1// <numeric> -*- C++ -*- 2 3// Copyright (C) 2001-2019 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 213 enable_if_t<__and_v<is_object<_Tp>, bool_constant<sizeof(_Tp) != 0>>, _Tp*> 214 midpoint(_Tp* __a, _Tp* __b) noexcept 215 { 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 /// @addtogroup numeric_ops 231 /// @{ 232 233 /// @cond undocumented 234 template<typename _It, typename _Traits = iterator_traits<_It>, 235 typename _Cat = typename _Traits::iterator_category> 236 using __is_random_access_iter 237 = is_base_of<random_access_iterator_tag, _Cat>; 238 /// @endcond 239 240 /** 241 * @brief Calculate reduction of values in a range. 242 * 243 * @param __first Start of range. 244 * @param __last End of range. 245 * @param __init Starting value to add other values to. 246 * @param __binary_op A binary function object. 247 * @return The final sum. 248 * 249 * Reduce the values in the range `[first,last)` using a binary operation. 250 * The initial value is `init`. The values are not necessarily processed 251 * in order. 252 * 253 * This algorithm is similar to `std::accumulate` but is not required to 254 * perform the operations in order from first to last. For operations 255 * that are commutative and associative the result will be the same as 256 * for `std::accumulate`, but for other operations (such as floating point 257 * arithmetic) the result can be different. 258 */ 259 template<typename _InputIterator, typename _Tp, typename _BinaryOperation> 260 _Tp 261 reduce(_InputIterator __first, _InputIterator __last, _Tp __init, 262 _BinaryOperation __binary_op) 263 { 264 using __ref = typename iterator_traits<_InputIterator>::reference; 265 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, __ref>); 266 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, __ref, _Tp&>); 267 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, _Tp&, _Tp&>); 268 static_assert(is_invocable_r_v<_Tp, _BinaryOperation&, __ref, __ref>); 269 if constexpr (__is_random_access_iter<_InputIterator>::value) 270 { 271 while ((__last - __first) >= 4) 272 { 273 _Tp __v1 = __binary_op(__first[0], __first[1]); 274 _Tp __v2 = __binary_op(__first[2], __first[3]); 275 _Tp __v3 = __binary_op(__v1, __v2); 276 __init = __binary_op(__init, __v3); 277 __first += 4; 278 } 279 } 280 for (; __first != __last; ++__first) 281 __init = __binary_op(__init, *__first); 282 return __init; 283 } 284 285 /** 286 * @brief Calculate reduction of values in a range. 287 * 288 * @param __first Start of range. 289 * @param __last End of range. 290 * @param __init Starting value to add other values to. 291 * @return The final sum. 292 * 293 * Reduce the values in the range `[first,last)` using addition. 294 * Equivalent to calling `std::reduce(first, last, init, std::plus<>())`. 295 */ 296 template<typename _InputIterator, typename _Tp> 297 inline _Tp 298 reduce(_InputIterator __first, _InputIterator __last, _Tp __init) 299 { return std::reduce(__first, __last, std::move(__init), plus<>()); } 300 301 /** 302 * @brief Calculate reduction of values in a range. 303 * 304 * @param __first Start of range. 305 * @param __last End of range. 306 * @return The final sum. 307 * 308 * Reduce the values in the range `[first,last)` using addition, with 309 * an initial value of `T{}`, where `T` is the iterator's value type. 310 * Equivalent to calling `std::reduce(first, last, T{}, std::plus<>())`. 311 */ 312 template<typename _InputIterator> 313 inline typename iterator_traits<_InputIterator>::value_type 314 reduce(_InputIterator __first, _InputIterator __last) 315 { 316 using value_type = typename iterator_traits<_InputIterator>::value_type; 317 return std::reduce(__first, __last, value_type{}, plus<>()); 318 } 319 320 /** 321 * @brief Combine elements from two ranges and reduce 322 * 323 * @param __first1 Start of first range. 324 * @param __last1 End of first range. 325 * @param __first2 Start of second range. 326 * @param __init Starting value to add other values to. 327 * @param __binary_op1 The function used to perform reduction. 328 * @param __binary_op2 The function used to combine values from the ranges. 329 * @return The final sum. 330 * 331 * Call `binary_op2(first1[n],first2[n])` for each `n` in `[0,last1-first1)` 332 * and then use `binary_op1` to reduce the values returned by `binary_op2` 333 * to a single value of type `T`. 