Export of internal Abseil changes.
-- ed3a3431eee9e48e6553b0320e0308d2dde6725c by Derek Mauro <dmauro@google.com>: Project import generated by Copybara. PiperOrigin-RevId: 258631680 GitOrigin-RevId: ed3a3431eee9e48e6553b0320e0308d2dde6725c Change-Id: I1d7ae86a79783842092d29504605ba039c369603
This commit is contained in:
Abseil Team
Derek Mauro
parent
44efe96dfc
commit
c6c3c1b498
32 changed files with 1168 additions and 657 deletions
|
|
@ -22,11 +22,18 @@
|
|||
|
||||
namespace absl {
|
||||
namespace random_internal {
|
||||
// Returns true if the input value is zero or a power of two. Useful for
|
||||
// determining if the range of output values in a URBG
|
||||
template <typename UIntType>
|
||||
constexpr bool IsPowerOfTwoOrZero(UIntType n) {
|
||||
return (n == 0) || ((n & (n - 1)) == 0);
|
||||
}
|
||||
|
||||
// Computes the length of the range of values producible by the URBG, or returns
|
||||
// zero if that would encompass the entire range of representable values in
|
||||
// URBG::result_type.
|
||||
template <typename URBG>
|
||||
constexpr typename URBG::result_type constexpr_range() {
|
||||
constexpr typename URBG::result_type RangeSize() {
|
||||
using result_type = typename URBG::result_type;
|
||||
return ((URBG::max)() == (std::numeric_limits<result_type>::max)() &&
|
||||
(URBG::min)() == std::numeric_limits<result_type>::lowest())
|
||||
|
|
@ -34,6 +41,42 @@ constexpr typename URBG::result_type constexpr_range() {
|
|||
: (URBG::max)() - (URBG::min)() + result_type{1};
|
||||
}
|
||||
|
||||
template <typename UIntType>
|
||||
constexpr UIntType LargestPowerOfTwoLessThanOrEqualTo(UIntType n) {
|
||||
return n < 2 ? n : 2 * LargestPowerOfTwoLessThanOrEqualTo(n / 2);
|
||||
}
|
||||
|
||||
// Given a URBG generating values in the closed interval [Lo, Hi], returns the
|
||||
// largest power of two less than or equal to `Hi - Lo + 1`.
|
||||
template <typename URBG>
|
||||
constexpr typename URBG::result_type PowerOfTwoSubRangeSize() {
|
||||
return LargestPowerOfTwoLessThanOrEqualTo(RangeSize<URBG>());
|
||||
}
|
||||
|
||||
// Computes the floor of the log. (i.e., std::floor(std::log2(N));
|
||||
template <typename UIntType>
|
||||
constexpr UIntType IntegerLog2(UIntType n) {
|
||||
return (n <= 1) ? 0 : 1 + IntegerLog2(n / 2);
|
||||
}
|
||||
|
||||
// Returns the number of bits of randomness returned through
|
||||
// `PowerOfTwoVariate(urbg)`.
|
||||
template <typename URBG>
|
||||
constexpr size_t NumBits() {
|
||||
return RangeSize<URBG>() == 0
|
||||
? std::numeric_limits<typename URBG::result_type>::digits
|
||||
: IntegerLog2(PowerOfTwoSubRangeSize<URBG>());
|
||||
}
|
||||
|
||||
// Given a shift value `n`, constructs a mask with exactly the low `n` bits set.
|
||||
// If `n == 0`, all bits are set.
|
||||
template <typename UIntType>
|
||||
constexpr UIntType MaskFromShift(UIntType n) {
|
||||
return ((n % std::numeric_limits<UIntType>::digits) == 0)
|
||||
? ~UIntType{0}
|
||||
: (UIntType{1} << n) - UIntType{1};
|
||||
}
|
||||
|
||||
// FastUniformBits implements a fast path to acquire uniform independent bits
|
||||
// from a type which conforms to the [rand.req.urbg] concept.
|
||||
// Parameterized by:
|
||||
|
|
@ -45,14 +88,6 @@ constexpr typename URBG::result_type constexpr_range() {
|
|||
// generator that will outlive the std::independent_bits_engine instance.
|
||||
template <typename UIntType = uint64_t>
|
||||
class FastUniformBits {
|
||||
static_assert(std::is_unsigned<UIntType>::value,
|
||||
"Class-template FastUniformBits<> must be parameterized using "
|
||||
"an unsigned type.");
|
||||
|
||||
// `kWidth` is the width, in binary digits, of the output. By default it is
|
||||
// the number of binary digits in the `result_type`.
