15   Complete Command and Settings Reference

Use this chapter to find a key, check operand order, or determine what a command changes. The keyboard maps include every main and alternate legend. The alphabetical entries group closely related operations while identifying their individual formulas and restrictions. The explanatory chapters provide longer examples; chapter C supplies the numerical conventions behind the results.

This reference describes the exposed calculator controls. Both entry modes support scientific, financial, statistical, and memory operations. ALG uses explicit CPT and labeled worksheets where RPN uses stack operands; the mode-specific procedure matters.

15.1   Reading an entry and following an example

A key shown after f or g identifies the physical main key to press, unless its alternate legend is explicitly named. Thus f PMT selects AMORT; g PMT selects RND. The INT legends have two meanings: orange ENTER in RPN and orange \(1/x\) in ALG truncate a number, while blue financial i selects simple interest.

The following effect codes make the mathematical entries compact. They describe a successful RPN operation after an active number is committed. ALG uses the expression rules immediately below instead. Unless an entry says otherwise, a scientific function changes no memory bank or setting.

In RPN instructions, X is the current value in the visible S0 position; Y is the next value in S1. These are current stack positions. Last X and Last Y are separate saved operands from earlier operations, not other names for S0 and S1. Statistical coordinates and ALG fields labeled X and Y identify inputs; their labels do not imply RPN stack positions.

A fixed stack discards its deepest value on a lift and repeats its previous deepest value on an ordinary drop. An unlimited stack grows and shrinks, keeping one zero if DROP empties it. A binary function requires two positions. A unary function on a one-position unlimited stack preserves Last Y. For financial and statistical entries, the detailed stack procedure is RPN-specific; each entry also gives its ALG route separately. Special statistical and financial effects are stated separately; they must not be inferred from the number of inputs. With CMPLX off, each newly written value and each newly saved Last operand has an imaginary component of zero. Moving an existing stack value preserves its components. See chapter 2 and section 6.5.

In ALG, a unary function opens a call when an operand is expected; after an operand it applies to that preceding number, group, or function result. A binary key goes between its first and second operands. FUNC followed by a unary or binary key instead opens an explicit call; separate two arguments with g FUNC and close with ). The first argument corresponds to Y and the second to X. Constants insert a factor after an existing operand. ANS and recall instead replace a trailing operand. Successful equals, worksheet ENTER, and direct or worksheet computation update ANS. Worksheet calculations use a declared primary result; browsing outputs does not change it. These operations never alter the suspended RPN stack or its Last registers. See chapter 4.

The reference start

Every numerical example below starts independently in RPN, real mode, fixed depth 5, 600 working digits, and FIX 4, with no open tool, active shift, or pending command. Before its displayed sequence, press f \(1/x\) for CLEAR. The setup procedure is in section 2.2. Where an entry specifies ALG, select ALG, retain real mode, 600 digits and FIX 4, and start with its unshifted CLEAR instead. Examples involving angles specify DEG; date examples specify MDY and FIX 6. Results usually omit trailing display zeros. A negative input is entered as its magnitude followed by +/\(-\).

No example assumes an empty memory bank. Examples that store a register, clear statistics, or start cash flows deliberately replace that data. Financial examples initialize every input they use. A semicolon in a printed sequence only separates steps for readability; it is not a key.

15.2   Complete keyboard maps

Read each map top to bottom, with a rule separating physical rows where useful. A dash means there is no alternate binding; selecting that layer does not execute the main function. In portrait, swipe the top two rows left for Financial or right for Scientific. Paging preserves entry, shifts, and pending commands. In landscape, both panels are visible. The remaining rows stay fixed. RPN ENTER occupies two row heights. ALG’s left entry column has normal-size EEX, \(1/x\), +/\(-\), and equals keys from top to bottom, placing equals on the bottom row. RPN has 49 key positions, with 39 visible in portrait; ALG has 50, with 40 visible in portrait. See section 1.5 for the arrangement.

For direct ALG computation, first finish or clear any unfinished compound expression; a lone scalar is allowed. In ALG, the five financial register keys always store the displayed operand. CPT then a register solves it; RCL then a register recalls it. CPT followed by NPV or IRR computes directly from the bank. Unprefixed cash-flow and multi-input financial keys open labeled worksheets. BEGIN/END, date order, CLfin, and CLcf retain their shared settings or clear scopes. Orange n/i and RND are direct calculations. See section 4.11 and section 4.12.

The shift keys themselves select a layer regardless of the current layer; pressing the same shift twice cancels it. Their map cells describe that control, rather than additional shifted commands. The ALG middle rows have no stack, roll, DROP, or LAST keys. CPT starts explicit computation; STAT and the associative-memory legends open worksheets. See section 4.11 and section 4.12.

FIX uses a different input sequence in each mode. SCI and ENG have no direct current key: use FSE to cycle to them. Orange 1, 2, and 3 have no binding. CONV, PREC, STACK, IRR[a,b], SHOW, and HELP open panels; their fields are separate from calculator operands.

15.3   Physical-keyboard shortcuts

Give the calculator display input focus before typing. These shortcuts select calculator keys; they are not a text field for pasted formulas or function names. Unless the table states otherwise, an active f or g layer changes the selected key in exactly the same way as a tap.

A parameter panel receives keyboard input in its own fields, and the stack inspector holds back calculator input while open. With the ALG FIX prompt active, digits collect its count and Return or equals accepts it; another keyboard character cancels the prompt without entering that character into the expression. No dedicated shortcut types an entire scientific-function name.

15.4   Alphabetical reference: A through F

ABS — absolute value

Keys/modes: f \(\times \), both modes; effect U. Return \(|X|\) in real mode, or the real magnitude \(\sqrt {a^2+b^2}\) of \(a+bi\) in complex mode. Angle and display settings do not change its mathematical meaning. Example from the reference start: 3 +/\(-\) f \(\times \) gives 3. See section 7.6 and chapter 8.

AMORT — a block of equal payments

RPN keys and effect: f PMT, RPN. X supplies an additional whole payment count, 0–100 000. Stored n is elapsed payments, i is periodic percent, PV the signed balance, and PMT the oppositely signed nonzero payment; all four must be explicitly stored. FV is unused. Require nonnegative integer n and \(i>-100\). An unlimited stack needs two operands even though old Y is not an input to the financial formula. Consume X and return total interest in X, total principal in Y, moving old Y to S2. Save old X/Y; update financial n and PV. BEGIN waives interest only on the first payment when initial n is zero. Intermediate amounts are not rounded to the display count.

Example, reference start with END selected: enter 0 STO n; 1 STO i; 1000 STO PV; 100 +/\(-\) STO PMT; 2 f PMT. Results are X = \(-19.1\), Y = \(-180.9\), n = 2, PV = 819.1. See section 11.11.

In ALG, the same key opens Amortization; accepted named inputs produce Interest, Principal, Balance, and updated n. See section 11.12.

ANS — previous ALG answer

Keys/modes: ANS, ALG only. Insert the last successful ALG result at an operand position, or replace the trailing operand or closed group. After a completed result it starts a new expression. It does not evaluate the expression or change ANS itself. CLEAR and failed evaluation preserve ANS; its initial value is zero. With CMPLX off, insertion copies only the real component and leaves the saved answer intact. Example from the ALG reference start: 2 + 3 =; CLEAR 10 \(\div \) ANS = gives 2. See section 4.8.

