feat(v4.0.0): Q.EXP bit for bit with v3; lighter D2*C and (UQ/)
Q.EXP is v3's q48_exp_approx: the Taylor series to 10 terms on |q|, stopping below 50 ulp, 1.0 Q./ e^|q| for q < 0, e^0 = 1.0, and for |q| >= 16.0 either 0 or Q max (v3 returned all ones, which is -ulp read signed under D-8). x, term, sum, sign and term index live in a new 8-cell variable (QE). Checked bit for bit against v3's q48_exp_approx (ported into the test) on 23 edge values and 3000 pseudo-random q in (-16.0, 16.0), at both cell widths, optimised and ASan+UBSan; dropping a term, moving the 50-ulp stop or skipping the reciprocal all fail. Q.EXP calls Q./, which calls (UQ/), which calls D2*C, and at first it left its caller no return entries. Lightened along the chain: - D2*C takes cin in A and builds 2hi+m with `over + +`: no ROT, no SWAP. - (UQ/) parks the quotient bit instead of using ROT, stores q without SWAP, and does its full trial subtraction (with borrow) in line instead of calling DNEGATE D+. - Q.EXP keeps its term index in (QE) instead of a FOR count. Headroom (data under args / return): (UQ/) 4/3 -> 4/4, Q./ 3/2 -> 3/3, Q.EXP 3/2. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
This commit is contained in:
rajames
co-authored by
Claude Opus 5.5
Claude Opus 5.5
parent
9e03bdab19
commit
29cf2688d2
@@ -147,8 +147,8 @@ IF body1 ELSE body2 THEN → if L1 drop body1 jump L2
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times, as on the F18. `FOR ... UNEXT` is the same but the body must fit in one instruction word.
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**Register conventions.** `A` and `B` are caller-saved. A word that uses them says so. Words in this
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document that clobber `A`: `@ ! +! -! 2@ 2! C@ C! UM* * UM/MOD Q.FROM-INT Q.TO-INT Q.* Q./ SEND RECV`. Words that clobber `B`:
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`Q./ SEND RECV`.
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document that clobber `A`: `@ ! +! -! 2@ 2! C@ C! UM* * UM/MOD Q.FROM-INT Q.TO-INT Q.* Q./ Q.EXP SEND RECV`. Words that clobber `B`:
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`Q./ Q.EXP SEND RECV`.
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**Return-stack words** (`>R R> R@ 2>R 2R> 2R@ I J UNLOOP` and the loop runtimes) are always IN.
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@@ -658,12 +658,14 @@ word. Per D-10 it occupies two cells on a 64-bit node too. Per D-8, v4 Q values
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| --- | --- | --- |
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| `Q.+` `Q.-` | CAP | `D+`, `D-` — executed on the golden model (2026-10-02) against v3's `q48_add`/`q48_sub` (`uint64_t` wrapping): bit-for-bit at 32-bit cells; at 64-bit cells the low cell is v3's, per D-10. |
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| `Q.*` | CAP | `SWAP push over over UM* drop push push over pop -if L1 SWAP jump L2 L1: SWAP drop 0 L2: pop SWAP - push push over pop UM* pop + ROT pop dup push over -if L3 drop dup jump L4 L3: drop 0 L4: push UM* pop - D+ ROT pop UM* SWAP push 0 D+ pop push over pop SWAP Q.TO-INT push Q.TO-INT pop SWAP` (`SWAP` and `ROT` in line) — `floor(a*b / 2^16)`, signed (D-8), cut to two cells. Cells 0–2 of the product come from the unsigned cell products `a1*b1` (low cell), `a0*b1`, `a1*b0`, `a0*b0`, in that order, each input dropped after its last use and `b0` waiting on the return stack. Reading `a1` and `b1` as signed takes `(b1<0 ? a0 : 0)` and `(a1<0 ? b0 : 0)` off cell 2; each is folded in as soon as its operands are adjacent. The result is cells 0–2 shifted right 16 with `Q.TO-INT` twice. Executed on the golden model (2026-10-02) against an independent limb-by-limb reference, and against v3's `q48_mul` for non-negative operands. Leaves its caller 3 data cells under its arguments and 3 return entries. Clobbers `A`. |
