Logic Toolbox #308

joecrop · 2022-12-27T06:04:15Z

Binary Logic Toolbox

Numworks is about to release some basic binary functions in Epsilon. I tried them out, and they are honestly pretty useless, with inputs of just 'True' and 'False' and just AND/OR/NOT functions. Here's my take on a toolbox with much more powerful logic functions to be used on both unsigned and signed integers. I have also extended the '...' (Additional Results) display to show the 2's complement binary/hex of negative numbers.

Additional Results

Negative integers can now be displayed in binary/hex. Simply navigate to the ellipsis ('...') on the right of a negative integer result to see a 2's complement representation of the number:

Functions Implemented

Basic Logic Operations

AND

// x = a & b
and(a, b); // and of 2 integers

// Examples
and(0b11,0b01) = 1;
and(0b100110,0b1011) = 2;

OR

// x = a | b
or(a, b); // or of 2 integers

// Examples
or(0b11,0b01) = 3 = 0b11;
or(0b100110,0b1011) = 47 = 0b101111;

XOR - Exclusive OR

// x = a ^ b
xor(a, b); // xor of 2 integers

// Examples
xor(0b11,0b01) = 1;
xor(0b100110,0b1011) = 45 = 0b101101;

NOT

// x = ~a
not(a); // logical inversion of 32-bit unsigend integer

// Examples
not(0b11) = 4294967292 = 0xFFFFFFFC;
not(0xFFFF0000) = 65535 = 0xFFFF;

Bit Shifts

Shift Logical Left

// x = a << s
sll(a, s) // shift 'a' left by 's' bit positions

// Examples
sll(0b11,2) = 12 = 0b1100;

Shift Logical Right

// x = a >> s
srl(a, s) // shift 'a' right by 's' bit positions

// Examples
srl(0b11,2) = 0;
srl(0b1100,1) = 6 = 0b110;

Arithmetic Shift Right

// x = a >>> s
sra(a, s) // shift 'a' right by 's' bit positions, perserving the MSB sign bit, where 'a' is presumed to a 32 bits

// Examples
sra(0b11,2) = 0;
sra(0b1100,1) = 6 = 0b110;
sra(0xFFFF0000,8) = 4294967040 = 0xFFFFFF00;

Rotate Left

// x = (a << r) | (a & 1)
rol(a, r) // rotate 'a' by 'r' bit positions, the MSB is warpped around to the LSB, where 'a' is presumed to a 32 bits

// Examples
rol(0b101,1) = 10 = 0b1010;
rol(0xFFFF0000,4) = 4293918735 = 0xFFF000F;

Rotate Right

// x = (a >> r) | ((a & 1) << 32)
ror(a, r) // rotate 'a' by 'r' bit positions, the LSB is warpped around to the MSB, where 'a' is presumed to a 32 bits

// Examples
ror(0b1010,1) = 5 = 0b101;
ror(0b101,1) = 1073741825 = 0x40000001;
ror(0xFFFF0000,4) = 268431360 = 0x0FFFF000;

Setting And Clearing Bits

Get Bit

// (a >> n) & 1
bit(a, n) // return the n-th bit of 'a'

// Examples
bit(0b1010,1) = 0;
bit(0b1010,2) = 1;

Set Bit

// x = a | (1 << n)
bset(a, n) // set the n-th bit of 'a'

// Examples
bset(0b1010,1) = 11 = 0b1011;
bset(0b1010,2) = 10 = 0b1010;

Clear Bit

// x = a & ~(1 << n)
bclr(a, n) // clear the n-th bit of 'a'

// Examples
bclr(0b1010,1) = 10 = 0b1010;
bclr(0b1010,2) = 8 = 0b1000;

Flip Bit

// x = a ^ (1 << n)
bflp(a, n) // flip the n-th bit of 'a'

// Examples
bflp(0b1010,1) = 11 = 0b1011;
bflp(0b1010,2) = 8 = 0b1000;

Clear 'a' With 'b'

// x = (a & ~b)
bic(a, b) // clear 'a' with 'b'

// Examples
bic(0b1010,1) = 10 = 0b1010;
bic(0b1010,0b10) = 8 = 0b1000;
bic(0b1010,0b1010) = 0;

Logic Operations (With Explicit Number of Bits)

Some logic operations (like NOT) end up generating large 32-bit numbers as the default precision is 32 bits. This adds frustration when 32 bits of precision is undesired. So some of the functions have overridden methods that have an extra argument that allows the user to control the number of output bits.

not(a,n);
sra(a,s,n);
rol(a,r,n);
ror(a,r,n);
bic(a,b,n);

// Examples
not(0b11) = 4294967292 = 0xFFFFFFFC;
not(0b11,8) = 252 = 0b11111100;
not(0b00,2) = 3 = 0b11;
not(0b10,1) = 1 = 0b1;
not(0b0,1) = 1 = 0b1;
not(0b1,1) = 0 = 0b0;

2'S Compliment Conversions/Helpers

2's Compliment Equivalent

// Converts an unsigned binary number to it's two-compliment equivalent Integer.
// Simply useful to decode binary numbers that are negative