|
||||
static constexpr size_t kWidth = std::numeric_limits<UIntType>::digits;
|
||||
|
||||
public:
|
||||
using result_type = UIntType;
|
||||
|
||||
|
|
@ -65,14 +100,47 @@ class FastUniformBits {
|
|||
result_type operator()(URBG& g); // NOLINT(runtime/references)
|
||||
|
||||
private:
|
||||
// Variate() generates a single random variate, always returning a value
|
||||
// in the closed interval [0 ... FastUniformBitsURBGConstants::kRangeMask]
|
||||
// (kRangeMask+1 is a power of 2).
|
||||
template <typename URBG>
|
||||
typename URBG::result_type Variate(URBG& g); // NOLINT(runtime/references)
|
||||
static_assert(std::is_unsigned<UIntType>::value,
|
||||
"Class-template FastUniformBits<> must be parameterized using "
|
||||
"an unsigned type.");
|
||||
|
||||
// generate() generates a random value, dispatched on whether
|
||||
// the underlying URNG must loop over multiple calls or not.
|
||||
// PowerOfTwoVariate() generates a single random variate, always returning a
|
||||
// value in the half-open interval `[0, PowerOfTwoSubRangeSize<URBG>())`. If
|
||||
// the URBG already generates values in a power-of-two range, the generator
|
||||
// itself is used. Otherwise, we use rejection sampling on the largest
|
||||
// possible power-of-two-sized subrange.
|
||||
struct PowerOfTwoTag {};
|
||||
struct RejectionSamplingTag {};
|
||||
template <typename URBG>
|
||||
static typename URBG::result_type PowerOfTwoVariate(
|
||||
URBG& g) { // NOLINT(runtime/references)
|
||||
using tag =
|
||||
typename std::conditional<IsPowerOfTwoOrZero(RangeSize<URBG>()),
|
||||
PowerOfTwoTag, RejectionSamplingTag>::type;
|
||||
return PowerOfTwoVariate(g, tag{});
|
||||
}
|
||||
|
||||
template <typename URBG>
|
||||
static typename URBG::result_type PowerOfTwoVariate(
|
||||
URBG& g, // NOLINT(runtime/references)
|
||||
PowerOfTwoTag) {
|
||||
return g() - (URBG::min)();
|
||||
}
|
||||
|
||||
template <typename URBG>
|
||||
static typename URBG::result_type PowerOfTwoVariate(
|
||||
URBG& g, // NOLINT(runtime/references)
|
||||
RejectionSamplingTag) {
|
||||
// Use rejection sampling to ensure uniformity across the range.
|
||||
typename URBG::result_type u;
|
||||
do {
|
||||
u = g() - (URBG::min)();
|
||||
} while (u >= PowerOfTwoSubRangeSize<URBG>());
|
||||
return u;
|
||||
}
|
||||
|
||||
// Generate() generates a random value, dispatched on whether
|
||||
// the underlying URBG must loop over multiple calls or not.
|
||||
template <typename URBG>
|
||||
result_type Generate(URBG& g, // NOLINT(runtime/references)
|
||||
std::true_type /* avoid_looping */);
|
||||
|
|
@ -82,196 +150,107 @@ class FastUniformBits {
|
|||
std::false_type /* avoid_looping */);
|
||||
};
|
||||
|
||||
// FastUniformBitsURBGConstants computes the URBG-derived constants used
|
||||
// by FastUniformBits::Generate and FastUniformBits::Variate.
|
||||
// Parameterized by the FastUniformBits parameter:
|
||||
// `URBG`: The underlying UniformRandomNumberGenerator.
|
||||
//
|
||||
// The values here indicate the URBG range as well as providing an indicator
|
||||
// whether the URBG output is a power of 2, and kRangeMask, which allows masking
|
||||
// the generated output to kRangeBits.
|
||||
template <typename UIntType>
|
||||
template <typename URBG>
|
||||
class FastUniformBitsURBGConstants {
|
||||
// Computes the floor of the log. (i.e., std::floor(std::log2(N));
|
||||
static constexpr size_t constexpr_log2(size_t n) {
|
||||
return (n <= 1) ? 0 : 1 + constexpr_log2(n / 2);
|
||||
}
|
||||
|
||||
// Computes a mask of n bits for the URBG::result_type.
|
||||
static constexpr typename URBG::result_type constexpr_mask(size_t n) {
|
||||
return (typename URBG::result_type(1) << n) - 1;
|
||||
}
|
||||
|
||||
public:
|
||||
using result_type = typename URBG::result_type;
|
||||
|
||||
// The range of the URNG, max - min + 1, or zero if that result would cause
|
||||
// overflow.
