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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__) || defined(__ARM_PCS_VFP)
67 i = floor(x + round_to_nearest);
68 #elif defined(__arm__)
69 // From 'ARMĀ®v7-M Architecture Reference Manual' page A7-569:
70 // "The floating-point to integer operation (vcvt) [normally] uses the Round towards Zero rounding mode"
71 // Because of this...we must use some less-than-straightforward logic to perform this operation without
72 // changing the rounding mode flags
74 /* The assembly below implements the following logic:
79 int_val = trunc(x+inc);
86 __asm__ __volatile__ (
87 "vmov.F64 d1,%[rnd_val] \n\t" // Copy round_to_nearest into a working register (d1 = 0.5)
88 "fcmpezd %P[value] \n\t" // Check value against zero (value == 0?)
89 "fmstat \n\t" // Copy the floating-point status flags into the general-purpose status flags
91 "vnegmi.F64 d1, d1 \n\t" // if N-flag is set, negate round_to_nearest (if (value < 0) d1 = -1 * d1)
92 "vadd.F64 d1,%P[value],d1 \n\t" // Add round_to_nearest to value, store result in working register (d1 += value)
93 "vcvt.S32.F64 s3,d1 \n\t" // Truncate(round towards zero) (s3 = (int)d1)
94 "vmov %[result],s3 \n\t" // Store the integer result in a general-purpose register (result = s3)
95 "vcvt.F64.S32 d1,s3 \n\t" // Convert back to floating-point (d1 = (double)s3)
96 "vsub.F64 d1,%P[value],d1 \n\t" // Calculate the error (d1 = value - d1)
97 "vmov.F64 d2,%[rnd_val] \n\t" // d2 = 0.5;
98 "fcmped d1, d2 \n\t" // (d1 == 0.5?)
99 "fmstat \n\t" // Copy the floating-point status flags into the general-purpose status flags
101 "addeq %[result],#1 \n\t" // (if (d1 == d2) result++;)
102 : [result] "=r"(i) // Outputs
103 : [rnd_val] "Dv" (round_to_nearest), [value] "w"(x) // Inputs
104 : "d1", "d2", "s3" // Clobbers
107 __asm__ __volatile__ (
112 : "=m"(i) : "u"(round_to_nearest), "t"(x) : "st"
119 /*! \brief Truncate to nearest integer.
120 This routine does fast truncation to an integer.
121 It should simply drop the fractional portion of the floating point number.
123 Make sure MathUtils::test() returns true for each implementation.
126 inline int truncate_int(double x)
128 assert(x > static_cast<double>(INT_MIN / 2) - 1.0);
129 assert(x < static_cast <double>(INT_MAX / 2) + 1.0);
131 #if !defined(__powerpc__) && !defined(__ppc__) && !defined(__arm__)
132 const float round_towards_m_i = -0.5f;
142 fadd round_towards_m_i
147 #if defined(__powerpc__) || defined(__ppc__)
149 #elif defined(__arm__)
150 __asm__ __volatile__ (
151 "vcvt.S32.F64 %[result],%P[value] \n\t" // Truncate(round towards zero) and store the result
152 : [result] "=w"(i) // Outputs
153 : [value] "w"(x) // Inputs
157 __asm__ __volatile__ (
163 : "=m"(i) : "u"(round_towards_m_i), "t"(x) : "st"
172 inline int64_t abs(int64_t a)
174 return (a < 0) ? -a : a;
179 // stupid hack to keep compiler from dropping these
180 // functions as unused
181 MathUtils::round_int(0.0);
182 MathUtils::truncate_int(0.0);
187 /*! \brief test routine for round_int and truncate_int
188 Must return true on all platforms.
192 for (int i = -8; i < 8; ++i)
195 int r = (i < 0) ? (i - 1) / 4 : (i + 2) / 4;
197 if (round_int(d) != r || truncate_int(d) != t)
203 } // namespace MathUtils