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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"
67 log2I(std::uint32_t n
)
69 GMX_ASSERT(n
> 0, "The behavior of log(0) is undefined");
71 // gcc, clang. xor with sign bit should be optimized out
72 return __builtin_clz(n
) ^ 31U;
73 #elif HAVE_BITSCANREVERSE
77 _BitScanReverse(&res
, static_cast<unsigned long>(n
));
78 return static_cast<unsigned int>(res
);
81 return 31 - __cntlz4(n
);
83 // http://graphics.stanford.edu/~seander/bithacks.html#IntegerLogLookup
85 static const std::array
<char, 256>
88 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
89 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
90 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
91 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
92 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
93 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
94 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
95 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
96 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
97 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
98 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
99 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
100 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
101 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
102 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
103 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
107 unsigned int tmp1
, tmp2
;
109 if ((tmp1
= n
>> 16) != 0)
111 result
= ((tmp2
= tmp1
>> 8) != 0) ? 24 + log2TableByte
[tmp2
] : 16 + log2TableByte
[tmp1
];
115 result
= ((tmp2
= n
>> 8) != 0) ? 8 + log2TableByte
[tmp2
] : log2TableByte
[n
];
123 log2I(std::uint64_t n
)
125 GMX_ASSERT(n
> 0, "The behavior of log(0) is undefined");
126 #if HAVE_BUILTIN_CLZLL
127 // gcc, icc, clang. xor with sign bit should be optimized out
128 return __builtin_clzll(n
) ^ 63U;
129 #elif HAVE_BITSCANREVERSE64
131 _BitScanReverse64(&res
, static_cast<unsigned __int64
>(n
));
132 return static_cast<unsigned int>(res
);
134 return 63 - __cntlz8(n
);
137 // No 64-bit log2 instrinsic available. Solve it by calling our internal
138 // 32-bit version (which in turn might defer to a software solution)
140 std::uint32_t high32Bits
= static_cast<std::uint32_t>(n
>>32);
141 std::uint32_t result
;
145 result
= log2I(high32Bits
) + 32;
149 result
= log2I(static_cast<std::uint32_t>(n
));
157 log2I(std::int32_t n
)
159 GMX_ASSERT(n
> 0, "The behavior of log(n) for n<=0 is undefined");
160 return log2I(static_cast<std::uint32_t>(n
));
164 log2I(std::int64_t n
)
166 GMX_ASSERT(n
> 0, "The behavior of log(n) for n<=0 is undefined");
167 return log2I(static_cast<std::uint64_t>(n
));
171 greatestCommonDivisor(std::int64_t p
,
176 std::int64_t tmp
= q
;
186 double xabs
= std::abs(x
);
195 return std::numeric_limits
<double>::infinity();
200 return -std::numeric_limits
<double>::infinity();
207 // Rational approximation in range [0,0.7]
209 double P
= (((-0.140543331 * z
+ 0.914624893) * z
- 1.645349621) * z
+ 0.886226899);
210 double Q
= ((((0.012229801 * z
- 0.329097515) * z
+ 1.442710462) * z
- 2.118377725) * z
+ 1.0);
215 // Rational approximation in range [0.7,1)
216 double z
= std::sqrt(-std::log((1.0 - std::abs(x
))/2.0));
217 double P
= ((1.641345311 * z
+ 3.429567803) * z
- 1.624906493) * z
- 1.970840454;
218 double Q
= (1.637067800 * z
+ 3.543889200) * z
+ 1.0;
219 res
= std::copysign(1.0, x
) * P
/Q
;
222 // Double precision requires two N-R iterations
223 res
= res
- (std::erf(res
) - x
)/( (2.0/std::sqrt(M_PI
))*std::exp(-res
*res
));
224 res
= res
- (std::erf(res
) - x
)/( (2.0/std::sqrt(M_PI
))*std::exp(-res
*res
));
232 float xabs
= std::abs(x
);
241 return std::numeric_limits
<float>::infinity();
246 return -std::numeric_limits
<float>::infinity();
253 // Rational approximation in range [0,0.7]
255 float P
= (((-0.140543331F
* z
+ 0.914624893F
) * z
- 1.645349621F
) * z
+ 0.886226899F
);
256 float Q
= ((((0.012229801F
* z
- 0.329097515F
) * z
+ 1.442710462F
) * z
- 2.118377725F
) * z
+ 1.0F
);
261 // Rational approximation in range [0.7,1)
262 float z
= std::sqrt(-std::log((1.0 - std::abs(x
))/2.0F
));
263 float P
= ((1.641345311F
* z
+ 3.429567803F
) * z
- 1.624906493F
) * z
- 1.970840454F
;
264 float Q
= (1.637067800F
* z
+ 3.543889200F
) * z
+ 1.0F
;
265 res
= std::copysign(1.0F
, x
) * P
/Q
;
268 // Single N-R iteration sufficient for single precision
269 res
= res
- (std::erf(res
) - x
)/( (2.0F
/std::sqrt(M_PI
))*std::exp(-res
*res
));