1// <numeric> -*- C++ -*- 2 3// Copyright (C) 2001-2022 Free Software Foundation, Inc. 4// 5// This file is part of the GNU ISO C++ Library. This library is free 6// software; you can redistribute it and/or modify it under the 7// terms of the GNU General Public License as published by the 8// Free Software Foundation; either version 3, or (at your option) 9// any later version. 10 11// This library is distributed in the hope that it will be useful, 12// but WITHOUT ANY WARRANTY; without even the implied warranty of 13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14// GNU General Public License for more details. 15 16// Under Section 7 of GPL version 3, you are granted additional 17// permissions described in the GCC Runtime Library Exception, version 18// 3.1, as published by the Free Software Foundation. 19 20// You should have received a copy of the GNU General Public License and 21// a copy of the GCC Runtime Library Exception along with this program; 22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23// <http://www.gnu.org/licenses/>. 24 25/* 26 * 27 * Copyright (c) 1994 28 * Hewlett-Packard Company 29 * 30 * Permission to use, copy, modify, distribute and sell this software 31 * and its documentation for any purpose is hereby granted without fee, 32 * provided that the above copyright notice appear in all copies and 33 * that both that copyright notice and this permission notice appear 34 * in supporting documentation. Hewlett-Packard Company makes no 35 * representations about the suitability of this software for any 36 * purpose. It is provided "as is" without express or implied warranty. 37 * 38 * 39 * Copyright (c) 1996,1997 40 * Silicon Graphics Computer Systems, Inc. 41 * 42 * Permission to use, copy, modify, distribute and sell this software 43 * and its documentation for any purpose is hereby granted without fee, 44 * provided that the above copyright notice appear in all copies and 45 * that both that copyright notice and this permission notice appear 46 * in supporting documentation. Silicon Graphics makes no 47 * representations about the suitability of this software for any 48 * purpose. It is provided "as is" without express or implied warranty. 49 */ 50 51/** @file include/numeric 52 * This is a Standard C++ Library header. 53 */ 54 55#ifndef _GLIBCXX_NUMERIC 56#define _GLIBCXX_NUMERIC 1 57 58#pragma GCC system_header 59 60#include <bits/c++config.h> 61#include <bits/stl_iterator_base_types.h> 62#include <bits/stl_numeric.h> 63 64#ifdef _GLIBCXX_PARALLEL 65# include <parallel/numeric> 66#endif 67 68#if __cplusplus >= 201402L 69# include <type_traits> 70# include <bit> 71# include <ext/numeric_traits.h> 72#endif 73 74#if __cplusplus >= 201703L 75# include <bits/stl_function.h> 76#endif 77 78#if __cplusplus > 201703L 79# include <limits> 80#endif 81 82/** 83 * @defgroup numerics Numerics 84 * 85 * Components for performing numeric operations. Includes support for 86 * complex number types, random number generation, numeric (n-at-a-time) 87 * arrays, generalized numeric algorithms, and mathematical special functions. 88 */ 89 90namespace std _GLIBCXX_VISIBILITY(default) 91{ 92_GLIBCXX_BEGIN_NAMESPACE_VERSION 93 94#if __cplusplus >= 201402L 95namespace __detail 96{ 97 // Like std::abs, but supports unsigned types and returns the specified type, 98 // so |std::numeric_limits<_Tp>::min()| is OK if representable in _Res. 99 template<typename _Res, typename _Tp> 100 constexpr _Res 101 __abs_r(_Tp __val) 102 { 103 static_assert(sizeof(_Res) >= sizeof(_Tp), 104 "result type must be at least as wide as the input type"); 105 106 if (__val >= 0) 107 return __val; 108#ifdef _GLIBCXX_ASSERTIONS 109 if (!