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28 #include <emmintrin.h>
31 // use real compiler defines in here as we want to
32 // avoid including system.h or other magic includes.
33 // use 'gcc -dM -E - < /dev/null' or similar to find them.
35 #if defined(__ppc__) || \
36 defined(__powerpc__) || \
37 (defined(__APPLE__) && defined(__arm__) && defined(__llvm__)) || \
38 (defined(__ANDROID__) && defined(__arm__)) || \
39 defined(TARGET_RASPBERRY_PI)
40 #define DISABLE_MATHUTILS_ASM_ROUND_INT
43 #if defined(__ppc__) || \
44 defined(__powerpc__) || \
45 (defined(__APPLE__) && defined(__llvm__)) || \
46 (defined(__ANDROID__) && defined(__arm__)) || \
47 defined(TARGET_RASPBERRY_PI)
48 #define DISABLE_MATHUTILS_ASM_TRUNCATE_INT
51 /*! \brief Math utility class.
52 Note that the test() routine should return true for all implementations
54 See http://ldesoras.free.fr/doc/articles/rounding_en.pdf for an explanation
55 of the technique used on x86.
59 // GCC does something stupid with optimization on release builds if we try
60 // to assert in these functions
62 /*! \brief Round to nearest integer.
63 This routine does fast rounding to the nearest integer.
64 In the case (k + 0.5 for any integer k) we round up to k+1, and in all other
65 instances we should return the nearest integer.
66 Thus, { -1.5, -0.5, 0.5, 1.5 } is rounded to { -1, 0, 1, 2 }.
67 It preserves the property that round(k) - round(k-1) = 1 for all doubles k.
69 Make sure MathUtils::test() returns true for each implementation.
70 \sa truncate_int, test
72 inline int round_int(double x)
74 assert(x > static_cast<double>(INT_MIN / 2) - 1.0);
75 assert(x < static_cast<double>(INT_MAX / 2) + 1.0);
76 const float round_to_nearest = 0.5f;
79 #if defined(DISABLE_MATHUTILS_ASM_ROUND_INT)
80 i = floor(x + round_to_nearest);
82 #elif defined(__arm__)
83 // From 'ARM-v7-M Architecture Reference Manual' page A7-569:
84 // "The floating-point to integer operation (vcvt) [normally] uses the Round towards Zero rounding mode"
85 // Because of this...we must use some less-than-straightforward logic to perform this operation without
86 // changing the rounding mode flags
88 /* The assembly below implements the following logic:
93 int_val = trunc(x+inc);
100 __asm__ __volatile__ (
101 #if defined(__ARM_PCS_VFP)
102 "fconstd d1,#%G[rnd_val] \n\t" // Copy round_to_nearest into a working register (d1 = 0.5)
104 "vmov.F64 d1,%[rnd_val] \n\t"
106 "fcmpezd %P[value] \n\t" // Check value against zero (value == 0?)
107 "fmstat \n\t" // Copy the floating-point status flags into the general-purpose status flags
109 "vnegmi.F64 d1, d1 \n\t" // if N-flag is set, negate round_to_nearest (if (value < 0) d1 = -1 * d1)
110 "vadd.F64 d1,%P[value],d1 \n\t" // Add round_to_nearest to value, store result in working register (d1 += value)
111 "vcvt.S32.F64 s3,d1 \n\t" // Truncate(round towards zero) (s3 = (int)d1)
112 "vmov %[result],s3 \n\t" // Store the integer result in a general-purpose register (result = s3)
113 "vcvt.F64.S32 d1,s3 \n\t" // Convert back to floating-point (d1 = (double)s3)
114 "vsub.F64 d1,%P[value],d1 \n\t" // Calculate the error (d1 = value - d1)
115 #if defined(__ARM_PCS_VFP)
116 "fconstd d2,#%G[rnd_val] \n\t" // d2 = 0.5;
118 "vmov.F64 d2,%[rnd_val] \n\t"
120 "fcmped d1, d2 \n\t" // (d1 == 0.5?)
121 "fmstat \n\t" // Copy the floating-point status flags into the general-purpose status flags
123 "addeq %[result],#1 \n\t" // (if (d1 == d2) result++;)
124 : [result] "=r"(i) // Outputs
125 : [rnd_val] "Dv" (round_to_nearest), [value] "w"(x) // Inputs
126 : "d1", "d2", "s3" // Clobbers
129 #elif defined(__SSE2__)
130 const float round_dn_to_nearest = 0.4999999f;
131 i = (x > 0) ? _mm_cvttsd_si32(_mm_set_sd(x + round_to_nearest)) : _mm_cvttsd_si32(_mm_set_sd(x - round_dn_to_nearest));
133 #elif defined(_WIN32)
138 fadd round_to_nearest
144 __asm__ __volatile__ (
149 : "=m"(i) : "u"(round_to_nearest), "t"(x) : "st"
157 /*! \brief Truncate to nearest integer.
158 This routine does fast truncation to an integer.
159 It should simply drop the fractional portion of the floating point number.
161 Make sure MathUtils::test() returns true for each implementation.
164 inline int truncate_int(double x)
166 assert(x > static_cast<double>(INT_MIN / 2) - 1.0);
167 assert(x < static_cast<double>(INT_MAX / 2) + 1.0);
170 #if defined(DISABLE_MATHUTILS_ASM_TRUNCATE_INT)
173 #elif defined(__arm__)
174 __asm__ __volatile__ (
175 "vcvt.S32.F64 %[result],%P[value] \n\t" // Truncate(round towards zero) and store the result
176 : [result] "=w"(i) // Outputs
177 : [value] "w"(x) // Inputs
181 #elif defined(_WIN32)
182 const float round_towards_m_i = -0.5f;
188 fadd round_towards_m_i
194 const float round_towards_m_i = -0.5f;
195 __asm__ __volatile__ (
201 : "=m"(i) : "u"(round_towards_m_i), "t"(x) : "st"
209 inline int64_t abs(int64_t a)
211 return (a < 0) ? -a : a;
214 inline unsigned bitcount(unsigned v)
218 v &= v - 1; // clear the least significant bit set
224 // stupid hack to keep compiler from dropping these
225 // functions as unused
226 MathUtils::round_int(0.0);
227 MathUtils::truncate_int(0.0);
232 /*! \brief test routine for round_int and truncate_int
233 Must return true on all platforms.
237 for (int i = -8; i < 8; ++i)
240 int r = (i < 0) ? (i - 1) / 4 : (i + 2) / 4;
242 if (round_int(d) != r || truncate_int(d) != t)
248 } // namespace MathUtils