Arithmetic — add, subtract, multiply, divide

Keys/modes: +, \(-\), \(\times \), \(\div \), both modes; effect B. Calculate \(Y+X\), \(Y-X\), \(YX\), or \(Y/X\), using both complex components when enabled. Division needs a nonzero divisor for a finite answer. ALG gives multiplication/division priority over addition/subtraction; equal-priority chains run left to right. Examples, each from the reference start: 12 ENTER 3 followed by the respective operator gives 15, 9, 36, or 4. A leading ALG minus has lower priority than a following power. See section 3.3 and section 4.2.

Associative storage and recall

Keys/modes: f STO and f RCL, both modes. In ALG these open Key/Value worksheets; accept inputs and choose STORE or RECALL, then Use value for insertion. See section 6.7. In RPN, store uses key X and value Y, saves both Last operands, and drops X. Recall replaces key X with its value, saving the key in Last X and preserving Last Y. A missing key returns zero without storing a pair. Numeric equality of the real components determines a match in both modes. The key is stored as a real value; an imaginary component is ignored and a NaN real component is invalid. Keys with equal real parts address the same entry, so storing again replaces its value. The value copied from Y or recalled into X includes both components with CMPLX on and only its real component with CMPLX off. Recall leaves the stored source unchanged.

Example: 42 ENTER 123 f STO; 123 f RCL returns 42, replacing any earlier pair for that key. The bank is distinct from R0–R9. See section 6.7.

atan2 — direction from two coordinates

Keys/modes: g HYP, both modes; effect B, real-only. Supply vertical coordinate Y first, horizontal X second. Return the quadrant-aware angle \(\operatorname {atan2}(Y,X)\) in the selected angle unit, within a half-turn on either side of zero. The origin has no geometric direction. Example, DEG: 1 ENTER 1 +/\(-\) g HYP gives \(135\) degrees. See section 7.4.

Backspace — delete the trailing character or element

Keys/modes: \(\leftarrow \), both modes. During entry, delete the selected component’s last character, removing exponent digits before its exponent marker. In real RPN, deleting the final character leaves zero in the reserved X position; it does not undo the original lift. Idle RPN backspace performs CLx and saves old X. In ALG, idle backspace removes the last expression element, or clears a completed working expression while retaining ANS. Pending-command cancellation takes priority, including MCLR: backspace cancels it without clearing memory. Example: 12.36 \(\leftarrow \) 5 ENTER gives 12.35 in RPN. See section 3.8 and section 4.7.

BGN — BEGIN/END payment timing

Keys/modes: g n, both modes. Toggle beginning-of-period payments; BGN present means BEGIN, absent means END. In RPN, accept active entry without moving the committed stack or changing the Last registers; preserve TVM store/solve readiness. ALG preserves its main expression. Timing affects TVM and AMORT, not explicit cash-flow dates, bonds, or depreciation. Example: with BGN absent, this key sequence shows BGN; repeating it restores END. Bank clears preserve the setting. See section 11.3.

CAL — digit ruler

Keys/modes: header CAL, both modes when a number overflows its display. Toggle the ruler that marks coefficient digits in groups of five. It neither changes the value nor commits entry, and it preserves any pending shift or command. Example: open PREC, set display digits to 100, apply, then insert \(\pi \) with f 0; use CAL and horizontal scrolling to inspect the long result. The ruler is a position aid, not an accuracy indicator. See section 5.5.

CANCEL — dismiss a pending shift or command

Keys/modes: header CANCEL, both modes. Appears while an ALG worksheet is active or a shift or command is waiting for another key: f, g, STO (including arithmetic modifiers), RCL, MCLR, HYP/INVHYP, FUNC, CPT, a notation digit selector, or the ALG FIX prompt. Cancels the whole selection, including any associated shift, and dismisses a displayed error. Does not commit or edit a number, evaluate an expression, clear a value or bank, or change settings. The cancellation is saved. Numeric entry or an unfinished expression alone does not show this button. Its fixed position beside the branding does not depend on CAL visibility. Example: 42 STO CANCEL 3 continues the same entry as 423 without storing it. An ALG worksheet provides its own CANCEL and physical Escape shortcut. Canceling the worksheet discards its unaccepted field edits and closes it; earlier accepted values, ANS updates, and completed operations remain. See table 1.3, section 14.4 and section 4.12.

Cash-flow entry — CF0, CFj, Nj

RPN keys and effect: \(\mathrm {CF}_0\), \(\mathrm {CF}_j\), \(N_j\), RPN. CF0 replaces the whole list with X and stores n = 0. CFj appends X to an existing list and stores its final index in n. Nj takes an integer count 1–1000 and appends count-minus-one copies of the actual last flow, then updates n. Each accepts entry, preserves the committed stack and both Last registers, and requires the expanded list to fit 1000 entries including CF0. CF0 and CFj accept finite signed amounts, including zero. A repeated amount has separate period indices, not an editable group frequency.

Example: 100 +/\(-\) \(\mathrm {CF}_0\); 30 \(\mathrm {CF}_j\); 3 \(N_j\) creates \((-100,30,30,30)\), with n = 3 and X still the frequency 3. See section 12.3.

In ALG, these keys open initial-flow, next-flow, and frequency worksheets. Accept fields and choose STORE, APPEND, or REPEAT; see section 12.9.

Cash-flow indexed STO and RCL

RPN keys and effect: STO \(\mathrm {CF}_j\) or RCL \(\mathrm {CF}_j\), RPN; CFj is unshifted. An index in X must identify an existing entry, starting at 0. Recall replaces it with the flow and saves the index in Last X. Store uses amount Y and index X, drops the index, and leaves the amount in X; it also saves only Last X. Last Y, n, and list length are unchanged. STO followed by an arithmetic operator before CFj applies \(\text {old flow}\mathbin {\mathrm {op}}Y\); division requires nonzero Y. The adjustment remains on the stack.

Example: 100 +/\(-\) \(\mathrm {CF}_0\); 110 \(\mathrm {CF}_j\); 120 ENTER 1 STO \(\mathrm {CF}_j\); 1 RCL \(\mathrm {CF}_j\) gives 120 with n still 1. There is no indexed insertion or deletion. See section 12.4.

In ALG, the same sequences open indexed worksheets with a Cash-flow index and, for storage, Value. Arithmetic STO chooses the corresponding modification. See section 12.9.

Ceiling and floor

Keys/modes: g 5 for ceiling, g 6 for floor, both modes; effect U, real-only. Ceiling returns the least integer at least X; floor returns the greatest integer at most X. Neither depends on display digits. Examples from separate reference starts: 2.75 +/\(-\) followed by blue 5 gives \(-2\); blue 6 gives \(-3\). See section 7.6.

CLEAR and CLx — working-area clears

Keys/modes: RPN CLEAR is f \(1/x\); ALG has unshifted CLEAR. Both modes use g \(\leftarrow \) for CLx. RPN CLEAR discards entry, fills a fixed stack with zeros or leaves one unlimited zero, and preserves both Last registers. RPN CLx commits and saves old X in Last X, then replaces X with zero, preserving deeper values and Last Y. ALG CLEAR discards the whole expression; CLx removes current entry or the trailing operand/group. Both preserve ANS. These clears preserve all memory banks and settings. Cancel an ordinary pending prefix before clearing; otherwise the first clear only cancels that prefix.

Example: 8 ENTER 3 g \(\leftarrow \) leaves X = 0, Y = 8 in RPN; then f \(1/x\) zeros the whole stack. See section 2.8, section 4.9 and chapter 14.

