Glossary and Mathematical Symbols

The terms below describe SpicyRPN as implemented. A key legend, a register name, and a mathematical variable can use the same letters with different meanings. The symbol tables following the alphabetical glossary distinguish these uses. For key sequences, see the command reference; for formulas and numerical limits, see the mathematical reference.

Alphabetical glossary

A

Absolute value. The nonnegative size of a real number. For a complex number, ABS returns its magnitude, \(\sqrt {a^2+b^2}\), rather than the absolute value of its real component. See complex functions.

Accrued interest. The portion of a bond’s next coupon attributable to the time from the previous coupon date to settlement. Clean price plus accrued interest is dirty price. See bond calculations.

Accumulator. A running total summarizing statistical observations. The statistical bank holds a count and five sums, not the original observations; removing a point requires entering it again. See the six accumulators.

Accuracy. Closeness to the intended mathematical or measured value. More working digits can reduce rounding error but cannot correct inaccurate inputs, an unsuitable model, or a coarser solver tolerance. See precision and accuracy.

Actual day count. The difference between two Gregorian date ordinals. Consecutive dates differ by one day; the calculation does not add an extra day for the starting date. See date differences.

Affine conversion. A conversion using both scale and offset, such as Celsius to Fahrenheit. Temperature conversions act on readings; an interval needs different handling because offsets do not apply to differences. See temperature conversions.

ALG (algebraic entry). The mode in which operands and operators form an expression, with precedence and parentheses, evaluated by =. It retains its own unfinished expression and answer. Financial inputs use explicit storage and CPT; multi-input financial, statistical, and associative operations use labeled worksheets. See ALG mode.

Amortization. Splitting loan payments into interest and principal while updating the balance and elapsed payment count. It differs from a TVM solve, which finds one unknown for the whole payment stream. See amortization and the ALG procedure.

Angle unit. The shared DEG, RAD, or GRAD setting used for trigonometric arguments, inverse results, and polar angles. A full turn is \(360^\circ \), \(2\pi \) radians, or 400 gradians. Turn is also a conversion unit. See angle settings.

Annuity. Equal payments separated by equal periods. END places each payment at its period’s end; BEGIN places it at the beginning. The TVM register PMT is the signed payment amount. See payment timing.

Annunciator. A short display indicator, called a flag in this manual, identifying a setting, pending command, active entry, or occupied bank. Reading it does not execute a command. See display flags.

ANS. ALG’s saved successful answer, retained when the expression is cleared. It is separate from the RPN stack and its Last X and Last Y operands. See answer updates and reuse.

Arbitrary precision. Arithmetic with selectable working precision rather than a fixed hardware width. SpicyRPN accepts 16–10,000 decimal working digits and defaults to 600. Calculations still have finite precision and resource limits. See PREC.

Arithmetic storage. Updating a memory value by adding, subtracting, multiplying, or dividing by the current operand through a STO modifier. It changes the target’s stored value. See arithmetic storage.

Associative memory. A bank addressed by numeric keys rather than register numbers. Numeric equality of the real components identifies keys, so equal real keys address one entry. See storage and recall and ALG worksheets.

Associativity. The grouping rule for operators of equal precedence. ALG powers associate rightward: \(2^{3^2}=2^{(3^2)}\). Multiplication and division group leftward, including implicit multiplication. This parsing rule does not guarantee mathematical associativity of rounded arithmetic. See ALG precedence.

Autosave. Saving state after actions without a separate Save command. The local database includes values, settings, unfinished entries, and pending prefixes. It is not cloud synchronization. See saved state.

Avoirdupois. The mass convention used for ounces and pounds: 16 ounces make one pound, and one pound is exactly 0.45359237 kilograms. These are neither troy nor fluid-volume units. See mass conversions.

B

Bank. A separately maintained collection of values: ordinary registers, associative memory, statistics, finance, or cash flows. Occupancy flags and clearing commands apply to these collections. Both entry modes share the banks. See memory banks.

Basis, depreciable. Asset cost minus salvage value. The secondary depreciation result is remaining depreciable basis, excluding salvage: RPN Y or the ALG output Book value less salvage. It is not full book value. See depreciation inputs.

BEGIN. Payment timing with the first regular TVM payment at time zero, identified by BGN. In amortization, only the first payment with elapsed count n=0 has no preceding interest period. See BEGIN and END.

