Statistics

The statistics subsystem reads list data, accumulates moments, solves regressions, and writes named results such as x̄, Σx, Sx, a, b, r, and r². This page separates the CALC, STAT-TESTS, and DISTR command families.

The CALC paths read L1–L6 through the VAT and use the BCD floating-point engine. The engine lives on Flash page 3A; raw disassembly supplies indexed-bit and cross-page operations that the decompiler can mis-render.

statVars result block [confirmed]

Every STAT-CALC result is a 9-byte TIFloat (see floating-point.md) written into a fixed RAM table beginning at statVars = 0x8A3A (statVars EQU 8A3Ah in ti83plus.inc). Entries are packed at the 9-byte FPLEN stride. These are the system variables recalled by name ([2nd][STAT] ▸ VARS):

These 31 consecutive values form the typed prefix used by the Ghidra database:

typedef struct {
    TIFloat StatN, XMean, SumX, SumXSqr, StdX, StdPX, MinX, MaxX;
    TIFloat MinY, MaxY, YMean, SumY, SumYSqr, StdY, StdPY, SumXY;
    TIFloat Corr, MedX, Q1, Q3, QuadA, QuadB, QuadC, CubeD, QuartE;
    TIFloat MedX1, MedX2, MedX3, MedY1, MedY2, MedY3;
} TIStatResultsPrefix; /* 31 × 9 bytes at statVars */

This makes, for example, statVars.XMean and statVars.Corr distinct fields rather than unrelated constants 0x8A43 and 0x8ACA. The address table remains the byte-level evidence for the layout. [confirmed]

Continuing past the table (also .inc): PStat/ZStat/TStat/ChiStat/ FStat/DF/Phat…/MeanX1/StdX1/StatN1/MeanX2/StdX2/StatN2/StdXP2/ SLower/SUpper/SStat — these hold the inferential-stats outputs (the STAT-TESTS menu) and are written by the test commands, not by 1/2-Var Stats. An ANOVA block anovaf_vars (F_DF/F_SS/F_MS/E_DF/E_SS/E_MS) follows.

STAT-TESTS are separate command handlers. [confirmed] Z-Test/T-Test/χ²-Test/ 2-SampFTest/ANOVA( etc. come in as their own 2-byte t2ByteTok (0xBB)-prefixed command tokens — e.g. LinRegTTest=34h in the STAT command token map — and are not dispatched through _OneVar (whose token map is only F2–FF). They fill the PStat…SStat/anovaf_vars block above directly. Test handlers and helpers appear alongside accumulation, variance, median, and regression code within 3A:4A00–3A:7E60; that span also contains coefficients and UI data, not one continuous test engine. See STAT-TESTS engine. The per-test entry addresses are not exposed as named routines and remain [hypothesis].

A scratch byte stat_calc_command (0x8A36, immediately below statVars) holds the stat-command discriminator (the model index set from the command token) for the duration of the computation. Working list/element pointers used by the loop live in the OP-scratch RAM 0x84AF…0x84DB (84D3=median data ptr, 84D5/84D7=current x/y element ptr, 84D9=sums matrix base, 84DB=freq list ptr, 84B1/84B2=loop counters, 84B3=element count). [confirmed]

Recall by name: _Rcl_StatVar (00:2149, id 0x42DC) is a page-0 bcall wrapper (CALL 0x3E07, then RST 20h) that loads the named statVar into OP1; the VAT-level recall (_RclVarSym/rcl_var_push, see sub-vat-archive.md) routes the stat-var name tokens (tRegEq 0x01, tStatN 0x02, tXMean 0x03, … tCorr 0x12, the STATVARS token group) to it. The name-token values are in ti83plus.inc (tStatN=02h … tSumXY=11h, tCorr=12h, tMedX=13h, regression coefficients via tokens 16h–1Ah). [standard]

_OneVar STAT-CALC entry [confirmed]

bcall(_OneVar) enters the shared 1-Var, 2-Var, and polynomial/transformed regression path. Separate nonlinear regression entries require their own caller analysis. The parser invokes it after pushing the list arguments; the normalized selector derived from the command token selects the behavior.