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| `Q./` | CAP | `over over OR if ZERO drop push over pop SWAP over xor (Q/) 4 + b! !b -if L1 DNEGATE L1: push push -if L2 DNEGATE L2: pop pop dup if CHK drop jump DIV CHK: drop over -131072 and if CHK2 drop jump DIV CHK2: drop push push dup pop dup push N-18 FOR 2* UNEXT over over xor -if SAME drop drop -if NOOV jump OV SAME: drop push inv pop + inv -if OV NOOV: drop pop pop jump DIV OV: drop drop drop pop pop drop drop (Q/) 4 + b! @b -if OVP drop 0 MSB ; OVP: drop -1 MAXHI ; DIV: (UQ/) (Q/) 4 + b! @b -if L3 drop DNEGATE ; L3: drop ; ZERO: drop drop drop NODE-ERROR b! -1 !b over over OR if Z0 drop -if ZP drop drop 0 MSB ; ZP: drop drop -1 MAXHI ; Z0: drop ;` — D-11: `a * 2^16 / b`, rounded toward zero; saturated to Q max / Q min on overflow; on division by zero, Q max / Q min by the dividend's sign (0 for `0 / 0`) and `NODE-ERROR` set. The sign of the result waits in `(Q/)`. Overflow needs no division: the quotient reaches `2^(2N-1)` exactly when `|a| * 2^16 >= |b| * 2^(2N-1)`, possible only for `|b| < 2^17`, where it is `a1 >= b0 << (N-17)` unsigned. `MSB` and `MAXHI` are the high cells of Q min and Q max. Executed on the golden model (2026-10-02) against an independent limb-by-limb reference (including `NODE-ERROR`), on width-native edge values, and against v3's `q48_div` for non-negative `a < 2^48`. Leaves its caller 3 data cells under its arguments and 2 return entries. Clobbers `A` and `B`. |
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| `(UQ/)` | CAP | Internal to `Q./`: unsigned `floor(a * 2^16 / b)` for `b != 0` and no overflow. Restoring division, `2N+16` steps, on one shifting register — quotient (starting as `a`) above remainder — with the quotient and divisor in `(Q/)` so the stacks carry only the remainder, the quotient bit and the loop count. Each step's quotient bit enters at the next step's shift; with no overflow the bits leaving the quotient in the last 16 steps are zeros. Trial subtraction by in-line sign tests (`x - y` with `y` on top is `push inv pop + inv`). Executed on the golden model (2026-10-02). Clobbers `A` and `B`. |
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| `D2*C` | CAP | `( lo hi cin -- lo' hi' cout )`: the double shifted left one bit, `cin` entering at the bottom and `cout` the bit leaving the top (both 0 or 1). `ROT dup -if L1 drop 1 jump L2 L1: drop 0 L2: push 2* + SWAP dup -if L3 drop 1 jump L4 L3: drop 0 L4: push 2* pop pop ROT + SWAP`, `ROT` and `SWAP` in line. Executed on the golden model (2026-10-02). |
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| `Q./` | CAP | `over over OR if ZERO drop push over pop SWAP over xor (Q/) 4 + b! !b -if L1 DNEGATE L1: push push -if L2 DNEGATE L2: pop pop dup if CHK drop jump DIV CHK: drop over -131072 and if CHK2 drop jump DIV CHK2: drop push push dup pop dup push N-18 FOR 2* UNEXT over over xor -if SAME drop drop -if NOOV jump OV SAME: drop push inv pop + inv -if OV NOOV: drop pop pop jump DIV OV: drop drop drop pop pop drop drop (Q/) 4 + b! @b -if OVP drop 0 MSB ; OVP: drop -1 MAXHI ; DIV: (UQ/) (Q/) 4 + b! @b -if L3 drop DNEGATE ; L3: drop ; ZERO: drop drop drop NODE-ERROR b! -1 !b over over OR if Z0 drop -if ZP drop drop 0 MSB ; ZP: drop drop -1 MAXHI ; Z0: drop ;` — D-11: `a * 2^16 / b`, rounded toward zero; saturated to Q max / Q min on overflow; on division by zero, Q max / Q min by the dividend's sign (0 for `0 / 0`) and `NODE-ERROR` set. The sign of the result waits in `(Q/)`. Overflow needs no division: the quotient reaches `2^(2N-1)` exactly when `|a| * 2^16 >= |b| * 2^(2N-1)`, possible only for `|b| < 2^17`, where it is `a1 >= b0 << (N-17)` unsigned. `MSB` and `MAXHI` are the high cells of Q min and Q max. Executed on the golden model (2026-10-02) against an independent limb-by-limb reference (including `NODE-ERROR`), on width-native edge values, and against v3's `q48_div` for non-negative `a < 2^48`. Leaves its caller 3 data cells under its arguments and 3 return entries. Clobbers `A` and `B`. |
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| `(UQ/)` | CAP | Internal to `Q./`: unsigned `floor(a * 2^16 / b)` for `b != 0` and no overflow. Restoring division, `2N+16` steps, on one shifting register — quotient (starting as `a`) above remainder — with the quotient and divisor in `(Q/)` so the stacks carry only the remainder, the quotient bit and the loop count. Each step's quotient bit enters at the next step's shift; with no overflow the bits leaving the quotient in the last 16 steps are zeros. Trial subtraction by in-line sign tests (`x - y` with `y` on top is `push inv pop + inv`), including the full double subtraction with its borrow, so the loop calls nothing but `D2*C`. Executed on the golden model (2026-10-02). Clobbers `A` and `B`. |