Binary operation. An operation requiring two operands. RPN uses \(Y\mathbin {\mathrm {op}}X\); an ordinary binary result replaces the pair and drops the stack. Percentage functions instead retain Y. See stack effects.

Bit. A binary digit. MPFR precision counts binary significand bits; a request for \(d\) decimal working digits becomes \(\lceil d\log _2 10\rceil \) bits. See numeric representation.

Bond. A security represented here by regular semiannual coupons and redemption of 100 per 100 of face value. The app uses a maturity-anchored schedule and actual coupon-period day counts. See the supported bond model.

Book value. Asset cost less accumulated depreciation, including retained salvage. Add salvage to the remaining-basis result to obtain book value. See depreciation results.

Bracket, root. Lower and upper bounds whose function values have opposite signs, or whose endpoint is a root. An IRR bracket restricts the search and can select among multiple returns. See IRR bounds.

Branch cut. A boundary across which a chosen single-valued complex function can be discontinuous. Logarithms, roots, and inverse functions require branch conventions; real and complex modes can return different valid roots. See principal branches.

Build. A compiled application or the process producing it. A target defines what is built, a scheme selects actions and configuration, and a destination selects the Mac, device, or Simulator environment. See building the source.

C

CANCEL. A control that dismisses a pending selection or an ALG worksheet’s unaccepted edits. It does not undo accepted values or completed operations. See cancellation scope and controls.

Cancellation, numerical. Loss of significant digits when subtracting nearly equal approximations. Increased precision can help, but stable formulas also matter. Composed calculations and custom special-function approximations can remain sensitive to cancellation even when each primitive is correctly rounded. See complex numerical limits.

Cash flow. A signed payment or receipt at a specified time. In the cash-flow bank, \(CF_0\) occurs at time zero and each expanded entry advances one equal period. Outflows are negative and receipts positive from the chosen viewpoint. See cash-flow timing.

Cash-flow index. A zero-based position in the expanded cash-flow list. Register n selects the final included index for NPV and IRR, not the number of stored entries. SHOW has a separate inspection position. See calculation selection.

Ceiling. The least integer greater than or equal to a real value. For example, \(\lceil -1.2\rceil =-1\). It differs from floor and nearest-integer rounding. See integer functions.

Checksum. A value computed from file contents to check that a source or library archive matches an expected artifact. It identifies bytes rather than establishing program correctness. See source acquisition.

Clean price. Bond price excluding accrued interest, per 100 of face value. PRC produces this amount and stores it in PV; YTM uses it as the price input. See price and yield.

Clear. An operation whose scope depends on the command: X, an expression, the stack, or a selected bank. Stack clearing does not reset every bank or setting. A pending prefix can consume a clear key as cancellation. See clearing scope.

Code signing. Attaching identity and integrity information to an application for its execution or installation environment. Device deployment can require a team and provisioning configuration. See signing and installation.

Combination. A selection of \(r\) objects from \(n\) distinct objects without regard to order, counted by \(\binom nr=n!/[r!(n-r)!]\). Inputs must be integers with \(0\le r\le n\le 10{,}000\). See counting functions.

Commit, entry. Converting a numeric draft into a calculator value. Committing a number differs from evaluating an entire ALG expression or duplicating a stack value. See RPN ENTER behavior and ALG evaluation.

Complex number. A single value \(z=a+bi\) with real and imaginary components. Both components occupy one stack or memory position; rectangular and polar views represent the same value. See complex entry, representation, and mode behavior.

Compound interest. Growth in which each period’s interest contributes to the balance used in later periods. Fractional periodic rate \(r\) produces factor \((1+r)^n\). TVM expects percentage \(i=100r\). See rates and periods.

Constant recall. Repeatedly retrieving a value without changing its stored source. Ordinary-register RCL pushes the value in RPN and does not consume the register. See using a stored constant.

Conversion family. Compatible units grouped by quantity, such as length, pressure, or energy. CONV selects source and destination within a family and returns a number; values acquire no persistent unit tags. See unit selection.

Correlation coefficient. The dimensionless measure \(r\) of linear association returned with a regression estimate. It requires variation in both coordinates. A constant response can have a valid fitted line but undefined correlation. See estimation and correlation.

