1/*
2 * Copyright 2015 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8#include "SkPoint3.h"
9
10// Returns the square of the Euclidian distance to (x,y,z).
11static inline float get_length_squared(float x, float y, float z) {
12    return x * x + y * y + z * z;
13}
14
15// Calculates the square of the Euclidian distance to (x,y,z) and stores it in
16// *lengthSquared.  Returns true if the distance is judged to be "nearly zero".
17//
18// This logic is encapsulated in a helper method to make it explicit that we
19// always perform this check in the same manner, to avoid inconsistencies
20// (see http://code.google.com/p/skia/issues/detail?id=560 ).
21static inline bool is_length_nearly_zero(float x, float y, float z, float *lengthSquared) {
22    *lengthSquared = get_length_squared(x, y, z);
23    return *lengthSquared <= (SK_ScalarNearlyZero * SK_ScalarNearlyZero);
24}
25
26SkScalar SkPoint3::Length(SkScalar x, SkScalar y, SkScalar z) {
27    float magSq = get_length_squared(x, y, z);
28    if (SkScalarIsFinite(magSq)) {
29        return sk_float_sqrt(magSq);
30    } else {
31        double xx = x;
32        double yy = y;
33        double zz = z;
34        return (float)sqrt(xx * xx + yy * yy + zz * zz);
35    }
36}
37
38/*
39 *  We have to worry about 2 tricky conditions:
40 *  1. underflow of magSq (compared against nearlyzero^2)
41 *  2. overflow of magSq (compared w/ isfinite)
42 *
43 *  If we underflow, we return false. If we overflow, we compute again using
44 *  doubles, which is much slower (3x in a desktop test) but will not overflow.
45 */
46bool SkPoint3::normalize() {
47    float magSq;
48    if (is_length_nearly_zero(fX, fY, fZ, &magSq)) {
49        this->set(0, 0, 0);
50        return false;
51    }
52
53    float scale;
54    if (SkScalarIsFinite(magSq)) {
55        scale = 1.0f / sk_float_sqrt(magSq);
56    } else {
57        // our magSq step overflowed to infinity, so use doubles instead.
58        // much slower, but needed when x, y or z is very large, otherwise we
59        // divide by inf. and return (0,0,0) vector.
60        double xx = fX;
61        double yy = fY;
62        double zz = fZ;
63#ifdef SK_CPU_FLUSH_TO_ZERO
64        // The iOS ARM processor discards small denormalized numbers to go faster.
65        // Casting this to a float would cause the scale to go to zero. Keeping it
66        // as a double for the multiply keeps the scale non-zero.
67        double dscale = 1.0f / sqrt(xx * xx + yy * yy + zz * zz);
68        fX = x * dscale;
69        fY = y * dscale;
70        fZ = z * dscale;
71        return true;
72#else
73        scale = (float)(1.0f / sqrt(xx * xx + yy * yy + zz * zz));
74#endif
75    }
76    fX *= scale;
77    fY *= scale;
78    fZ *= scale;
79    return true;
80}
81