CLcf, CLfin, and CL\(\Sigma \) — dedicated bank clears

Keys/modes: In both modes, g FV removes cash flows and stores n = 0; f FV removes all five financial registers but retains cash flows. RPN f \(\Sigma +\) removes the six statistics accumulators; ALG provides Clear statistics under STAT. In RPN these commands commit active entry and preserve the committed stack and both Last registers. ALG preserves its expression; its CLEAR STATISTICS action updates ANS to zero. Settings are retained. CLcf therefore leaves FIN lit; CLfin can leave CF lit. Copies of statistics in R4–R9 survive CL\(\Sigma \). Example: 0 \(\mathrm {CF}_0\) lights FIN and CF; g FV removes CF while FIN remains. Use MCLR for a group clear that preserves unfinished entry. See section 6.10, section 12.11 and section 10.1.

CMPLX and complex component controls

Keys/modes: both modes. Finish any incomplete ALG number before changing complex mode or representation, even if ALG is the inactive workspace. f \(\div \) toggles complex mode. With complex mode enabled, f 4 selects the other component; f 5 toggles rectangular/polar entry and presentation; f 6 swaps the rectangular real and imaginary parts. Mode and representation changes commit pending numbers in both workspaces without evaluating an ALG expression.

Re/Im stays within one operand; on an accepted value it reopens the second component, and a new digit replaces that component. In ALG, a closed group or function call is replaced by its edited value; the surrounding expression and ANS are preserved until evaluation. Swapping accepts entry and replaces the pair in place, preserving the RPN Last registers. Polar form uses magnitude and the selected angle unit; swapping still exchanges rectangular parts. Disabling CMPLX hides existing imaginary parts but retains them until a later operation replaces the value. New calculations, stores, recalls, Last-register captures, and idle ENTER copies made with CMPLX off write zero imaginary components. A real-mode recall leaves its source memory unchanged; turning CMPLX back on does not restore a component in the newly recalled copy.

Example from the reference start: f \(\div \) enables complex mode; select rectangular form if needed, then enter 3 f 4 4 ENTER. The pair is \(3+4i\). Orange 6 gives \(4+3i\); applying it again restores \(3+4i\). In DEG, orange 5 shows magnitude 5 and phase 53.1301 degrees. ALG keeps its expression visible and accessible alongside the two component rows. See chapter 8 for ALG component-editing examples.

Constants — pi, Euler’s e, and ln 2

Keys/modes: f 0, f ., and f \(\leftarrow \), respectively, both modes; effect Z. Generate the real constant at current working precision. ALG inserts an implicit product after an operand, or starts new work after a completed result. No FUNC is needed. From separate reference starts, these keys display 3.1416, 2.7183, and 0.6931 under FIX 4. They preserve both RPN Last registers. See section 7.12.

CONV — unit conversion

Keys/modes: g 8, both modes. First enter or recall the value to convert, then open CONV. Choose Dimension, From, and To, then Apply. Conversion uses the current real component, including an active number, and returns one real value. RPN replaces X with no movement and preserves both Last registers. ALG replaces the trailing operand or closed group; after a completed result, it starts a new expression. It does not update ANS until equals. Close leaves entry untouched; Apply rejects a nonfinite result. Units are not attached to the stored number.

Example: enter 12, open CONV, choose Length, inch to foot, and Apply: X becomes 1. Source memory and settings remain unchanged. The full inventory appears in section 15.10; factors, affine temperatures, and numerical caveats are in chapter 9.

CPT and STAT — ALG computation and worksheets

Keys/modes: main CPT; orange FUNC = STAT, ALG only. Finish or clear an unfinished compound expression before solving; a lone scalar is allowed. Then press CPT and an unshifted n, i, PMT, PV, FV, NPV, or IRR target. Successful computation becomes a completed result and ANS. CANCEL discards the prefix, and a saved prefix resumes without running the computation.

STAT opens the add-sample worksheet with an operation selector for sample removal, means, weighted mean, sample deviations, regression, estimation, summation recall, and statistical clear. Related finance and associative-memory commands use the same worksheet interaction. Equals evaluates a selected field; ENTER accepts it. Both update ANS. The named action uses accepted inputs and updates ANS with its primary output. Financial-register fields write their registers on acceptance. Use value inserts the selected output in the suspended main expression; output browsing does not change ANS. CANCEL discards unaccepted edits and closes; completed work remains. All worksheet inputs, exact drafts, outputs, and selections are retained across relaunch. See section 4.12 and section 10.10.

DATE and \(\Delta \)DAYS

RPN keys and effect: f \(\mathrm {CF}_0\) adds an integer count X to date Y; g \(\mathrm {CF}_0\) finds the interval from date Y to date X. RPN, real-only. DATE consumes two operands and returns one encoded date. \(\Delta \)DAYS replaces the two dates with actual days in X and the implemented 30/360 count in Y. Both save original X/Y, use MDY/DMY, and leave financial banks unchanged. Gregorian years are 1–9999; DATE’s count must be within \(\pm 3\,652\,058\) and its result within that calendar.

Examples, MDY selected with f \(\mathrm {CF}_j\) and FIX 6 selected with 6 f 7: 2.282024 ENTER 2 f \(\mathrm {CF}_0\) gives 3.012024. From a fresh clear, 1.312023 ENTER 3.312023 g \(\mathrm {CF}_0\) gives X = 59 and Y = 60. The 30/360 rule has no February-end adjustment and is not generally antisymmetric when dates are reversed. See section 13.4 and section 13.5.

In ALG, the same shifted keys open labeled date worksheets. DATE returns the result date; \(\Delta \)DAYS returns Actual days and 30/360 days. See section 13.12.

DEG, RAD, GRAD, and DRG — angle settings

Keys/modes: f SIN, f COS, f TAN select degrees, radians, gradians; orange 9 cycles DEG, RAD, GRAD. Both modes. Committed values, stack positions, and Last registers stay unchanged. Unfinished entry keeps its typed digits; for a pending polar number, however, the new unit changes the meaning of the typed phase when it is committed. A committed complex value keeps its direction and is displayed in the new angle unit. The setting governs trig arguments/results and polar angles, not hyperbolic functions or the imaginary part of a logarithm. ALG trig functions retain the unit from their insertion. Example: from DEG, orange 9 selects RAD; orange SIN returns to DEG. CONV changes an angle’s numerical units instead. See section 7.4 and section 8.3.

Depreciation — DB, DB to SL, SL, and SYD

RPN keys and effect: RPN: orange NPV = DB; blue NPV = DB\(\to \)SL; orange Nj = SL; blue Nj = SYD. Explicitly store life n, cost PV, salvage FV, and, for DB methods, positive factor i in percent. X is integer year \(j\geq 1\). Require \(n>0\) and \(PV\geq FV\geq 0\); PMT is unused. Lift depreciation into X and remaining value above salvage into Y, retaining year in S2 if capacity permits. Preserve financial inputs and both Last registers. Each request recomputes from original cost; it does not advance a ledger.

SL spreads the depreciable base across life; SYD uses descending year weights. DB multiplies opening book value by \((i/100)/n\), capped at salvage, and writes off the remainder in the final year. Crossover uses the larger of DB and remaining-life SL before that final write-off. Fractional lives have the conventions in section 13.11; active DB years are limited to 100 000. Years beyond \(\lceil n\rceil \) return two zeros.

Example: 5 STO n; 1000 STO PV; 100 STO FV; 200 STO i. Clear the stack, enter 2, and select each method separately. SL returns 180 and 540; SYD 240 and 360; DB and DB\(\to \)SL both return 240 and 260. These are year-2 amount and remaining depreciable value. See section 13.8.

In ALG, the same legends open worksheets for Year, Life, Cost, Salvage, and the DB factor where needed. Depreciation is primary; Book value less salvage is separately available. See section 13.12.

