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39 * Implements simple math functions
41 * \author Erik Lindahl <erik.lindahl@gmail.com>
42 * \ingroup module_math
47 #include "functions.h"
56 #if GMX_NATIVE_WINDOWS
57 # include <intrin.h> // _BitScanReverse, _BitScanReverse64
60 #include "gromacs/math/utilities.h"
61 #include "gromacs/utility/gmxassert.h"
66 unsigned int log2I(std::uint32_t n)
68 GMX_ASSERT(n > 0, "The behavior of log(0) is undefined");
70 // gcc, clang. xor with sign bit should be optimized out
71 return __builtin_clz(n) ^ 31U;
72 #elif HAVE_BITSCANREVERSE
76 _BitScanReverse(&res, static_cast<unsigned long>(n));
77 return static_cast<unsigned int>(res);
80 return 31 - __cntlz4(n);
82 // http://graphics.stanford.edu/~seander/bithacks.html#IntegerLogLookup
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 }
97 unsigned int tmp1, tmp2;
99 if ((tmp1 = n >> 16) != 0)
101 result = ((tmp2 = tmp1 >> 8) != 0) ? 24 + log2TableByte[tmp2] : 16 + log2TableByte[tmp1];
105 result = ((tmp2 = n >> 8) != 0) ? 8 + log2TableByte[tmp2] : log2TableByte[n];
112 unsigned int log2I(std::uint64_t n)
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
120 _BitScanReverse64(&res, static_cast<unsigned __int64>(n));
121 return static_cast<unsigned int>(res);
123 return 63 - __cntlz8(n);
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)
129 std::uint32_t high32Bits = static_cast<std::uint32_t>(n >> 32);
130 std::uint32_t result;
134 result = log2I(high32Bits) + 32;
138 result = log2I(static_cast<std::uint32_t>(n));
145 unsigned int log2I(std::int32_t n)
147 GMX_ASSERT(n > 0, "The behavior of log(n) for n<=0 is undefined");
148 return log2I(static_cast<std::uint32_t>(n));
151 unsigned int log2I(std::int64_t n)
153 GMX_ASSERT(n > 0, "The behavior of log(n) for n<=0 is undefined");
154 return log2I(static_cast<std::uint64_t>(n));
157 std::int64_t greatestCommonDivisor(std::int64_t p, std::int64_t q)
161 std::int64_t tmp = q;
168 double erfinv(double x)
170 double xabs = std::abs(x);
179 return std::numeric_limits<double>::infinity();
184 return -std::numeric_limits<double>::infinity();
191 // Rational approximation in range [0,0.7]
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);
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;
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));
213 float erfinv(float x)
215 float xabs = std::abs(x);
224 return std::numeric_limits<float>::infinity();
229 return -std::numeric_limits<float>::infinity();
236 // Rational approximation in range [0,0.7]
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);
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;
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));