|
||||
static constexpr result_type kRange = constexpr_range<URBG>();
|
||||
|
||||
static constexpr bool kPowerOfTwo =
|
||||
(kRange == 0) || ((kRange & (kRange - 1)) == 0);
|
||||
|
||||
// kRangeBits describes the number number of bits suitable to mask off of URNG
|
||||
// variate, which is:
|
||||
// kRangeBits = floor(log2(kRange))
|
||||
static constexpr size_t kRangeBits =
|
||||
kRange == 0 ? std::numeric_limits<result_type>::digits
|
||||
: constexpr_log2(kRange);
|
||||
|
||||
// kRangeMask is the mask used when sampling variates from the URNG when the
|
||||
// width of the URNG range is not a power of 2.
|
||||
typename FastUniformBits<UIntType>::result_type
|
||||
FastUniformBits<UIntType>::operator()(URBG& g) { // NOLINT(runtime/references)
|
||||
// kRangeMask is the mask used when sampling variates from the URBG when the
|
||||
// width of the URBG range is not a power of 2.
|
||||
// Y = (2 ^ kRange) - 1
|
||||
static constexpr result_type kRangeMask =
|
||||
kRange == 0 ? (std::numeric_limits<result_type>::max)()
|
||||
: constexpr_mask(kRangeBits);
|
||||
|
||||
static_assert((URBG::max)() != (URBG::min)(),
|
||||
"Class-template FastUniformBitsURBGConstants<> "
|
||||
static_assert((URBG::max)() > (URBG::min)(),
|
||||
"URBG::max and URBG::min may not be equal.");
|
||||
|
||||
static_assert(std::is_unsigned<result_type>::value,
|
||||
"Class-template FastUniformBitsURBGConstants<> "
|
||||
"URBG::result_type must be unsigned.");
|
||||
|
||||
static_assert(kRangeMask > 0,
|
||||
"Class-template FastUniformBitsURBGConstants<> "
|
||||
"URBG does not generate sufficient random bits.");
|
||||
|
||||
static_assert(kRange == 0 ||
|
||||
kRangeBits < std::numeric_limits<result_type>::digits,
|
||||
"Class-template FastUniformBitsURBGConstants<> "
|
||||
"URBG range computation error.");
|
||||
};
|
||||
|
||||
// FastUniformBitsLoopingConstants computes the looping constants used
|
||||
// by FastUniformBits::Generate. These constants indicate how multiple
|
||||
// URBG::result_type values are combined into an output_value.
|
||||
// Parameterized by the FastUniformBits parameters:
|
||||
// `UIntType`: output type.
|
||||
// `URNG`: The underlying UniformRandomNumberGenerator.
|
||||
//
|
||||
// The looping constants describe the sets of loop counters and mask values
|
||||
// which control how individual variates are combined the final output. The
|
||||
// algorithm ensures that the number of bits used by any individual call differs
|
||||
// by at-most one bit from any other call. This is simplified into constants
|
||||
// which describe two loops, with the second loop parameters providing one extra
|
||||
// bit per variate.
|
||||
//
|
||||
// See [rand.adapt.ibits] for more details on the use of these constants.
|
||||
template <typename UIntType, typename URBG>
|
||||
class FastUniformBitsLoopingConstants {
|
||||
private:
|
||||
static constexpr size_t kWidth = std::numeric_limits<UIntType>::digits;
|
||||
using urbg_result_type = typename URBG::result_type;
|
||||
using uint_result_type = UIntType;
|
||||
|
||||
public:
|
||||
using result_type =
|
||||
typename std::conditional<(sizeof(urbg_result_type) <=
|
||||
sizeof(uint_result_type)),
|
||||
uint_result_type, urbg_result_type>::type;
|
||||
|
||||
private:
|
||||
// Estimate N as ceil(width / urng width), and W0 as (width / N).
|
||||
static constexpr size_t kRangeBits =
|
||||
FastUniformBitsURBGConstants<URBG>::kRangeBits;
|
||||
|
||||
// The range of the URNG, max - min + 1, or zero if that result would cause
|
||||
// overflow.
|
||||
static constexpr result_type kRange = constexpr_range<URBG>();
|
||||
static constexpr size_t kEstimateN =
|
||||
kWidth / kRangeBits + (kWidth % kRangeBits != 0);
|
||||
static constexpr size_t kEstimateW0 = kWidth / kEstimateN;
|
||||
static constexpr result_type kEstimateY0 = (kRange >> kEstimateW0)
|
||||
<< kEstimateW0;
|
||||
|
||||
public:
|
||||
// Parameters for the two loops:
|
||||
// kN0, kN1 are the number of underlying calls required for each loop.
