diff --git a/docs/v4.0.0/DECOMPOSITION.md b/docs/v4.0.0/DECOMPOSITION.md index 2e81fb92..48ccf306 100644 --- a/docs/v4.0.0/DECOMPOSITION.md +++ b/docs/v4.0.0/DECOMPOSITION.md @@ -147,8 +147,8 @@ IF body1 ELSE body2 THEN → if L1 drop body1 jump L2 times, as on the F18. `FOR ... UNEXT` is the same but the body must fit in one instruction word. **Register conventions.** `A` and `B` are caller-saved. A word that uses them says so. Words in this -document that clobber `A`: `@ ! +! -! 2@ 2! C@ C! UM* * UM/MOD Q.FROM-INT Q.TO-INT Q.* Q./ Q.EXP Q.SQRT SEND RECV`. Words that clobber `B`: -`Q./ Q.EXP Q.SQRT SEND RECV`. +document that clobber `A`: `@ ! +! -! 2@ 2! C@ C! UM* * UM/MOD Q.FROM-INT Q.TO-INT Q.* Q./ Q.EXP Q.SQRT Q.LOG SEND RECV`. Words that clobber `B`: +`Q./ Q.EXP Q.SQRT Q.LOG SEND RECV`. **Return-stack words** (`>R R> R@ 2>R 2R> 2R@ I J UNLOOP` and the loop runtimes) are always IN. @@ -664,7 +664,9 @@ word. Per D-10 it occupies two cells on a 64-bit node too. Per D-8, v4 Q values | `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`. | | `(Q/)` | CAP | Variable, 5 cells: `Q./`'s quotient register, divisor and result sign. Like `BASE` and the hold buffer, it lives in node memory. | | `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. | -| `Q.LOG` `Q.SIN` `Q.COS` | CAP | Algorithms ported from `q48_words.c`; the hosted C versions are the golden model. | +| `Q.SIN` `Q.COS` | CAP | Algorithms ported from `q48_words.c`; the hosted C versions are the golden model. | +| `Q.LOG` | CAP | v3's `q48_log_approx`: `x = 2^k * m` with `1.0 <= m < 2.0`; `ln m` by up to 6 Newton rounds on `e^y = m` from `y = m - 1.0`, stopping once `|m - e^y| < 100` ulp; result `y + k * ln 2` with `ln 2 = 45426`. `e^y` is `Q.EXP`'s Taylor loop **written in line** (flattened, ruled 2026-10-02), so `Q.LOG` calls only `Q.*`, `Q./` and `UM*` and the call chain is one level shorter than through `Q.EXP`. After the reduction `m`, `y`, the Taylor term and its sum each fit one cell at either width, so the variable `(QL)` holds single cells. `x <= 0` returns 0 and sets `NODE-ERROR` (D-12). Executed on the golden model (2026-10-03): bit for bit v3's result for every `x > 0` tested, including a sweep of the reduced `m`. v3's clamp `y = max(y - corr, 0)` is kept for fidelity but cannot fire: over all 65536 values of `m` it is never reached, and the iteration never needs more than 4 rounds. Leaves its caller 3 data cells under its argument and 2 return entries. Clobbers `A` and `B`. | +| `(QL)` | CAP | Variable, 7 cells: `Q.LOG`'s `m`, `y`, `k`, rounds left, Taylor term (then `delta`), sum, and `n * 1.0`. | | `Q.SQRT` | CAP | v3's `q48_sqrt_approx`: Newton from `x0 = q/2 + 0.25`, up to 8 rounds of `x' = (x + q/x) / 2`, returning `x` as soon as `|x' - x| < 10` ulp; `sqrt(0) = 0`, `sqrt(1.0) = 1.0`. `q < 0` returns 0 and sets `NODE-ERROR` (D-12). `q`, `x` and the rounds left live in the variable `(QR)`. The halving is a logical double shift, `push a! 0 pop +* MAXHI and push drop a pop`. Executed on the golden model (2026-10-02): bit for bit v3's result for `0 <= q < 2^48`; above that v3's `q48_div` saturates and v4 divides correctly, so they part. Leaves its caller 3 data cells under its argument and 2 return entries. Clobbers `A` and `B`. | | `(QR)` | CAP | Variable, 5 cells: `Q.SQRT`'s `q`, `x` and rounds left. | | `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`. | diff --git a/v4/tests/test_foundation.c b/v4/tests/test_foundation.c index 71ecc00a..b0b0eaeb 100644 --- a/v4/tests/test_foundation.c +++ b/v4/tests/test_foundation.c @@ -29,7 +29,9 @@ * values, and against v3's q48_div where v4 keeps v3's meaning. * Q.EXP is checked bit for bit against v3's q48_exp_approx for |q| < 16.0. * Q.SQRT is checked bit for bit against v3's q48_sqrt_approx for - * 0 <= q < 2^48, and for 0 with NODE-ERROR below zero (D-12). Every word is + * 0 <= q < 2^48, and for 0 with NODE-ERROR below zero (D-12). + * Q.LOG is checked bit for bit against v3's q48_log_approx for x > 0, and + * for 0 with NODE-ERROR at or below zero. Every word is * also probed for how much of the 10- and 9-deep circular stacks (D-2) it * leaves to its caller. * @@ -56,6 +58,8 @@ static int failures = 0, checks = 0; #define QE ((v4_cell)(V4_NODE_WORDS - 16u)) /* (QR), Q.SQRT's 5-cell variable: q, x (two cells each), rounds left. */ #define QR ((v4_cell)(V4_NODE_WORDS - 24u)) +/* (QL), Q.LOG's 7-cell variable: m, y, k, rounds left, term, sum, n*1.0. */ +#define QL ((v4_cell)(V4_NODE_WORDS - 32u)) #define MAXU ((v4_ucell)~(v4_ucell)0) #define FLAG(c) ((c) ? V4_ALL_ONES : (v4_cell)0) @@ -69,7 +73,7 @@ static v4_cell w_nip, w_swap, w_or, w_negate, w_rot, w_zless, w_zequal, w_ugreater, w_abs, w_s2d, w_dplus, w_dnegate, w_dabs, w_smrem, w_slashmod, w_mplus, w_dminus, w_d0equal, w_dequal, w_qfromint, w_qtoint, w_less, w_equal, w_dless, w_2swap, w_2over, - w_dmax, w_dmin, w_qgt_doc, w_qgt, w_dltkeep, w_qstar, w_d2starc, w_uqdiv, w_qslash, w_qexp, w_qsqrt; + w_dmax, w_dmin, w_qgt_doc, w_qgt, w_dltkeep, w_qstar, w_d2starc, w_uqdiv, w_qslash, w_qexp, w_qsqrt, w_qlog; #define O(name) v4_asm_op(&as, V4_OP_##name) #define LIT(v) v4_asm_lit(&as, (v4_cell)(v)) @@ -1018,6 +1022,156 @@ static void build(void) #undef FETCH2 #undef STORE2 #undef HERE_ +#undef FWD + + /* : Q.LOG ( x -- ln x ) 5.26, v3's q48_log_approx + * x = 2^k * m with 1.0 <= m < 2.0; ln m by up to 6 Newton rounds on + * e^y = m from y = m - 1.0; result y + k * ln 2 (ln 2 = 45426). e^y is + * Q.EXP's Taylor loop written here in line, so Q.LOG calls only Q.