// Examples:
// If argument 1 is positive, the output will be converted to two-s comp (i.e. look at sign bit in MSB)
tc(0xFF, 8) = -1;
tc(0x0F, 8) = 15;

// if argument 1 is negative, it is always converted to unsigned
tc(-1, 8) = 255;

Ceiling Log2

// Returns the numver of bits required to represent a number in binary.
clog2(255) = 8;
clog2(3) = 2;

//NOTE: this is not the same as ceil(log(x,2)), as negative inputs to this function will instead be treated as 2's compliment numbers it report the number of bits needed to represent a signed 2's compliment number.
clog2(-3) = 2; // -3 in binary 2's compliment is 0b100
// If you want to konw the number of bits of an unsigend number in 2'c compliment number, just add 1 to the result for a sign bit.

Other Information

Please find a lengthy discussion and planing here: Add arithmetical and logical operations on integers: and, or, xor, etc. numworks/epsilon#146
Contributors: @debrouxl, @bmuessig

- negative numbers can now be displayed in 2's compliment binary

github-actions · 2022-12-27T06:10:49Z

	.text	.rodata	.bss	.data	Total (RAM)	Total (ROM)
Base	821684 bytes	478173 bytes	226384 bytes	1816 bytes	228200 bytes	1301673 bytes
Head	834324 bytes	486889 bytes	226376 bytes	1816 bytes	228192 bytes	1323029 bytes
	+12640 bytes	+8716 bytes	-8 bytes	+0 bytes	-8 bytes	+21356 bytes
	+1.5 %	+1.8 %	-0.0 %	+0.0 %	-0.0 %	+1.6 %

apps/toolbox.fr.i18n

lolocomotive · 2023-01-13T17:51:16Z

apps/toolbox.fr.i18n

+LogicalRotateLeft = "Rotation gauche de a par r bits"
+LogicalRotateRight= "Rotation droite de a par r bits"
+TwosComplementToBits = "Equivalent en complément à deux"
+CeilingLog2 = "Nombre de bits nécessaires pour stocker a"


The text is too long (maybe shortening Nombre to nb would help)

'Nombre de bits nécessaires pour stocker a' is now 'Nb de bits nécessaires pour stocker a'

lolocomotive · 2023-01-13T17:53:44Z

apps/toolbox.fr.i18n

+LogicalBitClear = "Effacer le bit numéro b dans a"
+LogicalBitFlip = "Inverser le bit numéro b dans a"
+LogicalBitGet = "Obtenir le bit numéro b dans a"
+LogicalBitSet = "Allumer le bit numéro b dans a"


Allumer is not the right word here. I'd use something like mettre/définir

Changed 'Allumer' to 'Mettre'

github-actions · 2023-01-22T05:18:37Z

	.text	.rodata	.bss	.data	Total (RAM)	Total (ROM)
Base	821684 bytes	478173 bytes	226384 bytes	1816 bytes	228200 bytes	1301673 bytes
Head	834324 bytes	486881 bytes	226376 bytes	1816 bytes	228192 bytes	1323021 bytes
	+12640 bytes	+8708 bytes	-8 bytes	+0 bytes	-8 bytes	+21348 bytes
	+1.5 %	+1.8 %	-0.0 %	+0.0 %	-0.0 %	+1.6 %

joecrop added 4 commits December 5, 2022 20:07

logic toolbox with logic functions

42d8fea

- Added clog2 function

fc95028

- negative numbers can now be displayed in 2's compliment binary

moved logic toolbox to the bottom of the list

81dc1bd

removed shift functions with explicit number of bits

d7f54ad

lolocomotive suggested changes Jan 13, 2023

View reviewed changes

Updated french translations after feedback

8041c7a

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Logic Toolbox #308

Logic Toolbox #308

joecrop commented Dec 27, 2022

github-actions bot commented Dec 27, 2022

lolocomotive Jan 13, 2023

joecrop Jan 22, 2023

lolocomotive Jan 13, 2023

joecrop Jan 22, 2023

github-actions bot commented Jan 22, 2023

Logic Toolbox #308

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Logic Toolbox #308

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joecrop commented Dec 27, 2022

Binary Logic Toolbox

Additional Results

Functions Implemented

Basic Logic Operations

AND

OR

XOR - Exclusive OR

NOT

Bit Shifts

Shift Logical Left

Shift Logical Right

Arithmetic Shift Right

Rotate Left

Rotate Right

Setting And Clearing Bits

Get Bit

Set Bit

Clear Bit

Flip Bit

Clear 'a' With 'b'

Logic Operations (With Explicit Number of Bits)

2'S Compliment Conversions/Helpers

2's Compliment Equivalent

Ceiling Log2

Other Information

github-actions bot commented Dec 27, 2022

lolocomotive Jan 13, 2023

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joecrop Jan 22, 2023

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lolocomotive Jan 13, 2023

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joecrop Jan 22, 2023

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github-actions bot commented Jan 22, 2023