1// <numeric> -*- C++ -*- 2 3// Copyright (C) 2001-2020 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#include <ext/numeric_traits.h> 64 65#ifdef _GLIBCXX_PARALLEL 66# include <parallel/numeric> 67#endif 68 69/** 70 * @defgroup numerics Numerics 71 * 72 * Components for performing numeric operations. Includes support for 73 * complex number types, random number generation, numeric (n-at-a-time) 74 * arrays, generalized numeric algorithms, and mathematical special functions. 75 */ 76 77#if __cplusplus >= 201402L 78#include <type_traits> 79 80namespace std _GLIBCXX_VISIBILITY(default) 81{ 82_GLIBCXX_BEGIN_NAMESPACE_VERSION 83 84namespace __detail 85{ 86 // std::abs is not constexpr, doesn't support unsigned integers, 87 // and std::abs(std::numeric_limits<T>::min()) is undefined. 88 template<typename _Up, typename _Tp> 89 constexpr _Up 90 __absu(_Tp __val) 91 { 92 static_assert(is_unsigned<_Up>::value, "result type must be unsigned"); 93 static_assert(sizeof(_Up) >= sizeof(_Tp), 94 "result type must be at least as wide as the input type"); 95 return __val < 0 ? -(_Up)__val : (_Up)__val; 96 } 97 98 template<typename _Up> void __absu(bool) = delete; 99 100 // GCD implementation 101 template<typename _Tp> 102 constexpr _Tp 103 __gcd(_Tp __m, _Tp __n) 104 { 105 static_assert(is_unsigned<_Tp>::value, "type must be unsigned"); 106 return __m == 0 ? __n 107 : __n == 0 ? __m 108 : __detail::__gcd(__n, _Tp(__m % __n)); 109 } 110 111 // LCM implementation 112 template<typename _Tp> 113 constexpr _Tp 114 __lcm(_Tp __m, _Tp __n) 115 { 116 return (__m != 0 && __n != 0) 117 ? (__m / __detail::__gcd(__m, __n)) * __n 118 : 0; 119 } 120} // namespace __detail 121 122#if __cplusplus >= 201703L 123 124#define __cpp_lib_gcd_lcm 201606 125// These were used in drafts of SD-6: 126#define __cpp_lib_gcd 201606 127#define __cpp_lib_lcm 201606 128 129 /// Greatest common divisor 130 template<typename _Mn, typename _Nn> 131 constexpr common_type_t<_Mn, _Nn> 132 gcd(_Mn __m, _Nn __n) noexcept 133 { 134 static_assert(is_integral_v<_Mn>, "std::gcd arguments must be integers"); 135 static_assert(is_integral_v<_Nn>, "std::gcd arguments must be integers"); 136 static_assert(_Mn(2) != _Mn(1), "std::gcd arguments must not be bool"); 137 static_assert(_Nn(2) != _Nn(1), "std::gcd arguments must not be bool"); 138 using _Up = make_unsigned_t<common_type_t<_Mn, _Nn>>; 139 return __detail::__gcd(__detail::__absu<_Up>(__m), 140 __detail::__absu<_Up>(__n)); 141 } 142 143 /// Least common multiple 144 template<typename _Mn, typename _Nn> 145 constexpr common_type_t<_Mn, _Nn> 146 lcm(_Mn __m, _Nn __n) noexcept 147 { 148 static_assert(is_integral_v<_Mn>, "std::lcm arguments must be integers"); 149 static_assert(is_integral_v<_Nn>, "std::lcm arguments must be integers"); 150 static_assert(_Mn(2) == 2, "std::lcm arguments must not be bool"); 151 static_assert(_Nn(2) == 2, "std::lcm arguments must not be bool"); 152 using _Up = make_unsigned_t<common_type_t<_Mn, _Nn>>; 153 return __detail::__lcm(__detail::__absu<_Up>(__m), 154 __detail::__absu<_Up>(__n)); 155 } 156 157#endif // C++17 158 159_GLIBCXX_END_NAMESPACE_VERSION 160} // namespace std 161 162#endif // C++14 163 164#if __cplusplus > 201703L 165#include <limits> 166 167namespace std _GLIBCXX_VISIBILITY(default) 168{ 169_GLIBCXX_BEGIN_NAMESPACE_VERSION 170 // midpoint 171# define __cpp_lib_interpolate 201902L 172 173 template<typename _Tp> 174 constexpr 175 enable_if_t<__and_v<is_arithmetic<_Tp>, is_same<remove_cv_t<_Tp>, _Tp>, 176 __not_<is_same<_Tp, bool>>>, 177 _Tp> 178 midpoint(_Tp __a, _Tp __b) noexcept 179 { 180 if constexpr (is_integral_v<_Tp>) 181 { 182 using _Up = make_unsigned_t<_Tp>; 183 184 int __k = 1; 185 _Up __m = __a; 186 _Up __M = __b; 187 if (__a > __b) 188 { 189 __k = -1; 190 __m = __b; 191 __M = __a; 192 } 193 return __a + __k * _Tp(_Up(__M - __m) / 2); 194 } 195 else // is_floating 196 { 197 constexpr _Tp __lo = numeric_limits<_Tp>::min() * 2; 198 constexpr _Tp __hi = numeric_limits<_Tp>::max() / 2; 199 const _Tp __abs_a = __a < 0 ? -__a : __a; 200 const _Tp __abs_b = __b < 0 ? -__b : __b; 201 if (__abs_a <= __hi && __abs_b <= __hi) [[likely]] 202 return (__a + __b) / 2; // always correctly rounded 203 if (__abs_a < __lo) // not safe to halve __a 204 return __a + __b/2; 205 if (__abs_b < __lo) // not safe to halve __b 206 return __a/2 + __b; 207 return __a/2 + __b/2; // otherwise correctly rounded 208 } 209 } 210 211 template<typename _Tp> 212 constexpr enable_if_t<is_object_v<_Tp>, _Tp*> 213 midpoint(_Tp* __a, _Tp* __b) noexcept 214 { 215 static_assert( sizeof(_Tp) != 0, "type must be complete" ); 216 return __a + (__b - __a) / 2; 217 } 218_GLIBCXX_END_NAMESPACE_VERSION 219} // namespace std 220 221#endif // C++20 222 223#if __cplusplus > 201402L 224#include <bits/stl_function.h> 225 226namespace std _GLIBCXX_VISIBILITY(default) 227{ 228_GLIBCXX_BEGIN_NAMESPACE_VERSION 229 230#if __cplusplus > 201703L 231#define __cpp_lib_constexpr_numeric 201911L 232#endif 233 234 /// @addtogroup numeric_ops 235 /// @{ 236 237 /** 238 * @brief Calculate reduction of values in a range. 239 * 240 * @param __first Start of range. 241 * @param __last End of range. 242 * @param __init Starting value to add other values to. 243 * @param __binary_op A binary function object. 244 * @return The final sum. 245 * 246 * Reduce the values in the range `[first,last)` using a binary operation. 247 * The initial value is `init`. The values are not necessarily processed 248 * in order. 249 * 250 * This algorithm is similar to `std::accumulate` but is not required to 251 * perform the operations in order from first to last. For operations 252 * that are commutative and associative the result will be the same as 253 * for `std::accumulate`, but for other operations (such as floating point 254 * arithmetic) the result can be different. 255 */ 256 template<typename _InputIterator, typename _Tp, typename _BinaryOperation> 257 _GLIBCXX20_CONSTEXPR 258 _Tp 259 reduce(_InputIterator __first, _InputIterator __last, _Tp __init, 260 _BinaryOperation __binary_op) 261 { 262 using value_type = typename iterator_traits<_InputIterator>::value_type; 263 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, _Tp&>); 264 static_assert(is_convertible_v<value_type, _Tp>); 265 if constexpr (__is_random_access_iter<_InputIterator>::value) 266 { 267 while ((__last - __first) >= 4) 268 { 269 _Tp __v1 = __binary_op(__first[0], __first[1]); 270 _Tp __v2 = __binary_op(__first[2], __first[3]); 271 _Tp __v3 = __binary_op(__v1, __v2); 272 __init = __binary_op(__init, __v3); 273 __first += 4; 274 } 275 } 276 for (; __first != __last; ++__first) 277 __init = __binary_op(__init, *__first); 278 return __init; 279 } 280 281 /** 282 * @brief Calculate reduction of values in a range. 283 * 284 * @param __first Start of range. 285 * @param __last End of range. 286 * @param __init Starting value to add other values to. 287 * @return The final sum. 288 * 289 * Reduce the values in the range `[first,last)` using addition. 290 * Equivalent to calling `std::reduce(first, last, init, std::plus<>())`. 291 */ 292 template<typename _InputIterator, typename _Tp> 293 _GLIBCXX20_CONSTEXPR 294 inline _Tp 295 reduce(_InputIterator __first, _InputIterator __last, _Tp __init) 296 { return std::reduce(__first, __last, std::move(__init), plus<>()); } 297 298 /** 299 * @brief Calculate reduction of values in a range. 300 * 301 * @param __first Start of range. 302 * @param __last End of range. 