010101111010

Note that the rightmost bits are simply dropped.
Note that the leftmost bits are filled with the leftmost bit of the operand.
Note that shift magnitude is used as modulo 32.

BITWISE SHIFTRIGHT 32-bit example

expression binary

a 01001001011101010110010101111010

a>>1 00100100101110101011001010111101

a>>7 00000000100100101110101011001010

a>>31 00000000000000000000000000000000

a>>32 01001001011101010110010101111010

BITWISE SHIFTRIGHT 32-bit example
expression	binary
a	11001001011101010110010101111010
a>>1	11100100101110101011001010111101
a>>7	11111111100100101110101011001010
a>>31	11111111111111111111111111111111
a>>32	11001001011101010110010101111010

BITWISE SHIFTRIGHT 32-bit example
expression	binary
a	01001001011101010110010101111010
a>>1	00100100101110101011001010111101
a>>7	00000000100100101110101011001010
a>>31	00000000000000000000000000000000
a>>32	01001001011101010110010101111010

LOGICAL

LOGICAL NOT !

false when the operand is true
true when the operand is false

LOGICAL NOT

a !a

false true

true false

0 1

Note that the default unambiguous numeric value for true is 1.

LOGICAL NOT
a	!a
false	true
true	false
0	1

LOGICAL AND &&

false when any operand is false
true when both operands are true

LOGICAL AND

a b a && b

false false false

false true false

true false false

true true true

LOGICAL AND
a	b	a && b
false	false	false
false	true	false
true	false	false
true	true	true

LOGICAL OR ||

false when both operands are false
true when any operand is true

LOGICAL OR

a b a || b

false false false

false true true

true false true

true true true

LOGICAL OR
a	b	a \|\| b
false	false	false
false	true	true
true	false	true
true	true	true

LOGICAL XOR ^^ (not ANSI-C)

false when operands are boolean equal
true when operands are not boolean equal

LOGICAL XOR

a b a ^^ b

false false false

false true true

true false true

true true false

Note that a^^b is equivalent to (a!=0)^(b!=0)

LOGICAL XOR
a	b	a ^^ b
false	false	false
false	true	true
true	false	true
true	true	false

Relational

Less Than <

LESS THAN

a b a < b

-1 0 true

0 0 false

+1 0 false

LESS THAN
a	b	a < b
-1	0	true
0	0	false
+1	0	false

Greater Than >

GREATER THAN

a b a > b

-1 0 false

0 0 false

+1 0 true

GREATER THAN
a	b	a > b
-1	0	false
0	0	false
+1	0	true

Less Than or Equal <=

LESS THAN OR EQUAL

a b a <= b

-1 0 true

0 0 true

+1 0 false

LESS THAN OR EQUAL
a	b	a <= b
-1	0	true
0	0	true
+1	0	false

Greater Than or Equal >=

GREATER THAN OR EQUAL

a b a >= b

-1 0 false

0 0 true

+1 0 true

GREATER THAN OR EQUAL
a	b	a >= b
-1	0	false
0	0	true
+1	0	true

Equality

Equal ==

EQUAL

a b a == b

-1 0 false

0 0 true

+1 0 false

EQUAL
a	b	a == b
-1	0	false
0	0	true
+1	0	false

Not Equal !=

NOT EQUAL

a b a != b

-1 0 true

0 0 false

+1 0 true

NOT EQUAL
a	b	a != b
-1	0	true
0	0	false
+1	0	true

Conditional ?:

a ? b : c
Standard algorithmic if then else
If a then b else c

CONDITIONAL

a b c a ? b : c

true any any b

false any any c

CONDITIONAL
a	b	c	a ? b : c
true	any	any	b
false	any	any	c

WinHoldEm Exclusive Group Operators []{} (not ANSI-C)

Note that WinHoldEm uses the []{} operators differently than ANSI C. Brackets [] and Braces {} are used by WinHoldEm as exlusive group operators. The exclusive group operators cannot be nested. They must be closed before starting another group of the same type. The following example is allowable syntax:
{ [ a * (b+c) ] && [ d / (h-k) ] }
The following example is not allowable syntax:
{ { [ 2 + 3 ] * 2 } / 7 }
because this expression uses two open brace '{' groups simultaneously. Also, note that parenthesis are not treated this way. You can have multiple open parenthisis groups simultaneously.

WinHoldem Formula Numeric Constants

By default all numeric constants are treated as double floating point values in base 10.

Floating Point
Numeric Constants

123.456

0.987

192837465

.5

17.

5.4321e-76

Floating Point Numeric Constants
123.456
0.987
192837465
.5
17.
5.4321e-76

Integer Numeric Base

There are 4 additional integer options available as well that allow you to select the base of the constant. The 4 available bases are: 16, 8, 4, 2. You must prefix a numeric constant with a zero followed by a letter that selects the specific base you desire. The letters to select each base are as follows:

Integer Numeric Base

Letter Base Name

x 16 Hex

o 8 Octal*

q 4 Quadal*

b 2 Binary*

* non-standard ANSI C

Integer Numeric Constants

Decimal Hex Octal Quadal Binary

0 0x0 0o0 0q0 0b0

1 0x1 0o1 0q1 0b1

2 0x2 0o2 0q2 0b10

3 0x3 0o3 0q3 0b11

4 0x4 0o4 0q10 0b100

5 0x5 0o5 0q11 0b101

6 0x6 0o6 0q12 0b110

7 0x7 0o7 0q13 0b111

8 0x8 0o10 0q20 0b1000

9 0x9 0o11 0q21 0b1001

10 0xa 0o12 0q22 0b1010

11 0xb 0o13 0q23 0b1011

12 0xc 0o14 0q30 0b1100

13 0xd 0o15 0q31 0b1101

14 0xe 0o16 0q32 0b1110

15 0xf 0o17 0q33 0b1111

16 0x10 0o20 0q100 0b10000

31 0x1f 0o37 0q133 0b11111

63 0x3f 0o77 0q333 0b111111

127 0x7f 0o177 0q1333 0b1111111

255 0xff 0o377 0q3333 0b11111111

Integer Numeric Constants
Decimal	Hex	Octal	Quadal	Binary
0	0x0	0o0	0q0	0b0
1	0x1	0o1	0q1	0b1
2	0x2	0o2	0q2	0b10
3	0x3	0o3	0q3	0b11
4	0x4	0o4	0q10	0b100
5	0x5	0o5	0q11	0b101
6	0x6	0o6	0q12	0b110
7	0x7	0o7	0q13	0b111
8	0x8	0o10	0q20	0b1000
9	0x9	0o11	0q21	0b1001
10	0xa	0o12	0q22	0b1010
11	0xb	0o13	0q23	0b1011
12	0xc	0o14	0q30	0b1100
13	0xd	0o15	0q31	0b1101
14	0xe	0o16	0q32	0b1110
15	0xf	0o17	0q33	0b1111
16	0x10	0o20	0q100	0b10000
31	0x1f	0o37	0q133	0b11111
63	0x3f	0o77	0q333	0b111111
127	0x7f	0o177	0q1333	0b1111111
255	0xff	0o377	0q3333	0b11111111