OpenTTD Source  20241120-master-g6d3adc6169
math_func.hpp
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5  * See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with OpenTTD. If not, see <http://www.gnu.org/licenses/>.
6  */
7 
10 #ifndef MATH_FUNC_HPP
11 #define MATH_FUNC_HPP
12 
13 #include "strong_typedef_type.hpp"
14 
22 template <typename T>
23 constexpr T abs(const T a)
24 {
25  return (a < static_cast<T>(0)) ? -a : a;
26 }
27 
36 template <typename T>
37 constexpr T Align(const T x, uint n)
38 {
39  assert((n & (n - 1)) == 0 && n != 0);
40  n--;
41  return static_cast<T>((x + n) & ~static_cast<T>(n));
42 }
43 
54 template <typename T>
55 constexpr T *AlignPtr(T *x, uint n)
56 {
57  static_assert(sizeof(uintptr_t) == sizeof(void *));
58  return reinterpret_cast<T *>(Align(reinterpret_cast<uintptr_t>(x), n));
59 }
60 
78 template <typename T>
79 constexpr T Clamp(const T a, const T min, const T max)
80 {
81  assert(min <= max);
82  if (a <= min) return min;
83  if (a >= max) return max;
84  return a;
85 }
86 
101 template <typename T>
102 constexpr T SoftClamp(const T a, const T min, const T max)
103 {
104  if (min > max) {
105  using U = std::make_unsigned_t<T>;
106  return min - (U(min) - max) / 2;
107  }
108  if (a <= min) return min;
109  if (a >= max) return max;
110  return a;
111 }
112 
129 constexpr int Clamp(const int a, const int min, const int max)
130 {
131  return Clamp<int>(a, min, max);
132 }
133 
150 constexpr uint ClampU(const uint a, const uint min, const uint max)
151 {
152  return Clamp<uint>(a, min, max);
153 }
154 
166 template <typename To, typename From, std::enable_if_t<std::is_integral<From>::value, int> = 0>
167 constexpr To ClampTo(From value)
168 {
169  static_assert(std::numeric_limits<To>::is_integer, "Do not clamp from non-integer values");
170  static_assert(std::numeric_limits<From>::is_integer, "Do not clamp to non-integer values");
171 
172  if constexpr (sizeof(To) >= sizeof(From) && std::numeric_limits<To>::is_signed == std::numeric_limits<From>::is_signed) {
173  /* Same signedness and To type is larger or equal than From type, no clamping is required. */
174  return static_cast<To>(value);
175  }
176 
177  if constexpr (sizeof(To) > sizeof(From) && std::numeric_limits<To>::is_signed) {
178  /* Signed destination and a larger To type, no clamping is required. */
179  return static_cast<To>(value);
180  }
181 
182  /* Get the bigger of the two types based on essentially the number of bits. */
183  using BiggerType = typename std::conditional<sizeof(From) >= sizeof(To), From, To>::type;
184 
185  if constexpr (std::numeric_limits<To>::is_signed) {
186  /* The output is a signed number. */
187  if constexpr (std::numeric_limits<From>::is_signed) {
188  /* Both input and output are signed. */
189  return static_cast<To>(std::clamp<BiggerType>(value,
190  std::numeric_limits<To>::lowest(), std::numeric_limits<To>::max()));
191  }
192 
193  /* The input is unsigned, so skip the minimum check and use unsigned variant of the biggest type as intermediate type. */
194  using BiggerUnsignedType = typename std::make_unsigned<BiggerType>::type;
195  return static_cast<To>(std::min<BiggerUnsignedType>(std::numeric_limits<To>::max(), value));
196  }
197 
198  /* The output is unsigned. */
199 
200  if constexpr (std::numeric_limits<From>::is_signed) {
201  /* Input is signed; account for the negative numbers in the input. */
202  if constexpr (sizeof(To) >= sizeof(From)) {
203  /* If the output type is larger or equal to the input type, then only clamp the negative numbers. */
204  return static_cast<To>(std::max<From>(value, 0));
205  }
206 
207  /* The output type is smaller than the input type. */
208  using BiggerSignedType = typename std::make_signed<BiggerType>::type;
209  return static_cast<To>(std::clamp<BiggerSignedType>(value,
210  std::numeric_limits<To>::lowest(), std::numeric_limits<To>::max()));
211  }
212 
213  /* The input and output are unsigned, just clamp at the high side. */
214  return static_cast<To>(std::min<BiggerType>(value, std::numeric_limits<To>::max()));
215 }
216 
220 template <typename To, typename From, std::enable_if_t<std::is_base_of<StrongTypedefBase, From>::value, int> = 0>
221 constexpr To ClampTo(From value)
222 {
223  return ClampTo<To>(value.base());