303 * @return The final sum. 304 * 305 * Reduce the values in the range `[first,last)` using addition, with 306 * an initial value of `T{}`, where `T` is the iterator's value type. 307 * Equivalent to calling `std::reduce(first, last, T{}, std::plus<>())`. 308 */ 309 template<typename _InputIterator> 310 _GLIBCXX20_CONSTEXPR 311 inline typename iterator_traits<_InputIterator>::value_type 312 reduce(_InputIterator __first, _InputIterator __last) 313 { 314 using value_type = typename iterator_traits<_InputIterator>::value_type; 315 return std::reduce(__first, __last, value_type{}, plus<>()); 316 } 317 318 /** 319 * @brief Combine elements from two ranges and reduce 320 * 321 * @param __first1 Start of first range. 322 * @param __last1 End of first range. 323 * @param __first2 Start of second range. 324 * @param __init Starting value to add other values to. 325 * @param __binary_op1 The function used to perform reduction. 326 * @param __binary_op2 The function used to combine values from the ranges. 327 * @return The final sum. 328 * 329 * Call `binary_op2(first1[n],first2[n])` for each `n` in `[0,last1-first1)` 330 * and then use `binary_op1` to reduce the values returned by `binary_op2` 331 * to a single value of type `T`. 332 * 333 * The range beginning at `first2` must contain at least `last1-first1` 334 * elements. 335 */ 336 template<typename _InputIterator1, typename _InputIterator2, typename _Tp, 337 typename _BinaryOperation1, typename _BinaryOperation2> 338 _GLIBCXX20_CONSTEXPR 339 _Tp 340 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, 341 _InputIterator2 __first2, _Tp __init, 342 _BinaryOperation1 __binary_op1, 343 _BinaryOperation2 __binary_op2) 344 { 345 if constexpr (__and_v<__is_random_access_iter<_InputIterator1>, 346 __is_random_access_iter<_InputIterator2>>) 347 { 348 while ((__last1 - __first1) >= 4) 349 { 350 _Tp __v1 = __binary_op1(__binary_op2(__first1[0], __first2[0]), 351 __binary_op2(__first1[1], __first2[1])); 352 _Tp __v2 = __binary_op1(__binary_op2(__first1[2], __first2[2]), 353 __binary_op2(__first1[3], __first2[3])); 354 _Tp __v3 = __binary_op1(__v1, __v2); 355 __init = __binary_op1(__init, __v3); 356 __first1 += 4; 357 __first2 += 4; 358 } 359 } 360 for (; __first1 != __last1; ++__first1, (void) ++__first2) 361 __init = __binary_op1(__init, __binary_op2(*__first1, *__first2)); 362 return __init; 363 } 364 365 /** 366 * @brief Combine elements from two ranges and reduce 367 * 368 * @param __first1 Start of first range. 369 * @param __last1 End of first range. 370 * @param __first2 Start of second range. 371 * @param __init Starting value to add other values to. 372 * @return The final sum. 373 * 374 * Call `first1[n]*first2[n]` for each `n` in `[0,last1-first1)` and then 375 * use addition to sum those products to a single value of type `T`. 376 * 377 * The range beginning at `first2` must contain at least `last1-first1` 378 * elements. 379 */ 380 template<typename _InputIterator1, typename _InputIterator2, typename _Tp> 381 _GLIBCXX20_CONSTEXPR 382 inline _Tp 383 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, 384 _InputIterator2 __first2, _Tp __init) 385 { 386 return std::transform_reduce(__first1, __last1, __first2, 387 std::move(__init), 388 plus<>(), multiplies<>()); 389 } 390 391 /** 392 * @brief Transform the elements of a range and reduce 393 * 394 * @param __first Start of range. 395 * @param __last End of range. 396 * @param __init Starting value to add other values to. 397 * @param __binary_op The function used to perform reduction. 398 * @param __unary_op The function used to transform values from the range. 399 * @return The final sum. 400 * 401 * Call `unary_op(first[n])` for each `n` in `[0,last-first)` and then 402 * use `binary_op` to reduce the values returned by `unary_op` 403 * to a single value of type `T`. 