Digits, decimal point, EEX, and sign

Keys/modes: 0–9, ., EEX, +/\(-\), both modes. Digits build one number. RPN’s first digit, decimal, or EEX lifts once; ENTER commits without a second lift. A new ALG number replaces a trailing accepted operand, except after a closing group where it starts an implicit product; after equals it starts a new expression. EEX introduces an integer power of ten, using mantissa 1 if it starts an ordinary new number. An empty second complex component needs an explicit mantissa. Sign edits the mantissa or active exponent; outside entry it negates the complete operand (U in RPN). ALG requires exponent digits before evaluation; RPN accepts an empty exponent as zero. Repeated decimal points or EEX markers are ignored.

Example: 4 +/\(-\) EEX +/\(-\) 3 ENTER gives \(-0.004\). See section 3.2, section 4.1 and section 8.2.

DROP — discard X

Keys/modes: f R\(\downarrow \), RPN. Commit entry and remove X, moving Y down. A fixed stack repeats its deepest value; unlimited shrinks, leaving zero if emptied. Preserve both Last registers and all memories. Example: 8 ENTER 3 f R\(\downarrow \) returns 8. Use this before entering an accepted operand’s replacement. See section 2.7.

ENTER and equals

Keys/modes: tall ENTER in RPN, = in ALG. RPN ENTER finishes active entry without duplication; idle ENTER lifts a copy of X. With CMPLX off, the new X copy is real, while the original moved to Y retains its components. Both preserve Last X/Y. ALG equals commits entry, evaluates the complete expression, and updates ANS; repeated equals leaves a completed answer unchanged and records it as ANS again. Missing parentheses are not supplied. Example in RPN: 6 ENTER ENTER + gives 12. In ALG: 2 + 3 \(\times \) 4 = gives 14. Under an ALG FIX prompt, equals accepts the display setting instead. See section 2.3 and section 4.1.

erf and erfc — error functions

Keys/modes: blue square root = erf; blue \(e^x\) = erfc, both modes; effect U. Compute \(\operatorname {erf}X=(2/\sqrt \pi )\int _0^X e^{-t^2}\,dt\) and its complement. All finite real arguments are allowed. Use erfc directly for a small complement. Nonreal complex arguments have an approximate magnitude limit of 100 and may fail to converge. Examples from separate reference starts: 0 g \(\sqrt {x}\) gives 0; 0 g \(e^x\) gives 1. See section 7.11 and section 8.9.

Exponential functions — e to x and 10 to x

Keys/modes: \(e^x\) and \(10^x\), both modes; effect U. Raise the named base to X, with complex extensions when enabled. Real inputs have no finite-domain restriction, but exponent range is finite. Angle units do not change these functions; the imaginary argument of \(e^{a+bi}\) is in radians. Examples, each from a fresh reference start: 1 \(e^x\) displays 2.7183; 3 \(10^x\) gives 1000. EEX types an exponent within a number instead. See section 7.3.

Factorial and logarithmic factorial

Keys/modes: \(x!\) and f \(x!\), both modes; effect U. In real mode, factorial requires integer \(0\leq X\leq 10\,000\), with \(0!=1\). Logarithmic factorial requires a finite nonnegative integer and calculates \(\ln \Gamma (X+1)\) without the 10 000 argument limit. Complex mode uses the Gamma extension, including noninteger real inputs, but retains its poles. Examples from separate reference starts: 5 \(x!\) gives 120; 5 f \(x!\) displays 4.7875. See section 7.9 and section 7.10.

FIX, FSE, SCI, and ENG

Keys/modes: FIX is orange 7; FSE is orange 8, both modes. RPN FIX takes a whole count from X, commits and drops it, preserving both Last registers. ALG FIX suspends the expression, collects digits, and accepts them with equals. Counts range from zero to working digits. FSE cycles FIX, SCI, ENG while preserving the count and unfinished entry. There are no direct SCI/ENG keys. Formatting leaves numeric values and memories unchanged; FIX can fall back to scientific notation.

Example in RPN: 42 ENTER 2 f 7 displays 42.00; orange 8 then shows \(4.20\times 10^1\). ALG selects the same count with f 7 2 = without evaluating its expression. PREC can change the count without using a stack position. See section 5.3 and section 5.4.

FUNC and the argument comma

Keys/modes: FUNC and g FUNC, ALG. FUNC waits for a unary or binary mathematical key, including a shifted one, then inserts its function name and opening parenthesis. It starts an implicit product after an operand. Constants and HYP do not use this prefix. The comma separates two arguments; closing parenthesis ends the call. This does not update ANS until successful equals.

Example from the ALG reference start: FUNC g \(y^x\) 2 g FUNC 8 ) = gives 3, evaluating \(\log _2 8\). Backspace cancels a pending FUNC without editing the expression. See section 4.6.

15.5   Alphabetical reference: G through N

Gamma and logarithmic Gamma

Keys/modes: \(\Gamma \) and f \(\Gamma \), both modes; effect U. Compute \(\Gamma (X)\) or \(\ln \Gamma (X)\). Gamma has poles at zero and negative integers; real log-Gamma is finite where Gamma is finite and positive, not the logarithm of its absolute value. For nonreal inputs, logarithmic Gamma is the principal logarithm of the computed Gamma, not an unwrapped analytic log-Gamma. Examples from separate starts: 5 \(\Gamma \) gives 24; 5 f \(\Gamma \) displays 3.1781. See section 7.10 and section 8.8.

GOAT — play the bundled sound

Keys/modes: g +, both modes. Play the goat audio. There are no numeric operands, results, stack movements, or memory changes, and unfinished entry is preserved. Example: use blue plus with no pending prefix to hear it. You can continue calculating while it sounds. Missing audio or a playback failure reports a message if GOAT is still the latest command; a delayed failure does not replace feedback from later input. This command is independent of scientific or financial calculation. See section 1.5.

HELP — key guide

Keys/modes: g RCL, both modes. Open the Key guide, with Entry, Memory, and Tools topics. Close returns to the same working value or entry; there is no calculation or Last-register change. Example: open HELP, choose Memory, then Close. For precise current prefix routing, use this chapter’s key maps and MCLR entry; indexed cash-flow memory uses unshifted CFj after STO/RCL. See section 1.9.

HYP and inverse HYP — hyperbolic function families

Keys/modes: HYP followed by unshifted SIN, COS, or TAN selects sinh, cosh, or tanh; f HYP followed by those keys selects asinh, acosh, or atanh. Both modes; effect U. The prefix applies once. Another shift cancels HYP, so do not insert it before the final SIN/COS/TAN key.

Angle settings are irrelevant. Finite real sinh, cosh, tanh, and asinh accept any finite real argument; acosh requires \(X\geq 1\), and finite atanh requires \(-1<X<1\). Complex extensions use the branch conventions in chapter 8. Examples from separate starts: 0 HYP SIN gives 0; 0 HYP COS gives 1; 0 HYP TAN gives 0. 1 f HYP COS gives 0. Use HYP directly in ALG, without FUNC. See section 7.5.

INT and FRAC — integer and fractional parts

Keys/modes: RPN: orange ENTER = INT, blue ENTER = FRAC. ALG: orange \(1/x\) = INT, blue \(1/x\) = FRAC. ALG equals has no shifted functions. Effect U, real-only. INT truncates toward zero; FRAC returns \(X-\operatorname {trunc}X\), so a negative input has a negative nonzero fractional part. Display digits have no effect. From separate reference starts, 2.75 +/\(-\) followed by orange ENTER gives \(-2\), or blue ENTER gives \(-0.75\). These are unrelated to blue financial i’s simple-interest INT. See section 7.6.