_OneVar (3A:6420):
  SET 5,(IY+9)            ; statFlags: "stat computation active"
  LD B,0                  ; arg counter
  RES 1,(IY+0)
  RES 1,(IY+1a)
  LD (9817),0             ; clear a status byte
  LD HL,8499
  CALL 1b33  ; stage the parsed arg descriptor at 8499
  LD A,0FF
  LD (84af),A
  CALL _CkOP1Real (1942-ish) / arg-class checks …
  ; ---- argument parsing (6442..64de) ----
  ;   walks the parser argument list, accepting list-name tokens (0x24 list,
  ;   0x2A list-element, 0x1C/0x25/0x19 = freq/list variants); validates count;
  ;   _JError(0x8A) ARGUMENT / 0x88 SYNTAX on a bad arg list.
  ; ---- set up the data pointers (64e1..6503) ----
  LD HL,847a
  LD DE,8d2a
  CALL 1a9a  ; resolve the x-list (and y/freq) → 84D3..84DB
  POP AF
  LD (8a36),A          ; *** save the command code → model discriminator ***
  LD HL,6352
  CALL 27da        ; install an on-error cleanup frame
  CALL 6572                     ; accumulation pass
  CALL 2800
  CALL 6345         ; tear down frame
  ; ---- coefficient ordering (6506..652f) ----
  LD A,(8a36)
  CP 4
  JR NC,..  ; other selectors take further ordering checks
       ; A<4: exchange coefficient slots through IDs 16h and 17h
       LD HL,8aee      ; read the first coefficient
  …
  SET 7,(IY+9)                  ; mark results valid
  CALL 67c1 …                   ; finalize / median

Key facts read from the disassembly:

• The command byte is saved in stat_calc_command and steers everything afterward.
• LD HL,0x8AEE (= QuadA) is the regression coefficient destination; the solver writes a,b,c,d,e there in descending order of power.
• _ErrStat (00:2741, id 0x44C2, code 0x15 “STAT”) and _ErrStatPlot (00:2759, code 0x1B) are the STAT-specific error raisers; the _OneVar body jumps to 0x2741 on e.g. fewer than the required data points. _ErrDimMismatch (0x2715) is raised if L1 and L2/freq lengths differ (the 21bb length compare at 6584/658a).

STAT command token map [confirmed]

The parser normalizes command selectors before the calculation path stores them in stat_calc_command (0x8A36). The source token bytes below must not be used directly as model indices. From ti83plus.inc:

CubicReg/QuartReg use single-byte tokens FAh/FBh; SinReg=32h, Logistic=33h, LinRegTTest=34h are 2-byte t2ByteTok (0xBB)-prefixed tokens (their 32h/33h/34h values are the second byte after 0xBB). The stored model selector is not the polynomial degree: the dimension setup at 3A:65A8–3A:65C1 handles special selectors before subtracting two from the selected value. The coefficient fan-out depends on the resulting matrix dimensions. [confirmed]

SortA(/SortD( are separate tokens (tSortA=E3h, tSortD=E4h) with their own command handler — not _OneVar. The sort used here, stat_sort (3A:7935), is stat-internal: its only callers are stat_median_quartile (3A:79B9) and medmed_partition (3A:760F) (xref-confirmed), so it powers the 1-Var median/ quartile and Med-Med paths in Median, quartiles, extrema, and sorting. The SortA(/SortD( command sort is a different routine on page 0x02 (≈02:5939, comparator _CpOP1OP2) — see Matrices and lists.

Accumulation pass [confirmed]

This builds the power-sums for 1/2-Var Stats and the regression sum-setup. It makes a single pass over the data list(s), accumulating the power-sums needed for the mean, variance, and least-squares normal equations. Read from disassembly:

6572: CALL 6f90/6f7d         ; default freq = 1 if no freq list given
6584: CALL 21bb              ; if freq list present, length-check vs x-list
                             ;   → _ErrDimMismatch (2715) on mismatch
658a: LD HL,(84d3)          ; HL = first element ptr; DE = element count
6590: LD A,(8a36)           ; dispatch on command:
   CP 8 (Med-Med) → jump to the resistant-line path (760f/75e4 → 79b9)
   else compute the matrix dimension from the degree:
        CP 1c/25/19/9 → dim=4
        CP 5 (CubicReg) NC → dim+? ; default
   65c1: A = dim
   SUB 2
   PUSH AF
65cd: set up x/y element pointers (84d5/84d7/84db)
65f0: ---- per-element accumulator init ----
   LD DE,8a3a ; … CALL 1a92  ; StatN slot
   LD DE,8a94                ; YMean/Σy slots
   CALL 110f                 ; allocate the sums matrix (84d9 = base)
6646..66fe: ---- per-element loop ----
   6f6a  : conditionally logarithm-transform the current operand
   28e4/2297 : loop bound (RST FPSub / compare)
   6567  : helper = (RST 8: OP1→OP2)
   LD HL,(84af)
   CALL 6f7d ; _FPMult (238b)
           → forms the running power x^k · freq
   238a  : _FPSquare (Σx²)
   238b  : _FPMult   (Σxy, Σx^(i+j))
   RST 30: _FPAdd    → accumulate into the matrix cell / Σ-slot
   2999/29db/29a2 : guard-clear / OP-shuffle helpers
   66fe: JP C,6655  ; loop while elements remain