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| `D2*C` | CAP | `( lo hi cin -- lo' hi' cout )`: the double shifted left one bit, `cin` entering at the bottom and `cout` the bit leaving the top (both 0 or 1). `a! dup -if L1 drop 1 jump L2 L1: drop 0 L2: push over -if L3 drop 1 jump L4 L3: drop 0 L4: over + + push 2* a + pop pop` — `cin` waits in `A`, and `2hi + m` is `over + +`, so it needs one return entry. Executed on the golden model (2026-10-02). Clobbers `A`. |
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| `(Q/)` | CAP | Variable, 5 cells: `Q./`'s quotient register, divisor and result sign. Like `BASE` and the hold buffer, it lives in node memory. |
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| `Q.ABS` `Q.NEG` | CAP | `DABS`, `DNEGATE` — executed on the golden model (2026-10-02) against v3's `q48_abs` and `0 - q`: bit-for-bit at 32-bit cells, including v3's wrap of Q min to itself; at 64-bit cells the low cell is v3's and the high cell is the true sign, per D-10. |
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| `Q.LOG` `Q.EXP` `Q.SQRT` `Q.SIN` `Q.COS` | CAP | Algorithms ported from `q48_words.c`; the hosted C versions are the golden model. |
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| `Q.LOG` `Q.SQRT` `Q.SIN` `Q.COS` | CAP | Algorithms ported from `q48_words.c`; the hosted C versions are the golden model. |
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| `Q.EXP` | CAP | v3's `q48_exp_approx`: `1 + x + x^2/2! + …` to 10 terms on `x = |q|`, stopping once a term is below 50 ulp; `1.0 Q./ e^|q|` for `q < 0`; `e^0 = 1.0`; `|q| >= 16.0` gives 0 (`q < 0`) or **Q max** (v3 returned all ones, which reads as −ulp under D-8). `x`, the term, the sum, the sign and the term index live in the variable `(QE)`, so only `Q.*` and `Q./` arguments sit on the stacks. Executed on the golden model (2026-10-02): bit for bit v3's result for `|q| < 16.0` (at 64-bit cells as the same value, high cell 0). Leaves its caller 3 data cells under its argument and 2 return entries. Clobbers `A` and `B`. |
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| `(QE)` | CAP | Variable, 8 cells: `Q.EXP`'s `x`, term, sum, sign and term index. |
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| `Q.FROM-INT` | CAP | `push 0 a! 0 pop 15 FOR +* UNEXT push drop a pop` — `n * 2^16` as a signed double. `+*` with `S = 0` never adds, so each step is an exact arithmetic right shift of `T:A`; starting from `T:A = n:0` (that is, `n * 2^N`) and shifting `N-16` bits leaves `n * 2^16`. The count is `N-17`: 15 at 32-bit cells, 47 at 64. Negative values are no longer clamped to 0. Executed on the golden model (2026-10-02): matches v3's `q48_from_u64` for `n >= 0` (at 64-bit cells in the low cell, where v3 wraps for `n >= 2^47`, per D-10). Clobbers `A`. |
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| `Q.TO-INT` | CAP | `push a! 0 pop 15 FOR +* UNEXT drop drop a` — the same `+*` shift, 16 bits at every cell width, leaving the low cell in `A`. Rounds toward minus infinity, as v3's arithmetic shift does (−1.5 gives −2). Executed on the golden model (2026-10-02): v3's `q48_to_u64` exactly at 64-bit cells, its low cell at 32. Clobbers `A`. |
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| `Q.1` `Q.0` `Q.SCALE` | IN | Double-cell constants. |
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+206
-25
@@ -26,7 +26,8 @@
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* reference, signed, and against v3's q48_mul for non-negative operands.
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* Q./ (D-11) and its core (UQ/) are checked against an independent
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* limb-by-limb long division, including NODE-ERROR, on width-native edge
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* values, and against v3's q48_div where v4 keeps v3's meaning. Every word is
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* values, and against v3's q48_div where v4 keeps v3's meaning.
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* Q.EXP is checked bit for bit against v3's q48_exp_approx for |q| < 16.0. Every word is
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* also probed for how much of the 10- and 9-deep circular stacks (D-2) it
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* leaves to its caller.
