281 lines
11 KiB
C
281 lines
11 KiB
C
// Fold (´)
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// Optimized operands:
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// ⊣⊢ on all types
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// +-∧∨=≠ and synonyms on booleans
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// ≤<>≥ on booleans, monadic only, with a search
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// +⌈⌊× on numbers
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// Integer +: sum blocks associatively as long as sum can't exceed +-2⋆53
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// COULD implement fast numeric -´
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// ∨ on boolean-valued integers, stopping at 1
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// •math.Sum: +´ with faster and more precise SIMD code for i32, f64
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#include "../core.h"
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#include "../builtins.h"
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#if SINGELI
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#pragma GCC diagnostic push
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#pragma GCC diagnostic ignored "-Wunused-variable"
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#include "../singeli/gen/fold.c"
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#pragma GCC diagnostic pop
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#endif
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static bool fold_ne(u64* x, u64 am) {
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u64 r = 0;
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for (u64 i = 0; i < (am>>6); i++) r^= x[i];
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if (am&63) r^= x[am>>6]<<(64-am & 63);
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return POPC(r) & 1;
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}
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static i64 bit_diff(u64* x, u64 am) {
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i64 r = 0;
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u64 a = 0xAAAAAAAAAAAAAAAA;
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for (u64 i = 0; i < (am>>6); i++) r+= POPC(x[i]^a);
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if (am&63) r+= POPC((x[am>>6]^a)<<(64-am & 63));
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return r - (i64)(am/2);
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}
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// It's safe to sum a block of integers as long as the current total
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// is far enough from +-1ull<<53 (and integer, in dyadic fold).
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static const usz sum_small_max = 1<<16;
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#define DEF_INT_SUM(T,W,M,A) \
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static i64 sum_small_##T(void* xv, usz ia) { \
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i##A s=0; for (usz i=0; i<ia; i++) s+=((T*)xv)[i]; return s; \
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} \
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static f64 sum_##T(void* xv, usz ia, f64 init) { \
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usz b=1<<(M-W); i64 lim = (1ull<<53) - (1ull<<M); \
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T* xp = xv; \
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f64 r=init; i64 c=init; usz i0=ia; \
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if (c == init) { \
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while (i0>0 && -lim<=c && c<=lim) { \
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usz e=i0; i0=(i0-1)&~(b-1); \
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c+=sum_small_##T(xp+i0, e-i0); \
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} \
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r = c; \
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} \
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while (i0--) r+=xp[i0]; \
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return r; \
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}
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DEF_INT_SUM(i8 ,8 ,32,32)
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DEF_INT_SUM(i16,16,32,32)
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DEF_INT_SUM(i32,32,52,64)
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#undef DEF_SUM
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static f64 sum_f64(void* xv, usz i, f64 r) {
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while (i--) r += ((f64*)xv)[i];
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return r;
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}
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static i64 (*const sum_small_fns[])(void*, usz) = { sum_small_i8, sum_small_i16, sum_small_i32 };
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static f64 (*const sum_fns[])(void*, usz, f64) = { sum_i8, sum_i16, sum_i32, sum_f64 };
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B sum_c1(B t, B x) {
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if (isAtm(x) || RNK(x)!=1) thrF("•math.Sum: Argument must be a list (%H ≡ ≢𝕩)", x);
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usz ia = IA(x);
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if (ia==0) return m_f64(0);
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u8 xe = TI(x,elType);
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if (!elNum(xe)) {
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x = any_squeeze(x); xe = TI(x,elType);
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if (!elNum(xe)) thrF("•math.Sum: Argument elements must be numbers", x);
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}
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f64 r;
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void* xv = tyany_ptr(x);
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if (xe == el_bit) {
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r = bit_sum(xv, ia);
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} else if (xe <= el_i32) {
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u8 sel = xe - el_i8;
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i64 s = 0; r = 0;
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i64 m = 1ull<<48;
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usz b = sum_small_max;
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for (usz i=0; i<ia; i+=b) {
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s += sum_small_fns[sel]((u8*)xv + (i<<sel), ia-i<b? ia-i : b);
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if (s >= m) { r+=m; s-=m; }
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if (s <= -m) { r-=m; s+=m; }
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}
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r += s;
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} else {
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#if SINGELI
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r = avx2_sum_f64(xv, ia);
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#else
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r=0; for (usz i=0; i<ia; i++) r+=((f64*)xv)[i];
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#endif
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}
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decG(x); return m_f64(r);