INT — simple interest

RPN keys and effect: g i, RPN, real-only. Explicitly store nonnegative days in n, annual percent in i, and signed principal in PV. PMT and FV are unused. Return \((-PV)(i/100)n/360\) in X, \(-PV\) in Y, and \((-PV)(i/100)n/365\) in S2. Discard old X and insert these three values above old Y; save old X/Y and preserve all financial inputs. An unlimited stack needs two positions; a fixed depth of at least three retains every result. Fractional days and negative annual rates are accepted if finite.

Example: 90 STO n; 6 STO i; 1000 +/\(-\) STO PV; g i gives 15, 1000, and 14.7945 in X, Y, S2. Adding immediately gives principal plus 360-day interest, 1015. See section 13.2.

In ALG, blue i opens Simple interest with Days, Annual interest %, and Present value. The three outputs are labeled; 360-day interest is primary. See section 13.12.

IRR and IRR[a,b] — internal rate of return

RPN keys and effect: IRR for automatic search; f IRR for bounds, RPN. Use the stored cash-flow prefix CF0 through integer n. At least two selected flows, with positive and negative amounts, are required. Automatic search uses stored i as its guess, or zero if i is unset. Bounds are typed lower and upper periodic percentages: finite, strictly ordered, and greater than \(-100\); endpoint NPV must be zero or the interval must bracket a sign change. Bounded search uses that interval instead of the guess.

Lift the periodic percentage into X, preserving both Last registers, all flows, n, and i. IRR does not automatically store its result in i. Multiple roots and roots without a sign change require care; a failed search is not proof that the mathematical problem has no solution.

Example: 100 +/\(-\) \(\mathrm {CF}_0\); 110 \(\mathrm {CF}_j\); 0 STO i; IRR gives 10 percent. Alternatively open orange IRR, set Lower % to 0 and Upper % to 20, and Apply for the same answer. Store the returned rate explicitly before checking it with NPV. See section 12.7 and section 12.8.

In ALG, main IRR opens a worksheet; orange IRR adds bound fields. For direct computation, first finish or clear a pending compound expression, then use CPT IRR to compute from the bank. A lone scalar is allowed. No variant overwrites i with its result. See section 12.9.

LAST X and LAST Y — saved RPN operands

Keys/modes: blue swap = LAST X; blue reciprocal = LAST Y, RPN. Lift the saved operand into X (visible S0) while preserving both Last registers. A Last register holds an earlier operand; it is not the current S0 or S1 position. A new state starts them at zero. Their contents depend on the last command that saved them, not necessarily the last command pressed. They cannot undo bank clears, recover discarded deepest values, or restore a whole earlier stack. With CMPLX off, new Last captures and recalls copy only the real component. Toggling the mode or recalling a Last operand does not change the stored source operand.

Example: 12 ENTER 3 +; f R\(\downarrow \); g \(1/x\); g \(x\leftrightarrow y\); \(\div \) gives 4 by recovering the operands of the addition. See section 2.9.

LN, LOG, LOG2, and logarithm to base Y

Keys/modes: orange \(e^x\) = LN; orange \(10^x\) = LOG; blue \(10^x\) = LOG2; blue \(y^x\) = \(\log _Y X\). Both modes. The first three have effect U, the last effect B. Finite real logarithms require a positive argument; the binary form also requires base \(Y>0\), \(Y\ne 1\). Base precedes argument. Complex mode uses principal logarithms, with \(\log _Y X=\operatorname {Log}X/\operatorname {Log}Y\). Logarithm’s imaginary component is in radians regardless of angle mode.

Examples from separate starts: 1 f \(e^x\) gives 0; 100 f \(10^x\) gives 2; 32 g \(10^x\) gives 5; 2 ENTER 8 g \(y^x\) gives 3. See section 7.3 and section 8.8.

L.R. and estimated Y — linear statistics

RPN keys and effect: L.R. fits the stored pairs; f L.R. estimates at X, RPN, real-only. For \(\hat y=a+bx\), L.R. lifts slope b into X and intercept a into Y, saving old X/Y. It requires at least two observations and positive x variance. Estimate consumes its supplied x, returns \(\hat y\) in X and correlation r in Y, moves old Y to S2, and saves only Last X. It also requires positive y variance. Both preserve the accumulators. A horizontal line is valid for L.R. but has undefined correlation.

Example: f \(\Sigma +\); 2 ENTER 1 \(\Sigma +\); 4 ENTER 2 \(\Sigma +\); L.R. gives slope 2, intercept 0. Then 3 f L.R. gives estimate 6 and correlation 1. See section 10.7 and section 10.8.

In ALG, STAT provides Linear regression and Linear estimate worksheets. Slope or Estimated Y is primary; companion outputs are labeled. Regression retains a valid horizontal line if correlation is undefined. See section 10.10.

MCLR — select a group to clear

Keys/modes: g STO, both modes. The very next key’s group selects the clear before its normal function can run. No individual memory address follows this prefix. The selectors below are convenient representatives of their entire groups.

ALG parentheses, FUNC, CPT, CLEAR, and reciprocal also select ordinary and associative clearing. Scientific keys, STO/RCL, and ALG ANS cancel MCLR without acting. Memory-bank clears preserve the exact unfinished entry, stack, Last registers, and settings; stack clear preserves both Last registers and banks. Example: g STO 0 removes all ordinary and associative entries, not only R0. Use CANCEL, backspace, either shift, or physical Escape to cancel without clearing. See section 6.10 and chapter 14.

MDY and DMY — date order

Keys/modes: orange CFj = MDY; blue CFj = DMY, both modes. Select month-first (Month.DDYYYY) or day-first (Day.MMYYYY) interpretation. Stored numbers, unfinished entry, stack, and Last registers do not change. This shared saved setting governs date and bond calculations. Example: orange CFj selects MDY, under which 2.032026 means February 3, 2026; blue CFj would interpret the same number as March 2. It does not convert one encoding into the other. See section 13.3.

Mean and weighted mean

RPN keys and effect: \(\bar x\) and orange \(\bar x\), RPN, real-only. Mean lifts \(\sum x/n\) into X and \(\sum y/n\) into Y, saving old X/Y. Weighted mean returns \(\sum xy/\sum y\) by replacing X, saving only Last X. Both require data; weighted mean also requires nonzero total weight. Y-coordinates are weights only for weighted mean. The bank is unchanged.

Example: f \(\Sigma +\); 2 ENTER 10 \(\Sigma +\); 3 ENTER 20 \(\Sigma +\). Unshifted mean returns X = 15, Y = 2.5; orange mean then gives 16, since \((2\times 10+3\times 20)/(2+3)=16\). Negative weights are accepted; SD and regression still count each pair once. See section 10.5.

In ALG, select Mean or Weighted mean under STAT. Mean X is the primary paired output. See section 10.10.

MOD and REM — two remainder rules

Keys/modes: blue division = MOD, blue multiplication = REM, both modes; effect B, real-only. With dividend Y and nonzero divisor X, return \(Y-qX\). MOD truncates \(Y/X\) toward zero; REM chooses the nearest integer quotient, ties even. MOD’s nonzero remainder has Y’s sign; REM may have the opposite sign. Examples from separate starts: 7 ENTER 4 followed by blue division gives 3, or blue multiplication gives \(-1\). Neither function is restricted to integers. In a worksheet field expression, a typed percent symbol denotes truncating remainder; the calculator’s percentage key is a different binary function. See section 7.7.

n, i, PMT, PV, FV — financial register keys

RPN keys and effect: five main Financial keys, RPN. A bare key stores X after number entry, ordinary arithmetic, stack actions, or recall. After a financial-register store, a TVM solve, or the 12-times/divide shortcuts, the next bare key solves its variable. BEGIN/END preserves this readiness. Explicit STO always stores, and RCL always recalls. There is no store/solve readiness annunciator.