__is_constant_evaluated()) // overflow already detected in constexpr 110 __glibcxx_assert(__val != __gnu_cxx::__int_traits<_Res>::__min); 111#endif 112 return -static_cast<_Res>(__val); 113 } 114 115 template<typename> void __abs_r(bool) = delete; 116 117 // GCD implementation, using Stein's algorithm 118 template<typename _Tp> 119 constexpr _Tp 120 __gcd(_Tp __m, _Tp __n) 121 { 122 static_assert(is_unsigned<_Tp>::value, "type must be unsigned"); 123 124 if (__m == 0) 125 return __n; 126 if (__n == 0) 127 return __m; 128 129 const int __i = std::__countr_zero(__m); 130 __m >>= __i; 131 const int __j = std::__countr_zero(__n); 132 __n >>= __j; 133 const int __k = __i < __j ? __i : __j; // min(i, j) 134 135 while (true) 136 { 137 if (__m > __n) 138 { 139 _Tp __tmp = __m; 140 __m = __n; 141 __n = __tmp; 142 } 143 144 __n -= __m; 145 146 if (__n == 0) 147 return __m << __k; 148 149 __n >>= std::__countr_zero(__n); 150 } 151 } 152} // namespace __detail 153 154#if __cplusplus >= 201703L 155 156#define __cpp_lib_gcd_lcm 201606L 157// These were used in drafts of SD-6: 158#define __cpp_lib_gcd 201606L 159#define __cpp_lib_lcm 201606L 160 161 /// Greatest common divisor 162 template<typename _Mn, typename _Nn> 163 constexpr common_type_t<_Mn, _Nn> 164 gcd(_Mn __m, _Nn __n) noexcept 165 { 166 static_assert(is_integral_v<_Mn> && is_integral_v<_Nn>, 167 "std::gcd arguments must be integers"); 168 static_assert(_Mn(2) == 2 && _Nn(2) == 2, 169 "std::gcd arguments must not be bool"); 170 using _Ct = common_type_t<_Mn, _Nn>; 171 const _Ct __m2 = __detail::__abs_r<_Ct>(__m); 172 const _Ct __n2 = __detail::__abs_r<_Ct>(__n); 173 return __detail::__gcd<make_unsigned_t<_Ct>>(__m2, __n2); 174 } 175 176 /// Least common multiple 177 template<typename _Mn, typename _Nn> 178 constexpr common_type_t<_Mn, _Nn> 179 lcm(_Mn __m, _Nn __n) noexcept 180 { 181 static_assert(is_integral_v<_Mn> && is_integral_v<_Nn>, 182 "std::lcm arguments must be integers"); 183 static_assert(_Mn(2) == 2 && _Nn(2) == 2, 184 "std::lcm arguments must not be bool"); 185 using _Ct = common_type_t<_Mn, _Nn>; 186 const _Ct __m2 = __detail::__abs_r<_Ct>(__m); 187 const _Ct __n2 = __detail::__abs_r<_Ct>(__n); 188 if (__m2 == 0 || __n2 == 0) 189 return 0; 190 _Ct __r = __m2 / __detail::__gcd<make_unsigned_t<_Ct>>(__m2, __n2); 191 192 if constexpr (is_signed_v<_Ct>) 193 if (__is_constant_evaluated()) 194 return __r * __n2; // constant evaluation can detect overflow here. 195 196 bool __overflow = __builtin_mul_overflow(__r, __n2, &__r); 197 __glibcxx_assert(!__overflow); 198 return __r; 199 } 200 201#endif // C++17 202#endif // C++14 203 204#if __cplusplus > 201703L 205 206 // midpoint 207# define __cpp_lib_interpolate 201902L 208 209 template<typename _Tp> 210 constexpr 211 enable_if_t<__and_v<is_arithmetic<_Tp>, is_same<remove_cv_t<_Tp>, _Tp>, 212 __not_<is_same<_Tp, bool>>>, 213 _Tp> 214 midpoint(_Tp __a, _Tp __b) noexcept 215 { 216 if constexpr (is_integral_v<_Tp>) 217 { 218 using _Up = make_unsigned_t<_Tp>; 219 220 int __k = 1; 221 _Up __m = __a; 222 _Up __M = __b; 223 if (__a > __b) 224 { 225 __k = -1; 226 __m = __b; 227 __M = __a; 228 } 229 return __a + __k * _Tp(_Up(__M - __m) / 2); 230 } 231 else // is_floating 232 { 233 constexpr _Tp __lo = numeric_limits<_Tp>::min() * 2; 234 constexpr _Tp __hi = numeric_limits<_Tp>::max() / 2; 235 const _Tp __abs_a = __a < 0 ? -__a : __a; 236 const _Tp __abs_b = __b < 0 ? -__b : __b; 237 if (__abs_a <= __hi && __abs_b <= __hi) [[likely]] 238 return (__a + __b) / 2; // always correctly rounded 239 if (__abs_a < __lo) // not safe to halve __a 240 return __a + __b/2; 241 if (__abs_b < __lo) // not safe to halve __b 242 return __a/2 + __b; 243 return __a/2 + __b/2; // otherwise correctly rounded 244 } 245 } 246 247 template<typename _Tp> 248 constexpr enable_if_t<is_object_v<_Tp>, _Tp*> 249 midpoint(_Tp* __a, _Tp* __b) noexcept 250 { 251 static_assert( sizeof(_Tp) != 0, "type must be complete" ); 252 return __a + (__b - __a) / 2; 253 } 254#endif // C++20 255 256#if __cplusplus >= 201703L 257 258#if __cplusplus > 201703L 259#define __cpp_lib_constexpr_numeric 201911L 260#endif 261 262 /// @addtogroup numeric_ops 263 /// @{ 264 265 /** 266 * @brief Calculate reduction of values in a range. 