From f2893b2bca70e1ba6732b10288c02caac792eb3c Mon Sep 17 00:00:00 2001 From: Yi Xu Date: Wed, 10 Aug 2022 22:38:28 +0800 Subject: [PATCH] [Doc] [type] Add introduction to quantized types (#5705) * [Doc] [type] Add introduction to quantized types * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix * Apply suggestions from code review Co-authored-by: Ailing * Shuffle * Fix type Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Ailing --- docs/lang/articles/advanced/quant.md | 249 ++++++++++++++++++ .../bitpacked_fields_layout_example.png | Bin 0 -> 52825 bytes .../static/assets/floating-point_formats.png | Bin 0 -> 138507 bytes .../assets/quant_array_layout_example.png | Bin 0 -> 10329 bytes 4 files changed, 249 insertions(+) create mode 100644 docs/lang/articles/advanced/quant.md create mode 100644 docs/lang/articles/static/assets/bitpacked_fields_layout_example.png create mode 100644 docs/lang/articles/static/assets/floating-point_formats.png create mode 100644 docs/lang/articles/static/assets/quant_array_layout_example.png diff --git a/docs/lang/articles/advanced/quant.md b/docs/lang/articles/advanced/quant.md new file mode 100644 index 00000000000000..3ed4972b42f606 --- /dev/null +++ b/docs/lang/articles/advanced/quant.md @@ -0,0 +1,249 @@ +--- +sidebar_position: 3 +--- + +# Using quantized data types + +High-resolution simulations can deliver great visual quality, but they are often +limited by available memory, especially on GPUs. For the sake of saving memory, +Taichi provides low-precision ("quantized") data types. You can define your own integers, +fixed-point numbers or floating-point numbers with non-standard number of bits so +that you can choose a proper setting with minimum memory for your applications. +Taichi provides a suite of tailored domain-specific optimizations to ensure the +runtime performance with quantized data types close to that with full-precision +data types. + +:::note +Quantized data types are only supported on CPU and CUDA backends for now. +::: + +## Quantized data types + +### Quantized integers + +Modern computers represent integers using the [two's complement](https://en.wikipedia.org/wiki/Two%27s_complement) +format. *Quantized integers* in Taichi adopt the same format, and can contain +non-standard number of bits: + +```python +i10 = ti.types.quant.int(bits=10) # 10-bit signed (default) integer type +u5 = ti.types.quant.int(bits=5, signed=False) # 5-bit unsigned integer type +``` + +### Quantized fixed-point numbers + +[Fixed-point numbers](https://en.wikipedia.org/wiki/Fixed-point_arithmetic) are +an old way to represent real numbers. The internal representation of a fixed-point number is simply an integer, and +its actual value equals to the integer multiplied by a predefined scaling +factor. Based on the support for quantized integers, Taichi provides *quantized +fixed-point numbers* as follows: + +```python +fixed_type_a = ti.types.quant.fixed(bits=10, max_value=20.0) # 10-bit signed (default) fixed-point type within [-20.0, 20.0] +fixed_type_b = ti.types.quant.fixed(bits=5, signed=False, max_value=100.0) # 5-bit unsigned fixed-point type within [0.0, 100.0] +fixed_type_c = ti.types.quant.fixed(bits=6, signed=False, scale=1.0) # 6-bit unsigned fixed-point type within [0, 64.0] +``` + +`scale` is the scaling factor mentioned above. Because fixed-point numbers are +especially useful when you know the actual value is guaranteed to be within a +range, Taichi allows you to simply set `max_value` and will calculate the +scaling factor accordingly. + +### Quantized floating-point numbers + +[Floating-point numbers](https://en.wikipedia.org/wiki/Floating-point_arithmetic) +are the standard way to represent real numbers on modern computers. A +floating-point number is composed of exponent bits, fraction bits, and a sign +bit. There are various floating-point formats: + +![image](../static/assets/floating-point_formats.png) + +In Taichi, you can define a *quantized floating-point number* with arbitrary +combination of exponent bits and fraction bits (the sign bit is made part of +fraction bits): + +```python +float_type_a = ti.types.quant.float(exp=5, frac=10) # 15-bit signed (default) floating-point type with 5 exponent bits +float_type_b = ti.types.quant.float(exp=6, frac=9, signed=False) # 15-bit unsigned floating-point type with 6 exponent bits +``` + +### Compute types + +All the parameters you've seen above are specifying the *storage type* of a +quantized data type. However, most quantized data types have no native support +on hardware, so an actual value of that quantized data type needs to convert to +a primitive type ("*compute type*") when it is involved in computation. + +The default compute type for quantized integers is `ti.i32`, while the default +compute type for quantized fixed-point/floating-point numbers is `ti.f32`. You +can change the compute type by specifying the `compute` parameter: + +```python +i21 = ti.types.quant.int(bits=21, compute=ti.i64) +bfloat16 = ti.types.quant.float(exp=8, frac=8, compute=ti.f32) +``` + +## Data containers for quantized data types + +Because the storage types are not primitive types, you may now wonder how +quantized data types can work together with data containers that Taichi +provides. In fact, some special constructs are introduced to eliminate the gap. + +### Bitpacked fields + +`ti.BitpackedFields` packs a group of fields whose `dtype`s are +quantized data types together so that they are stored with one primitive type. +You can then place a `ti.BitpackedFields` instance under any SNode as if each member field +is placed individually. + +```python +a = ti.field(float_type_a) # 15 bits +b = ti.field(fixed_type_b) # 5 bits +c = ti.field(fixed_type_c) # 6 bits +d = ti.field(u5) # 5 bits +bitpack = ti.BitpackedFields(max_num_bits=32) +bitpack.place(a, b, c, d) # 31 out of 32 bits occupied +ti.root.dense(ti.i, 10).place(bitpack) +``` + +#### Shared exponent + +When multiple fields with quantized floating-point types are packed together, +there is chance that they can share a common exponent. For example, in a 3D +velocity vector, if you know the x-component has a much larger absolute value +compared to y- and z-components, then you probably do not care about the exact +value of the y- and z-components. In this case, using a shared exponent can +leave more bits for components with larger absolute values. You can use +`place(x, y, z, shared_exponent=True)` to make fields `x, y, z` share a common +exponent. + +#### Your first program + +You probably cannot wait to write your first Taichi program with quantized data +types. The easiest way is to modify the data definitions of an existing example. +Assume you want to save memory for +[examples/simulation/euler.py](https://github.com/taichi-dev/taichi/blob/master/python/taichi/examples/simulation/euler.py). +Because most data definitions in the example are similar, here only field `Q` is +used for illustration: + +```python +Q = ti.Vector.field(4, dtype=ti.f32, shape=(N, N)) +``` + +An element of `Q` now occupies 4 x 32 = 128 bits. If you can fit it in +64 bits, then the memory usage is halved. A direct and first attempt is to +use quantized floating-point numbers with a shared exponent: + +```python +float_type_c = ti.types.quant.float(exp=8, frac=14) +Q_old = ti.Vector.field(4, dtype=float_type_c) +bitpack = ti.BitpackedFields(max_num_bits=64) +bitpack.place(Q_old, shared_exponent=True) +ti.root.dense(ti.ij, (N, N)).place(bitpack) +``` + +Surprisingly, you find that there is no obvious difference in visual effects +after the change, and you now successfully finish a Taichi program with +quantized data types! More attempts are left to you. + +#### More complicated quantization schemes + +Here comes a more complicated scenario. In a 3D Eulerian fluid simulation, a +voxel may need to store a 3D vector for velocity, and an integer value for cell +category with three possible values: "source", "Dirichlet boundary", and +"Neumann boundar". You can actually store all information with a single 32-bit +`ti.BitpackedFields`: + +```python +velocity_component_type = ti.types.quant.float(exp=6, frac=8, compute=ti.f32) +velocity = ti.Vector.field(3, dtype=velocity_component_type) + +# Since