*, Q./ + * and UM*. After the reduction m, y, the Taylor term and sum all fit one + * cell, so (QL) holds single cells: m y k rounds term sum n*1.0. + * x <= 0 gives 0 and sets NODE-ERROR (D-12). D2/ is the logical double + * shift right, as in Q.SQRT. + * dup -if POS drop jump ERR + * POS: drop over over OR if ZERO drop 0 QL 2 + b! !b + * DOWN: dup if CHKLO drop jump SHR + * CHKLO: drop over -131072 and if DOWNDONE drop + * SHR: D2/ QL 2 + b! @b 1 + !b jump DOWN x >= 2.0: halve, k+1 + * DOWNDONE: drop drop m + * UP: dup -65536 and if UPSHIFT drop jump NORM + * UPSHIFT: drop 2* QL 2 + b! @b -1 + !b jump UP m < 1.0: double, k-1 + * NORM: dup QL b! !b -65536 + QL 1 + b! !b 6 QL 3 + b! !b + * NEWTON: QL 1 + b! @b dup QL 4 + b! !b 65536 + QL 5 + b! !b + * 131072 QL 6 + b! !b + * EXPL: QL 4 + b! @b 0 QL 1 + b! @b 0 Q.* drop + * 0 QL 6 + b! @b 0 Q./ drop dup QL 4 + b! !b + * dup QL 5 + b! @b + !b + * -50 + -if EXPC drop jump EXPD + * EXPC: drop QL 6 + b! @b 65536 + dup !b -720896 + -if EXPD2 drop jump EXPL + * EXPD2: drop + * EXPD: QL b! @b QL 5 + b! @b push inv pop + inv delta = m - e^y + * dup QL 4 + b! !b delta waits in the term's cell + * if DZ -if DPOS + * inv 1 + 0 QL 5 + b! @b 0 Q./ drop corr = -delta / e^y + * QL 1 + b! @b SWAP push inv pop + inv -if KEEP drop 0 KEEP: QL 1 + b! !b + * jump TEST y = max(y - corr, 0) + * DPOS: 0 QL 5 + b! @b 0 Q./ drop QL 1 + b! @b + !b jump TEST + * DZ: drop + * TEST: QL 4 + b! @b -if AP inv 1 + AP: -100 + -if CONT drop jump FIN + * CONT: drop QL 3 + b! @b -1 + dup !b if FIN0 drop jump NEWTON + * FIN0: drop + * FIN: QL 1 + b! @b QL 2 + b! @b + * -if KP inv 1 + 45426 UM* drop inv 1 + jump KS KP: 45426 UM* drop + * KS: + dup -if SP drop -1 ; SP: drop 0 ; + * ZERO: drop ERR: drop drop NODE-ERROR b! -1 !b 0 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 JUMP_TO(l) v4_asm_branch(&as, V4_OP_JUMP, (l)) +#define VGET(a) do { LIT(a); O(BANG_B); O(FETCH_B); } while (0) +#define VSET(a) do { LIT(a); O(BANG_B); O(STORE_B); } while (0) +#define SWAP_INLINE() do { O(OVER); O(PUSH); O(PUSH); O(DROP); O(RPOP); O(RPOP); } while (0) +#define SUB_INLINE() do { O(PUSH); O(INV); O(RPOP); O(ADD); O(INV); } while (0) +#define D2SLASH() do { O(PUSH); O(BANG_A); LIT(0); O(RPOP); O(MUL_STEP); \ + LIT((v4_cell)(MAXU >> 1)); O(AND); O(PUSH); O(DROP); O(PUSH_A); O(RPOP); } while (0) + { + v4_asm_ref pos, j_err, zero, chklo, j_shr, downdone, upshift, j_norm, expc, j_expd, + expd2, dzero, dpos, keep, j_test, ap, contn, j_fin, fin0, kp, j_ks, sp; + v4_cell