267 * 268 * @param __first Start of range. 269 * @param __last End of range. 270 * @param __init Starting value to add other values to. 271 * @param __binary_op A binary function object. 272 * @return The final sum. 273 * 274 * Reduce the values in the range `[first,last)` using a binary operation. 275 * The initial value is `init`. The values are not necessarily processed 276 * in order. 277 * 278 * This algorithm is similar to `std::accumulate` but is not required to 279 * perform the operations in order from first to last. For operations 280 * that are commutative and associative the result will be the same as 281 * for `std::accumulate`, but for other operations (such as floating point 282 * arithmetic) the result can be different. 283 */ 284 template<typename _InputIterator, typename _Tp, typename _BinaryOperation> 285 _GLIBCXX20_CONSTEXPR 286 _Tp 287 reduce(_InputIterator __first, _InputIterator __last, _Tp __init, 288 _BinaryOperation __binary_op) 289 { 290 using __ref = typename iterator_traits<_InputIterator>::reference; 291 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, __ref>); 292 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, __ref, _Tp&>); 293 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, _Tp&>); 294 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, __ref, __ref>); 295 if constexpr (__is_random_access_iter<_InputIterator>::value) 296 { 297 while ((__last - __first) >= 4) 298 { 299 _Tp __v1 = __binary_op(__first[0], __first[1]); 300 _Tp __v2 = __binary_op(__first[2], __first[3]); 301 _Tp __v3 = __binary_op(__v1, __v2); 302 __init = __binary_op(__init, __v3); 303 __first += 4; 304 } 305 } 306 for (; __first != __last; ++__first) 307 __init = __binary_op(__init, *__first); 308 return __init; 309 } 310 311 /** 312 * @brief Calculate reduction of values in a range. 313 * 314 * @param __first Start of range. 315 * @param __last End of range. 316 * @param __init Starting value to add other values to. 317 * @return The final sum. 318 * 319 * Reduce the values in the range `[first,last)` using addition. 320 * Equivalent to calling `std::reduce(first, last, init, std::plus<>())`. 321 */ 322 template<typename _InputIterator, typename _Tp> 323 _GLIBCXX20_CONSTEXPR 324 inline _Tp 325 reduce(_InputIterator __first, _InputIterator __last, _Tp __init) 326 { return std::reduce(__first, __last, std::move(__init), plus<>()); } 327 328 /** 329 * @brief Calculate reduction of values in a range. 330 * 331 * @param __first Start of range. 332 * @param __last End of range. 333 * @return The final sum. 334 * 335 * Reduce the values in the range `[first,last)` using addition, with 336 * an initial value of `T{}`, where `T` is the iterator's value type. 337 * Equivalent to calling `std::reduce(first, last, T{}, std::plus<>())`. 338 */ 339 template<typename _InputIterator> 340 _GLIBCXX20_CONSTEXPR 341 inline typename iterator_traits<_InputIterator>::value_type 342 reduce(_InputIterator __first, _InputIterator __last) 343 { 344 using value_type = typename iterator_traits<_InputIterator>::value_type; 345 return std::reduce(__first, __last, value_type{}, plus<>()); 346 } 347 348 /** 349 * @brief Combine elements from two ranges and reduce 350 * 351 * @param __first1 Start of first range. 