404 */ 405 template<typename _InputIterator, typename _Tp, 406 typename _BinaryOperation, typename _UnaryOperation> 407 _GLIBCXX20_CONSTEXPR 408 _Tp 409 transform_reduce(_InputIterator __first, _InputIterator __last, _Tp __init, 410 _BinaryOperation __binary_op, _UnaryOperation __unary_op) 411 { 412 if constexpr (__is_random_access_iter<_InputIterator>::value) 413 { 414 while ((__last - __first) >= 4) 415 { 416 _Tp __v1 = __binary_op(__unary_op(__first[0]), 417 __unary_op(__first[1])); 418 _Tp __v2 = __binary_op(__unary_op(__first[2]), 419 __unary_op(__first[3])); 420 _Tp __v3 = __binary_op(__v1, __v2); 421 __init = __binary_op(__init, __v3); 422 __first += 4; 423 } 424 } 425 for (; __first != __last; ++__first) 426 __init = __binary_op(__init, __unary_op(*__first)); 427 return __init; 428 } 429 430 /** @brief Output the cumulative sum of one range to a second range 431 * 432 * @param __first Start of input range. 433 * @param __last End of input range. 434 * @param __result Start of output range. 435 * @param __init Initial value. 436 * @param __binary_op Function to perform summation. 437 * @return The end of the output range. 438 * 439 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 440 * to the output range. Each element of the output range contains the 441 * running total of all earlier elements (and the initial value), 442 * using `binary_op` for summation. 443 * 444 * This function generates an "exclusive" scan, meaning the Nth element 445 * of the output range is the sum of the first N-1 input elements, 446 * so the Nth input element is not included. 447 */ 448 template<typename _InputIterator, typename _OutputIterator, typename _Tp, 449 typename _BinaryOperation> 450 _GLIBCXX20_CONSTEXPR 451 _OutputIterator 452 exclusive_scan(_InputIterator __first, _InputIterator __last, 453 _OutputIterator __result, _Tp __init, 454 _BinaryOperation __binary_op) 455 { 456 while (__first != __last) 457 { 458 auto __v = __init; 459 __init = __binary_op(__init, *__first); 460 ++__first; 461 *__result++ = std::move(__v); 462 } 463 return __result; 464 } 465 466 /** @brief Output the cumulative sum of one range to a second range 467 * 468 * @param __first Start of input range. 469 * @param __last End of input range. 470 * @param __result Start of output range. 471 * @param __init Initial value. 472 * @return The end of the output range. 473 * 474 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 475 * to the output range. Each element of the output range contains the 476 * running total of all earlier elements (and the initial value), 477 * using `std::plus<>` for summation. 478 * 479 * This function generates an "exclusive" scan, meaning the Nth element 480 * of the output range is the sum of the first N-1 input elements, 481 * so the Nth input element is not included. 482 */ 483 template<typename _InputIterator, typename _OutputIterator, typename _Tp> 484 _GLIBCXX20_CONSTEXPR 485 inline _OutputIterator 486 exclusive_scan(_InputIterator __first, _InputIterator __last, 487 _OutputIterator __result, _Tp __init) 488 { 489 return std::exclusive_scan(__first, __last, __result, std::move(__init), 490 plus<>()); 491 } 492 493 /** @brief Output the cumulative sum of one range to a second range 494 * 495 * @param __first Start of input range. 496 * @param __last End of input range. 497 * @param __result Start of output range. 498 * @param __binary_op Function to perform summation. 499 * @param __init Initial value. 500 * @return The end of the output range. 501 * 502 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 503 * to the output range. Each element of the output range contains the 504 * running total of all earlier elements (and the initial value), 505 * using `binary_op` for summation. 506 * 507 * This function generates an "inclusive" scan, meaning the Nth element 508 * of the output range is the sum of the first N input elements, 509 * so the Nth input element is included. 