Storage commits entry and preserves stack and both Last registers. A solve uses all four other registers, treating unwritten ones as zero; it replaces the target register and lifts the answer into X while preserving both Last registers. n counts periods, i is percent per period, and PV, PMT, FV use opposite signs for money paid and received. All participating values must be finite; \(i>-100\), and n must be nonnegative, positive when solving i or PMT. Old target contents are ignored, including old i as a guess. Solved n is rounded to a whole period: a fractional part below 0.005 normally rounds down, otherwise up; a small numerical guard treats values extremely close to the cutoff as boundary cases. See section C.6 for the precise rule. Entered fractional n retains the continuous compound-annuity convention.

Example: select END and follow the sequence without inserting ENTER before the final FV solve: f FV; 2 n; 10 i; 100 +/\(-\) PV; 0 PMT; FV gives 121 and stores it in FV. For unambiguous solving after inspecting inputs, recall and explicitly restore a known input, then press the target. See chapter 11.

In ALG, each bare register key always stores the displayed operand; RCL recalls and CPT explicitly solves. A store preserves pending arithmetic. See section 11.12.

NINT — nearest integer

Keys/modes: g 9, both modes; effect U, real-only. Round to the nearest integer with an exact tie to even, independently of display digits. Examples, each from a fresh reference start: 2.5 g 9 gives 2; 3.5 g 9 gives 4. RND instead rounds to decimal places with ties away from zero. See section 7.6 and section 5.6.

NPV — net present value

RPN keys and effect: NPV, RPN, real-only. Require a nonempty flow list, an explicitly stored final index n, and explicitly stored periodic percentage \(i>-100\). Calculate \(\sum _{t=0}^{n}\mathrm {CF}_t/(1+i/100)^t\). Lift the result into X, preserving both Last registers, all financial registers, and cash flows. It does not store the result in PV. n = 0 uses only CF0; BGN does not shift the explicit times.

Example: 100 +/\(-\) \(\mathrm {CF}_0\); 110 \(\mathrm {CF}_j\); 10 STO i; NPV gives zero to ordinary monetary precision, possibly with a tiny nonzero floating-point residue. See section 12.5 and section 12.6.

In ALG, NPV opens its input worksheet. For direct computation, first finish or clear a pending compound expression; a lone scalar is also allowed. Then use CPT NPV to calculate from n, i, and the selected cash-flow prefix. See section 12.9.

15.6   Alphabetical reference: P through S

Parentheses — explicit ALG groups

Keys/modes: ( and ), ALG. Delimit a group; an opening group after an operand inserts multiplication. Closing a group previews its value but does not update ANS or evaluate the entire surrounding expression. Equals does not supply missing closing parentheses. Example from the ALG reference start: ( 2 + 3 ) \(\times \) 4 = gives 20. Groups are limited to 128 levels. See section 4.2.

Percent, percent change, and percent of total

Keys/modes: blue 1 = %, blue 2 = \(\Delta \%\), blue 3 = T%, both modes; effect P. Return respectively \(YX/100\), \(100(X-Y)/Y\), and \(100X/Y\). The last two need a nonzero base Y. Rates and answers use percent units: 10 means 10 percent. Complex mode extends the same formulas. In ALG each is an ordinary binary operation with no retained base.

Examples from separate starts: 200 ENTER 10 g 1 gives X = 20, retaining Y = 200; 80 ENTER 92 g 2 gives 15; 200 ENTER 50 g 3 gives 25. See section 7.8.

Permutations and combinations — nPr and nCr

Keys/modes: blue Gamma = nPr; blue factorial = nCr, both modes; effect B, real-only. Put the number available n in Y, number selected r in X. Require integers \(0\leq r\leq n\leq 10\,000\). Return \(n!/(n-r)!\) for ordered selections or \(n!/[r!(n-r)!]\) for unordered selections without replacement. Both give 1 when r = 0. From separate starts, 10 ENTER 3 followed by blue Gamma gives 720, or blue factorial gives 120. Large integer results can still exceed working precision. See section 7.9.

Power and indexed root

Keys/modes: \(y^x\) and its orange \(\sqrt [x]{y}\), both modes; effect B. Power uses base Y, exponent X. In real mode, a negative base needs an integer exponent for a real result. Root uses radicand Y, nonzero index X; a negative radicand requires an odd integer index. Integer indices are limited to \(\pm 1\,000\,000\). A negative index takes the reciprocal root. A noninteger real index uses \(Y^{1/X}\) for \(Y\geq 0\). Zero to a negative power has no finite result. Complex mode returns principal powers/roots and permits complex indices except zero.

Examples from separate starts: 2 ENTER 5 \(y^x\) gives 32; 125 +/\(-\) ENTER 3 f \(y^x\) gives \(-5\) in real mode. ALG powers associate from the right: \(2^{3^2}=512\). See section 7.2, section 4.3 and section 8.8.

PRC and YTM — bond price and yield

RPN keys and effect: orange PV = PRC; blue PV = YTM, RPN, real-only. First select the date order and explicitly store nonnegative annual coupon percent in PMT. For PRC, also store annual yield percent \(i>-200\); for YTM, store positive clean price per 100 in PV. Then enter settlement in Y and later maturity in X. n and FV are ignored. Coupons are semiannual, redemption 100, and the schedule is anchored to maturity using actual coupon-period fractions. One remaining coupon uses simple yield for the partial period; longer schedules use compound discounting.

PRC replaces the dates with clean price X and accrued interest Y, and stores clean price in PV. YTM consumes both dates, returns annual yield in X, and stores it in i. Both save original X/Y. No old i guess or user bracket is used by YTM. Example, MDY: store 6 STO PMT and 6 STO i; clear the stack and enter 1.012024 ENTER 1.012026 f PV. PRC returns clean 100, accrued 0. Clear and re-enter those dates with g PV; YTM returns 6, using the clean price just stored. See section 13.6 and section 13.7.

In ALG, the same keys open labeled bond worksheets. PRC returns Price per 100 and Accrued interest and stores PV; YTM returns Annual yield % and stores i. See section 13.12.

PREC — working and display precision

Keys/modes: g 7, both modes. Enter whole Working digits from 16 through 10 000 and Display digits from zero through the proposed working count, then Apply. Change subsequent arithmetic precision and presentation count without committing entry, evaluating an expression, moving the stack, or rewriting existing numbers. Retain the chosen FIX/SCI/ENG notation. Invalid fields leave settings unchanged and the panel open.

Example: open PREC, set working 80 and display 8, and Apply; a subsequent 1.25 ENTER under FIX shows 1.25000000. Raising precision cannot restore lost digits of an old value. The help label INFIX refers to working digits, not ALG. See section 5.2 and section 5.7.

RAN# — random number

Keys/modes: g 4, both modes; effect Z. Generate a real value \(0\leq u<1\) from random decimal digits at working precision. No seed or repeat-sequence control is exposed. Example: blue 4 from the reference start puts one draw in X; another blue 4 puts a new draw in X and the first in Y. Repetition is possible. FIX 4 can display 1.0000 after rounding a value below 1. ALG insertion follows the constant rule. See section 7.12.

RCL and STO — ordinary and financial memory

Keys/modes: RCL or STO, then one digit 0–9, both modes. Both also accept unshifted n, i, PMT, PV, FV as financial targets, and CFj with its separate indexed rules. In ALG, CFj opens a worksheet rather than consuming stack operands. Select the target to commit an active number. STO copies the current operand and preserves stack and Last registers; in ALG it stores the current operand/preview without evaluating the whole expression.

