Made tf.abs underflow-safe on CPU & GPU and added test for it. (#1391)

BUG

src/kernels/backend_cpu.ts

@@ -1122,7 +1122,7 @@ export class MathBackendCPU implements KernelBackend {
     for (let i = 0; i < x.size; ++i) {
       const real = values[i * 2];
       const imag = values[i * 2 + 1];
-      resultValues[i] = Math.sqrt(real * real + imag * imag);
+      resultValues[i] = Math.hypot(real, imag);
     }
     return Tensor.make(x.shape, {values: resultValues}) as T;
   }

src/kernels/webgl/complex_abs_gpu.ts

@@ -26,11 +26,16 @@ export class ComplexAbsProgram implements GPGPUProgram {
     this.outputShape = shape;
     this.userCode = `
       void main() {
-        float real = getRealAtOutCoords();
-        float imag = getImagAtOutCoords();
-        vec2 v = vec2(real, imag);
+        float re = abs(getRealAtOutCoords());
+        float im = abs(getImagAtOutCoords());
+        float mx = max(re, im);
 
-        setOutput(sqrt(dot(v, v)));
+        // sadly the length function in glsl is not underflow-safe
+        // (at least not on Intel GPUs). So the safe solution is
+        // to ensure underflow-safety in all cases.
+        setOutput(
+          mx == 0.0 ? 0.0 : mx * length(vec2(1, min(re, im)/mx))
+        );
       }
     `;
   }

src/ops/unary_ops_test.ts

@@ -19,6 +19,7 @@ import * as tf from '../index';
 import {describeWithFlags} from '../jasmine_util';
 import {ALL_ENVS, expectArraysClose, expectNumbersClose} from '../test_util';
 import * as util from '../util';
+import {ENV} from '../environment';
 
 import * as selu_util from './selu_util';
 
@@ -168,6 +169,34 @@ describeWithFlags('abs', ALL_ENVS, () => {
     expect(result.shape).toEqual([2, 2, 2]);
   });
 
+  it('is underflow-safe for complex64', () => {
+
+    const floatBits = ENV.backend.floatPrecision();
+    let small;
+    switch(floatBits) {
+      case 32: small = 1e-30; break;
+      case 16: small = 1e-4;  break;
+      default: throw new Error(
+        `Test not implemented for ENV.engine.floatPrecision()=${floatBits}.`
+      );
+    }
+
+    const a = tf.complex(
+       [small,     0, small, 0],
+       [small, small,     0, 0]
+    );
+    const result = tf.abs(a);
+    expectArraysClose(
+      result,
+      [Math.hypot(small, small),
+       Math.hypot(    0, small),
+       Math.hypot(small,     0),
+       Math.hypot(    0,     0)], 
+      /*tolerance=*/small/100
+    );
+    expect(result.shape).toEqual([4]);
+  });
+
   it('propagates NaNs', () => {
     const a = tf.tensor1d([1, -2, 0, 3, -0.1, NaN]);
     const result = tf.abs(a);