For a small original calculator, define the grammar, precedence, angle mode, and real-number error rules first. The example below is a bounded numeric expression pad with a shared parser for typed text and native buttons. Use its worked records to check the local HTML example's parser and results.
Choose a readable expression language
Support dot-decimal numbers, the constants pi and e, parentheses, unary signs, and the operators +, −, *, /, and ^. Use ^ to mean exponentiation in this calculator's language. Do not pass it through as JavaScript's operator syntax.
Allow only sqrt, ln, log, sin, cos, and tan, each with one parenthesized argument. Thus write log(100), not log100, and sin(30), not sin30. Multiplication is explicit: use 2pi, not 2pi, and 2(3+4), not 2(3+4).
The function names have distinct meanings. MDN's Math reference documents natural logarithm, base-10 logarithm, square root, powers, and trigonometric functions. This pad maps ln to the natural logarithm and log to base ten. It is not a graphing tool or symbolic equation solver.
An Excelsoft scientific-calculator manual hosted by New York State provides context for an on-screen function interface. Hosting does not make its vendor-authored manual government authorship or establish that this original calculator is permitted in an exam. The design here uses its own layout and examples.
Specify precedence with examples
Multiplication and division bind more tightly than addition and subtraction. Parentheses override that order. Powers associate to the right, and power binds more tightly than a unary minus on its left.
| Expression | Interpretation | Expected result |
|---|---|---|
| 2+3*4 | 2+(3*4) | 14 |
| (2+3)*4 | Parenthesized sum first | 20 |
| 2^3^2 | 2^(3^2) | 512 |
| -2^2 | -(2^2) | -4 |
| (-2)^2 | Negative base in parentheses | 4 |
| 2^-2 | 2^(-2) | 0.25 |
The last three rows are particularly useful parser tests. A blanket “unary signs always bind first” rule would break the fourth row; rejecting every sign after ^ would break the sixth.
A possible grammar contract is:
expression = sum
sum = product { ("+" | "-") product }
product = unary { ("*" | "/") unary }
unary = "+" unary | "-" unary | power
power = primary [ "^" unary ]
primary = number | "pi" | "e" | "(" expression ")"
| allowedFunction "(" expression ")"
The recursion on the right of power makes chained exponents associate to the right. Require the parser to consume the entire input: a valid prefix followed by unknown text is still an invalid expression.
Attach the angle mode to the result
Show DEG and RAD next to the expression field. DEG converts each trig argument to radians by multiplying by pi/180 before evaluation; RAD passes the argument through as radians. MDN documents radians as the JavaScript trig-function basis.
| Expression and mode | Expected value |
|---|---|
| sin(30), DEG | Approximately 0.5 |
| sin(pi/2), RAD | Approximately 1 |
| ln(e), either mode | Approximately 1 |
| log(100), either mode | 2 |
| sqrt(9), either mode | 3 |
Angle mode applies to sin, cos, and tan, not to all numbers in the expression. Changing mode invalidates the prior result until Calculate runs again. Keep the expression and mode in the displayed record so a copied number still has its context.
Return an error instead of a stale answer
This is a real, finite-number calculator. Reject sqrt(-1), ln(0), log(0), division by zero, and any nonfinite intermediate or final value. For power, reject a negative base with a noninteger exponent and zero raised to a negative exponent. Explicitly treat 0^0 as outside this pad's domain.
For tangent, reject an argument when the absolute cosine of its normalized radian value is at most 1e-12. This is a declared numerical policy near singularities, not a new mathematical definition. In DEG, tan(90) should produce that error rather than a huge approximate value presented as an ordinary answer.
Limit raw input to 100 characters and parser nesting/recursive depth to 20. Require decimal literals to have a leading digit; scientific notation is outside this version. Reject assignment, property access, strings, unknown function names, implicit multiplication, and incomplete parentheses. A whitelist parser must not execute input through eval or Function.
Any edit clears the previous result. Clear empties expression, result, and error while retaining the selected mode. Backspace removes the selected text or the character before the caret and then invalidates the result. Native function buttons insert their named function and opening parenthesis at the caret using the same expression field; Calculate always uses the shared parser.
Display double-precision results as approximate numerical values, with a documented formatting rule such as 12 significant digits. Preserve the unrounded value in the current record; do not claim exact symbolic fractions or exact trigonometric simplification.
Copyable calculator prompt
Create an original self-contained HTML/CSS/JavaScript scientific numeric expression pad with readable source and an acceptance-test report. Use a labeled expression field, DEG/RAD, native numeric/operator/function keys, Calculate/Clear/Backspace and text errors. No copied vendor layout or artwork.
Whitelist decimal literals with a leading digit, +,-,*,/,^, parentheses, unary signs, pi/e and single-argument sqrt,ln,log(base10),sin,cos,tan. Explicit multiplication only; functions require parentheses. No scientific notation, assignment, property access, strings, unknown calls, eval or Function. Limit raw input 100 characters and recursive/nesting depth 20; consume all input.
Grammar: sum is products joined by +/-. Product is unary expressions joined by */. Unary is +unary, -unary, or power. Power is primary optionally followed by ^unary. Primary is number, pi/e, grouped expression or allowed function call. This gives right-associative power and unary minus below power on the left, while allowing signed exponents.
Test 2+3*4=14;(2+3)*4=20;2^3^2=512;-2^2=-4;(-2)^2=4;2^-2=0.25. Treat ^ as grammar power, never JavaScript XOR. DEG trig arguments multiply by pi/180; RAD arguments are already radians. Test DEG sin(30)≈0.5, RAD sin(pi/2)≈1, ln(e)≈1,log(100)=2,sqrt(9)=3.
Real finite domain: reject sqrt(-1),ln(0),log(0),1/0, nonfinite intermediate/results, negative-base fractional powers,0 to negative exponent and 0^0. Reject tan when abs(cos(normalizedArgument))<=1e-12 as an explicit numerical policy; test DEG tan(90). Mode or expression edits clear stale result until Calculate. Clear retains mode but empties expression/result/error. Backspace respects caret/selection; native function keys insert name plus opening parenthesis at caret. All paths use the same parser.
Record expression, mode and approximate result; document 12-significant-digit display and retain internal double value without symbolic-exactness claims. Test syntax/limits/domain/precedence/trig/shared key behavior, focus, actual article width and 360 px. Mark unexecuted parser/security/runtime checks not_tested. No graphing, symbolic solve, exam approval, network, storage or tested-host promise.
Keep the interpretation beside the HTML
The native source and parser acceptance cases remain the reference when changing this calculator. If you prepare an HTML version in NOS, the supplied product documentation supports HTML saving and rendering; verify its parser, native keys, modes, and errors in the actual workspace before calling that version a tested calculator. Explore NOS with prepared HTML, keeping the expression and angle mode beside each result so the next reader can tell what was actually calculated.