So one pass builds, for a degree-d fit, the symmetric moment matrix of power-sums Σxⁱ (i = 0 … 2d) and the right-hand side Σxⁱy, stored as a small 2-D array reached by the RAM trampoline helpers 00:3A8F/3AA1/3AA7/3AAD/3AB9 (matrix-element get/set by (row B, col C)). StatN, SumX, SumXSqr, SumY, SumYSqr, SumXY, MinX/MaxX/MinY/MaxY are filled here directly. [confirmed]

Non-polynomial regressions transform first [confirmed]: the front-end at 658a+ checks the command code and, for ExpReg/PwrReg (ln y), LnReg/PwrReg (ln x), pre-applies the logarithm to each element before accumulating, then exponentiates the resulting linear coefficients off page 0x3A. The per-element ln is selected by the transform helper at 3A:6F6A:

LD A,(8A36)
CP 4
RET NC
AND B
RET Z

It bcalls _LnX at 3A:6F72 only when the model code is below four and its intersection with the caller’s mask in B is nonzero. This helper neither loads an element nor advances a data pointer. The back-transform _EToX/_TenX lives on page 02; see Transcendentals. This is the standard “linearize, fit a line, transform back” method; r is the correlation of the transformed data.

Mean and standard deviation [confirmed]

After the pass, _OneVar finalizes the moments (3A:6762+):

6762: LD DE,8a67
CALL 6984   ; σx  (population) from Σx², Σx, n
6786: LD DE,8a5e
CALL 6989   ; Sx  (sample), via _Minus1 (n→n-1) at 677c
6798: LD DE,8a55
CALL 6998   ; Σx² slot
67a7: LD DE,8aa6
CALL 6998   ; Σy²   (2-Var)

The variance helpers (3A:6984/6989/6998) implement the one-pass formula var = (Σx² − n·x̄²)/N then √:

6998: _FPSquare(x̄) ; recall Σx² (15da) ; _FPMult ; (RST 30 _FPAdd / subtract) ; …
6989: CALL _FPDiv (2541)
CALL 3939 (_SqRoot wrapper) ; store

The only difference between σx (population) and Sx (sample) is the divisor: the population path divides by n, the sample path first does _Minus1 (00:2294, n−1) — confirmed at 3A:677C. x̄ = Σx / n via _FPDiv. [confirmed]

Regression solver [confirmed]

For a polynomial fit the moment matrix from the accumulation pass is the augmented normal-equations matrix [ M | Σxⁱy ]. _OneVar solves it in place by Gauss-Jordan elimination (not a closed-form determinant), then writes the coefficients to QuadA…QuartE.

67c6: build/copy the augmented matrix; 84d9 = base
67d4..67e3: scale the pivot row
67ec: LD BC,0202
CALL 3aad        ; pivot element (2,2)
67f7: CALL 212d                     ; zero guard -> _ErrDomain (84h)
67fa: RST 8 ; …                     ; pivot reciprocal
6804: CALL 2541 (_FPDiv)            ; divide row by pivot
680d..6815: elimination loop

The 3A:6845–6891 cluster, byte by byte:

6845  CALL 3939  (cross_page_jump)   ; OP1 = √OP1 (_SqRoot at 02:6E38)
6848  RST 08h   (_OP1ToOP2)          ; OP2 = √…
6849  CALL 1674  (_CpyTo1FPST)       ; OP1 ← FPS−9 (the saved numerator sum)
684C  CALL 2541  (_FPDiv)            ; OP1 = numerator/denominator = r
684F  LD A,0x12 ; CALL 213D          ; _Sto_StatVar(tCorr): Corr (8ACA) ← r
6854  CALL 1BA4  (_OP1Set0)          ; accumulator = 0
6857  POP BC / PUSH BC               ; BC = augmented-matrix row count
685B  LD B,2                         ; start at row 2 (first data column)
685D  loop:
        CALL 19EC (_OP1ToOP4); CALL 150A (_PopRealO2)   ; OP2 ← popped FPS value
        CALL 3AA7 (cross_page_jump)  ; matrix element (col B) → OP1
        CALL 238B (_FPMult)          ; element · value
        CALL 19FE; RST 30h (_FPAdd)  ; accumulate into OP4/OP1
        INC B until B = H            ; walk the column
6878  CALL 2903 (fp_st_slot7_op3)    ; stash the column sum
687B  CALL 1DEE  (_CkOP2FP0)         ; denominator zero?
687E  JR Z,6891                      ; yes → skip r² store
6880  CALL 2541  (_FPDiv)            ; ratio for r²/R²
6885  LD A,B; CP 2                   ; model order == 2 (linear)?
6888  LD A,0x35 / 0x36               ; id 0x35 = r² (slot 8C05), 0x36 = R² (8C0E)
688E  CALL 213D  (_Sto_StatVar)