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*
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@@ -49,6 +50,8 @@ static int failures = 0, checks = 0;
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#define NODE_ERROR ((v4_cell)(V4_NODE_WORDS - 2u))
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/* (Q/), Q./'s 5-cell scratch variable: q0 q1 b0 b1 sign. */
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#define QS ((v4_cell)(V4_NODE_WORDS - 8u))
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/* (QE), Q.EXP's 8-cell variable: x, term, sum (two cells each), sign, n. */
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#define QE ((v4_cell)(V4_NODE_WORDS - 16u))
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#define MAXU ((v4_ucell)~(v4_ucell)0)
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#define FLAG(c) ((c) ? V4_ALL_ONES : (v4_cell)0)
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@@ -62,7 +65,7 @@ static v4_cell w_nip, w_swap, w_or, w_negate, w_rot, w_zless, w_zequal,
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w_ugreater, w_abs, w_s2d, w_dplus, w_dnegate, w_dabs, w_smrem,
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w_slashmod, w_mplus, w_dminus, w_d0equal, w_dequal,
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w_qfromint, w_qtoint, w_less, w_equal, w_dless, w_2swap, w_2over,
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w_dmax, w_dmin, w_qgt_doc, w_qgt, w_dltkeep, w_qstar, w_d2starc, w_uqdiv, w_qslash;
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w_dmax, w_dmin, w_qgt_doc, w_qgt, w_dltkeep, w_qstar, w_d2starc, w_uqdiv, w_qslash, w_qexp;
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#define O(name) v4_asm_op(&as, V4_OP_##name)
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#define LIT(v) v4_asm_lit(&as, (v4_cell)(v))
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@@ -605,37 +608,34 @@ static void build(void)
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/* : D2*C ( lo hi cin -- lo' hi' cout ) 5.26, for Q./
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* The double shifted left one bit, cin (0 or 1) entering at the bottom,
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* cout (0 or 1) the bit that left the top.
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* ROT dup -if L1 drop 1 jump L2 L1: drop 0 L2: push hi cin lo R: m
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* 2* + SWAP lo' hi
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* dup -if L3 drop 1 jump L4 L3: drop 0 L4: push R: m cout
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* 2* pop pop ROT + SWAP ; lo' hi' cout
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* ROT and SWAP in line. */
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#define SWAP_INLINE() do { O(OVER); O(PUSH); O(PUSH); O(DROP); O(RPOP); O(RPOP); } while (0)
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#define ROT_INLINE() do { O(PUSH); SWAP_INLINE(); O(RPOP); SWAP_INLINE(); } while (0)
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* cout (0 or 1) the bit that left the top. cin waits in A.
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* a! dup -if L1 drop 1 jump L2 L1: drop 0 L2: push lo hi R: cout
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* over -if L3 drop 1 jump L4 L3: drop 0 L4: lo hi m m: lo's top bit
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* over + + lo 2hi+m
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* push 2* a + pop pop ; lo' hi' cout
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* Clobbers A. */
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{
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v4_asm_ref l1, l2, l3, l4;
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w_d2starc = v4_asm_label(&as);
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ROT_INLINE(); O(DUP);
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O(BANG_A); O(DUP);
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l1 = v4_asm_branch_fwd(&as, V4_OP_MINUS_IF);
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O(DROP); LIT(1);
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l2 = v4_asm_branch_fwd(&as, V4_OP_JUMP);
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v4_asm_resolve(&as, l1, v4_asm_label(&as));
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O(DROP); LIT(0);
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v4_asm_resolve(&as, l2, v4_asm_label(&as));
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O(PUSH); O(TWO_STAR); O(ADD); SWAP_INLINE();
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O(DUP);
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O(PUSH); O(OVER);
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l3 = v4_asm_branch_fwd(&as, V4_OP_MINUS_IF);
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O(DROP); LIT(1);
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l4 = v4_asm_branch_fwd(&as, V4_OP_JUMP);
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v4_asm_resolve(&as, l3, v4_asm_label(&as));
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O(DROP); LIT(0);
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v4_asm_resolve(&as, l4, v4_asm_label(&as));
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O(PUSH); O(TWO_STAR); O(RPOP); O(RPOP); ROT_INLINE(); O(ADD); SWAP_INLINE();
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O(OVER); O(ADD); O(ADD);
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O(PUSH); O(TWO_STAR); O(PUSH_A); O(ADD); O(RPOP); O(RPOP);
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O(SEMI);
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}
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#undef ROT_INLINE
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#undef SWAP_INLINE
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/* : (UQ/) ( a0 a1 b0 b1 -- q0 q1 ) 5.26, core of Q./
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* Unsigned floor(a * 2^16 / b), for b != 0 and a quotient below
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@@ -648,8 +648,8 @@ static void build(void)
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* stacks hold only r, the quotient bit and the loop count.
