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37 /*! \internal \file
38 * \brief
39 * Implements simple math functions
40 *
41 * \author Erik Lindahl <erik.lindahl@gmail.com>
42 * \ingroup module_math
43 */
44
45 #include "gmxpre.h"
46
47 #include "functions.h"
48
49 #include "config.h"
50
51 #include <cstdint>
52
53 #include <array>
54 #include <limits>
55
56 #if GMX_NATIVE_WINDOWS
57 # include <intrin.h> // _BitScanReverse, _BitScanReverse64
58 #endif
59
60 #include "gromacs/math/utilities.h"
61 #include "gromacs/utility/gmxassert.h"
62
63 namespace gmx
64 {
65
log2I(std::uint32_t n)66 unsigned int log2I(std::uint32_t n)
67 {
68 GMX_ASSERT(n > 0, "The behavior of log(0) is undefined");
69 #if HAVE_BUILTIN_CLZ
70 // gcc, clang. xor with sign bit should be optimized out
71 return __builtin_clz(n) ^ 31U;
72 #elif HAVE_BITSCANREVERSE
73 // icc, MSVC
74 {
75 unsigned long res;
76 _BitScanReverse(&res, static_cast<unsigned long>(n));
77 return static_cast<unsigned int>(res);
78 }
79 #elif HAVE_CNTLZ4
80 return 31 - __cntlz4(n);
81 #else
82 // http://graphics.stanford.edu/~seander/bithacks.html#IntegerLogLookup
83
84 static const std::array<char, 256> log2TableByte = {
85 { 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
86 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
87 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
88 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
89 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
90 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
91 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
92 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
93 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 }
94 };
95
96 unsigned int result;
97 unsigned int tmp1, tmp2;
98
99 if ((tmp1 = n >> 16) != 0)
100 {
101 result = ((tmp2 = tmp1 >> 8) != 0) ? 24 + log2TableByte[tmp2] : 16 + log2TableByte[tmp1];
102 }
103 else
104 {
105 result = ((tmp2 = n >> 8) != 0) ? 8 + log2TableByte[tmp2] : log2TableByte[n];
106 }
107 return result;
108 #endif
109 }
110
111
log2I(std::uint64_t n)112 unsigned int log2I(std::uint64_t n)
113 {
114 GMX_ASSERT(n > 0, "The behavior of log(0) is undefined");
115 #if HAVE_BUILTIN_CLZLL
116 // gcc, icc, clang. xor with sign bit should be optimized out
117 return __builtin_clzll(n) ^ 63U;
118 #elif HAVE_BITSCANREVERSE64
119 unsigned long res;
120 _BitScanReverse64(&res, static_cast<unsigned __int64>(n));
121 return static_cast<unsigned int>(res);
122 #elif HAVE_CNTLZ8
123 return 63 - __cntlz8(n);
124 #else
125
126 // No 64-bit log2 instrinsic available. Solve it by calling our internal
127 // 32-bit version (which in turn might defer to a software solution)
128
129 std::uint32_t high32Bits = static_cast<std::uint32_t>(n >> 32);
130 std::uint32_t result;
131
132 if (high32Bits)
133 {
134 result = log2I(high32Bits) + 32;
135 }
136 else
137 {
138 result = log2I(static_cast<std::uint32_t>(n));
139 }
140
141 return result;
142 #endif
143 }
144
log2I(std::int32_t n)145 unsigned int log2I(std::int32_t n)
146 {
147 GMX_ASSERT(n > 0, "The behavior of log(n) for n<=0 is undefined");
148 return log2I(static_cast<std::uint32_t>(n));
149 }
150
log2I(std::int64_t n)151 unsigned int log2I(std::int64_t n)
152 {
153 GMX_ASSERT(n > 0, "The behavior of log(n) for n<=0 is undefined");
154 return log2I(static_cast<std::uint64_t>(n));
155 }
156
greatestCommonDivisor(std::int64_t p,std::int64_t q)157 std::int64_t greatestCommonDivisor(std::int64_t p, std::int64_t q)
158 {
159 while (q != 0)
160 {
161 std::int64_t tmp = q;
162 q = p % q;
163 p = tmp;
164 }
165 return p;
166 }
167
erfinv(double x)168 double erfinv(double x)
169 {
170 double xabs = std::abs(x);
171
172 if (xabs > 1.0)
173 {
174 return std::nan("");
175 }
176
177 if (x == 1.0)
178 {
179 return std::numeric_limits<double>::infinity();
180 }
181
182 if (x == -1.0)
183 {
184 return -std::numeric_limits<double>::infinity();
185 }
186
187 double res;
188
189 if (xabs <= 0.7)
190 {
191 // Rational approximation in range [0,0.7]
192 double z = x * x;
193 double P = (((-0.140543331 * z + 0.914624893) * z - 1.645349621) * z + 0.886226899);
194 double Q = ((((0.012229801 * z - 0.329097515) * z + 1.442710462) * z - 2.118377725) * z + 1.0);
195 res = x * P / Q;
196 }
197 else
198 {
199 // Rational approximation in range [0.7,1)
200 double z = std::sqrt(-std::log((1.0 - std::abs(x)) / 2.0));
201 double P = ((1.641345311 * z + 3.429567803) * z - 1.624906493) * z - 1.970840454;
202 double Q = (1.637067800 * z + 3.543889200) * z + 1.0;
203 res = std::copysign(1.0, x) * P / Q;
204 }
205
206 // Double precision requires two N-R iterations
207 res = res - (std::erf(res) - x) / ((2.0 / std::sqrt(M_PI)) * std::exp(-res * res));
208 res = res - (std::erf(res) - x) / ((2.0 / std::sqrt(M_PI)) * std::exp(-res * res));
209
210 return res;
211 }
212
erfinv(float x)213 float erfinv(float x)
214 {
215 float xabs = std::abs(x);
216
217 if (xabs > 1.0F)
218 {
219 return std::nan("");
220 }
221
222 if (x == 1.0F)
223 {
224 return std::numeric_limits<float>::infinity();
225 }
226
227 if (x == -1.0F)
228 {
229 return -std::numeric_limits<float>::infinity();
230 }
231
232 float res;
233
234 if (xabs <= 0.7F)
235 {
236 // Rational approximation in range [0,0.7]
237 float z = x * x;
238 float P = (((-0.140543331F * z + 0.914624893F) * z - 1.645349621F) * z + 0.886226899F);
239 float Q = ((((0.012229801F * z - 0.329097515F) * z + 1.442710462F) * z - 2.118377725F) * z + 1.0F);
240 res = x * P / Q;
241 }
242 else
243 {
244 // Rational approximation in range [0.7,1)
245 float z = std::sqrt(-std::log((1.0 - std::abs(x)) / 2.0F));
246 float P = ((1.641345311F * z + 3.429567803F) * z - 1.624906493F) * z - 1.970840454F;
247 float Q = (1.637067800F * z + 3.543889200F) * z + 1.0F;
248 res = std::copysign(1.0F, x) * P / Q;
249 }
250
251 // Single N-R iteration sufficient for single precision
252 res = res - (std::erf(res) - x) / ((2.0F / std::sqrt(M_PI)) * std::exp(-res * res));
253
254 return res;
255 }
256
257 } // namespace gmx
258