Coupon. A bond’s periodic interest payment. PMT stores the annual coupon percentage; each semiannual coupon is \(PMT/2\) per 100 of face value. Coupon rate and yield are different inputs. See bond inputs.

CPT. The ALG prefix for explicitly computing a financial result. It distinguishes solving from storing an input. See computation targets and procedure.

Crossover depreciation. Declining balance that switches to straight line when distributing remaining basis over remaining life gives a larger deduction. The final period reaches salvage. See DB to SL.

D

Database. The local SQLite store containing calculator state and value records. Saving is transactional; a failed save is handled by restoring the previous saved state where possible. See storage errors.

Date order. MDY or DMY interpretation of numeric dates. In MDY, the month precedes .DDYYYY; in DMY, the day precedes .MMYYYY. Changing the setting changes interpretation, not stored digits. See date entry.

Day-count convention. A rule translating dates or days into a financial interval. Actual days, the implemented 30/360 date rule, and simple interest divided by 360 or 365 are separate conventions. See day counts.

Decimal place. A position after the decimal point. FIX, SCI, and ENG specify fractional places in the displayed mantissa; this differs from working digits. See display notation.

Declining-balance depreciation. Depreciation based on current book value and rate \((F/100)/L\), where \(F\) is factor percentage and \(L\) useful life. Deductions respect salvage and remove remaining basis in the final year. See declining balance.

Depreciation. Allocating an asset’s depreciable cost over useful life. Each requested year is computed from cost, salvage, life, and method; the app does not maintain a cumulative depreciation ledger. See depreciation.

Digit ruler. The CAL display aid marking positions in groups of five during long-number inspection. It counts digits, not their accuracy. See long-number inspection.

Dirty price. Bond settlement price including accrued interest: clean price plus accrued interest. PRC returns clean price. See bond pricing.

Discount rate. The rate translating future cash flows into present values. NPV uses percentage i per interval between cash-flow entries; the rate and interval must agree. See net present value.

Display precision. The fractional-digit count requested for display notation. Formatting normally preserves the stored value; RND separately changes it. See displaying and rounding.

Domain. Inputs on which a function is defined in the selected mode. Negative values are outside the real square-root domain but have principal complex square roots. See function domains.

Drop. Removing X and shifting deeper values toward it. A fixed stack repeats its deepest value; an unlimited stack shrinks and retains zero X if otherwise emptied. See stack drop.

E

Effective rate. Actual growth over an interval after compounding. With \(m\) periods per year and fractional periodic rate \(r\), the effective annual rate is \((1+r)^m-1\). See rate conventions.

END. Timing with regular payments at times 1 through \(n\). This is the default TVM timing; BGN is absent. See payment timing.

Engineering notation. ENG display with an exponent divisible by three and one to three digits before the mantissa’s decimal point. Fractional places do not specify a fixed significant-digit count. See SCI and ENG.

Entry. The draft being edited. ENTRY means an active numeric draft in RPN and an entire unfinished expression in ALG. Drafts survive mode switches and saved-state restoration. See the ENTRY flag.

Ephemeral test mode. A development configuration with nonpersistent state, protecting normal on-disk state from test changes. A uniquely named test database is another isolation mechanism. See test environments.

Error function. The function \(\operatorname {erf}(x)=2\pi ^{-1/2}\int _0^x e^{-t^2}\,dt\). Its complement is \(\operatorname {erfc}(x)=1-\operatorname {erf}(x)\); using erfc directly preserves small real-tail values better than subtraction. See erf and erfc.

Exponent. The power in \(a^b\), or the power of ten in a literal such as \(1.2\times 10^5\). EEX edits the latter; it is not the general power operator. See scientific-number entry.

Expression. Operands, operators, groups, and function calls representing a calculation. ALG retains this structure until evaluation; RPN executes operations on available operands. See ALG expressions.

F

Factorial. For a nonnegative integer \(n\), \(n!=1\cdot 2\cdots n\), with \(0!=1\). Real-mode factorial accepts integers through 10,000. Complex mode extends it through \(\Gamma (z+1)\), including noninteger real inputs, subject to poles and numerical limits. See factorials.

Financial register. One of n, i, PV, PMT, or FV. Financial families reuse them with different meanings; check retained values before a calculation. See financial registers and the context table below.

