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implement erf #59

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merged 4 commits into from
Dec 12, 2023
Merged

implement erf #59

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69d45f8
implement erf
mei1127 Nov 29, 2023
6d80908
modifeid erf.js
mei1127 Nov 29, 2023
095fc07
Optimize erf implementation
mei1127 Nov 29, 2023
c4da65b
modified unary.js
mei1127 Dec 5, 2023
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25 changes: 24 additions & 1 deletion src/unary.js
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Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
'use strict';

import {Tensor} from './lib/tensor.js';
import {Scalar, Tensor} from './lib/tensor.js';
import {add, div, mul, sub} from '../src/binary.js';

/**
* Compute the element-wise unary operation for input tensor.
Expand Down Expand Up @@ -30,3 +31,25 @@ export const tan = (input) => unary(input, Math.tan);
export const copy = (input) => unary(input, (x) => x);
export const reciprocal = (input) => unary(input, (x) => 1 / x);
export const sqrt = (input) => unary(input, Math.sqrt);
export const sign = (input) => unary(input, Math.sign);

export const erf = (input) => {
/**
*reference 1:https://en.wikipedia.org/wiki/Error_function
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FYI, thanks.

Here we refer to an "Approximation with elementary function" with maximum error: 1.5×10−7 of Error function in Wikipedia as below figure:

image

and erf function of WebGL backend for TensorFlow.js.

const ERF = `
  // Error function is calculated approximately with elementary function.
  // See "Handbook of Mathematical Functions with Formulas,
  // Graphs, and Mathematical Tables", Abramowitz and Stegun.
  float p = ${backend_util.ERF_P};
  float a1 = ${backend_util.ERF_A1};
  float a2 = ${backend_util.ERF_A2};
  float a3 = ${backend_util.ERF_A3};
  float a4 = ${backend_util.ERF_A4};
  float a5 = ${backend_util.ERF_A5};

  float sign = sign(x);
  x = abs(x);
  float t = 1.0 / (1.0 + p * x);
  return sign * (1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*exp(-x*x));
`;

*reference 2:https://github.com/tensorflow/tfjs/blob/master/tfjs-backend-webgl/src/kernels/Erf.ts
*/
const a1 = new Scalar(0.254829592);
const a2 = new Scalar(-0.284496736);
const a3 = new Scalar(1.421413741);
const a4 = new Scalar(-1.453152027);
const a5 = new Scalar(1.061405429);
const p = new Scalar(0.3275911);
const ones = new Scalar(1);
input = input.shape.length === 0 ? new Scalar(input.data) : input;
const signInput = sign(input);
input = abs(input);
const t = div(ones, add(ones, mul(p, input)));
const y = mul(add(mul(add(mul(add(mul(add(mul(a5, t), a4), t), a3), t), a2), t), a1), t);
const result = mul(signInput, sub(ones, mul(y, exp(neg(mul(input, input))))));
return result;
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};
27 changes: 27 additions & 0 deletions test/unary_test.js
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Original file line number Diff line number Diff line change
Expand Up @@ -141,6 +141,33 @@ describe('test unary', function() {
[3, 2, 2, 1]);
});

it('erf', function() {
// erf 1D
testUnary(
'erf',
[-0.25, 0.25, 0.5, 0.75, -0.4],
[
-0.2763262613535272,
0.2763262613535272,
0.5205000163047472,
0.7111555696366565,
-0.42839242346728446,
],
[5]);
// erf 2D
testUnary(
'erf',
[
0.2, 0.3,
0.4, 0.5,
],
[
0.22270245785831588, 0.32862668272901174,
0.42839242346728446, 0.5205000163047472,
],
[2, 2]);
});

it('exp', function() {
testUnary('exp', [-1, 0, 1], [0.36787944117144233, 1, 2.718281828459045], [3]);
testUnary(
Expand Down