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* QS 2 + a! SWAP !+ ! QS a! SWAP !+ ! 0 0 0 r0 r1 qb
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* 2N+15 FOR
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* QS a! @+ @ ROT D2*C r0 r1 q0 q1 c
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* push SWAP QS a! !+ ! pop D2*C r0 r1 t
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* push QS a! @+ @ pop D2*C r0 r1 q0 q1 c
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* push QS 1 + a! ! QS a! ! pop D2*C r0 r1 t
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* if CMP drop jump TAKE
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* CMP: drop QS 3 + b! @b r0 r1 b1
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* over over xor if EQH -if SAMEH
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@@ -663,11 +663,15 @@ static void build(void)
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* -if T4 drop jump NOTAKEL T4: drop jump TAKEL
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* TAKEL: drop QS 2 + b! @b push inv pop + inv 0 1 jump END
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* NOTAKEL: 0 jump END
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* TAKE: QS 2 + a! @+ @ DNEGATE D+ 1 jump END
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* TAKE: push QS 2 + b! @b over over push inv pop + inv push r0 b0 R: r1 d0
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* over over xor -if SB drop NIP -if NB drop 1 jump BD NB: drop 0 jump BD
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* SB: drop push inv pop + inv -if NB2 drop 1 jump BD NB2: drop 0
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* BD: pop pop QS 3 + b! @b push inv pop + inv borrow d0 r1-b1
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* push SWAP pop SWAP - 1 jump END d0 r1-b1-borrow 1
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* NOTAKE: 0
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* END:
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* NEXT
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* QS a! @+ @ ROT D2*C drop push push drop drop pop pop ;
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* push QS a! @+ @ pop D2*C drop push push drop drop pop pop ;
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* x - y with y on top is push inv pop + inv. SWAP, ROT in line.
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* Clobbers A and B. */
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#define SWAP_INLINE() do { O(OVER); O(PUSH); O(PUSH); O(DROP); O(RPOP); O(RPOP); } while (0)
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@@ -687,8 +691,8 @@ static void build(void)
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LIT(0); LIT(0); LIT(0);
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LIT(2 * V4_CELL_BITS + 15); O(PUSH);
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loop = v4_asm_label(&as);
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LIT(QS); O(BANG_A); O(FETCH_INC); O(FETCH_A); ROT_INLINE(); CALL(w_d2starc);
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O(PUSH); SWAP_INLINE(); LIT(QS); O(BANG_A); O(STORE_INC); O(STORE_A); O(RPOP);
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O(PUSH); LIT(QS); O(BANG_A); O(FETCH_INC); O(FETCH_A); O(RPOP); CALL(w_d2starc);
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O(PUSH); LIT(QS + 1); O(BANG_A); O(STORE_A); LIT(QS); O(BANG_A); O(STORE_A); O(RPOP);
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CALL(w_d2starc);
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cmp = FWD(IF);
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O(DROP); j_take[nt++] = FWD(JUMP);
