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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).
get_length_squared(float x,float y,float z)11 static 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 ).
is_length_nearly_zero(float x,float y,float z,float * lengthSquared)21 static 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 
Length(SkScalar x,SkScalar y,SkScalar z)26 SkScalar 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  */
normalize()46 bool 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