Ordinary RPN RCL lifts the value and saves old X in Last X, preserving Last Y. Financial RCL also lifts but preserves both Last registers. ALG RCL inserts or replaces the trailing operand; it does not update ANS. An unset register recalls zero without becoming occupied. Stored zero remains occupied. STO followed by \(+, -, \times ,\div \) and a target changes that destination from M to \(M\mathbin {\mathrm {op}}v\), leaving the current operand v in place; division by zero is rejected. Stores and recalls copy full complex pairs with CMPLX on; with it off, they write purely real values. Recall leaves the source memory unchanged. Arithmetic storage also follows the current complex setting; see section 6.5.

Example: 20 STO 1; 5 STO \(-\) 1; RCL 1 returns 15. In RPN, financial storage arms the next bare TVM key to solve; recall arms it to store. In ALG, bare financial keys always store and CPT explicitly computes. See chapter 6.

RCL\(\Sigma \) — copy statistical accumulators

RPN keys and effect: g L.R., RPN. Commit entry, then copy the six accumulators into ordinary R4–R9 in this order:

Overwrite those six ordinary registers, without moving the stack or changing either Last register or the statistical bank. Later data changes do not refresh the copies, and editing them does not edit statistics. There is no inverse load command.

Example: f \(\Sigma +\); 2 ENTER 1 \(\Sigma +\); g L.R.; RCL 9 gives 2, the sum of products. Copying an empty bank writes six zeros and lights MEM without lighting STAT. See section 10.9.

In ALG, choose Recall summations under STAT, then RECALL SUMMATIONS. The same copy to R4–R9 occurs, all six totals are labeled, and count is primary. See section 10.10.

Reciprocal — one divided by X

Keys/modes: \(1/x\), both modes; effect U. Return \(1/X\), including the full complex reciprocal when enabled. A zero denominator has no finite answer. Example: 8 \(1/x\) gives 0.125. In ALG its orange and blue functions are INT and FRAC; in RPN those layers are CLEAR and LAST Y. See section 7.2.

RND — round the working value to decimal places

RPN keys and effect: g PMT, RPN, real-only. Round X to the current display count of decimal places, with ties away from zero. Replace X and save its old value in Last X; preserve deeper values, Last Y, and source memories. The count is decimal places in the value even when SCI or ENG is selected. This changes a value, unlike formatting. Example: 2 f 7; .125 g PMT gives 0.13, whereas FIX 2 alone displays exact 0.125 as 0.12 by ties-to-even rounding. Store the result explicitly to replace a financial payment. See section 5.6 and section 11.13.

In ALG, first finish or clear a pending compound expression; a lone scalar is also allowed. Then use the same key to round the displayed operand, display a completed result, and update ANS. The mathematical rounding rule is unchanged.

Roll down and roll up

Keys/modes: R\(\downarrow \) and its blue R\(\uparrow \), RPN with a fixed stack. Commit entry and cyclically move every value. Down sends Y to X and old X to the deepest position; up sends the deepest value to X. No values or Last registers are replaced. Roll is unavailable in unlimited mode. Example: 1 ENTER 2 ENTER R\(\downarrow \) shows 1; blue roll then restores 2 in X. See section 2.7.

RPN and ALG — workspace selection

Keys/modes: header mode buttons. Select the independent stack or expression workspace without evaluating, committing, or copying an operand. Shared memories and settings remain shared. Mode selection normally clears shifts and pending commands; an ALG FIX prompt consumes the first press as cancellation without switching. Example: type 12.30 in RPN, select ALG, then return to RPN; the unfinished literal still reads 12.30. Store and recall ordinary memory to transfer a value deliberately. See section 1.7.

SD — sample standard deviations

RPN keys and effect: g \(\bar x\), RPN, real-only. Use at least two stored observations; lift x sample deviation into X and y sample deviation into Y, saving old X/Y. Preserve all accumulators. Each variance divides the centered sum of squares by \(n-1\). Constant coordinates return zero; negative implied variance is rejected. This is neither population nor frequency-weighted SD.

Example: f \(\Sigma +\); 0 ENTER 8 \(\Sigma +\); 0 ENTER 10 \(\Sigma +\); 0 ENTER 12 \(\Sigma +\); g \(\bar x\) gives X = 2, Y = 0. See section 10.6.

In ALG, choose Sample standard deviation under STAT. The X deviation is primary and Y is separately labeled; no stack operands are used. See section 10.10.

Shifts and prefix cancellation

Keys/modes: f and g, both modes. Select a one-key alternate layer; repeating the same shift cancels, and pressing the other selects that layer. Shifts preserve STO, RCL, and FUNC while allowing a shifted target; they cancel HYP. Missing alternate legends report an error without performing the main action. Example: blue 7 opens PREC; Close returns without applying a setting.

Header CANCEL dismisses the entire pending selection without editing, including simultaneous shifts and prefixes. Unshifted backspace, CLx, or CLEAR also cancels an ordinary pending prefix instead of editing. For HYP, use CANCEL or unshifted backspace because a shift first cancels HYP and arms its own layer. MCLR consumes backspace or either shift as cancellation without clearing anything. Physical Escape cancels any current shift, prefix, or error before performing CLx on a later press. See CANCEL (p. 486), section 1.6 and chapter 14.

SHOW — inspect and recall cash flows

RPN keys and effect: g IRR, RPN. Open Cash flows; use the index stepper to inspect the entire stored list, including any entries after the NPV/IRR cutoff n. The selected amount uses up to 32 significant digits. Inspection and Close preserve entry, stack, n, and Last registers. Recall into X commits entry and replaces X without lift or Last-register changes. An empty bank cannot be recalled.

Example: 100 +/\(-\) \(\mathrm {CF}_0\); 110 \(\mathrm {CF}_j\); open SHOW, select index 0, and choose Recall into X to obtain \(-100\), with n still 1. This panel does not edit amounts or frequencies. See section 12.4.

In ALG, SHOW opens the indexed Recall cash flow worksheet. Accept an index and choose RECALL; Use value inserts the selected amount. Opening alone does not read or insert a value. See section 12.9.

Sigma plus and minus — add or remove a pair

RPN keys and effect: \(\Sigma +\) and its blue \(\Sigma -\), RPN, real-only. For single-variable data use y = 0 for each observation. Supply x in X and y in Y by entering y first, ENTER, then x. Add or subtract the pair’s contributions to the six accumulators; replace X with the new count, preserve Y and deeper values, and save both original operands in Last X/Y. Removal requires a positive count but cannot verify that the pair was previously entered.

Both sample real components and all six existing and proposed totals must be finite. A rejected addition or removal shows an error and preserves the bank, committed stack values, and Last X/Y; active entry is finished before validation. Imaginary components remain ignored.

Example: f \(\Sigma +\); 4 ENTER 2 \(\Sigma +\) gives count 1. Re-enter 4 ENTER 2 g \(\Sigma +\) to return the count to zero. STAT remains lit until the bank is cleared. The bank stores sums, not a retrievable sample list; use finite values. See section 10.2 and section 10.4.

In ALG, choose Add sample or Remove sample under STAT. Accept X and Y, then ADD SAMPLE or REMOVE SAMPLE. Validation precedes all accumulator updates. See section 10.10.

Square and square root

Keys/modes: orange square root = \(x^2\); unshifted \(\sqrt {x}\), both modes; effect U. Square multiplies X by itself. Real square root requires \(X\geq 0\) and returns the nonnegative root. Complex square root uses the principal branch, with \(\sqrt {-r}=+i\sqrt r\) on the negative real axis. Examples from separate starts: 12 f \(\sqrt {x}\) gives 144; 81 \(\sqrt {x}\) gives 9. Squaring then taking a real square root returns absolute value, not the original sign. See section 7.2 and section 8.8.