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}
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// Try to keep to i32 product, go to f64 on overflow or non-i32 initial
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#define DEF_INT_PROD(T) \
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static NOINLINE f64 prod_##T(void* xv, usz i, f64 init) { \
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while (i--) init*=((T*)xv)[i]; return init; \
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} \
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static f64 prod_int_##T(void* xv, usz ia, i32 init) { \
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T* xp = xv; \
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while (ia--) { \
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i32 i0=init; \
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if (mulOn(init,xp[ia])) return prod_##T(xv, ia+1, i0); \
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} \
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return init; \
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}
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DEF_INT_PROD(i8)
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DEF_INT_PROD(i16)
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DEF_INT_PROD(i32)
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#undef DEF_PROD
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static f64 prod_f64(void* xv, usz i, f64 r) {
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while (i--) r *= ((f64*)xv)[i];
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return r;
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}
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static f64 (*const prod_int_fns[])(void*, usz, i32) = { prod_int_i8, prod_int_i16, prod_int_i32 };
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static f64 (*const prod_fns[])(void*, usz, f64) = { prod_i8, prod_i16, prod_i32, prod_f64 };
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#define MIN_MAX(T,C) \
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T* xp = xv; T r = xp[0]; \
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for (usz i=1; i<ia; i++) if (xp[i] C r) r=xp[i]; \
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return r;
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#define DEF_MIN_MAX(T) \
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static f64 min_##T(void* xv, usz ia) { MIN_MAX(T,<) } \
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static f64 max_##T(void* xv, usz ia) { MIN_MAX(T,>) }
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DEF_MIN_MAX(i8) DEF_MIN_MAX(i16) DEF_MIN_MAX(i32)
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#if SINGELI
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static f64 min_f64(void* xv, usz ia) { return avx2_fold_min_f64(xv,ia); }
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static f64 max_f64(void* xv, usz ia) { return avx2_fold_max_f64(xv,ia); }
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#else
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DEF_MIN_MAX(f64)
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#endif
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#undef DEF_MIN_MAX
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#undef MIN_MAX
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static f64 (*const min_fns[])(void*, usz) = { min_i8, min_i16, min_i32, min_f64 };
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static f64 (*const max_fns[])(void*, usz) = { max_i8, max_i16, max_i32, max_f64 };
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B fold_c1(Md1D* d, B x) { B f = d->f;
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if (isAtm(x) || RNK(x)!=1) thrF("´: Argument must be a list (%H ≡ ≢𝕩)", x);
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usz ia = IA(x);
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if (ia==0) {
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decG(x);
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if (isFun(f)) {
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B r = TI(f,identity)(f);
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if (!q_N(r)) return inc(r);
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}
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thrM("´: No identity found");
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}
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u8 xe = TI(x,elType);
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if (isFun(f) && v(f)->flags) {
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u8 rtid = v(f)->flags-1;
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if (rtid==n_ltack) { B r = IGet(x, 0 ); decG(x); return r; }
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if (rtid==n_rtack) { B r = IGet(x, ia-1); decG(x); return r; }
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if (xe>el_f64) goto base;
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if (xe==el_bit) {
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u64* xp = bitarr_ptr(x);
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f64 r;
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switch (rtid) { default: goto base;
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case n_add: r = bit_sum (xp, ia); break;
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case n_sub: r = bit_diff(xp, ia); break;
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case n_and: case n_mul: case n_floor: r = bit_has (xp, ia, 0) ^ 1; break;
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case n_or: case n_ceil: r = bit_has (xp, ia, 1) ; break;
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case n_ne: r = fold_ne (xp, ia) ; break;
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case n_eq: r = fold_ne (xp, ia) ^ (1&~ia); break;
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case n_lt: r = bit_find(xp, ia, 1) == ia-1; break;
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case n_le: r = bit_find(xp, ia, 0) != ia-1; break;
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case n_gt: r = bit_find(xp, ia, 0) & 1; break;
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case n_ge: r =~bit_find(xp, ia, 1) & 1; break;
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}
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decG(x); return m_f64(r);
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}
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if (rtid==n_add) { // +
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void *xv = tyany_ptr(x);
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bool small = xe<=el_i32 & ia<=sum_small_max;
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u8 sel = xe - el_i8;
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f64 r = small ? sum_small_fns[sel](xv, ia)
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: sum_fns[sel](xv, ia, 0);
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decG(x); return m_f64(r);
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}
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if (rtid==n_floor) { f64 r=min_fns[xe-el_i8](tyany_ptr(x), ia); decG(x); return m_f64(r); } // ⌊
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if (rtid==n_ceil ) { f64 r=max_fns[xe-el_i8](tyany_ptr(x), ia); decG(x); return m_f64(r); } // ⌈
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if (rtid==n_mul | rtid==n_and) { // ×/∧
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void *xv = tyany_ptr(x);
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u8 sel = xe - el_i8;
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f64 r = xe<=el_i32 ? prod_int_fns[sel](xv, ia, 1)
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: prod_fns[sel](xv, ia, 1);
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decG(x); return m_f64(r);
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}
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if (rtid==n_or) { // ∨
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if (xe==el_i8 ) { i8* xp = i8any_ptr (x); usz i=ia; while (i--) { i8 c=xp[i]; if (c==1) break; if (c!=0) goto base; } decG(x); return m_i32(i+1 > 0); }
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if (xe==el_i16) { i16* xp = i16any_ptr(x); usz i=ia; while (i--) { i16 c=xp[i]; if (c==1) break; if (c!=0) goto base; } decG(x); return m_i32(i+1 > 0); }
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if (xe==el_i32) { i32* xp = i32any_ptr(x); usz i=ia; while (i--) { i32 c=xp[i]; if (c==1) break; if (c!=0) goto base; } decG(x); return m_i32(i+1 > 0); }
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}
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}
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base:;
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SLOW2("𝕎´ 𝕩", f, x);
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SGet(x)
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BBB2B fc2 = c2fn(f);
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B c;
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if (TI(x,elType)==el_i32) {
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i32* xp = i32any_ptr(x);
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c = m_i32(xp[ia-1]);
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for (usz i = ia-1; i>0; i--) c = fc2(f, m_i32(xp[i-1]), c);
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} else {
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c = Get(x, ia-1);
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for (usz i = ia-1; i>0; i--) c = fc2(f, Get(x, i-1), c);
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}
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decG(x);
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return c;
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}
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B fold_c2(Md1D* d, B w, B x) { B f = d->f;
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if (isAtm(x) || RNK(x)!=1) thrF("´: 𝕩 must be a list (%H ≡ ≢𝕩)", x);
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usz ia = IA(x);
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u8 xe = TI(x,elType);
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if (isFun(f) && v(f)->flags) {
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u8 rtid = v(f)->flags-1;
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if (rtid==n_ltack) {
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B r = w;
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if (ia) { dec(w); r=IGet(x, 0); }
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decG(x); return r;
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}
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if (rtid==n_rtack) { decG(x); return w; }
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if (!isF64(w) || xe>el_f64) goto base;
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f64 wf = o2fG(w);
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if (xe==el_bit) {
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i32 wi = wf; if (wi!=wf) goto base;
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u64* xp = bitarr_ptr(x);
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if (rtid==n_add) { B r = m_f64(wi + bit_sum (xp, ia)); decG(x); return r; }
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if (rtid==n_sub) { B r = m_f64((ia&1?-wi:wi) + bit_diff(xp, ia)); decG(x); return r; }
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if (wi!=(wi&1)) goto base;
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if (rtid==n_and | rtid==n_mul | rtid==n_floor) { B r = m_i32(wi && !bit_has(xp, ia, 0)); decG(x); return r; }
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if (rtid==n_or | rtid==n_ceil ) { B r = m_i32(wi || bit_has(xp, ia, 1)); decG(x); return r; }
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if (rtid==n_ne) { bool r=wi^fold_ne(xp, ia) ; decG(x); return m_i32(r); }
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if (rtid==n_eq) { bool r=wi^fold_ne(xp, ia) ^ (1&ia); decG(x); return m_i32(r); }
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goto base;
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}
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if (rtid==n_add) { // +
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u8 sel = xe - el_i8;
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f64 r = sum_fns[sel](tyany_ptr(x), ia, wf);
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decG(x); return m_f64(r);
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}
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if (rtid==n_floor) { f64 r=wf; if (ia>0) { f64 m=min_fns[xe-el_i8](tyany_ptr(x), ia); if (m<r) r=m; } decG(x); return m_f64(r); } // ⌊
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if (rtid==n_ceil ) { f64 r=wf; if (ia>0) { f64 m=max_fns[xe-el_i8](tyany_ptr(x), ia); if (m>r) r=m; } decG(x); return m_f64(r); } // ⌈
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i32 wi = wf;
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if (rtid==n_mul | rtid==n_and) { // ×/∧
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void *xv = tyany_ptr(x);
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bool isint = xe<=el_i32 && wi==wf;
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u8 sel = xe - el_i8;
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f64 r = isint ? prod_int_fns[sel](xv, ia, wi)
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: prod_fns[sel](xv, ia, wf);
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decG(x); return m_f64(r);
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}
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if (rtid==n_or && (wi&1)==wf) { // ∨
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if (xe==el_i8 ) { i8* xp = i8any_ptr (x); usz i=ia; if (!wi) while (i--) { i8 c=xp[i]; if (c==1) break; if (c!=0) goto base; } decG(x); return m_i32(i+1 > 0); }
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if (xe==el_i16) { i16* xp = i16any_ptr(x); usz i=ia; if (!wi) while (i--) { i16 c=xp[i]; if (c==1) break; if (c!=0) goto base; } decG(x); return m_i32(i+1 > 0); }
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if (xe==el_i32) { i32* xp = i32any_ptr(x); usz i=ia; if (!wi) while (i--) { i32 c=xp[i]; if (c==1) break; if (c!=0) goto base; } decG(x); return m_i32(i+1 > 0); }
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}
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}
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base:;
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SLOW3("𝕨 F´ 𝕩", w, x, f);
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B c = w;
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SGet(x)
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BBB2B fc2 = c2fn(f);
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for (usz i = ia; i>0; i--) c = fc2(f, Get(x, i-1), c);
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decG(x);
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return c;
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}
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