A fascinating read (An RPN/Hierarchy treatise)

[Matt Agajanian]

Hi all.

Just browsing around fiddling with the PEDMAS conundrum, I came across this report. The dissertation on RPN is quite fascinating.

Hierarchy and Postfix Analyses

Enjoy

[Steve Simpkin]

That is awesome!

"Why did HP use RPN?
In the years that followed the development of postfix notation, computer scientists realized that RPN was very efficient for computer use since calculations with postfix notation are done faster, requiring less processor time, than those with infix notation. As a postfix expression is scanned from left to right, operands are placed into the LIFO stack and operators may be immediately applied to the operands at the top of the stack. By contrast, expressions with parentheses and precedence (infix notation) require that operators be delayed until some later point. For example, the expression (75 - (6 + 4) * 3) / 5 requires the interpreter, human or machine, to make decisions about the operands and operators. This occurs only after the entire expression is scanned from left to right which demands extra processing time. Thus, the compilers of most modern computers of this time converted statements to RPN for execution. (In fact, some computer manufacturers designed their computers around postfix notation.)

At the time Hewlett Packard introduced its first calculator using RPN, other pocket calculators typically used a partial algebraic model. That meant they could evaluate simple expressions like 3 + 4 but couldn't handle anything that involved parentheses or order of operations. The technology available didn't allow for full algebraic compilers in pocket calculators.

The development of RPN allowed HP to produce a pocket calculator that could evaluate arbitrary, complex expressions using the available technology. For many, learning a new style of entry was a small price to pay to be able to evaluate these expressions on a calculator. Once the technology to produce algebraic compilers could fit into a pocket calculator, most RPN users had decided that RPN was more efficient and consistent for the user as well as for the calculator. Also, because subexpressions are evaluated as they are entered, entry errors are more obvious with RPN. On an algebraic calculator, omitting an opening parenthesis may not lead to a calculation error until much later when an entire expression has been evaluated. "


I agree. RPN may not have been for everyone but the early TI models without parenthesis keys (for example the SR-50 or SR-51) were not easy to use on complex calculations. The mental gyrations needed for calculating parenthesis heavy formulas could be daunting if you didn't break down the equation into simpler subsets first. Even then, this may have required intermediate results to be written down and re-entered in order to solve some problems.

Conversely, HP models, with their RPN logic and a four level stack, were able to provide a workable entry system that allowed most problems to be solved without writing down intermittent results. The methods used to break down a problem and to work it from the inside out also had the added advantage of mimicking the methods you would have used to solve the problem with a pencil and paper (or a slide rule).

HP wrote a detailed 16-page comparative analysis of the differences between RPN and the early algebraic entry systems.
See:"Advanced Calculator Logic HP RPN/Algebraic - A Comparative Analysis"

Thank you for that reference, Matt

[Massimo Gnerucci]

First mentioned by SlideRule

[Matt Agajanian]

(05-01-2024 07:36 AM)Steve Simpkin Wrote:  That is awesome!

"Why did HP use RPN?
In the years that followed the development of postfix notation, computer scientists realized that RPN was very efficient for computer use since calculations with postfix notation are done faster, requiring less processor time, than those with infix notation. As a postfix expression is scanned from left to right, operands are placed into the LIFO stack and operators may be immediately applied to the operands at the top of the stack. By contrast, expressions with parentheses and precedence (infix notation) require that operators be delayed until some later point. For example, the expression (75 - (6 + 4) * 3) / 5 requires the interpreter, human or machine, to make decisions about the operands and operators. This occurs only after the entire expression is scanned from left to right which demands extra processing time. Thus, the compilers of most modern computers of this time converted statements to RPN for execution. (In fact, some computer manufacturers designed their computers around postfix notation.)

At the time Hewlett Packard introduced its first calculator using RPN, other pocket calculators typically used a partial algebraic model. That meant they could evaluate simple expressions like 3 + 4 but couldn't handle anything that involved parentheses or order of operations. The technology available didn't allow for full algebraic compilers in pocket calculators.