STACK and full-stack inspection

Keys/modes: f \(x\leftrightarrow y\) opens RPN stack depth; the display triangle opens the RPN inspector. STACK accepts a typed depth of 2–1000, or 0 for unlimited. Apply commits active entry; shrinking retains the positions nearest X and discards deeper values, while enlarging adds zero positions. Last registers and memories remain unchanged. Example: open STACK, enter 4, Apply to select a fixed four-register stack. No number is entered on the stack by typing in that field.

The inspector is read-only, preserving entries and pending commands. Deeper positions appear above X/S0; each row can scroll horizontally. Close with its collapse control, outside tap, or physical Escape. Example: type 12.30 and open the triangle to inspect the unfinished X without committing it. See section 2.10 and section 2.6.

SWAP — exchange X and Y

Keys/modes: \(x\leftrightarrow y\), RPN. Commit entry and exchange the two nearest complete operands, preserving deeper positions and both Last registers. Unlimited mode requires two positions. This is separate from orange 6’s complex-component swap. Example: 3 ENTER 12 \(x\leftrightarrow y\) \(\div \) gives 4, calculating \(12/3\). See section 2.7.

15.7   Alphabetical reference: T through Z and numeric legends

Trigonometric functions and their inverses

Keys/modes: SIN, COS, TAN and their blue inverse functions, both modes; effect U. The current DEG/RAD/GRAD setting controls argument and inverse-result units. In ALG the function retains the unit selected at insertion. In complex mode both components of a trig argument or inverse result are scaled to that unit; these are not hyperbolic functions.

Use equivalent ranges in RAD or GRAD. Examples, each from a fresh reference start with DEG selected: 30 SIN gives 0.5; 60 COS gives 0.5; 45 TAN gives 1; .5 g SIN gives 30; .5 g COS gives 60; 1 g TAN gives 45. The inverse legend means inverse function, not reciprocal. Complex branches and numerical precision conventions are in section 8.8 and section 8.9; real use is in section 7.4.

12 times and 12 divide — monthly TVM shortcuts

RPN keys and effect: orange n multiplies X by 12 and stores n; orange i divides X by 12 and stores i. RPN, real-only. Each replaces X without movement or Last-register changes, then arms the next bare TVM key to solve. Require a finite result. They do not set a calendar or payments-per-year option. Example: 30 f n sets n and X to 360; 6 f i sets i and X to 0.5. Division by 12 converts a nominal annual monthly rate, not an effective annual rate. See section 11.2.

In ALG, first finish or clear a pending compound expression; a lone scalar is also allowed. Then use the same shortcuts to store the scaled operand in n or i and publish a completed result with ANS updated. See section 11.12.

Finding an alternate legend by name

Several alphabetized families above cover more than one legend. table 15.10 provides a direct route without implying additional commands.

15.8   Display flags and pending indicators

The main display and expanded stack use the same indicators. A memory flag reports occupied storage, not validity, a count of entries, or which operation will run next. Explicitly stored zero counts as occupied; recalling an unset register does not. The same bank flags appear in both modes because the banks are shared.

A restored state can also contain TURN, an angle unit not offered by the current DEG/RAD/GRAD keys, or DIGITS, an older notation count prompt. These are not extra current keyboard selections. DRG returns TURN to DEG; DIGITS accepts one unshifted digit 0–9 or can be canceled as an ordinary prefix. A selected turn in the conversion menu is a unit choice and does not select the TURN angle setting.

There is no dedicated indicator for TVM store/solve readiness, a particular occupied register, a depreciation crossover year, or an HP odd-period C setting. Read the status line as well as the flags. CF0 and CLcf store n = 0 and therefore light FIN; clearing only cash flows does not extinguish it. See section 6.1.

15.9   Settings, defaults, and tool fields

The following defaults describe a new calculator state. Relaunch restores saved work; it is not a reset to this table. RPN and ALG retain independent operands and editors, but precision, display, complex settings, angle unit, date order, payment timing, and memory banks are shared.

ALG worksheets use separate accepted inputs and expression drafts. Equals evaluates a field, ENTER accepts it, and the named action computes from accepted inputs. Use value transfers a selected output; CANCEL discards unaccepted edits. See section 4.12.

The precision and depth panels refresh their fields from the actual current settings when opened. Editing a field does not place a value on the calculator stack. PREC Apply preserves unfinished entry; STACK Apply commits it before changing depth. Conversion Apply commits and replaces the active operand. In RPN, bounded IRR Apply calculates and lifts a result. RPN SHOW’s Recall into X commits and replaces X; its stepper only inspects. In ALG, bounded IRR and SHOW follow the worksheet ENTER, COMPUTE or RECALL, and Use value procedure. A tool’s Close control does not perform its operation. Invalid settings keep the panel available for correction without partially changing precision settings.

Numeric entry and all state-changing actions are saved locally as you work, including unfinished literals, prefixes, and panel inputs. There is no Save button, user undo/history browser, cloud synchronization, or single factory-reset key in this interface. Grouped clearing retains settings. For persistence failures and recovery, see chapter 14; for display rounding and old-value precision, see chapter 5.

15.10   Complete conversion-unit inventory

Open CONV with blue 8, select Dimension first, then From and To. The names below identify every selectable unit. Each conversion stays within one family; no cross-family inference or stored unit tag is provided. Chapter 9 explains exact and approximate factors, US/Imperial distinctions, offsets, and examples; chapter C gives the numerical definitions.

Temperature choices convert readings with offsets, not temperature intervals; readings below absolute zero are not screened for physical plausibility. Mass ounces are avoirdupois, and US volume choices are liquid measures. A day in the Time family is a fixed 24 hours, unrelated to date arithmetic or civil time zones. Angle conversion is independent of the trig angle setting and does not change it. Conversions use real components even in complex mode, including a same-unit conversion.

15.11   Domains and operational limits

Use the individual entries for their mathematical domains. This table collects capacities and restrictions that cannot be changed by selecting more display digits. Working precision is finite and does not guarantee the same number of correct answer digits, particularly for sensitive formulas and iterative results.

Numerical magnitude is not limited to \(10^{\pm p}\) when working precision is p digits. Exponent range is a separate, finite property; increasing p does not generally cure overflow or underflow. Ordinary real operations and each MPC primitive’s components use nearest, ties-even rounding. Display rounding is also nearest, ties even; financial RND uses ties away from zero, and solved TVM n has its separate 0.005 rule. Complex and financial formulas composed from multiple operations do not inherit a blanket guarantee of correct rounding for the entire calculation.

In complex mode, integer/fraction operations, remainders, counting, atan2, conversions, statistics, and finance use real components. ABS instead uses the complete complex magnitude. With complex mode off, scientific calculations use real components while stored pairs can remain intact. Branch choices can make a complex root differ from the real odd root. See chapter 5, chapter 8 and chapter C.

15.12   Errors, warnings, and recovery cues

Messages identify different kinds of failure. A domain error does not mean a stored bank was cleared, and a numerical search failure does not prove that an equation lacks a root. An active entry can be committed before a command fails; check ENTRY before expecting backspace to remove one digit. The following messages are grouped by the correction they require rather than by internal error names.

Some RPN operations return NaN (“not a number”) or \(\pm \infty \) without a domain message. These are not finite answers. Check settings and operands; absence of a warning does not establish accuracy. See chapter 14 for recovery.