The region forms r = num/den and stores it to Corr at 0x8ACA. It then accumulates a column-weighted residual sum over the augmented matrix. When the denominator is nonzero, it stores r² for linear fits or R² for higher-order fits in separate statVar slots at 0x8C05 and 0x8C0E. [confirmed]

68d6..6953: back-substitution — each coeff = (rhs − Σ known·M) / pivot
   (3aa7/3aa1 matrix access, 238b _FPMult, RST 30/RST 8 accumulate,
    24bd _InvOP1S to subtract, 2541 _FPDiv)
   each solved coefficient is stored via 69af → CALL 3ab9 (matrix set)
       then copied out to the QuadA..QuartE statVars block.

• The zero guard at 3A:67F7 calls ram:212D. That helper calls _CkOP1FP0 and jumps to _ErrDomain on zero; this site raises DOMAIN (0x84), not SINGULAR MAT. Other matrix/regression guards must be classified separately. [confirmed]

• The solver is dimension-generic: LinReg (2×2) → a,b; QuadReg (3×3) → a,b,c; CubicReg (4×4) → a,b,c,d; QuartReg (5×5) → a,b,c,d,e. The coefficients land in QuadA(8AEE) downward. [confirmed]

• Correlation r and r² are computed for the linear models from the centred sums: $$r=\frac{\sum (x-\bar x)(y-\bar y)}{\sqrt{\sum (x-\bar x)^2\,\sum (y-\bar y)^2}}=\frac{n\sum xy-\sum x\sum y}{\sqrt{\big(n\sum x^2-(\sum x)^2\big)\big(n\sum y^2-(\sum y)^2\big)}}$$

  assembled with _FPMult/_FPSub/_SqRoot/ _FPDiv (the 6845/684c cluster) and stored to Corr (8ACA). The store offset is pinned: at 3A:684F the code does LD A,0x12
CALL 0x213D, and 0x213D is _Sto_StatVar (the store counterpart of _Rcl_StatVar 00:2149 — both funnel through the 0x3E07 statVar dispatcher with the name id in A). Id 0x12 = tCorr = the Corr slot, so this single sequence is exactly r → Corr (8ACA). The preceding 3A:6845 _SqRoot/_FPDiv cluster forms the ratio; r² (and R² for higher-order fits) is the coefficient of determination derived by the following column-weighted pass. It is stored separately through IDs 0x35 and 0x36, at 0x8C05 and 0x8C0E respectively. [confirmed]

• The fitted equation is also written to RegEQ (the Y=-style regression equation system var, recalled via token tRegEq=0x01) so RegEQ can be pasted or graphed. [standard]

The Med-Med model (F8) takes the resistant-line branch (3A:760F/79B9): it sorts, splits the x-sorted data into three equal partitions, takes the median (x,y) of each (MedX1/2/3, MedY1/2/3 at 8B1B…), and fits the line through the outer two summary points adjusted toward the middle — classic Tukey median-median. [standard]

Median, quartiles, extrema, and sorting [confirmed]

For 1-Var Stats the five-number summary needs the data sorted:

• MinX/MaxX are tracked during the accumulation pass with running min/max compares.
• The median/quartile path (3A:79B9 → 7A0B …) sorts a working copy via the internal sort stat_sort (3A:7935), then:
  • Med (MedX, 8AD3) = middle element (or mean of the two middle for even n),
  • Q1 (8ADC) = median of the lower half, Q3 (8AE5) = median of the upper half (TI’s “exclude the overall median when n is odd” convention), with frequency-weighted positions (the 7B30/7B4C/7B6E helpers walk the cumulative-frequency index, and 198d/238b interpolate the rank). The ROM path is [confirmed]. The quartile rule is [standard].