there are only three cell categories, 2 bits are enough. +cell_category_type = ti.types.quant.int(bits=2, signed=False, compute=ti.i32) +cell_category = ti.field(dtype=cell_category_type) + +voxel = ti.BitpackedFields(max_num_bits=32) +# Place three components of velocity into the voxel, and let them share the exponent. +voxel.place(velocity, shared_exponent=True) +# Place the 2-bit cell category. +voxel.place(cell_category) +# Create 512 x 512 x 256 voxels. +ti.root.dense(ti.ijk, (512, 512, 256)).place(voxel) +``` + +The compression scheme above allows you to store 13 bytes (4B x 3 + 1B) into +just 4 bytes. Note that you can still use velocity and cell_category in the +computation code, as if they are `ti.f32` and `ti.u8`. + +![image](../static/assets/bitpacked_fields_layout_example.png) + +### Quant arrays + +Bitpacked fields are actually laid in an array of structure (AOS) order. +However, there are also cases where a single quantized type is required to get +laid in an array. For example, you may want to store 8 x u4 values in a single +u32 type, to represent bin values of a histogram: + +![image](../static/assets/quant_array_layout_example.png) + +Quant array is exactly what you need. A `quant_array` is a SNode which +can reinterpret a primitive type into an array of a quantized type: + +```python +bin_value_type = ti.types.quant.int(bits=4, signed=False) + +# The quant array for 512 x 512 bin values +array = ti.root.dense(ti.ij, (512, 64)).quant_array(ti.j, 8, max_num_bits=32) +# Place the unsigned 4-bit bin value into the array +array.place(bin_value_type) +``` + +:::note +1. Only one field can be placed under a `quant_array`. +2. Only quantized integer types and quantized fixed-point types are supported as +the `dtype` of the field under a `quant_array`. +3. The size of the `dtype` of the field times the shape of the `quant_array` +must be less than or equal to the `max_num_bits` of the `quant_array`. +::: + +#### Bit vectorization + +For quant arrays of 1-bit quantized integer types ("boolean"), Taichi provides +an additional optimization - bit vectorization. It aims at vectorizing +operations on such quant arrays under struct fors: + +```python +u1 = ti.types.quant.int(1, False) +N = 512 +M = 32 +x = ti.field(dtype=u1) +y = ti.field(dtype=u1) +ti.root.dense(ti.i, N // M).quant_array(ti.i, M, max_num_bits=M).place(x) +ti.root.dense(ti.i, N // M).quant_array(ti.i, M, max_num_bits=M).place(y) + +@ti.kernel +def assign_vectorized(): + ti.loop_config(bit_vectorize=True) + for i, j in x: + y[i, j] = x[i, j] # 32 bits are handled at a time + +assign_vectorized() +``` + +## Advanced examples + +The following examples are picked from the +[QuanTaichi paper](https://yuanming.taichi.graphics/publication/2021-quantaichi/quantaichi.pdf), +so you can dig into details there. + +### [Game of Life](https://github.com/taichi-dev/quantaichi/tree/main/gol) + +![image](https://github.com/taichi-dev/quantaichi/raw/main/pics/teaser_gol.jpg) + +### [Eulerian Fluid](https://github.com/taichi-dev/quantaichi/tree/main/eulerian_fluid) + +![image](https://github.com/taichi-dev/quantaichi/raw/main/pics/smoke_result.png) + +### [MLS-MPM](https://github.com/taichi-dev/taichi_elements/blob/master/demo/demo_quantized_simulation_letters.py) + +![image](https://github.com/taichi-dev/quantaichi/raw/main/pics/mpm-235.jpg) diff --git a/docs/lang/articles/static/assets/bitpacked_fields_layout_example.png b/docs/lang/articles/static/assets/bitpacked_fields_layout_example.png new file mode 100644 index 0000000000000000000000000000000000000000..4184cd60c274950f5346a51aa1885ea0e9487990 GIT binary patch literal 52825 zcmeFZbySsI`!#wa-6frZfpkeXNQ$I%halbE-H1weN{4iJi=>ovNO$+QIN$ia&+~p~ zjPu9&^Nh2HL)^Ic+V{QIy5=?KysouF<=;!7qY$G&5QHuzDW(WP2ngWci%5@u^GllU zf*)}9B2vmo;NgK}6aqn%kd&CPvP;VDyt9Yw1_k2b@KAFiXL5)b7F-3g)NZrcL~)JE zo@`NJ)!R|pu*ou->felS72JD5h+>df`#z`kE!1D6EmFj+>eSEB_HEp`xiicf1c)({vS_cV*mZ}3E6Z3vWA8RNhzuJ zjzCm>bMvB@w6wISVZjH|moHyF{<`o(k)DNxmU!+9w+l(GD`xEfc{Iz~(cQu4wWpG&pIQ&Lj0o%#8bUalcD6!|%hl&@;vP27yQ 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