|
||||
// KW0, kW1 are shift widths for each loop.
|
||||
//
|
||||
static constexpr size_t kN1 = (kRange - kEstimateY0) >
|
||||
(kEstimateY0 / kEstimateN)
|
||||
? kEstimateN + 1
|
||||
: kEstimateN;
|
||||
static constexpr size_t kN0 = kN1 - (kWidth % kN1);
|
||||
static constexpr size_t kW0 = kWidth / kN1;
|
||||
static constexpr size_t kW1 = kW0 + 1;
|
||||
|
||||
static constexpr result_type kM0 = (result_type(1) << kW0) - 1;
|
||||
static constexpr result_type kM1 = (result_type(1) << kW1) - 1;
|
||||
|
||||
static_assert(
|
||||
kW0 <= kRangeBits,
|
||||
"Class-template FastUniformBitsLoopingConstants::kW0 too large.");
|
||||
|
||||
static_assert(
|
||||
kW0 > 0,
|
||||
"Class-template FastUniformBitsLoopingConstants::kW0 too small.");
|
||||
};
|
||||
|
||||
template <typename UIntType>
|
||||
template <typename URBG>
|
||||
typename FastUniformBits<UIntType>::result_type
|
||||
FastUniformBits<UIntType>::operator()(
|
||||
URBG& g) { // NOLINT(runtime/references)
|
||||
using constants = FastUniformBitsURBGConstants<URBG>;
|
||||
return Generate(
|
||||
g, std::integral_constant<bool, constants::kRangeMask >= (max)()>{});
|
||||
}
|
||||
|
||||
template <typename UIntType>
|
||||
template <typename URBG>
|
||||
typename URBG::result_type FastUniformBits<UIntType>::Variate(
|
||||
URBG& g) { // NOLINT(runtime/references)
|
||||
using constants = FastUniformBitsURBGConstants<URBG>;
|
||||
if (constants::kPowerOfTwo) {
|
||||
return g() - (URBG::min)();
|
||||
}
|
||||
|
||||
// Use rejection sampling to ensure uniformity across the range.
|
||||
typename URBG::result_type u;
|
||||
do {
|
||||
u = g() - (URBG::min)();
|
||||
} while (u > constants::kRangeMask);
|
||||
return u;
|
||||
constexpr urbg_result_type kRangeMask =
|
||||
RangeSize<URBG>() == 0
|
||||
? (std::numeric_limits<urbg_result_type>::max)()
|
||||
: static_cast<urbg_result_type>(PowerOfTwoSubRangeSize<URBG>() - 1);
|
||||
return Generate(g, std::integral_constant<bool, (kRangeMask >= (max)())>{});
|
||||
}
|
||||
|
||||
template <typename UIntType>
|
||||
template <typename URBG>
|
||||
typename FastUniformBits<UIntType>::result_type
|
||||
FastUniformBits<UIntType>::Generate(
|
||||
URBG& g, // NOLINT(runtime/references)
|
||||
std::true_type /* avoid_looping */) {
|
||||
FastUniformBits<UIntType>::Generate(URBG& g, // NOLINT(runtime/references)
|
||||
std::true_type /* avoid_looping */) {
|
||||
// The width of the result_type is less than than the width of the random bits
|
||||
// provided by URNG. Thus, generate a single value and then simply mask off
|
||||
// provided by URBG. Thus, generate a single value and then simply mask off
|
||||
// the required bits.
|
||||
return Variate(g) & (max)();
|
||||
|
||||
return PowerOfTwoVariate(g) & (max)();
|
||||
}
|
||||
|
||||
template <typename UIntType>
|
||||
template <typename URBG>
|
||||
typename FastUniformBits<UIntType>::result_type
|
||||
FastUniformBits<UIntType>::Generate(
|
||||
URBG& g, // NOLINT(runtime/references)
|
||||
std::false_type /* avoid_looping */) {
|
||||
// The width of the result_type is wider than the number of random bits
|
||||
// provided by URNG. Thus we merge several variates of URNG into the result
|
||||
// using a shift and mask. The constants type generates the parameters used
|
||||
// ensure that the bits are distributed across all the invocations of the
|
||||
// underlying URNG.