334 * 335 * The range beginning at `first2` must contain at least `last1-first1` 336 * elements. 337 */ 338 template<typename _InputIterator1, typename _InputIterator2, typename _Tp, 339 typename _BinaryOperation1, typename _BinaryOperation2> 340 _Tp 341 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, 342 _InputIterator2 __first2, _Tp __init, 343 _BinaryOperation1 __binary_op1, 344 _BinaryOperation2 __binary_op2) 345 { 346 if constexpr (__and_v<__is_random_access_iter<_InputIterator1>, 347 __is_random_access_iter<_InputIterator2>>) 348 { 349 while ((__last1 - __first1) >= 4) 350 { 351 _Tp __v1 = __binary_op1(__binary_op2(__first1[0], __first2[0]), 352 __binary_op2(__first1[1], __first2[1])); 353 _Tp __v2 = __binary_op1(__binary_op2(__first1[2], __first2[2]), 354 __binary_op2(__first1[3], __first2[3])); 355 _Tp __v3 = __binary_op1(__v1, __v2); 356 __init = __binary_op1(__init, __v3); 357 __first1 += 4; 358 __first2 += 4; 359 } 360 } 361 for (; __first1 != __last1; ++__first1, (void) ++__first2) 362 __init = __binary_op1(__init, __binary_op2(*__first1, *__first2)); 363 return __init; 364 } 365 366 /** 367 * @brief Combine elements from two ranges and reduce 368 * 369 * @param __first1 Start of first range. 370 * @param __last1 End of first range. 371 * @param __first2 Start of second range. 372 * @param __init Starting value to add other values to. 373 * @return The final sum. 374 * 375 * Call `first1[n]*first2[n]` for each `n` in `[0,last1-first1)` and then 376 * use addition to sum those products to a single value of type `T`. 377 * 378 * The range beginning at `first2` must contain at least `last1-first1` 379 * elements. 380 */ 381 template<typename _InputIterator1, typename _InputIterator2, typename _Tp> 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 _Tp 408 transform_reduce(_InputIterator __first, _InputIterator __last, _Tp __init, 409 _BinaryOperation __binary_op, _UnaryOperation __unary_op) 410 { 411 if constexpr (__is_random_access_iter<_InputIterator>::value) 412 { 413 while ((__last - __first) >= 4) 414 { 415 _Tp __v1 = __binary_op(__unary_op(__first[0]), 416 __unary_op(__first[1])); 417 _Tp __v2 = __binary_op(__unary_op(__first[2]), 418 __unary_op(__first[3])); 419 _Tp __v3 = __binary_op(__v1, __v2); 420 __init = __binary_op(__init, __v3); 421 __first += 4; 422 } 423 } 424 for (; __first != __last; ++__first) 425 __init = __binary_op(__init, __unary_op(*__first)); 426 return __init; 427 } 428 429 /** @brief Output the cumulative sum of one range to a second range 430 * 431 * @param __first Start of input range. 432 * @param __last End of input range. 433 * @param __result Start of output range. 434 * @param __init Initial value. 435 * @param __binary_op Function to perform summation. 436 * @return The end of the output range. 437 * 438 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 439 * to the output range. Each element of the output range contains the 440 * running total of all earlier elements (and the initial value), 441 * using `binary_op` for summation. 442 * 443 * This function generates an "exclusive" scan, meaning the Nth element 444 * of the output range is the sum of the first N-1 input elements, 445 * so the Nth input element is not included. 446 */ 447 template<typename _InputIterator, typename _OutputIterator, typename _Tp, 448 typename _BinaryOperation> 449 _OutputIterator 450 exclusive_scan(_InputIterator __first, _InputIterator __last, 451 _OutputIterator __result, _Tp __init, 452 _BinaryOperation __binary_op) 453 { 454 while (__first != __last) 455 { 456 auto __v = __init; 457 __init = __binary_op(__init, *__first); 458 ++__first; 459 *__result++ = std::move(__v); 460 } 461 return __result; 462 } 463 464 /** @brief Output the cumulative sum of one range to a second range 465 * 466 * @param __first Start of input range. 467 * @param __last End of input range. 468 * @param __result Start of output range. 469 * @param __init Initial value. 470 * @return The end of the output range. 471 * 472 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 473 * to the output range. Each element of the output range contains the 474 * running total of all earlier elements (and the initial value), 475 * using `std::plus<>` for summation. 476 * 477 * This function generates an "exclusive" scan, meaning the Nth element 478 * of the output range is the sum of the first N-1 input elements, 479 * so the Nth input element is not included. 