352 * @param __last1 End of first range. 353 * @param __first2 Start of second range. 354 * @param __init Starting value to add other values to. 355 * @param __binary_op1 The function used to perform reduction. 356 * @param __binary_op2 The function used to combine values from the ranges. 357 * @return The final sum. 358 * 359 * Call `binary_op2(first1[n],first2[n])` for each `n` in `[0,last1-first1)` 360 * and then use `binary_op1` to reduce the values returned by `binary_op2` 361 * to a single value of type `T`. 362 * 363 * The range beginning at `first2` must contain at least `last1-first1` 364 * elements. 365 */ 366 template<typename _InputIterator1, typename _InputIterator2, typename _Tp, 367 typename _BinaryOperation1, typename _BinaryOperation2> 368 _GLIBCXX20_CONSTEXPR 369 _Tp 370 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, 371 _InputIterator2 __first2, _Tp __init, 372 _BinaryOperation1 __binary_op1, 373 _BinaryOperation2 __binary_op2) 374 { 375 if constexpr (__and_v<__is_random_access_iter<_InputIterator1>, 376 __is_random_access_iter<_InputIterator2>>) 377 { 378 while ((__last1 - __first1) >= 4) 379 { 380 _Tp __v1 = __binary_op1(__binary_op2(__first1[0], __first2[0]), 381 __binary_op2(__first1[1], __first2[1])); 382 _Tp __v2 = __binary_op1(__binary_op2(__first1[2], __first2[2]), 383 __binary_op2(__first1[3], __first2[3])); 384 _Tp __v3 = __binary_op1(__v1, __v2); 385 __init = __binary_op1(__init, __v3); 386 __first1 += 4; 387 __first2 += 4; 388 } 389 } 390 for (; __first1 != __last1; ++__first1, (void) ++__first2) 391 __init = __binary_op1(__init, __binary_op2(*__first1, *__first2)); 392 return __init; 393 } 394 395 /** 396 * @brief Combine elements from two ranges and reduce 397 * 398 * @param __first1 Start of first range. 399 * @param __last1 End of first range. 400 * @param __first2 Start of second range. 401 * @param __init Starting value to add other values to. 402 * @return The final sum. 403 * 404 * Call `first1[n]*first2[n]` for each `n` in `[0,last1-first1)` and then 405 * use addition to sum those products to a single value of type `T`. 406 * 407 * The range beginning at `first2` must contain at least `last1-first1` 408 * elements. 409 */ 410 template<typename _InputIterator1, typename _InputIterator2, typename _Tp> 411 _GLIBCXX20_CONSTEXPR 412 inline _Tp 413 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, 414 _InputIterator2 __first2, _Tp __init) 415 { 416 return std::transform_reduce(__first1, __last1, __first2, 417 std::move(__init), 418 plus<>(), multiplies<>()); 419 } 420 421 /** 422 * @brief Transform the elements of a range and reduce 423 * 424 * @param __first Start of range. 425 * @param __last End of range. 426 * @param __init Starting value to add other values to. 427 * @param __binary_op The function used to perform reduction. 428 * @param __unary_op The function used to transform values from the range. 429 * @return The final sum. 430 * 431 * Call `unary_op(first[n])` for each `n` in `[0,last-first)` and then 432 * use `binary_op` to reduce the values returned by `unary_op` 433 * to a single value of type `T`. 434 */ 435 template<typename _InputIterator, typename _Tp, 436 typename _BinaryOperation, typename _UnaryOperation> 437 _GLIBCXX20_CONSTEXPR 438 _Tp 439 transform_reduce(_InputIterator __first, _InputIterator __last, _Tp __init, 440 _BinaryOperation __binary_op, _UnaryOperation __unary_op) 441 { 442 if constexpr (__is_random_access_iter<_InputIterator>::value) 443 { 444 while ((__last - __first) >= 4) 445 { 446 _Tp __v1 = __binary_op(__unary_op(__first[0]), 447 __unary_op(__first[1])); 448 _Tp __v2 = __binary_op(__unary_op(__first[2]), 449 __unary_op(__first[3])); 450 _Tp __v3 = __binary_op(__v1, __v2); 451 __init = __binary_op(__init, __v3); 452 __first += 4; 453 } 454 } 455 for (; __first != __last; ++__first) 456 __init = __binary_op(__init, __unary_op(*__first)); 457 return __init; 458 } 459 460 /** @brief Output the cumulative sum of one range to a second range 461 * 462 * @param __first Start of input range. 