The five-number summary (minX, Q1, Med, Q3, maxX) is what the MED/box-plot stat plot reads back out of statVars.

Worked two-variable statistics and regression flow [hypothesis]

1. Parser pushes the list args, sets A = command token, bcall(_OneVar).
2. _OneVar parses args → x-list ptr (84D3), y-list (84D5), freq (84DB); saves the model code to stat_calc_command.
3. Accumulation pass: one walk of L1/L2 building n, Σx, Σx², Σy, Σy², Σxy and minX/maxX/minY/maxY into statVars, plus the 2×2 moment matrix.
4. Moments: $\bar x=\tfrac{\sum x}{n}$, $\bar y=\tfrac{\sum y}{n}$; the sample/population spreads $S_x,\sigma_x,S_y,\sigma_y$ via the variance helper (divide by $n-1$ vs $n$).
5. Solve: Gauss-Jordan on the normal equations $\left[\begin{array}{cc|c}\sum 1&\sum x&\sum y\\\sum x&\sum x^2&\sum xy\end{array}\right]$ → b=slope, a=intercept → QuadA/QuadB; r → Corr, r² → its separate stat-variable slot; equation → RegEQ, pasted into Y1.
6. Results displayed by the STAT-CALC report screen; all of x̄/Σx/…/a/b/r persist in statVars for later recall by name (_Rcl_StatVar).

Stat plots [standard]

Stat plots (Scatter tScatter=FE, xyLine FD, Histogram tHist=FC, box plots tBoxIcon, normal-prob) are drawn by the graphing subsystem, reading the five-number summary and the raw L1/L2 lists. _ErrStatPlot (00:2759, code 0x1B) guards an invalid/undefined plot configuration; _ZmStats (33:65DC, id 0x47A4) is the ZoomStat routine that auto-scales the window to the plotted list data (sets Xmin/Xmax/Ymin/Ymax from minX/maxX/minY/maxY). See sub-graphing.md. [standard]

DISTR functions

Distribution functions use the BB token family. For example, BB 0F is normalcdf( and BB 1B is normalpdf(; they are expression functions rather than _OneVar commands. The complete numerical caller paths remain open on this page. [standard]

The macro tools/macros/distr-normalcdf.macro enters normalcdf(0,1) through the interactive UI. Its visits to 39:4A02–39:4F5B belong to the MathPrint editor/layout family documented in Equation display. Whole-run coverage of those routines does not identify the distribution calculation. A reduced trace anchored around numeric evaluation is needed.

The coefficient table at 3A:554F below directly establishes a normal-tail approximation in the statistics code. Which DISTR entries use that approximation, and which use other integration or special-function routines, remains [hypothesis].

STAT-TESTS engine on page 3A [confirmed]

The inferential-statistics commands execute in their own engine on page 3A, sharing the bank with _OneVar but distinct from it. Three byte-pinned structures locate it:

Candidate PStat–SStat references. A ROM-wide byte-pattern scan (tools/ti84re/rom/scan_stat_writers.py, immediate or absolute operands landing in 0x8B5A–0x8C37) finds about 50 opcode-shaped candidates on page 3A (3A:4B15–3A:6BDC) plus candidates on pages 06, 35, 37, and 39. Because the scan does not recover instruction boundaries, these hits locate a search cluster but do not by themselves establish a writer count or exclude references on other pages. [hypothesis]

A TStat output stage at 3A:54C0–3A:54D9. The code loads StdX (0x8A5E) at 3A:54C1, divides through _FPDiv at 3A:54C5, and calls the subtraction/division helper at 3A:544C through 3A:54D4. It stores the result with LD A,24h at 3A:54D7 followed by _Sto_StatVar at 3A:54D9. The common resolver at 38:618A maps ID 24h to TStat at 0x8B6C. This pins a result-store stage, not every command caller. 3A:5500 instead belongs to the normal-tail arithmetic below. [confirmed]

The normal p-value coefficient table at 3A:554F. [confirmed] Nine-byte TIFloat constants, byte-verified in sequence:

For nonnegative $z$, this coefficient set gives the Zelen–Severo upper-tail approximation $Q(z)\approx\varphi(z),(b_1t+b_2t^2+b_3t^3+b_4t^4+b_5t^5)$, where $Q(z)=1-\Phi(z)$ and $t=1/(1+pz)$. The loop at 3A:551F evaluates the five coefficients in descending order by Horner steps; LD HL,554Fh at 3A:550E pins the table start. The type bytes at 3A:5561 and 3A:5573 are 0x80, which supplies the negative signs on b4 and b2. The routine evaluates the polynomial using the absolute standardized argument (3A:550A). After multiplying by the normal density, it tests the saved argument’s sign at 3A:553F and conditionally calls 3A:447A to replace the result with 1-Q(|z|). Thus the returned tail has the correct symmetry for negative arguments. Caller-level conversion to a test’s PStat must be checked separately. [confirmed]