510 */ 511 template<typename _InputIterator, typename _OutputIterator, 512 typename _BinaryOperation, typename _Tp> 513 _GLIBCXX20_CONSTEXPR 514 _OutputIterator 515 inclusive_scan(_InputIterator __first, _InputIterator __last, 516 _OutputIterator __result, _BinaryOperation __binary_op, 517 _Tp __init) 518 { 519 for (; __first != __last; ++__first) 520 *__result++ = __init = __binary_op(__init, *__first); 521 return __result; 522 } 523 524 /** @brief Output the cumulative sum of one range to a second range 525 * 526 * @param __first Start of input range. 527 * @param __last End of input range. 528 * @param __result Start of output range. 529 * @param __binary_op Function to perform summation. 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, using `binary_op` for summation. 535 * 536 * This function generates an "inclusive" scan, meaning the Nth element 537 * of the output range is the sum of the first N input elements, 538 * so the Nth input element is included. 539 */ 540 template<typename _InputIterator, typename _OutputIterator, 541 typename _BinaryOperation> 542 _GLIBCXX20_CONSTEXPR 543 _OutputIterator 544 inclusive_scan(_InputIterator __first, _InputIterator __last, 545 _OutputIterator __result, _BinaryOperation __binary_op) 546 { 547 if (__first != __last) 548 { 549 auto __init = *__first; 550 *__result++ = __init; 551 ++__first; 552 if (__first != __last) 553 __result = std::inclusive_scan(__first, __last, __result, 554 __binary_op, std::move(__init)); 555 } 556 return __result; 557 } 558 559 /** @brief Output the cumulative sum of one range to a second range 560 * 561 * @param __first Start of input range. 562 * @param __last End of input range. 563 * @param __result Start of output range. 564 * @return The end of the output range. 565 * 566 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 567 * to the output range. Each element of the output range contains the 568 * running total of all earlier elements, using `std::plus<>` for summation. 569 * 570 * This function generates an "inclusive" scan, meaning the Nth element 571 * of the output range is the sum of the first N input elements, 572 * so the Nth input element is included. 573 */ 574 template<typename _InputIterator, typename _OutputIterator> 575 _GLIBCXX20_CONSTEXPR 576 inline _OutputIterator 577 inclusive_scan(_InputIterator __first, _InputIterator __last, 578 _OutputIterator __result) 579 { return std::inclusive_scan(__first, __last, __result, plus<>()); } 580 581 /** @brief Output the cumulative sum of one range to a second range 582 * 583 * @param __first Start of input range. 584 * @param __last End of input range. 585 * @param __result Start of output range. 586 * @param __init Initial value. 587 * @param __binary_op Function to perform summation. 588 * @param __unary_op Function to transform elements of the input range. 589 * @return The end of the output range. 590 * 591 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 592 * to the output range. Each element of the output range contains the 593 * running total of all earlier elements (and the initial value), 594 * using `__unary_op` to transform the input elements 595 * and using `__binary_op` for summation. 596 * 597 * This function generates an "exclusive" scan, meaning the Nth element 598 * of the output range is the sum of the first N-1 input elements, 599 * so the Nth input element is not included. 