Fixed-point display. FIX formatting with a selected number of fractional places. Scientific fallback can occur when fixed formatting cannot usefully show the value. It is a display choice, not fixed-point arithmetic. See FIX.

Fixed stack. An RPN stack with a configured position count. Default depth is five; the UI accepts 2–1,000. Lifting can discard the deepest value; dropping repeats it. See stack depth.

Fixture, test. Known inputs, expected results, and setup for a repeatable test. Oracle fixtures can supply expectations calculated outside the application. See oracle data.

Flag. An annunciator reporting state. MEM, ASSOC, STAT, FIN, and CF identify occupied banks, including stored zero; ENTRY and prefix flags identify unfinished work. Occupancy does not certify a complete or valid problem. See all flags.

Floating-point number. A finite-precision significand with an exponent, permitting a wide magnitude range. MPFR uses binary significands; many finite decimal fractions therefore require rounding. See number representation.

Floor. The greatest integer no larger than a real value. For example, \(\lfloor -1.2\rfloor =-2\), whereas truncation gives \(-1\). See integer functions.

Fractional part. The signed remainder after truncation: \(\operatorname {FRAC}(x)=x-\operatorname {INT}(x)\). Thus FRAC of \(-1.2\) is \(-0.2\). See INT and FRAC.

FUNC. The ALG prefix making a selected function start an explicit call, with groups or comma-separated arguments where applicable. See function-call entry.

Future value. The signed terminal TVM amount at time \(n\). The FV register instead holds salvage value for depreciation. See TVM registers.

G

Gamma function. The factorial extension satisfying \(\Gamma (n+1)=n!\) for nonnegative integers, with poles at zero and negative integers. Real log-gamma is not a general \(\ln |\Gamma (x)|\) command. See gamma and log-gamma.

GMP. The GNU Multiple Precision Arithmetic Library, used beneath MPFR. Building the app requires appropriate library artifacts for each target platform. See numeric libraries.

Gradian. One hundredth of a right angle; a full turn contains 400 gradians. GRAD selects this interpretation for trigonometric and polar angles. See angle units.

Gregorian calendar. The calendar used for dates, extended backward with the same leap-year rules throughout years 1–9999. Numeric dates have no time zone or time of day. See calendar dates.

Guard digits. Extra intermediate precision reducing rounding loss. They improve numerical calculations without making approximations exact or removing domain limits. See complex arithmetic.

H

Hyperbolic functions. The exponential-based sinh, cosh, and tanh functions and their inverses. HYP and INVHYP select them through trigonometric keys. Their arguments are not interpreted as DEG, RAD, or GRAD angles. See hyperbolic functions.

I

Imaginary unit. The number \(i\) satisfying \(i^2=-1\), used in \(a+bi\). It is unrelated to financial i, which holds a real percentage rate or depreciation factor. See complex components.

Immutable value. A value whose stored components and creation precision do not change in place. Raising precision affects subsequent calculations and cannot reconstruct digits lost earlier. See existing values.

Implicit multiplication. ALG multiplication inserted between adjacent compatible operands or groups. It has the same precedence as explicit multiplication and division. Use parentheses for another intended grouping. See implicit multiplication.

Infix. Notation placing operators between operands, as in \(2+3\). ALG uses infix expressions. Separately, INFIX in precision help means working decimal digits; it does not select ALG. See precision terminology.

Integer part (INT). Truncation toward zero. Scientific INT, on orange-shift ENTER in RPN or orange-shift \(1/x\) in ALG, differs from blue-shift financial i, whose INT legend means simple interest. See integer and fractional parts.

Interest rate. A proportion charged, earned, or used for discounting over an interval. Financial i uses percentages: enter 5 for 5%. Its period is context dependent: periodic for TVM and NPV, annual for simple interest and bond yield. See rate units.

Intermediate result. A value calculated for later use in a larger calculation. The RPN stack retains several such values; ordinary memory can preserve them beyond subsequent stack operations. See intermediate results.

Internal rate of return (IRR). A periodic percentage at which selected cash flows have zero NPV. There may be no root, one, or several; a guess or bracket influences the search. The result does not automatically replace i. See IRR.

Inverse function. A function reversing another on a chosen domain or branch. Inverse trigonometry returns an angle, not the reciprocal of the corresponding trigonometric value. See inverse trigonometry.