463 * @param __last End of input range. 464 * @param __result Start of output range. 465 * @param __init Initial value. 466 * @param __binary_op Function to perform summation. 467 * @return The end of the output range. 468 * 469 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 470 * to the output range. Each element of the output range contains the 471 * running total of all earlier elements (and the initial value), 472 * using `binary_op` for summation. 473 * 474 * This function generates an "exclusive" scan, meaning the Nth element 475 * of the output range is the sum of the first N-1 input elements, 476 * so the Nth input element is not included. 477 */ 478 template<typename _InputIterator, typename _OutputIterator, typename _Tp, 479 typename _BinaryOperation> 480 _GLIBCXX20_CONSTEXPR 481 _OutputIterator 482 exclusive_scan(_InputIterator __first, _InputIterator __last, 483 _OutputIterator __result, _Tp __init, 484 _BinaryOperation __binary_op) 485 { 486 while (__first != __last) 487 { 488 auto __v = __init; 489 __init = __binary_op(__init, *__first); 490 ++__first; 491 *__result++ = std::move(__v); 492 } 493 return __result; 494 } 495 496 /** @brief Output the cumulative sum of one range to a second range 497 * 498 * @param __first Start of input range. 499 * @param __last End of input range. 500 * @param __result Start of output range. 501 * @param __init Initial value. 502 * @return The end of the output range. 503 * 504 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 505 * to the output range. Each element of the output range contains the 506 * running total of all earlier elements (and the initial value), 507 * using `std::plus<>` for summation. 508 * 509 * This function generates an "exclusive" scan, meaning the Nth element 510 * of the output range is the sum of the first N-1 input elements, 511 * so the Nth input element is not included. 512 */ 513 template<typename _InputIterator, typename _OutputIterator, typename _Tp> 514 _GLIBCXX20_CONSTEXPR 515 inline _OutputIterator 516 exclusive_scan(_InputIterator __first, _InputIterator __last, 517 _OutputIterator __result, _Tp __init) 518 { 519 return std::exclusive_scan(__first, __last, __result, std::move(__init), 520 plus<>()); 521 } 522 523 /** @brief Output the cumulative sum of one range to a second range 524 * 525 * @param __first Start of input range. 526 * @param __last End of input range. 527 * @param __result Start of output range. 528 * @param __binary_op Function to perform summation. 529 * @param __init Initial value. 530 * @return The end of the output range. 531 * 532 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 533 * to the output range. Each element of the output range contains the 534 * running total of all earlier elements (and the initial value), 535 * using `binary_op` for summation. 536 * 537 * This function generates an "inclusive" scan, meaning the Nth element 538 * of the output range is the sum of the first N input elements, 539 * so the Nth input element is included. 540 */ 541 template<typename _InputIterator, typename _OutputIterator, 542 typename _BinaryOperation, typename _Tp> 543 _GLIBCXX20_CONSTEXPR 544 _OutputIterator 545 inclusive_scan(_InputIterator __first, _InputIterator __last, 546 _OutputIterator __result, _BinaryOperation __binary_op, 547 _Tp __init) 548 { 549 for (; __first != __last; ++__first) 550 *__result++ = __init = __binary_op(__init, *__first); 551 return __result; 552 } 553 554 /** @brief Output the cumulative sum of one range to a second range 555 * 556 * @param __first Start of input range. 