600 */ 601 template<typename _InputIterator, typename _OutputIterator, typename _Tp, 602 typename _BinaryOperation, typename _UnaryOperation> 603 _GLIBCXX20_CONSTEXPR 604 _OutputIterator 605 transform_exclusive_scan(_InputIterator __first, _InputIterator __last, 606 _OutputIterator __result, _Tp __init, 607 _BinaryOperation __binary_op, 608 _UnaryOperation __unary_op) 609 { 610 while (__first != __last) 611 { 612 auto __v = __init; 613 __init = __binary_op(__init, __unary_op(*__first)); 614 ++__first; 615 *__result++ = std::move(__v); 616 } 617 return __result; 618 } 619 620 /** @brief Output the cumulative sum of one range to a second range 621 * 622 * @param __first Start of input range. 623 * @param __last End of input range. 624 * @param __result Start of output range. 625 * @param __binary_op Function to perform summation. 626 * @param __unary_op Function to transform elements of the input range. 627 * @param __init Initial value. 628 * @return The end of the output range. 629 * 630 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 631 * to the output range. Each element of the output range contains the 632 * running total of all earlier elements (and the initial value), 633 * using `__unary_op` to transform the input elements 634 * and using `__binary_op` for summation. 635 * 636 * This function generates an "inclusive" scan, meaning the Nth element 637 * of the output range is the sum of the first N input elements, 638 * so the Nth input element is included. 639 */ 640 template<typename _InputIterator, typename _OutputIterator, 641 typename _BinaryOperation, typename _UnaryOperation, typename _Tp> 642 _GLIBCXX20_CONSTEXPR 643 _OutputIterator 644 transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 645 _OutputIterator __result, 646 _BinaryOperation __binary_op, 647 _UnaryOperation __unary_op, 648 _Tp __init) 649 { 650 for (; __first != __last; ++__first) 651 *__result++ = __init = __binary_op(__init, __unary_op(*__first)); 652 return __result; 653 } 654 655 /** @brief Output the cumulative sum of one range to a second range 656 * 657 * @param __first Start of input range. 658 * @param __last End of input range. 659 * @param __result Start of output range. 660 * @param __binary_op Function to perform summation. 661 * @param __unary_op Function to transform elements of the input range. 662 * @return The end of the output range. 663 * 664 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 665 * to the output range. Each element of the output range contains the 666 * running total of all earlier elements, 667 * using `__unary_op` to transform the input elements 668 * and using `__binary_op` for summation. 669 * 670 * This function generates an "inclusive" scan, meaning the Nth element 671 * of the output range is the sum of the first N input elements, 672 * so the Nth input element is included. 673 */ 674 template<typename _InputIterator, typename _OutputIterator, 675 typename _BinaryOperation, typename _UnaryOperation> 676 _GLIBCXX20_CONSTEXPR 677 _OutputIterator 678 transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 679 _OutputIterator __result, 680 _BinaryOperation __binary_op, 681 _UnaryOperation __unary_op) 682 { 683 if (__first != __last) 684 { 685 auto __init = __unary_op(*__first); 686 *__result++ = __init; 687 ++__first; 688 if (__first != __last) 689 __result = std::transform_inclusive_scan(__first, __last, __result, 690 __binary_op, __unary_op, 691 std::move(__init)); 692 } 693 return __result; 694 } 695 696 // @} group numeric_ops 697 698_GLIBCXX_END_NAMESPACE_VERSION 699} // namespace std 700 701// Parallel STL algorithms 702# if _PSTL_EXECUTION_POLICIES_DEFINED 703// If <execution> has already been included, pull in implementations 704# include <pstl/glue_numeric_impl.h> 705# else 706// Otherwise just pull in forward declarations 707# include <pstl/glue_numeric_defs.h> 708# define _PSTL_NUMERIC_FORWARD_DECLARED 1 709# endif 710 711// Feature test macro for parallel algorithms 712# define __cpp_lib_parallel_algorithm 201603L 713#endif // C++17 714 715#endif /* _GLIBCXX_NUMERIC */ 716