l_down, l_up, l_newton, l_expl, l_test, l_err; + + w_qlog = v4_asm_label(&as); + O(DUP); pos = FWD(MINUS_IF); + O(DROP); j_err = FWD(JUMP); + HERE_(pos); + O(DROP); O(OVER); O(OVER); CALL(w_or); zero = FWD(IF); + O(DROP); LIT(0); VSET(QL + 2); + l_down = v4_asm_label(&as); + O(DUP); chklo = FWD(IF); + O(DROP); j_shr = FWD(JUMP); + HERE_(chklo); + O(DROP); O(OVER); LIT(-131072); O(AND); downdone = FWD(IF); + O(DROP); + HERE_(j_shr); + D2SLASH(); VGET(QL + 2); LIT(1); O(ADD); O(STORE_B); JUMP_TO(l_down); + HERE_(downdone); + O(DROP); O(DROP); + l_up = v4_asm_label(&as); + O(DUP); LIT(-65536); O(AND); upshift = FWD(IF); + O(DROP); j_norm = FWD(JUMP); + HERE_(upshift); + O(DROP); O(TWO_STAR); VGET(QL + 2); LIT(-1); O(ADD); O(STORE_B); JUMP_TO(l_up); + HERE_(j_norm); + O(DUP); VSET(QL); LIT(-65536); O(ADD); VSET(QL + 1); LIT(6); VSET(QL + 3); + l_newton = v4_asm_label(&as); + VGET(QL + 1); O(DUP); VSET(QL + 4); LIT(65536); O(ADD); VSET(QL + 5); + LIT(131072); VSET(QL + 6); + l_expl = v4_asm_label(&as); + VGET(QL + 4); LIT(0); VGET(QL + 1); LIT(0); CALL(w_qstar); O(DROP); + LIT(0); VGET(QL + 6); LIT(0); CALL(w_qslash); O(DROP); + O(DUP); VSET(QL + 4); + O(DUP); VGET(QL + 5); O(ADD); O(STORE_B); + LIT(-50); O(ADD); expc = FWD(MINUS_IF); + O(DROP); j_expd = FWD(JUMP); + HERE_(expc); + O(DROP); VGET(QL + 6); LIT(65536); O(ADD); O(DUP); O(STORE_B); + LIT(-720896); O(ADD); expd2 = FWD(MINUS_IF); + O(DROP); JUMP_TO(l_expl); + HERE_(expd2); + O(DROP); + HERE_(j_expd); + VGET(QL); VGET(QL + 5); SUB_INLINE(); O(DUP); VSET(QL + 4); + dzero = FWD(IF); + dpos = FWD(MINUS_IF); + O(INV); LIT(1); O(ADD); LIT(0); VGET(QL + 5); LIT(0); CALL(w_qslash); O(DROP); + VGET(QL + 1); SWAP_INLINE(); SUB_INLINE(); + keep = FWD(MINUS_IF); O(DROP); LIT(0); HERE_(keep); + VSET(QL + 1); j_test = FWD(JUMP); + HERE_(dpos); + LIT(0); VGET(QL + 5); LIT(0); CALL(w_qslash); O(DROP); + VGET(QL + 1); O(ADD); O(STORE_B); + { + v4_asm_ref j_test2 = FWD(JUMP); + HERE_(dzero); + O(DROP); + l_test = v4_asm_label(&as); + v4_asm_resolve(&as, j_test2, l_test); + } + VGET(QL + 4); + ap = FWD(MINUS_IF); O(INV); LIT(1); O(ADD); HERE_(ap); + LIT(-100); O(ADD); contn = FWD(MINUS_IF); + O(DROP); j_fin = FWD(JUMP); + HERE_(contn); + O(DROP); VGET(QL + 3); LIT(-1); O(ADD); O(DUP); O(STORE_B); + fin0 = FWD(IF); + O(DROP); JUMP_TO(l_newton); + HERE_(fin0); + O(DROP); + HERE_(j_fin); + VGET(QL + 1); VGET(QL + 2); + kp = FWD(MINUS_IF); + O(INV); LIT(1); O(ADD); LIT(45426); CALL(w_umstar); O(DROP); O(INV); LIT(1); O(ADD); + j_ks = FWD(JUMP); + HERE_(kp); + LIT(45426); CALL(w_umstar); O(DROP); + HERE_(j_ks); + O(ADD); O(DUP); sp = FWD(MINUS_IF); + O(DROP); LIT(-1); O(SEMI); + HERE_(sp); O(DROP); LIT(0); O(SEMI); + HERE_(zero); + O(DROP); + l_err = v4_asm_label(&as); + O(DROP); O(DROP); LIT(NODE_ERROR); O(BANG_B); LIT(-1); O(STORE_B); LIT(0); LIT(0); O(SEMI); + + v4_asm_resolve(&as, j_err, l_err); + v4_asm_resolve(&as, j_test, l_test); + } +#undef D2SLASH +#undef SUB_INLINE +#undef SWAP_INLINE +#undef VSET +#undef VGET +#undef JUMP_TO +#undef HERE_ #undef FWD CHECK(v4_asm_ok(&as), "foundation words assemble"); @@ -1034,7 +1188,7 @@ static int call(v4_cell word, unsigned argc, v4_cell a, v4_cell b, v4_cell c) if (argc > 0) v4_dstack_push(&n.ds, a); if (argc > 1) v4_dstack_push(&n.ds, b); if (argc > 2) v4_dstack_push(&n.ds, c); - return v4_test_call(&n, &es, &h, word, 100000) > 0; + return v4_test_call(&n, &es, &h, word, 4000000) > 0; } /* The same with four arguments. */ @@ -1048,7 +1202,7 @@ static int call4(v4_cell word, v4_cell a, v4_cell b, v4_cell c, v4_cell d) v4_dstack_push(&n.ds, b); v4_dstack_push(&n.ds, c); v4_dstack_push(&n.ds, d); - return v4_test_call(&n, &es, &h, word, 100000) > 0; + return v4_test_call(&n, &es, &h, word, 4000000) > 0; } /* The results, top first, then the canary. */ @@ -1422,6 +1576,42 @@ static uint64_t v3_q48_sqrt(uint64_t q) return x; } +/* v3's q48_log_approx, verbatim but for the names. */ +static uint64_t v3_q48_log(uint64_t x) +{ + const uint64_t LN2_Q48 = 45426; + int k = 0, iter; + uint64_t m = x, y, result; + + if (x == 0) return 0; + if (x == 65536) return 0; + if (m >= 131072) { + while (m >= 131072) { m >>= 1; k++; } + } else if (m < 65536) { + while (m < 65536) { m <<= 1; k--; } + } + y = (m > 65536) ? (m - 65536) : 0; + for (iter = 0; iter < 6; iter++) { + uint64_t exp_y = v3_q48_exp(y), correction; + int64_t delta_signed; + if (exp_y == 0) break; + delta_signed = (int64_t)m - (int64_t)exp_y; + if (delta_signed > 0) { + correction = v3_q48_div((uint64_t)delta_signed, exp_y); + y = y + correction; + } else if (delta_signed < 0) { + correction = v3_q48_div((uint64_t)(-delta_signed), exp_y); + if (y > correction) y = y - correction; + else y = 0; + } + if (delta_signed < 100 && delta_signed > -100) break; + } + result = y; + if (k > 0) result = result + v3_q48_mul((uint64_t)k << 16, LN2_Q48); + else if (k < 0) result = result - v3_q48_mul((uint64_t)(-k) << 16, LN2_Q48); + 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 @@ -1440,7 +1630,7 @@ static int fits(v4_cell word, unsigned argc, const v4_cell *arg, v4_rstack_reset(&n.rs); v4_exec_reset(&es); for (i = 0; i < argc; i++) v4_dstack_push(&n.ds, arg[i]); - if (v4_test_call(&n, &es, &h, word, 100000) <= 0) return 0; + if (v4_test_call(&n, &es, &h, word, 4000000) <= 0) return 0; if (nres > V4_DATA_DEPTH) return 0; for (i = 0; i < nres; i++) want[i] = v4_dstack_pop(&n.ds); @@ -1451,7 +1641,7 @@ static int fits(v4_cell word, unsigned argc, const v4_cell *arg, v4_dstack_push(&n.ds, CANARY); for (i = 0; i < argc; i++) v4_dstack_push(&n.ds, arg[i]); for (i = 0; i < rfill; i++) v4_rstack_push(&n.rs, RFILL(i)); - if (v4_test_call(&n, &es, &h, word, 100000) <= 0) return 0; + if (v4_test_call(&n, &es, &h, word, 4000000) <= 0) return 0; for (i = 0; i < nres; i++) if (v4_dstack_pop(&n.ds) != want[i]) return 0; if (v4_dstack_pop(&n.ds) != CANARY) return 0; for (i = dfill; i-- > 0; ) if (v4_dstack_pop(&n.ds) != DFILL(i)) return 0; @@ -2105,6 +2295,43 @@ int main(void) } } + /* Q.LOG against v3's q48_log_approx for x > 0, bit for bit; x <= 0 + * gives 0 and NODE-ERROR (D-12). */ + { + static const int64_t ql[] = { + 1, 2, 3, 0x7FFF, 0x8000, 0xFFFF, 0x10000, 0x10001, 0x18000, 0x1FFFF, 0x20000, + 0x2B7E1, 0x30000, 0xA0000, 0x640000, 0x7FFFFFFF, 0x80000000, 0xFFFFFFFF, + 0x100000000, ((int64_t)1 << 47), ((int64_t)1 << 62) + 12345, + (int64_t)(((uint64_t)1 << 63) - 1u), 0, -1, -0x10000 + }; + uint64_t x = 0xA0761D6478BD642Fu; + for (unsigned i = 0; i < sizeof ql / sizeof ql[0] + 2000u; i++) { + int64_t q; + v4_cell xl, xh, el, eh; + if (i < sizeof ql / sizeof ql[0]) q = ql[i]; + else { + x ^= x << 13; x ^= x >> 7; x ^= x << 17; + q = (int64_t)((x >> 1) >> (x & 63u)); /* every magnitude */ + if (q == 0) q = 1; + } + qcells((uint64_t)q, &xl, &xh); + if (q <= 0) { el = 0; eh = 0; } + else qcells(v3_q48_log((uint64_t)q), &el, &eh); + v4_node_store(&n, NODE_ERROR, 0); + CHECK(call(w_qlog, 2, xl, xh, 0) && left2(el, eh) + && v4_node_load(&n, NODE_ERROR) == (q <= 0 ? -1 : 0), + "Q.LOG [%u] x=%lld", i, (long long)q); + } + /* The reduced m takes only 65536 values, 1.0 <= m < 2.0; sweep every + * 17th directly (k = 0), which covers the Newton iteration itself. */ + for (int64_t m = 65536; m < 131072; m += 17) { + v4_cell xl, xh, el, eh; + qcells((uint64_t)m, &xl, &xh); + qcells(v3_q48_log((uint64_t)m), &el, &eh); + CHECK(call(w_qlog, 2, xl, xh, 0) && left2(el, eh), "Q.LOG m=%lld", (long long)m); + } + } + /* Q./ at the overflow boundary: |a| * 2^16 against |b| * 2^(2N-1), for * divisors around 2^16 and 2^17, every sign. */ { @@ -2218,6 +2445,12 @@ int main(void) }; headroom("Q.SQRT", w_qsqrt, 2, qsqrt_args, 5, 2, &dh, &rh); CHECK(dh >= 2 && rh >= 2, "Q.SQRT leaves room"); + static const v4_cell qlog_args[][4] = { + { 0x10000, 0, 0, 0 }, { 0x2B7E1, 0, 0, 0 }, { 3, 0, 0, 0 }, { -1, 0x7FFF, 0, 0 }, + { 0, 0, 0, 0 }, { 5, -1, 0, 0 } + }; + headroom("Q.LOG", w_qlog, 2, qlog_args, 6, 2, &dh, &rh); + CHECK(dh >= 2 && rh >= 2, "Q.LOG 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);