The development of RPN allowed HP to produce a pocket calculator that could evaluate arbitrary, complex expressions using the available technology. For many, learning a new style of entry was a small price to pay to be able to evaluate these expressions on a calculator. Once the technology to produce algebraic compilers could fit into a pocket calculator, most RPN users had decided that RPN was more efficient and consistent for the user as well as for the calculator. Also, because subexpressions are evaluated as they are entered, entry errors are more obvious with RPN. On an algebraic calculator, omitting an opening parenthesis may not lead to a calculation error until much later when an entire expression has been evaluated. "


I agree. RPN may not have been for everyone but the early TI models without parenthesis keys (for example the SR-50 or SR-51) were not easy to use on complex calculations. The mental gyrations needed for calculating parenthesis heavy formulas could be daunting if you didn't break down the equation into simpler subsets first. Even then, this may have required intermediate results to be written down and re-entered in order to solve some problems.

Conversely, HP models, with their RPN logic and a four level stack, were able to provide a workable entry system that allowed most problems to be solved without writing down intermittent results. The methods used to break down a problem and to work it from the inside out also had the added advantage of mimicking the methods you would have used to solve the problem with a pencil and paper (or a slide rule).

HP wrote a detailed 16-page comparative analysis of the differences between RPN and the early algebraic entry systems.
See:"Advanced Calculator Logic HP RPN/Algebraic - A Comparative Analysis"

Thank you for that reference, Matt

That Comparative Analysis one of my favorite. And you're welcome.

[Steve Simpkin]

(05-01-2024 07:57 AM)Massimo Gnerucci Wrote:  First mentioned by SlideRule

I somehow missed that post. Thank you SlideRule!

[Matt Agajanian]

(05-01-2024 07:36 AM)Steve Simpkin Wrote:  That is awesome!

"Why did HP use RPN?
In the years that followed the development of postfix notation, computer scientists realized that RPN was very efficient for computer use since calculations with postfix notation are done faster, requiring less processor time, than those with infix notation. As a postfix expression is scanned from left to right, operands are placed into the LIFO stack and operators may be immediately applied to the operands at the top of the stack. By contrast, expressions with parentheses and precedence (infix notation) require that operators be delayed until some later point. For example, the expression (75 - (6 + 4) * 3) / 5 requires the interpreter, human or machine, to make decisions about the operands and operators. This occurs only after the entire expression is scanned from left to right which demands extra processing time. Thus, the compilers of most modern computers of this time converted statements to RPN for execution. (In fact, some computer manufacturers designed their computers around postfix notation.)

At the time Hewlett Packard introduced its first calculator using RPN, other pocket calculators typically used a partial algebraic model. That meant they could evaluate simple expressions like 3 + 4 but couldn't handle anything that involved parentheses or order of operations. The technology available didn't allow for full algebraic compilers in pocket calculators.

The development of RPN allowed HP to produce a pocket calculator that could evaluate arbitrary, complex expressions using the available technology. For many, learning a new style of entry was a small price to pay to be able to evaluate these expressions on a calculator. Once the technology to produce algebraic compilers could fit into a pocket calculator, most RPN users had decided that RPN was more efficient and consistent for the user as well as for the calculator. Also, because subexpressions are evaluated as they are entered, entry errors are more obvious with RPN. On an algebraic calculator, omitting an opening parenthesis may not lead to a calculation error until much later when an entire expression has been evaluated. "


I agree. RPN may not have been for everyone but the early TI models without parenthesis keys (for example the SR-50 or SR-51) were not easy to use on complex calculations. The mental gyrations needed for calculating parenthesis heavy formulas could be daunting if you didn't break down the equation into simpler subsets first. Even then, this may have required intermediate results to be written down and re-entered in order to solve some problems.

Conversely, HP models, with their RPN logic and a four level stack, were able to provide a workable entry system that allowed most problems to be solved without writing down intermittent results. The methods used to break down a problem and to work it from the inside out also had the added advantage of mimicking the methods you would have used to solve the problem with a pencil and paper (or a slide rule).

HP wrote a detailed 16-page comparative analysis of the differences between RPN and the early algebraic entry systems.
See:"Advanced Calculator Logic HP RPN/Algebraic - A Comparative Analysis"

Thank you for that reference, Matt

That Comparative Analysis one of my favorite. And you're welcome.