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Switch constantIsGreaterEqual to use greaterEqual #95

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76 changes: 23 additions & 53 deletions inc/zoo/swar/SWAR.h
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Original file line number Diff line number Diff line change
Expand Up @@ -340,10 +340,6 @@ struct BooleanSWAR: SWAR<NBits, T> {
friend constexpr auto
equals(SWAR<NB, TT>, SWAR<NB, TT>) noexcept;

template<int N, int NB, typename TT>
friend constexpr BooleanSWAR<NB, TT>
constantIsGreaterEqual(SWAR<NB, TT>) noexcept;

template<int N, int NB, typename TT>
friend constexpr BooleanSWAR<NB, TT>
constantIsGreaterEqual_MSB_off(SWAR<NB, TT>) noexcept;
Expand Down Expand Up @@ -374,36 +370,31 @@ convertToBooleanSWAR(SWAR<NBits, T> arg) noexcept {
return SWAR<NBits, T>{SWAR<NBits, T>::MostSignificantBit} & arg;
}

template<typename T, typename U, typename V>
constexpr T median(T x, U y, V z) {
return (x | y) & (y | z) & (x | z);
}

template<int NBits, typename T>
constexpr BooleanSWAR<NBits, T>
greaterEqual(SWAR<NBits, T> left, SWAR<NBits, T> right) noexcept {
// Adapted from TAOCP V4 P152
// h is msbselector, x is right, l is lower/left. Sets MSB to 1 in lanes
// in test variable t for when xi < yi for lane i . Invert for greaterEqual.
// t = h & ~<x~yz>
// z = (x|h) - (y&~h)
using S = swar::SWAR<NBits, T>;
const auto h = S::MostSignificantBit, x = left.value(), y = right.value(); // x=left, y= right is x < y
const auto z = (x|h) - (y&~h);
// bitwise ternary median!
const auto t = h & ~median(x, ~y, z);
return ~BooleanSWAR<NBits, T>{static_cast<T>(t)}; // ~(x<y) === x >= y
}

template<int N, int NBits, typename T>
constexpr BooleanSWAR<NBits, T>
constantIsGreaterEqual(SWAR<NBits, T> subtrahend) noexcept {
static_assert(1 < NBits, "Degenerated SWAR");
constexpr auto MSB_Position = NBits - 1;
constexpr auto MSB = T(1) << MSB_Position;
constexpr auto MSB_Mask =
SWAR<NBits, T>{meta::BitmaskMaker<T, MSB, NBits>::value};
constexpr auto Minuend =
SWAR<NBits, T>{meta::BitmaskMaker<T, N, NBits>::value};
constexpr auto N_MSB = MSB & N;

auto subtrahendWithMSB_on = MSB_Mask & subtrahend;
auto subtrahendWithMSB_off = ~subtrahendWithMSB_on;
auto subtrahendMSBs_turnedOff = subtrahend ^ subtrahendWithMSB_on;
if constexpr(N_MSB) {
auto leastSignificantComparison = Minuend - subtrahendMSBs_turnedOff;
auto merged =
subtrahendMSBs_turnedOff | // the minuend MSBs are on
leastSignificantComparison;
return MSB_Mask & merged;
} else {
auto minuendWithMSBs_turnedOn = Minuend | MSB_Mask;
auto leastSignificantComparison =
minuendWithMSBs_turnedOn - subtrahendMSBs_turnedOff;
auto merged =
subtrahendWithMSB_off & // the minuend MSBs are off
leastSignificantComparison;
return MSB_Mask & merged;
}
return greaterEqual(SWAR<NBits, T>{N}, subtrahend);
}

template<int N, int NBits, typename T>
Expand All @@ -428,27 +419,6 @@ constantIsGreaterEqual_MSB_off(SWAR<NBits, T> subtrahend) noexcept {
}
}

template<typename T, typename U, typename V>
constexpr T median(T x, U y, V z) {
return (x | y) & (y | z) & (x | z);
}

template<int NBits, typename T>
constexpr BooleanSWAR<NBits, T>
greaterEqual(SWAR<NBits, T> left, SWAR<NBits, T> right) noexcept {
// Adapted from TAOCP V4 P152
// h is msbselector, x is right, l is lower/left. Sets MSB to 1 in lanes
// in test variable t for when xi < yi for lane i . Invert for greaterEqual.
// t = h & ~<x~yz>
// z = (x|h) - (y&~h)
using S = swar::SWAR<NBits, T>;
const auto h = S::MostSignificantBit, x = left.value(), y = right.value(); // x=left, y= right is x < y
const auto z = (x|h) - (y&~h);
// bitwise ternary median!
const auto t = h & ~median(x, ~y, z);
return ~BooleanSWAR<NBits, T>{static_cast<T>(t)}; // ~(x<y) === x >= y
}

// In the condition where only MSBs will be on, we can fast lookup with 1 multiply the index of the most signficant byte that is on.
// This appears to be a mapping from the (say) 256 unique values of a 64 bit int where only MSBs of each 8 bits can be on, but I don't fully understand it.
// Adapted from TAOCP Vol 4A Page 153 Eq 94.
Expand All @@ -473,7 +443,7 @@ greaterEqual_MSB_off(SWAR<NBits, T> left, SWAR<NBits, T> right) noexcept {
template<int NB, typename T>
constexpr auto
booleans(SWAR<NB, T> arg) noexcept {
return ~constantIsGreaterEqual<0>(arg);
return ~greaterEqual(SWAR<NB, T>{0}, arg);
}

template<int NBits, typename T>
Expand Down