|
||||
using constants = FastUniformBitsLoopingConstants<UIntType, URBG>;
|
||||
FastUniformBits<UIntType>::Generate(URBG& g, // NOLINT(runtime/references)
|
||||
std::false_type /* avoid_looping */) {
|
||||
// See [rand.adapt.ibits] for more details on the constants calculated below.
|
||||
//
|
||||
// It is preferable to use roughly the same number of bits from each generator
|
||||
// call, however this is only possible when the number of bits provided by the
|
||||
// URBG is a divisor of the number of bits in `result_type`. In all other
|
||||
// cases, the number of bits used cannot always be the same, but it can be
|
||||
// guaranteed to be off by at most 1. Thus we run two loops, one with a
|
||||
// smaller bit-width size (`kSmallWidth`) and one with a larger width size
|
||||
// (satisfying `kLargeWidth == kSmallWidth + 1`). The loops are run
|
||||
// `kSmallIters` and `kLargeIters` times respectively such
|
||||
// that
|
||||
//
|
||||
// `kTotalWidth == kSmallIters * kSmallWidth
|
||||
// + kLargeIters * kLargeWidth`
|
||||
//
|
||||
// where `kTotalWidth` is the total number of bits in `result_type`.
|
||||
//
|
||||
constexpr size_t kTotalWidth = std::numeric_limits<result_type>::digits;
|
||||
constexpr size_t kUrbgWidth = NumBits<URBG>();
|
||||
constexpr size_t kTotalIters =
|
||||
kTotalWidth / kUrbgWidth + (kTotalWidth % kUrbgWidth != 0);
|
||||
constexpr size_t kSmallWidth = kTotalWidth / kTotalIters;
|
||||
constexpr size_t kLargeWidth = kSmallWidth + 1;
|
||||
//
|
||||
// Because `kLargeWidth == kSmallWidth + 1`, it follows that
|
||||
//
|
||||
// `kTotalWidth == kTotalIters * kSmallWidth + kLargeIters`
|
||||
//
|
||||
// and therefore
|
||||
//
|
||||
// `kLargeIters == kTotalWidth % kSmallWidth`
|
||||
//
|
||||
// Intuitively, each iteration with the large width accounts for one unit
|
||||
// of the remainder when `kTotalWidth` is divided by `kSmallWidth`. As
|
||||
// mentioned above, if the URBG width is a divisor of `kTotalWidth`, then
|
||||
// there would be no need for any large iterations (i.e., one loop would
|
||||
// suffice), and indeed, in this case, `kLargeIters` would be zero.
|
||||
constexpr size_t kLargeIters = kTotalWidth % kSmallWidth;
|
||||
constexpr size_t kSmallIters =
|
||||
(kTotalWidth - (kLargeWidth * kLargeIters)) / kSmallWidth;
|
||||
|
||||
static_assert(
|
||||
kTotalWidth == kSmallIters * kSmallWidth + kLargeIters * kLargeWidth,
|
||||
"Error in looping constant calculations.");
|
||||
|
||||
result_type s = 0;
|
||||
for (size_t n = 0; n < constants::kN0; ++n) {
|
||||
auto u = Variate(g);
|
||||
s = (s << constants::kW0) + (u & constants::kM0);
|
||||
|
||||
constexpr size_t kSmallShift = kSmallWidth % kTotalWidth;
|
||||
constexpr result_type kSmallMask = MaskFromShift(result_type{kSmallShift});
|
||||
for (size_t n = 0; n < kSmallIters; ++n) {
|
||||
s = (s << kSmallShift) +
|
||||
(static_cast<result_type>(PowerOfTwoVariate(g)) & kSmallMask);
|
||||
}
|
||||
for (size_t n = constants::kN0; n < constants::kN1; ++n) {
|
||||
auto u = Variate(g);
|
||||
s = (s << constants::kW1) + (u & constants::kM1);
|
||||
|
||||
constexpr size_t kLargeShift = kLargeWidth % kTotalWidth;
|
||||
constexpr result_type kLargeMask = MaskFromShift(result_type{kLargeShift});
|
||||
for (size_t n = 0; n < kLargeIters; ++n) {
|
||||
s = (s << kLargeShift) +
|
||||
(static_cast<result_type>(PowerOfTwoVariate(g)) & kLargeMask);
|
||||
}
|
||||
|
||||
static_assert(
|
||||
kLargeShift == kSmallShift + 1 ||
|
||||
(kLargeShift == 0 &&
|
||||
kSmallShift == std::numeric_limits<result_type>::digits - 1),
|
||||
"Error in looping constant calculations");
|
||||
|
||||
return s;
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue