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28 /*! \brief Math utility class.
29 Note that the test() routine should return true for all implementations
31 See http://ldesoras.free.fr/doc/articles/rounding_en.pdf for an explanation
32 of the technique used on x86.
36 // GCC does something stupid with optimization on release builds if we try
37 // to assert in these functions
39 /*! \brief Round to nearest integer.
40 This routine does fast rounding to the nearest integer.
41 In the case (k + 0.5 for any integer k) we round up to k+1, and in all other
42 instances we should return the nearest integer.
43 Thus, { -1.5, -0.5, 0.5, 1.5 } is rounded to { -1, 0, 1, 2 }.
44 It preserves the property that round(k) - round(k-1) = 1 for all doubles k.
46 Make sure MathUtils::test() returns true for each implementation.
47 \sa truncate_int, test
49 inline int round_int (double x)
51 assert(x > static_cast<double>(INT_MIN / 2) - 1.0);
52 assert(x < static_cast <double>(INT_MAX / 2) + 1.0);
53 const float round_to_nearest = 0.5f;
66 #if defined(__powerpc__) || defined(__ppc__)
67 i = floor(x + round_to_nearest);
68 #elif defined(__arm__)
69 //BIG FIXME here (still has issues with rounding -0.5 to zero and not -1)
70 //the asm codes below do the following - trunc(x+0.5)
71 //this isn't correct for negativ x - values - for example
72 //-1 gets rounded to zero because trunc(-1+0.5) == 0
73 //this is a dirty hack until someone fixes this propably in asm
74 //i've created a trac ticket for this #11767
75 //this hacks decrements the x by 1 if it is negativ
76 // so for -1 it would be trunc(-2+0.5) - which would be correct -1 then ...
79 __asm__ __volatile__ (
80 "vmov.F64 d1,%[rnd_val] \n\t" // Copy round_to_nearest into a working register
81 "vadd.F64 %P[value],%P[value],d1 \n\t" // Add round_to_nearest to value
82 "vcvt.S32.F64 %[result],%P[value] \n\t" // Truncate(round towards zero) and store the result
83 : [result] "=w"(i), [value] "+w"(x) // Outputs
84 : [rnd_val] "Dv" (round_to_nearest) // Inputs
87 __asm__ __volatile__ (
92 : "=m"(i) : "u"(round_to_nearest), "t"(x) : "st"
99 /*! \brief Truncate to nearest integer.
100 This routine does fast truncation to an integer.
101 It should simply drop the fractional portion of the floating point number.
103 Make sure MathUtils::test() returns true for each implementation.
106 inline int truncate_int(double x)
108 assert(x > static_cast<double>(INT_MIN / 2) - 1.0);
109 assert(x < static_cast <double>(INT_MAX / 2) + 1.0);
111 #if !defined(__powerpc__) && !defined(__ppc__) && !defined(__arm__)
112 const float round_towards_m_i = -0.5f;
122 fadd round_towards_m_i
127 #if defined(__powerpc__) || defined(__ppc__) || defined(__arm__)
130 __asm__ __volatile__ (
136 : "=m"(i) : "u"(round_towards_m_i), "t"(x) : "st"
145 inline int64_t abs(int64_t a)
147 return (a < 0) ? -a : a;
152 // stupid hack to keep compiler from dropping these
153 // functions as unused
154 MathUtils::round_int(0.0);
155 MathUtils::truncate_int(0.0);
160 /*! \brief test routine for round_int and truncate_int
161 Must return true on all platforms.
165 for (int i = -8; i < 8; ++i)
168 int r = (i < 0) ? (i - 1) / 4 : (i + 2) / 4;
170 if (round_int(d) != r || truncate_int(d) != t)
176 } // namespace MathUtils