Iteration. One repeated step of an algorithm. Financial solvers have iteration, evaluation, and tolerance limits independent of working-digit count. See solver policy.

K

Key. Either a keyboard control or, in associative memory, the numeric value identifying a stored item. A shifted legend selects an operation; an associative key is the real component of a numeric value, in either complex setting. See shifted keys and numeric keys.

L

Last X and Last Y. Separate RPN registers preserving earlier operands for recovery and reuse. They are not the current X and Y positions, shown as S0 and S1, and do not form an undo history. See which operations save and recall operands.

LaTeX. The source-document system for this manual. LuaLaTeX typesets it, and latexmk coordinates passes and index processing. The calculator is built separately. See manual builds.

Least squares. Fitting a model by minimizing squared residuals. SpicyRPN’s ordinary unweighted fit is \(y=a+bx\). See linear regression and ALG statistical outputs.

Lift. Moving stack values deeper to make room at X. Starting an RPN number lifts once; committing it does not lift again. A fixed stack can lose its deepest value. See stack lift.

Linear conversion. Conversion by scale without offset, such as meters to feet. Exact decimal or rational conversion factors are still evaluated at finite working precision. See conversion arithmetic.

Logarithm. The exponent needed to obtain a value from a base. LN uses base \(e\); LOG uses base 10. RPN’s arbitrary-base logarithm takes base Y and argument X. See logarithms.

M

Magnitude. The nonnegative radial component \(|z|\) of a complex value, paired with phase in polar display and returned by ABS. It generally differs from the real component. See polar representation.

Mantissa, display. The coefficient before the power of ten in SCI or ENG, such as 1.234 in \(1.234\times 10^6\). The stored binary significand is a different representation. See number notation.

Maturity. A bond’s final payment date. Preceding semiannual coupon dates are derived backward from maturity, preserving its month-end convention. See bond dates.

MCLR. A prefix that selects a group to clear, rather than an individual memory address. See selectors, clearing scope, and cancellation.

Mean, arithmetic. Observation sum divided by count. Paired data has a separate mean for each coordinate; this differs from the weighted mean. See means and their outputs.

Memory occupancy. The presence of stored data, including explicit zero. Recalling an unset register returns zero without occupying it. A zero display therefore does not establish whether a bank is empty. See empty and zero.

Mode. A setting selecting behavior, such as RPN/ALG, real/complex, or BEGIN/END. Their scopes differ; switching entry mode preserves each workspace. See shared and independent state.

Modulo and remainder. Operations subtracting an integer multiple of a divisor. SpicyRPN distinguishes truncating remainder from IEEE-style remainder using a nearest-even quotient. Neither implies an always-nonnegative mathematical modulo. See remainder conventions.

MPC. The GNU Multiple Precision Complex library, built on GMP and MPFR, used for SpicyRPN’s complex arithmetic and elementary functions. Each primitive’s real and imaginary results are individually rounded; composed calculations and custom special functions retain their own numerical limits. See complex arithmetic and MPC build setup.

MPFR. The multiple-precision floating-point library used for real arithmetic and many real functions. Precision is specified in bits; ordinary arithmetic rounds to nearest with ties to even. See MPFR representation.

N

NaN. “Not a Number,” representing an undefined numerical result. It is not a valid ordinary financial input or real component of an associative key. Invalid operation results commonly become displayed errors. See calculation errors.

Net present value (NPV). Selected cash flows discounted to time zero at percentage i, including undiscounted \(CF_0\). Register n selects the final included index. See NPV.

Nominal annual rate. An annual percentage quoted as a multiple of a periodic rate. For monthly compounding, divide the nominal annual percentage by 12; this does not convert an effective annual rate. See rate conversion.

Numeric literal. An entered number’s characters, including decimal and optional exponent. Drafts can preserve trailing zeros and unfinished exponents before conversion to values. See numeric entry.

O

Operand. A value an operation acts on. RPN unary functions use X; binary functions use Y followed by X. ALG precedence and grouping determine operands. See operand order.

Oracle, test. An independent source of expected results, such as a separate high-precision implementation and its fixtures. Agreement is evidence subject to matching conventions and inputs. See financial oracles.

