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lower memory uniform sampling (#2361)
* lower memory uniform * use fp32 * fix
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@ -92,29 +92,6 @@ T below_one() {
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return f;
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}
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// Get the next representable value above -1.0 for half precision
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// floating point types (fp16, bf16)
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template <typename T>
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T above_minus_one() {
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T f = T(-1.0);
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uint16_t* m = (uint16_t*)&f;
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*m -= 1;
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return f;
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}
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// Get the next representable value above -1.0 for half precision
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// use std::nextafter as default case.
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array above_minus_one_with_default(Dtype dtype) {
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switch (dtype) {
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case float16:
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return array(above_minus_one<float16_t>(), dtype);
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case bfloat16:
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return array(above_minus_one<bfloat16_t>(), dtype);
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default:
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return array(std::nextafter(-1.0f, 0.0f), dtype);
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}
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}
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array uniform(
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const array& low,
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const array& high,
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@ -139,31 +116,27 @@ array uniform(
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<< " from broadcasted shape " << out_shape << ".";
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throw std::invalid_argument(msg.str());
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}
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// Get random values between [0, nextafter(maxval, 0.0f)] since samples must
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// Get random values between [0, nextafter(1.0, 0.0)] since samples must
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// be in [low, high)
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auto get_limits = [&dtype]() {
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auto get_upper = [&dtype]() {
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switch (dtype) {
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case float32:
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return std::make_pair(
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array(std::nextafter(1.0f, 0.0f), float32),
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array(std::numeric_limits<uint32_t>::max(), float32));
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return array(std::nextafter(1.0f, 0.0f), float32);
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case float16:
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return std::make_pair(
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array(below_one<float16_t>(), float16),
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array(std::numeric_limits<uint16_t>::max(), float32));
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return array(below_one<float16_t>(), float32);
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case bfloat16:
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return std::make_pair(
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array(below_one<bfloat16_t>(), bfloat16),
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array(std::numeric_limits<uint16_t>::max(), float32));
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return array(below_one<bfloat16_t>(), float32);
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default:
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throw std::runtime_error("[uniform] Unsupported type.");
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}
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};
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auto [upper, maxval] = get_limits();
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auto out = bits(shape, size_of(dtype), key, stream);
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out = astype(divide(out, maxval, stream), dtype, stream);
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out = minimum(out, upper, stream);
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auto upper = get_upper();
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auto maxval = array(std::numeric_limits<uint32_t>::max(), float32);
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auto out = bits(shape, size_of(float32), key, stream);
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out = divide(out, maxval, stream);
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out = astype(minimum(out, upper, stream), dtype, stream);
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return add(multiply(range, out, stream), lo, stream);
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}
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@ -183,7 +156,7 @@ inline array complex_normal(
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const std::optional<array>& key,
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StreamOrDevice s) {
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auto stream = to_stream(s);
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auto low = above_minus_one_with_default(float32);
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auto low = array(std::nextafter(-1.0f, 0.0f), float32);
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auto high = array(1.0f, float32);
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shape.push_back(2);
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auto samples =
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@ -207,18 +180,23 @@ array normal(
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StreamOrDevice s /* = {} */) {
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if (dtype == complex64) {
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return complex_normal(shape, loc, scale, key, s);
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} else if (!issubdtype(dtype, floating)) {
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throw std::invalid_argument(
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"[normal] Can only generate uniform numbers with "
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"floating point type.");
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}
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auto stream = to_stream(s);
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auto low = above_minus_one_with_default(dtype);
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auto high = array(1.0f, dtype);
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auto samples = uniform(low, high, shape, dtype, key, stream);
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auto low = array(std::nextafter(-1.0f, 0.0f), float32);
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auto high = array(1.0f, float32);
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auto samples = uniform(low, high, shape, float32, key, stream);
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auto applied_scale = array(std::sqrt(2.0), dtype);
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if (scale.has_value()) {
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applied_scale =
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multiply(applied_scale, astype(*scale, dtype, stream), stream);
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}
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samples = multiply(applied_scale, erfinv(samples, stream), stream);
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samples = astype(erfinv(samples, stream), dtype, stream);
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samples = multiply(applied_scale, samples, stream);
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if (loc.has_value()) {
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samples = add(astype(*loc, dtype, stream), samples, stream);
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}
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@ -469,16 +447,23 @@ array laplace(
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const float scale /* = 1.0 */,
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const std::optional<array>& key /*= nullopt */,
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StreamOrDevice s /* = {} */) {
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if (!issubdtype(dtype, floating)) {
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throw std::invalid_argument(
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"[laplace] Can only generate uniform numbers with real"
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"floating point type.");
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}
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auto stream = to_stream(s);
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auto low = above_minus_one_with_default(dtype);
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auto high = array(1.0f, dtype);
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auto samples = uniform(low, high, shape, dtype, key, stream);
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auto low = array(std::nextafter(-1.0f, 0.0f), float32);
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auto high = array(1.0f, float32);
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auto samples = uniform(low, high, shape, float32, key, stream);
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// Use inverse CDF to generate Laplacian noise
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samples = multiply(
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sign(samples, stream),
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log1p(
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multiply(array(-1.0f, dtype), abs(samples, stream), stream), stream),
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stream);
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samples = astype(samples, dtype, stream);
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if (scale != 1.0) {
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samples = multiply(array(scale, dtype), samples, stream);
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@ -350,7 +350,7 @@ TEST_CASE("test random uniform") {
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// Check float16
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{
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auto key = random::key(0);
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auto out = random::uniform({100}, float16, key);
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auto out = random::uniform({1000}, float16, key);
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CHECK_EQ(out.dtype(), float16);
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CHECK(all(less(out, array(1.0f))).item<bool>());
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CHECK(all(greater_equal(out, array(0.0f))).item<bool>());
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@ -360,7 +360,7 @@ TEST_CASE("test random uniform") {
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{
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auto key = random::key(0);
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auto out = random::uniform({100}, bfloat16, key);
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auto out = random::uniform({1000}, bfloat16, key);
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CHECK_EQ(out.dtype(), bfloat16);
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CHECK(all(less(out, array(1.0f))).item<bool>());
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CHECK(all(greater_equal(out, array(0.0f))).item<bool>());
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