Medium-row ⊣˘ and ≠˘ with mask-aware carry
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@ -337,6 +337,34 @@ def avx2_loop_with_unaligned_mask{xp, rp, nw, l, scan_words, apply_carry} = {
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m = m>>d4 | m<<(l-d4)
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}
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}
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def avx2_loop_with_loose_mask{xp, rp, nw, l, id, scan_words, propagate, fix_carry, apply_carry} = {
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assert{l >= 64}
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def V = [4]u64
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c := V**id # carry, 0 or 1
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q := -make{V, 64*iota{4}} # distance to next row boundary
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def q_mod{} = { q = blend_top{q,q+V**l, q} }
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o:u64 = 256; while (o>l) { o-=l; q_mod{} }
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@for_masked{4} (x in tup{V, xp}, r in tup{V, rp} over nw) {
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# Get mask; <=1 bit per word
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m:= V**1 << q
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q-= V**o; q_mod{}
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# Within-word scan and carry info
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ml:= m - V**1
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{s, k}:= scan_words{x, m, ml}
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# Propagate carries and adjust result
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p:= propagate{k, c}
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t:= blend{shuf{V, p, 3,0,1,2}, c, 1,0,0,0}
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r = apply_carry{s, -fix_carry{t}, ml}
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c = shuf{V, p, 4**3}
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}
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}
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def avx2_loop_with_loose_mask{...a={xp, rp, nw, l, id, scan_words}, apply_carry} = {
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def passthrough{k, c} = {
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def bl{b,a} = blend_top{b,a, b}
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bl{make_scan_idem{f64, bl}{k}, c} # Can't be -1 now
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}
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avx2_loop_with_loose_mask{...a, passthrough, {k}=>k, apply_carry}
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}
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fn scan_rows_andor{id}(src:*u64, dst:*u64, nl:usz, l:usz) : void = {
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def qand = not id
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@ -375,31 +403,17 @@ fn scan_rows_andor{id}(src:*u64, dst:*u64, nl:usz, l:usz) : void = {
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a >> 63} # new c
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}}
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}
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} else if (l < 160) {
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} else if (l < (if (hasarch{'AVX2'}) 256 else 160)) {
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if (hasarch{'AVX2'}) {
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assert{l >= 64}
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def V = [4]u64
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c := V**id # carry, 0 or 1
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v1:= V**1; xk:= c - v1
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q := -make{V, 64*iota{4}} # distance to next row boundary
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def q_mod{} = { q = blend_top{q,q+V**l, q} }
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o:u64 = 256; while (o>l) { o-=l; q_mod{} }
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@for_masked{4} (x in tup{V, src}, r in tup{V, dst} over nw) {
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# Get mask; <=1 bit per word
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m:= v1 << q
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q-= V**o; q_mod{}
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# Within-word scan and carry info
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r = (if (qand) x &~ ((x+v1) & (x+m))
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def scan_words{x:V, m:V, _} = {
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s:= (if (qand) x &~ ((x+V**1) & (x+m))
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else x | ((-x) &~ (x-m)))
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p:= (if (qand) x&~m else x|m) == xk
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k:= r>>63 | p # Carry of 0 or 1, but -1 to propagate previous
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# Propagate carries and adjust result
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def bl{b,a} = blend_top{b,a, b}
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k = bl{make_scan_idem{f64, bl}{k}, c} # Can't be -1 now
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t:= blend{shuf{V, k, 3,0,1,2}, c, 1,0,0,0}
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r = apply_carry{r, -t, m-v1}
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c = shuf{V, k, 4**3}
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p:= (if (qand) x&~m == ~V**0
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else x| m == V**0)
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k:= s>>63 | p # Carry of 0 or 1, but -1 to propagate previous
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tup{s, k}
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}
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avx2_loop_with_loose_mask{src, dst, nw, l, id, scan_words, apply_carry}
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} else {
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q:usz = 0 # distance to next row boundary
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c:u64 = id # carry
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@ -443,6 +457,13 @@ fn scan_rows_andor{id}(src:*u64, dst:*u64, nl:usz, l:usz) : void = {
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fn scan_rows_neq(x:*u64, r:*u64, nl:usz, l:usz) : void = {
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def scan_word = prefix_byshift{^, <<}
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def scan_words = {
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def vec_prefix_byshift{op, sh} = {
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def pre{v:V, k} = if (k < elwidth{V}) pre{op{v, sh{v,k}}, 2*k} else v
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{v:T} => pre{v, 1}
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}
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vec_prefix_byshift{^, <<}
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}
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assert{l > 0}
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nw := cdiv{nl, 64}
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if (l < 64) {
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@ -455,11 +476,7 @@ fn scan_rows_neq(x:*u64, r:*u64, nl:usz, l:usz) : void = {
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}
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} else if (hasarch{'AVX2'}) {
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def scan_words{x, m} = {
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def vec_prefix_byshift{op, sh} = {
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def pre{v:V, k} = if (k < elwidth{V}) pre{op{v, sh{v,k}}, 2*k} else v
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{v:T} => pre{v, 1}
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}
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s:= vec_prefix_byshift{^, <<}{x}
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s:= scan_words{x}
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b:= s<<1 & m # last bit of previous row
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s ^ (b<<l - b)
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}
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@ -473,6 +490,22 @@ fn scan_rows_neq(x:*u64, r:*u64, nl:usz, l:usz) : void = {
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s ^ ((c & f) | (b<<l - b))
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}}
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}
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} else if (l < 320 and hasarch{'AVX2'}) {
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def scan_words{x:V, m:V, ml:V} = {
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s:= scan_words{x}
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s^= -(s<<1 & m)
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k:= s>>63 | (V**(1<<63) &~ ml) # Top bit 1 to stop, so 0 is identity
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tup{s, k}
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}
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def propagate{k:V, c:V} = {
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def bl{b,a} = blend_top{a^b,b, b}
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k = bl{k, vec_shift_right_128{k, 1}}
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k = bl{k, shuf{V, blend{V**0, k, 0,1,0,1}, 0,0,1,1}}
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bl{k, c}
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}
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def fix_carry{t:V} = t & V**1
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def apply_carry{r, a, ml} = r ^ (a & ml)
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avx2_loop_with_loose_mask{x, r, nw, l, 0, scan_words, propagate, fix_carry, apply_carry}
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} else {
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i :usz = 0 # row bit index
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iw:usz = 0 # starting word
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@ -491,7 +524,6 @@ fn scan_rows_neq(x:*u64, r:*u64, nl:usz, l:usz) : void = {
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}
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fn scan_rows_left(x:*u64, r:*u64, nl:usz, l:usz) : void = {
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def scan_word = prefix_byshift{^, <<}
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assert{l > 0}
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nw := cdiv{nl, 64}
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if (l < 64) {
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@ -509,6 +541,13 @@ fn scan_rows_left(x:*u64, r:*u64, nl:usz, l:usz) : void = {
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(c & f) | (b<<l - b)
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}}
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}
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} else if (l < 176 and hasarch{'AVX2'}) {
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def scan_words{x:V, m:V, _} = {
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s:= -(x & m)
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tup{s, s>>63 | (m == V**0)}
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}
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def apply_carry{r, a, ml} = r | (a & ml)
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avx2_loop_with_loose_mask{x, r, nw, l, 0, scan_words, apply_carry}
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} else {
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i :usz = 0 # row bit index
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wn:usz = 0 # starting word of next row
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