224 }
225 
233 template <typename T>
234 constexpr T Delta(const T a, const T b)
235 {
236  return (a < b) ? b - a : a - b;
237 }
238 
251 template <typename T>
252 constexpr bool IsInsideBS(const T x, const size_t base, const size_t size)
253 {
254  return static_cast<size_t>(x - base) < size;
255 }
256 
267 template <typename T, std::enable_if_t<std::disjunction_v<std::is_convertible<T, size_t>, std::is_base_of<StrongTypedefBase, T>>, int> = 0>
268 constexpr bool IsInsideMM(const T x, const size_t min, const size_t max) noexcept
269 {
270  if constexpr (std::is_base_of_v<StrongTypedefBase, T>) {
271  return static_cast<size_t>(x.base() - min) < (max - min);
272  } else {
273  return static_cast<size_t>(x - min) < (max - min);
274  }
275 }
276 
282 template <typename T>
283 constexpr void Swap(T &a, T &b)
284 {
285  T t = a;
286  a = b;
287  b = t;
288 }
289 
295 constexpr uint ToPercent8(uint i)
296 {
297  assert(i < 256);
298  return i * 101 >> 8;
299 }
300 
306 constexpr uint ToPercent16(uint i)
307 {
308  assert(i < 65536);
309  return i * 101 >> 16;
310 }
311 
312 int DivideApprox(int a, int b);
313 
320 constexpr uint CeilDiv(uint a, uint b)
321 {
322  return (a + b - 1) / b;
323 }
324 
331 constexpr uint Ceil(uint a, uint b)
332 {
333  return CeilDiv(a, b) * b;
334 }
335 
342 constexpr int RoundDivSU(int a, uint b)
343 {
344  if (a > 0) {
345  /* 0.5 is rounded to 1 */
346  return (a + static_cast<int>(b) / 2) / static_cast<int>(b);
347  } else {
348  /* -0.5 is rounded to 0 */
349  return (a - (static_cast<int>(b) - 1) / 2) / static_cast<int>(b);
350  }
351 }
352 
358 constexpr uint64_t PowerOfTen(int power)
359 {
360  assert(power >= 0 && power <= 20 /* digits in uint64_t */);
361  uint64_t result = 1;
362  for (int i = 0; i < power; i++) result *= 10;
363  return result;
364 }
365 
366 uint32_t IntSqrt(uint32_t num);
367 
368 #endif /* MATH_FUNC_HPP */
constexpr bool IsInsideBS(const T x, const size_t base, const size_t size)
Checks if a value is between a window started at some base point.
Definition: math_func.hpp:252
int DivideApprox(int a, int b)
Deterministic approximate division.
Definition: math_func.cpp:22
constexpr uint ToPercent16(uint i)
Converts a "fract" value 0..65535 to "percent" value 0..100.
Definition: math_func.hpp:306
constexpr T abs(const T a)
Returns the absolute value of (scalar) variable.
Definition: math_func.hpp:23
constexpr uint64_t PowerOfTen(int power)
Computes ten to the given power.
Definition: math_func.hpp:358
constexpr T Align(const T x, uint n)
Return the smallest multiple of n equal or greater than x.
Definition: math_func.hpp:37
uint32_t IntSqrt(uint32_t num)
Compute the integer square root.
Definition: math_func.cpp:42
constexpr int RoundDivSU(int a, uint b)
Computes round(a / b) for signed a and unsigned b.
Definition: math_func.hpp:342
constexpr T SoftClamp(const T a, const T min, const T max)
Clamp a value between an interval.
Definition: math_func.hpp:102
constexpr uint CeilDiv(uint a, uint b)
Computes ceil(a / b) for non-negative a and b.
Definition: math_func.hpp:320
constexpr T Delta(const T a, const T b)
Returns the (absolute) difference between two (scalar) variables.
Definition: math_func.hpp:234
constexpr uint ToPercent8(uint i)
Converts a "fract" value 0..255 to "percent" value 0..100.
Definition: math_func.hpp:295
constexpr uint Ceil(uint a, uint b)
Computes ceil(a / b) * b for non-negative a and b.
Definition: math_func.hpp:331
constexpr T Clamp(const T a, const T min, const T max)
Clamp a value between an interval.
Definition: math_func.hpp:79
constexpr uint ClampU(const uint a, const uint min, const uint max)
Clamp an unsigned integer between an interval.
Definition: math_func.hpp:150
constexpr T * AlignPtr(T *x, uint n)
Return the smallest multiple of n equal or greater than x Applies to pointers only.
Definition: math_func.hpp:55
constexpr To ClampTo(From value)
Clamp the given value down to lie within the requested type.
Definition: math_func.hpp:167
constexpr bool IsInsideMM(const T x, const size_t min, const size_t max) noexcept
Checks if a value is in an interval.
Definition: math_func.hpp:268
constexpr void Swap(T &a, T &b)
Type safe swap operation.
Definition: math_func.hpp:283
Type (helpers) for making a strong typedef that is a distinct type.