557 * @param __last End of input range. 558 * @param __result Start of output range. 559 * @param __binary_op Function to perform summation. 560 * @return The end of the output range. 561 * 562 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 563 * to the output range. Each element of the output range contains the 564 * running total of all earlier elements, using `binary_op` for summation. 565 * 566 * This function generates an "inclusive" scan, meaning the Nth element 567 * of the output range is the sum of the first N input elements, 568 * so the Nth input element is included. 569 */ 570 template<typename _InputIterator, typename _OutputIterator, 571 typename _BinaryOperation> 572 _GLIBCXX20_CONSTEXPR 573 _OutputIterator 574 inclusive_scan(_InputIterator __first, _InputIterator __last, 575 _OutputIterator __result, _BinaryOperation __binary_op) 576 { 577 if (__first != __last) 578 { 579 auto __init = *__first; 580 *__result++ = __init; 581 ++__first; 582 if (__first != __last) 583 __result = std::inclusive_scan(__first, __last, __result, 584 __binary_op, std::move(__init)); 585 } 586 return __result; 587 } 588 589 /** @brief Output the cumulative sum of one range to a second range 590 * 591 * @param __first Start of input range. 592 * @param __last End of input range. 593 * @param __result Start of output range. 594 * @return The end of the output range. 595 * 596 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 597 * to the output range. Each element of the output range contains the 598 * running total of all earlier elements, using `std::plus<>` for summation. 599 * 600 * This function generates an "inclusive" scan, meaning the Nth element 601 * of the output range is the sum of the first N input elements, 602 * so the Nth input element is included. 603 */ 604 template<typename _InputIterator, typename _OutputIterator> 605 _GLIBCXX20_CONSTEXPR 606 inline _OutputIterator 607 inclusive_scan(_InputIterator __first, _InputIterator __last, 608 _OutputIterator __result) 609 { return std::inclusive_scan(__first, __last, __result, plus<>()); } 610 611 /** @brief Output the cumulative sum of one range to a second range 612 * 613 * @param __first Start of input range. 614 * @param __last End of input range. 615 * @param __result Start of output range. 616 * @param __init Initial value. 617 * @param __binary_op Function to perform summation. 618 * @param __unary_op Function to transform elements of the input range. 619 * @return The end of the output range. 620 * 621 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 622 * to the output range. Each element of the output range contains the 623 * running total of all earlier elements (and the initial value), 624 * using `__unary_op` to transform the input elements 625 * and using `__binary_op` for summation. 626 * 627 * This function generates an "exclusive" scan, meaning the Nth element 628 * of the output range is the sum of the first N-1 input elements, 629 * so the Nth input element is not included. 630 */ 631 template<typename _InputIterator, typename _OutputIterator, typename _Tp, 632 typename _BinaryOperation, typename _UnaryOperation> 633 _GLIBCXX20_CONSTEXPR 634 _OutputIterator 635 transform_exclusive_scan(_InputIterator __first, _InputIterator __last, 636 _OutputIterator __result, _Tp __init, 637 _BinaryOperation __binary_op, 638 _UnaryOperation __unary_op) 639 { 640 while (__first != __last) 641 { 642 auto __v = __init; 643 __init = __binary_op(__init, __unary_op(*__first)); 644 ++__first; 645 *__result++ = std::move(__v); 646 } 647 return __result; 648 } 649 650 /** @brief Output the cumulative sum of one range to a second range 651 * 652 * @param __first Start of input range. 