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Define built-in constants and add two circle constants #4473
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Define built-in constants and add two circle constants #4473
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Previews, as seen when this build job started (df4bf8f):
WebGPU webgpu.idl | Explainer | Correspondence Reference
WGSL grammar.js | wgsl.lalr.txt
wgsl/index.bs
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Any other constants we need? e or phi for example?
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@Kangz I think that e is certainly a good addition in terms of practicality, though group decided to start with pi and tau initially. If there's consensus, I can certainly add to PR
mehmetoguzderin
commented
Feb 13, 2024
The PR now also has an example to demonstrate numerical accuracy improvement through constants. Your review would be highly appreciated!
Since spec is not the right place, I'm attaching calculation of absolute error here (I've used 128 dps for mpmath):
import mpmath import numpy as np mpmath.mp.dps = 128 # Calculate delta_x with high precision # Delta for interval from -PI/4 to 2 * TAU with 1024 steps mpmath_delta_x = (mpmath.mpf(4 * mpmath.pi) - mpmath.mpf(-mpmath.pi / 4)) / 1024 print(f"delta_x (128-bit precision): {mpmath_delta_x}") numpy_delta_x = ( (np.float64(4.0) * np.float64(np.pi)) - (-np.float64(np.pi) / np.float64(4.0)) ) / np.float64(1024) print(f"delta_x (64-bit precision): {numpy_delta_x}") numpy_delta_x_32 = ( (np.float32(4.0) * np.float32(np.pi)) - (-np.float32(np.pi) / np.float32(4.0)) ) / np.float32(1024) print(f"delta_x (32-bit precision): {numpy_delta_x_32}") M_PI_4 = np.float32(0.785398185253143310546875) TAU_X_2 = np.float32(12.56637096405029296875) numpy_delta_x_32_c = ( (TAU_X_2) - (-M_PI_4) ) / np.float32(1024) print(f"delta_x (32-bit precision constants): {numpy_delta_x_32_c}") print(f"absolute error for 64-bit: {mpmath.nstr(abs(numpy_delta_x - mpmath_delta_x))}") print(f"absolute error for 32-bit: {mpmath.nstr(abs(numpy_delta_x_32 - mpmath_delta_x))}") print(f"absolute error for 32-bit constants: {mpmath.nstr(abs(numpy_delta_x_32_c - mpmath_delta_x))}")
delta_x (128-bit precision): 0.013038836697027950452603744510681530525232392526703320057757338395808808326871472894696433601273435096605595085626415823486473476
delta_x (64-bit precision): 0.01303883669702795
delta_x (32-bit precision): 0.013038837350904942
delta_x (32-bit precision constants): 0.013038837350904942
absolute error for 64-bit: 3.59085e-19
absolute error for 32-bit: 6.53877e-10
absolute error for 32-bit constants: 6.53877e-10
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Isn't the argument for not including M_PI_2 (PI/2) a good argument for omitting TAU? It's just one more character to write PI*2.
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Certainly an argument in support of such thinking, although I think the consensus was to add TAU for widespread recognition, but if the group decides otherwise today, I can change it. Though even when precision is not an issue, similar constant collections seem to be including TAU these days, strengthening the case for inclusion.
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Fixes #4100
In accordance with the discussions, I have made sure to keep the normative definition concise and succinct, and move any exemplification or explanation into note since otherwise would be a denormalization of spec itself, especially for the rules of abstract float accuracy, directly linked in the text.
Per discussion at the Editors' call, I'm creating as draft. All feedback will be deeply appreciated.
TODO:
PI_2is redundant per WGSL definitions