Ordinary register. One of ten general-purpose memory locations R0–R9. They are separate from the current stack positions X (visible S0) and Y (visible S1), and from Last X and Last Y. See ordinary storage and recall.

P

Packed date. A number whose integer and six fractional decimal positions encode calendar fields under MDY or DMY. It has no attached date type; ordinary numeric arithmetic is not calendar arithmetic. See date encoding.

Payment. The signed equal periodic cash flow in PMT for TVM and amortization. For bonds, PMT instead contains an annual coupon percentage. See payment registers.

Percent. A proportion per hundred. RPN % computes \(YX/100\), retaining Y; percentage change and percentage of total use different formulas. In worksheet field text, infix % instead denotes truncating remainder. See percentage functions.

Period. The equal interval in a financial calculation. Rate, payment spacing, and period count must agree. No calendar unit is attached to a stored count. See period consistency.

Permutation. An ordered selection of \(r\) objects from \(n\), counted by \(n!/(n-r)!\). Inputs must be integers with \(0\le r\le n\le 10{,}000\). See permutations and combinations.

Persistence. Retaining state across launches, including both entry workspaces and shared banks and settings rather than only the visible answer. See resuming work.

Phase. A complex value’s polar angle, also called its argument. Display follows the angle unit; zero has phase zero by convention. See polar angles.

Polar representation. Magnitude and phase, \(r\angle \theta \), equivalent to \(r(\cos \theta +i\sin \theta )\). Stored components remain rectangular. See polar entry and display.

Pole. A singularity where a function becomes unbounded, such as gamma at a nonpositive integer. Complex mode does not make a pole a finite valid result. See gamma’s domain.

Postfix. Placing an operation after its operands, as in RPN arithmetic. Many ALG scientific keys instead act postfix on the trailing operand or closed group; FUNC starts an explicit call. See ALG functions.

Precedence. Operator priority in ALG grouping. Parentheses override it; multiplication and division precede addition and subtraction. See precedence rules.

Precision. Digits carried in a representation or calculation. Working precision, display places, and algorithmic stopping accuracy differ. More displayed digits are not necessarily more meaningful digits. See three precision concepts.

Prefix, command. A pending selection modifying subsequent keys, such as STO, RCL, HYP, FUNC, CPT, or MCLR. It is distinct from prefix mathematical notation and unit prefixes such as kilo. See canceling prefixes.

Present value. The signed TVM amount at time zero, in PV. Other families reuse PV for balance, negative simple-interest principal, bond clean price, or asset cost. See financial registers.

Primary result. The designated ALG output that becomes ANS after a successful computation. Selecting a companion output does not redefine the primary result or change ANS. See worksheet outputs and transfers.

Principal branch. The chosen standard value of a multivalued complex function. On negative real input, SpicyRPN’s logarithm uses imaginary part \(+\pi \), and square root uses the positive imaginary root. See branch conventions.

Principal, financial. Capital excluding interest. Simple interest uses \(P=-PV\); amortization separates principal from interest. This meaning is unrelated to a principal complex branch. See simple interest.

Provenance. Internal records linking a value to its operation and sources. They support storage and development inspection, rather than providing user-facing undo or calculation history. See stored state.

R

Radian. The angle subtending an arc equal in length to its radius. A full turn is \(2\pi \) radians. Complex exponential and logarithmic formulas use radian-valued imaginary arguments independently of display angle units. See complex conventions.

Real-only operation. An operation defined on real components, including finance, statistics, conversions, and several integer functions. A nonzero imaginary input in complex mode can produce “Used real portion only.” See real-only functions.

Recall. Retrieving a stored value without consuming its source. Insertion, stack movement, and Last-register effects depend on the memory bank and entry mode. See ordinary recall and specialized banks.

Reciprocal. The inverse \(1/x\), defined for nonzero \(x\). It is unary, unlike exchanging a division’s two operands. See powers and reciprocal.

Rectangular representation. Real and imaginary components \(a,b\) of \(a+bi\). Component Swap exchanges these components even in polar display. See component swapping.

Redemption value. The amount repaid at bond maturity, fixed here at 100 per 100 of face value. FV does not alter this amount. See bond assumptions.

Register. A named value location. Current RPN X and Y appear as S0 and S1; ordinary R0–R9, saved Last X and Last Y, and financial registers are separate locations. See register names.

Regression. Estimating a relationship from observations. SpicyRPN supports the ordinary linear fit \(y=a+bx\) from paired accumulators and can return fitted \(\hat y\) and correlation. See linear regression.

Repetition count, cash flow. The total equal consecutive occurrences specified by Nj, including the one already entered by CFj. Storage expands repetitions into period entries. See repeated flows.

Residual. The difference between a model result and its target. In regression, observed Y minus fitted Y; in a financial solve, the remaining equation value that should be zero. See financial solver policy.

Roll. A cyclic rearrangement of a fixed stack, up or down, without arithmetic. Unlimited stacks do not support roll. See stack rearrangement.

Root. Either an indexed root, such as a cube root, or a solution of \(f(x)=0\). Complex indexed roots use principal values; financial solvers seek real roots in allowed domains. See indexed roots and equation solving.

Rounding. Replacing a value with one representable at a selected precision or increment. Ordinary MPFR arithmetic, display, and NINT use nearest with ties to even. Financial RND rounds to decimal places with ties away from zero. See rounding rules.

RPN (Reverse Polish Notation). Entry in which operands precede the operation using them. The stack retains values and intermediate results, letting the user choose evaluation order without expression parentheses. See learning RPN.

S

Salvage value. The residual asset value retained after depreciation, in FV. Depreciable basis excludes it, and methods limit depreciation so salvage is not consumed. See asset inputs.

Sample, statistics. An entered pair of X and Y values; use Y equal to zero for single-variable work. Count records observation updates, not total Y weights. Original observations are not retained as a list. See statistical entry.

Scientific notation. SCI display with one digit before the decimal point and an explicit power of ten. For nonzero values, \(d\) fractional places normally show \(d+1\) significant digits. See display formats.

SDK. A Software Development Kit providing platform headers, libraries, and tools. Mac, iOS device, and Simulator remain different destinations even when CPU architectures coincide. See build prerequisites.

Settlement. The bond valuation date, which must precede maturity. A coupon due on settlement is excluded from the future-payment schedule. See settlement conventions.

Shift. A one-operation keyboard layer selected by orange f or blue g, identified by its flag. It selects a legend rather than multiplying by \(f\) or \(g\). See shift controls.

Sign convention. A consistent financial viewpoint: outflows are negative and receipts positive. Changing viewpoint reverses all relevant signs, not just one amount. See cash-flow signs.

Significand. Precision-bearing floating-point digits, separate from the exponent. Stored significands are binary although entry and display are decimal. See number representation.

Significant digits. Digits expressing numerical detail, counted from the first nonzero digit. They differ from places: 123.45 has five significant digits and two fractional places. See digit counts.

Simple interest (INT). Interest proportional to principal, annual rate, and elapsed days without compounding. Blue-shift financial i returns 360-day and 365-day basis amounts. This INT differs from integer part on orange-shift ENTER in RPN or orange-shift \(1/x\) in ALG. See simple interest.

Simulator. Apple’s environment for running iOS applications on a development Mac. A Simulator binary is not interchangeable with a device binary merely because both are arm64. See iOS destinations.

Solver. A procedure calculating an unknown from inputs. TVM solves one register using all four others, including unwritten zeros; rates can require iterative root finding. See store and solve.

SQLite. The embedded database engine for local persistence. The app uses transactions and write-ahead logging to maintain saved state. See source organization.

Stack. The ordered RPN collection with current X at the working end, displayed as S0, and Y next, displayed as S1. Deeper positions follow. The stack is separate from memory banks and from the saved Last X and Last Y operands. See the RPN stack.

Stack inspector. The read-only full-stack view opened from the display triangle, preserving entries and pending prefixes during inspection. See inspecting the stack.

Standard deviation. Dispersion measured in the original data units. SpicyRPN returns sample deviations using denominator \(n-1\), requiring at least two observations. See sample deviation.

Standard gravity. The defined acceleration \(g_0=9.80665\,\mathrm {m/s^2}\), a fixed conversion reference rather than measured local gravity. See mechanical units.

Static library. Compiled code linked into an application during build. It must match both platform and architecture; arm64 device and Simulator libraries differ. See library deployment.

Straight-line depreciation. Allocating basis evenly over useful life, with a fractional final year receiving a fractional annual deduction. See SL and SYD.