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@@ -719,13 +723,28 @@ static void build(void)
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l_notakel = v4_asm_label(&as); /* NOTAKEL */
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LIT(0); j_end[ne++] = FWD(JUMP);
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l_take = v4_asm_label(&as); /* TAKE */
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LIT(QS + 2); O(BANG_A); O(FETCH_INC); O(FETCH_A);
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CALL(w_dnegate); CALL(w_dplus); LIT(1); j_end[ne++] = FWD(JUMP);
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{
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v4_asm_ref sb, nb, bd, nb2, bd2;
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O(PUSH); LIT(QS + 2); O(BANG_B); O(FETCH_B);
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O(OVER); O(OVER); SUB_INLINE(); O(PUSH);
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O(OVER); O(OVER); O(XOR); sb = FWD(MINUS_IF);
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O(DROP); O(PUSH); O(DROP); O(RPOP); nb = FWD(MINUS_IF);
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O(DROP); LIT(1); bd = FWD(JUMP);
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HERE_(nb); O(DROP); LIT(0); bd2 = FWD(JUMP);
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HERE_(sb);
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O(DROP); SUB_INLINE(); nb2 = FWD(MINUS_IF);
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O(DROP); LIT(1); j_end[ne] = FWD(JUMP);
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HERE_(nb2); O(DROP); LIT(0);
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HERE_(bd); HERE_(bd2); v4_asm_resolve(&as, j_end[ne], v4_asm_label(&as));
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O(RPOP); O(RPOP); LIT(QS + 3); O(BANG_B); O(FETCH_B); SUB_INLINE();
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O(PUSH); SWAP_INLINE(); O(RPOP); SWAP_INLINE(); CALL(w_minus);
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LIT(1); j_end[ne++] = FWD(JUMP);
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}
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l_notake = v4_asm_label(&as); /* NOTAKE */
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LIT(0);
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l_end = v4_asm_label(&as); /* END */
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v4_asm_branch(&as, V4_OP_NEXT, loop);
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LIT(QS); O(BANG_A); O(FETCH_INC); O(FETCH_A); ROT_INLINE(); CALL(w_d2starc); O(DROP);
|
||||
O(PUSH); LIT(QS); O(BANG_A); O(FETCH_INC); O(FETCH_A); O(RPOP); CALL(w_d2starc); O(DROP);
|
||||
O(PUSH); O(PUSH); O(DROP); O(DROP); O(RPOP); O(RPOP); O(SEMI);
|
||||
|
||||
for (k = 0; k < nt; k++) v4_asm_resolve(&as, j_take[k], l_take);
|
||||
@@ -822,6 +841,101 @@ static void build(void)
|
||||
#undef SUB_INLINE
|
||||
#undef SWAP_INLINE
|
||||
|
||||
/* : Q.EXP ( q -- e ) 5.26, v3's q48_exp_approx
|
||||
* e^q by the Taylor series 1 + x + x^2/2! + ... to 10 terms, stopping
|
||||
* once a term is below 50 ulp, on x = |q|; for q < 0 the result is
|
||||
* 1.0 Q./ e^|q|. e^0 = 1.0; |q| >= 16.0 gives 0 (q < 0) or Q max (v3
|
||||
* returned all ones, which is -ulp read signed, D-8). x, the term and
|
||||
* the sum live in (QE), so only Q.* and Q./ arguments sit on the stack.
|
||||
* over over OR if ONE drop
|
||||
* dup QE 6 + b! !b -if L1 DNEGATE L1: x (QE)+6: sign
|
||||
* over over -1048576 -1 D+ push drop pop -if BIG drop
|
||||
* over over QE 2 + a! SWAP !+ ! over over QE a! SWAP !+ !