UI descriptor tables at 3A:7D00–3A:7E60. [confirmed] The same bank carries the test editor’s data. It includes alternative-hypothesis strings for the 1-PropZTest and 2-PropZTest menus, plus the F-test tail strings. It also contains SinReg and Logistic formula templates, three-byte dispatch stubs into fixed page 0 vectors, and an ascending handler-pointer array at 3A:7DF4–3A:7E1E. The mapping from array slots to menu items remains open.

Subsystem integration

  L1..L6 lists (VAT data)                 statVars (0x8A3A)  ← results, recall-by-name
        │ (VAT element access)                 ▲
        ▼                                       │ (_Rcl_StatVar 00:2149)
   _OneVar (3A:6420, id 0x4BA3)  ──►  per-element accumulation pass (3A:6572)
        │  cmd code → stat_calc_command          │  uses FP engine:
        │                                        │   RST30 _FPAdd, 238B _FPMult,
        ├─ moments / Sx,σx (3A:6984..)           │   238A _FPSquare, 2541 _FPDiv,
        ├─ Gauss-Jordan solve (3A:67C6..) ───►   │   3939 _SqRoot, 2294 _Minus1
        │     → QuadA..QuartE, Corr, RegEQ       │
        └─ sort + median/quartile (3A:7935/79B9) ┘
  errors: _ErrStat 00:2741 (0x15), _ErrStatPlot 00:2759 (0x1B),
          _ErrSingularMat 0x83, _ErrDimMismatch 00:2715 (0x8B)

The STAT subsystem is a thin data-driven front-end on page 0x3A that reads list data via the VAT, drives the page-0/page-02 BCD FP engine to build power-sums, then either finalizes the moments or runs an in-place Gauss-Jordan solve of the normal equations, depositing every output as a named TIFloat in the statVars block.

Routine index

RAM: statVars=0x8A3A, stat_calc_command=0x8A36, work pointers 0x84AF–0x84DB (84D3 x/median ptr, 84D5/84D7 element ptrs, 84D9 sums-matrix base, 84DB freq ptr, 84B1/84B2 loop counters, 84B3 element count). FP engine reused: RST 30h=_FPAdd, RST 08h=OP1→OP2, 00:238B=_FPMult, 00:238A=_FPSquare, 00:2541=_FPDiv, 00:2294=_Minus1, 02:6E38 via the fixed-page stub ram:3939 =_SqRoot, 24BD=_InvOP1S.

Remaining questions

• Correlation stores. 3A:684F does LD A,0x12
CALL 0x213D (_Sto_StatVar, ID 0x12 = tCorr), i.e. r → Corr (0x8ACA); r²/R² is the coefficient of determination from the following column-weighted pass, stored through IDs 0x35/0x36 at 0x8C05/0x8C0E. See the annotated 3A:6845–3A:6891 listing under Regression solver. [confirmed]
• DISTR numerical cores. The interactive normalcdf( trace visits MathPrint UI routines, but its numerical evaluator has not been isolated. The normal-tail coefficients on page 3A are decoded; the complete DISTR caller graph and algorithms remain open.
• STAT-TESTS (Z/T/χ²/F/ANOVA) fill PStat…SStat/anovaf_vars from their own engine on page 3A. A pinned TStat store, the normal-tail coefficient table, and the UI descriptor area provide separate anchors. See STAT-TESTS engine. The per-test entry addresses and the slot-to-menu mapping for the 3A:7DF4 pointer array remain [hypothesis]. The _Sto_StatVar/_Rcl_StatVar stubs (ram:213D/ram:2149) funnel through the stub at ram:3E07. Its descriptor 8A 61 78 selects the common stat-variable address resolver at 38:618A; the variable ID in A selects a RAM slot, not a separate cross-page descriptor.
• stat_sort (3A:7935) is a 49-byte setup that validates/counts the elements then dispatches the compare-swap via rst 28h (the bcall site isn’t fully analyzed in the DB). The SortA(/SortD( command sort is a different routine (page 0x02, comparator _CpOP1OP2) — its complex-list ordering is documented in Matrices and lists.