Sum-of-years’-digits depreciation. Allocating basis with descending life weights. Fractional life retains fractional weights, such as 2.5, 1.5, and 0.5, instead of first rounding life to three. See fractional life.

SwiftUI. Apple’s interface framework used by SpicyRPN. The source directory named Preview contains the live keyboard and display implementation. See project layout.

T

Ties to even. Nearest rounding that selects an even final retained digit at an exact halfway case. NINT maps both 1.5 and 2.5 to 2. See rounding conventions.

Time value of money (TVM). The relationship among periods, periodic interest, present value, equal payments, and future value. The five registers describe regular payments rather than arbitrary cash-flow sequences. See TVM calculations.

Tolerance. A threshold stopping an iterative calculation, such as interval width or residual size. It is independent of display places; 600 working digits do not imply a 600-digit solver stopping threshold. See solver tolerances.

Transaction, database. Storage changes saved together or rolled back together, helping prevent partially updated calculator state from becoming the saved state. See save failures.

Truncation. Removing the fractional part toward zero. Unlike floor, it moves negative nonintegers toward zero. Scientific INT and the quotient in truncating remainder use this rule. See integer operations.

U

Unary operation. An operation using one operand, such as reciprocal. In RPN it normally replaces X without consuming Y; in ALG it normally acts on the trailing operand or group. See unary functions.

Unit alias. A short conversion label such as lb, US gal, or Imp gal. Qualifiers matter: oz means mass, while US fl oz means volume. See the unit-symbol table.

Unlimited stack. The depth-zero RPN setting, growing and shrinking as needed within available resources. It retains a zero X when otherwise empty and does not support roll. See stack settings.

Useful life. The positive depreciation duration stored in n. It may be fractional; requested years must still be integers beginning at one. See fractional life.

V

Variance. The square of standard deviation. Sample variance divides the sum of squared deviations from the mean by \(n-1\). Positive X variation is required for a nondegenerate fitted line. See dispersion.

W

Weighted mean. The value \(\sum xy/\sum y\), treating each Y as its paired X’s weight. Weights do not alter count or make other statistical functions frequency-weighted. See weighted mean.

Working precision. Precision for new values and calculations, selected through PREC and shared across entry modes. Existing values retain their creation precision. See working digits.

Worksheet. An ALG panel with named inputs and outputs, separate from the main expression. Accepted inputs and unaccepted field drafts are distinct. See evaluation, acceptance, computation, and result transfer.

Workspace, entry. One mode’s independent state: RPN stack and draft, or ALG expression and answer. Memory banks and many settings are shared. See switching workspaces.

X–Z

Xcode. Apple’s environment for building and running the app and tests. Scheme, configuration, destination, and installed SDKs affect the build. See development tools.

Yield to maturity. The annual nominal percentage implied by clean bond price, coupons, redemption, and dates under the semiannual model. It differs from the bond’s coupon percentage. See bond price and yield.

Zero, stored and signed. A number that can occupy memory. Floating-point values can also distinguish positive and negative zero, affecting some branch-boundary angles. Neither distinction means an empty bank contains stored data. See stored zero and signed zero.

Mathematical symbols by context

Symbols are local to their formulas. Italic mathematical letters are not automatically register names or commands. In particular, \(i\), \(n\), \(r\), \(P\), and \(N\) have several meanings.

Entry, stack, and overloaded notation

Arithmetic, functions, and precision

Complex numbers

Statistics and regression

Financial registers, TVM, and simple interest

These are context-dependent meanings, not permanent types attached to the registers. Check the selected problem’s inputs before calculation.

Cash flows and numerical rate solving

Dates and bonds

Depreciation

Conversion symbols and aliases

These labels identify conversion choices; typing letters does not attach units to values. Prefix case matters: kilo k is \(10^3\), mega M is \(10^6\), giga G is \(10^9\), centi c is \(10^{-2}\), milli m is \(10^{-3}\), micro \(\mu \) is \(10^{-6}\), and nano n is \(10^{-9}\). The interface’s micro sign µ has the same unit meaning as Greek \(\mu \). Bare m means meter; mm means millimeter. The table below distinguishes easily confused symbols. Every selectable unit appears in the complete unit inventory; factors appear in the mathematical reference.