|
||||
* 65536 0 D+ QE 4 + a! SWAP !+ ! term = x, sum = 1 + x
|
||||
* 2 QE 7 + b! !b (QE)+7: n
|
||||
* LOOP:
|
||||
* QE 2 + a! @+ @ QE a! @+ @ Q.*
|
||||
* QE 7 + b! @b Q.FROM-INT Q./ term*x / n
|
||||
* over over QE 2 + a! SWAP !+ !
|
||||
* QE 4 + a! @+ @ D+ QE 4 + a! SWAP !+ ! sum += term
|
||||
* QE 2 + a! @+ @ if HI0 drop drop jump CONT
|
||||
* HI0: drop -if SM drop jump CONT
|
||||
* SM: -50 + -if CONT1 drop jump DONE term < 50: stop
|
||||
* CONT1: drop
|
||||
* CONT: QE 7 + b! @b 1 + dup !b -11 + -if DONE1 drop jump LOOP
|
||||
* DONE1: drop after n = 10
|
||||
* DONE: QE 4 + a! @+ @ QE 6 + b! @b -if POS drop 65536 0 2SWAP Q./ ;
|
||||
* POS: drop ;
|
||||
* BIG: drop drop drop QE 6 + b! @b -if BIGP drop 0 0 ; BIGP: drop -1 MAXHI ;
|
||||
* ONE: drop drop drop 65536 0 ;
|
||||
* Clobbers A and B. */
|
||||
#define FWD(op) v4_asm_branch_fwd(&as, V4_OP_##op)
|
||||
#define HERE_(r) v4_asm_resolve(&as, (r), v4_asm_label(&as))
|
||||
#define STORE2(addr) do { LIT(addr); O(BANG_A); O(OVER); O(PUSH); O(PUSH); O(DROP); O(RPOP); O(RPOP); \
|
||||
O(STORE_INC); O(STORE_A); } while (0)
|
||||
#define FETCH2(addr) do { LIT(addr); O(BANG_A); O(FETCH_INC); O(FETCH_A); } while (0)
|
||||
{
|
||||
v4_asm_ref one, l1, big, hi0, sm, cont1, j_cont1, j_cont2, j_done, pos, bigp;
|
||||
v4_cell loop, l_cont, l_done;
|
||||
|
||||
w_qexp = v4_asm_label(&as);
|
||||
O(OVER); O(OVER); CALL(w_or); one = FWD(IF);
|
||||
O(DROP);
|
||||
O(DUP); LIT(QE + 6); O(BANG_B); O(STORE_B);
|
||||
l1 = FWD(MINUS_IF); CALL(w_dnegate); HERE_(l1);
|
||||
O(OVER); O(OVER); LIT(-1048576); LIT(-1); CALL(w_dplus);
|
||||
O(PUSH); O(DROP); O(RPOP);
|
||||
big = FWD(MINUS_IF);
|
||||
O(DROP);
|
||||
O(OVER); O(OVER); STORE2(QE + 2);
|
||||
O(OVER); O(OVER); STORE2(QE);
|
||||
LIT(65536); LIT(0); CALL(w_dplus); STORE2(QE + 4);
|
||||
LIT(2); LIT(QE + 7); O(BANG_B); O(STORE_B);
|
||||
loop = v4_asm_label(&as);
|
||||
FETCH2(QE + 2); FETCH2(QE); CALL(w_qstar);
|
||||
LIT(QE + 7); O(BANG_B); O(FETCH_B); CALL(w_qfromint); CALL(w_qslash);
|
||||
O(OVER); O(OVER); STORE2(QE + 2);
|
||||
FETCH2(QE + 4); CALL(w_dplus); STORE2(QE + 4);
|
||||
FETCH2(QE + 2); hi0 = FWD(IF);
|
||||
O(DROP); O(DROP); j_cont1 = FWD(JUMP);
|
||||
HERE_(hi0);
|
||||
O(DROP); sm = FWD(MINUS_IF);
|
||||
O(DROP); j_cont2 = FWD(JUMP);
|
||||
HERE_(sm);
|
||||
LIT(-50); O(ADD); cont1 = FWD(MINUS_IF);
|
||||
O(DROP); j_done = FWD(JUMP);
|
||||
HERE_(cont1);
|
||||
O(DROP);
|
||||
l_cont = v4_asm_label(&as);
|
||||
LIT(QE + 7); O(BANG_B); O(FETCH_B); LIT(1); O(ADD); O(DUP); O(STORE_B);
|
||||
LIT(-11); O(ADD);
|
||||
{
|
||||
v4_asm_ref fin = FWD(MINUS_IF);
|
||||
O(DROP); v4_asm_branch(&as, V4_OP_JUMP, loop);
|
||||
HERE_(fin); O(DROP);
|
||||
}
|
||||
l_done = v4_asm_label(&as);
|
||||
FETCH2(QE + 4); LIT(QE + 6); O(BANG_B); O(FETCH_B);
|
||||
pos = FWD(MINUS_IF);
|
||||
O(DROP); LIT(65536); LIT(0); CALL(w_2swap); CALL(w_qslash); O(SEMI);
|
||||
HERE_(pos); O(DROP); O(SEMI);
|
||||
HERE_(big);
|
||||
O(DROP); O(DROP); O(DROP); LIT(QE + 6); O(BANG_B); O(FETCH_B);
|
||||
bigp = FWD(MINUS_IF);
|
||||
O(DROP); LIT(0); LIT(0); O(SEMI);
|
||||
HERE_(bigp); O(DROP); LIT(-1); LIT((v4_cell)(MAXU >> 1)); O(SEMI);
|
||||
HERE_(one);
|
||||
O(DROP); O(DROP); O(DROP); LIT(65536); LIT(0); O(SEMI);
|
||||
|
||||
v4_asm_resolve(&as, j_cont1, l_cont);
|
||||
v4_asm_resolve(&as, j_cont2, l_cont);
|
||||
v4_asm_resolve(&as, j_done, l_done);
|
||||
}
|
||||
#undef FETCH2
|
||||
#undef STORE2
|
||||
#undef HERE_
|
||||
#undef FWD
|
||||
|
||||
CHECK(v4_asm_ok(&as), "foundation words assemble");
|
||||
}
|
||||
|
||||
@@ -1172,6 +1286,40 @@ static void qdiv_ref(v4_ucell al, v4_ucell ah, v4_ucell bl, v4_ucell bh,