653 * @param __last End of input range. 654 * @param __result Start of output range. 655 * @param __binary_op Function to perform summation. 656 * @param __unary_op Function to transform elements of the input range. 657 * @param __init Initial value. 658 * @return The end of the output range. 659 * 660 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 661 * to the output range. Each element of the output range contains the 662 * running total of all earlier elements (and the initial value), 663 * using `__unary_op` to transform the input elements 664 * and using `__binary_op` for summation. 665 * 666 * This function generates an "inclusive" scan, meaning the Nth element 667 * of the output range is the sum of the first N input elements, 668 * so the Nth input element is included. 669 */ 670 template<typename _InputIterator, typename _OutputIterator, 671 typename _BinaryOperation, typename _UnaryOperation, typename _Tp> 672 _GLIBCXX20_CONSTEXPR 673 _OutputIterator 674 transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 675 _OutputIterator __result, 676 _BinaryOperation __binary_op, 677 _UnaryOperation __unary_op, 678 _Tp __init) 679 { 680 for (; __first != __last; ++__first) 681 *__result++ = __init = __binary_op(__init, __unary_op(*__first)); 682 return __result; 683 } 684 685 /** @brief Output the cumulative sum of one range to a second range 686 * 687 * @param __first Start of input range. 688 * @param __last End of input range. 689 * @param __result Start of output range. 690 * @param __binary_op Function to perform summation. 691 * @param __unary_op Function to transform elements of the input range. 692 * @return The end of the output range. 693 * 694 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 695 * to the output range. Each element of the output range contains the 696 * running total of all earlier elements, 697 * using `__unary_op` to transform the input elements 698 * and using `__binary_op` for summation. 699 * 700 * This function generates an "inclusive" scan, meaning the Nth element 701 * of the output range is the sum of the first N input elements, 702 * so the Nth input element is included. 703 */ 704 template<typename _InputIterator, typename _OutputIterator, 705 typename _BinaryOperation, typename _UnaryOperation> 706 _GLIBCXX20_CONSTEXPR 707 _OutputIterator 708 transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 709 _OutputIterator __result, 710 _BinaryOperation __binary_op, 711 _UnaryOperation __unary_op) 712 { 713 if (__first != __last) 714 { 715 auto __init = __unary_op(*__first); 716 *__result++ = __init; 717 ++__first; 718 if (__first != __last) 719 __result = std::transform_inclusive_scan(__first, __last, __result, 720 __binary_op, __unary_op, 721 std::move(__init)); 722 } 723 return __result; 724 } 725 726 /// @} group numeric_ops 727#endif // C++17 728 729_GLIBCXX_END_NAMESPACE_VERSION 730} // namespace std 731 732#if __cplusplus >= 201703L 733// Parallel STL algorithms 734# if _PSTL_EXECUTION_POLICIES_DEFINED 735// If <execution> has already been included, pull in implementations 736# include <pstl/glue_numeric_impl.h> 737# else 738// Otherwise just pull in forward declarations 739# include <pstl/glue_numeric_defs.h> 740# define _PSTL_NUMERIC_FORWARD_DECLARED 1 741# endif 742 743// Feature test macro for parallel algorithms 744# define __cpp_lib_parallel_algorithm 201603L 745#endif // C++17 746 747#endif /* _GLIBCXX_NUMERIC */ 748