|
||||
if (neg) dneg(*rl, *rh, rl, rh);
|
||||
}
|
||||
|
||||
/* v3's q48_div and q48_exp_approx (v3/src/word_source/q48_16_words.c),
|
||||
* verbatim but for the names, as the parity reference for Q.EXP. They use
|
||||
* v3_q48_mul above, which is v3's __int128 result. */
|
||||
static uint64_t v3_q48_div(uint64_t a, uint64_t b)
|
||||
{
|
||||
if (b == 0) return 0;
|
||||
if (a > 0x0000FFFFFFFFFFFFULL) return 0xFFFFFFFFFFFFFFFFULL;
|
||||
return (a << 16) / b;
|
||||
}
|
||||
static uint64_t v3_q48_exp(uint64_t q)
|
||||
{
|
||||
int64_t q_signed;
|
||||
int is_negative, nn;
|
||||
uint64_t x, result, term;
|
||||
|
||||
if (q == 0) return 65536;
|
||||
q_signed = (int64_t)q;
|
||||
if (q_signed >= 1048576) return 0xFFFFFFFFFFFFFFFFULL;
|
||||
if (q_signed <= -1048576) return 0;
|
||||
is_negative = (q_signed < 0);
|
||||
x = is_negative ? (uint64_t)(-q_signed) : q;
|
||||
result = 65536;
|
||||
term = x;
|
||||
result = result + term;
|
||||
for (nn = 2; nn <= 10; nn++) {
|
||||
term = v3_q48_mul(term, x);
|
||||
term = v3_q48_div(term, (uint64_t)nn << 16);
|
||||
result = result + term;
|
||||
if (term < 50) break;
|
||||
}
|
||||
if (is_negative) result = v3_q48_div(65536, result);
|
||||
return result;
|
||||
}
|
||||
|
||||
/* Stack headroom. Run `word` with `dfill` marked cells under the canary and
|
||||
* `rfill` marked cells under its return address, and report whether the
|
||||
* results, the canary and every marked cell come back intact. The F18 stacks
|
||||
@@ -1800,6 +1948,33 @@ int main(void)
|
||||
}
|
||||
}
|
||||
|
||||
/* Q.EXP against v3's q48_exp_approx for |q| < 16.0 (bit for bit at
|
||||
* 32-bit cells; the same value, high cell 0, at 64), and the limits. */
|
||||
{
|
||||
static const int64_t qx[] = {
|
||||
0, 1, -1, 0x8000, -0x8000, 0x10000, -0x10000, 0x18000, 0x20000, -0x20000,
|
||||
0x2B7E1, 0x50000, -0x50000, 0xA0000, -0xA0000, 0xFFFFF, -0xFFFFF,
|
||||
0x100000, -0x100000, 0x100001, -0x100001, 0x7FFFFFFF, -0x7FFFFFFF
|
||||
};
|
||||
uint64_t x = 0x9FB21C651E98DF25u;
|
||||
for (unsigned i = 0; i < sizeof qx / sizeof qx[0] + 3000u; i++) {
|
||||
int64_t q;
|
||||
uint64_t uq;
|
||||
v4_cell ql, qh, el, eh;
|
||||
if (i < sizeof qx / sizeof qx[0]) q = qx[i];
|
||||
else {
|
||||
x ^= x << 13; x ^= x >> 7; x ^= x << 17;
|
||||
q = (int64_t)(x % 0x200000u) - 0x100000; /* (-16.0, 16.0) */
|
||||
}
|
||||
uq = (uint64_t)q;
|
||||
qcells(uq, &ql, &qh);
|
||||
if (q >= 0x100000) { el = V4_ALL_ONES; eh = (v4_cell)(MAXU >> 1); }
|
||||
else if (q <= -0x100000) { el = 0; eh = 0; }
|
||||
else qcells(v3_q48_exp(uq), &el, &eh);
|
||||
CHECK(call(w_qexp, 2, ql, qh, 0) && left2(el, eh), "Q.EXP [%u] q=%lld", i, (long long)q);
|
||||
}
|
||||
}
|
||||
|
||||
/* Q./ at the overflow boundary: |a| * 2^16 against |b| * 2^(2N-1), for
|
||||
* divisors around 2^16 and 2^17, every sign. */
|
||||
{
|
||||
@@ -1901,6 +2076,12 @@ int main(void)
|
||||
headroom("(UQ/)", w_uqdiv, 4, qdiv_args, 2, 2, &dh, &rh);
|
||||
headroom("Q./", w_qslash, 4, qdiv_args, 7, 2, &dh, &rh);
|
||||
CHECK(dh >= 2 && rh >= 2, "Q./ leaves room");
|
||||
static const v4_cell qexp_args[][4] = {
|
||||
{ 0, 0, 0, 0 }, { 0x10000, 0, 0, 0 }, { -0x10000, -1, 0, 0 },
|
||||
{ 0x50000, 0, 0, 0 }, { 0x200000, 0, 0, 0 }, { -0x200000, -1, 0, 0 }
|
||||
};
|
||||
headroom("Q.EXP", w_qexp, 2, qexp_args, 6, 2, &dh, &rh);
|
||||
CHECK(dh >= 2 && rh >= 2, "Q.EXP leaves room");
|
||||
headroom("SM/REM", w_smrem, 3, smrem_args, 5, 2, &dh, &rh);
|
||||
CHECK(rh >= 1, "SM/REM leaves room for /MOD's return address");
|
||||
headroom("/MOD", w_slashmod, 2, slashmod_args, 4, 2, &dh, &rh);
|
||||
|
||||
Reference in New Issue
Block a user