480 */ 481 template<typename _InputIterator, typename _OutputIterator, typename _Tp> 482 inline _OutputIterator 483 exclusive_scan(_InputIterator __first, _InputIterator __last, 484 _OutputIterator __result, _Tp __init) 485 { 486 return std::exclusive_scan(__first, __last, __result, std::move(__init), 487 plus<>()); 488 } 489 490 /** @brief Output the cumulative sum of one range to a second range 491 * 492 * @param __first Start of input range. 493 * @param __last End of input range. 494 * @param __result Start of output range. 495 * @param __binary_op Function to perform summation. 496 * @param __init Initial value. 497 * @return The end of the output range. 498 * 499 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 500 * to the output range. Each element of the output range contains the 501 * running total of all earlier elements (and the initial value), 502 * using `binary_op` for summation. 503 * 504 * This function generates an "inclusive" scan, meaning the Nth element 505 * of the output range is the sum of the first N input elements, 506 * so the Nth input element is included. 507 */ 508 template<typename _InputIterator, typename _OutputIterator, 509 typename _BinaryOperation, typename _Tp> 510 _OutputIterator 511 inclusive_scan(_InputIterator __first, _InputIterator __last, 512 _OutputIterator __result, _BinaryOperation __binary_op, 513 _Tp __init) 514 { 515 for (; __first != __last; ++__first) 516 *__result++ = __init = __binary_op(__init, *__first); 517 return __result; 518 } 519 520 /** @brief Output the cumulative sum of one range to a second range 521 * 522 * @param __first Start of input range. 523 * @param __last End of input range. 524 * @param __result Start of output range. 525 * @param __binary_op Function to perform summation. 526 * @return The end of the output range. 527 * 528 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 529 * to the output range. Each element of the output range contains the 530 * running total of all earlier elements, using `binary_op` for summation. 531 * 532 * This function generates an "inclusive" scan, meaning the Nth element 533 * of the output range is the sum of the first N input elements, 534 * so the Nth input element is included. 535 */ 536 template<typename _InputIterator, typename _OutputIterator, 537 typename _BinaryOperation> 538 _OutputIterator 539 inclusive_scan(_InputIterator __first, _InputIterator __last, 540 _OutputIterator __result, _BinaryOperation __binary_op) 541 { 542 if (__first != __last) 543 { 544 auto __init = *__first; 545 *__result++ = __init; 546 ++__first; 547 if (__first != __last) 548 __result = std::inclusive_scan(__first, __last, __result, 549 __binary_op, std::move(__init)); 550 } 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 * @return The end of the output range. 560 * 561 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 562 * to the output range. Each element of the output range contains the 563 * running total of all earlier elements, using `std::plus<>` for summation. 564 * 565 * This function generates an "inclusive" scan, meaning the Nth element 566 * of the output range is the sum of the first N input elements, 567 * so the Nth input element is included. 568 */ 569 template<typename _InputIterator, typename _OutputIterator> 570 inline _OutputIterator 571 inclusive_scan(_InputIterator __first, _InputIterator __last, 572 _OutputIterator __result) 573 { return std::inclusive_scan(__first, __last, __result, plus<>()); } 574 575 /** @brief Output the cumulative sum of one range to a second range 576 * 577 * @param __first Start of input range. 578 * @param __last End of input range. 579 * @param __result Start of output range. 580 * @param __init Initial value. 581 * @param __binary_op Function to perform summation. 582 * @param __unary_op Function to transform elements of the input range. 583 * @return The end of the output range. 584 * 585 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 586 * to the output range. Each element of the output range contains the 587 * running total of all earlier elements (and the initial value), 588 * using `__unary_op` to transform the input elements 589 * and using `__binary_op` for summation. 590 * 591 * This function generates an "exclusive" scan, meaning the Nth element 592 * of the output range is the sum of the first N-1 input elements, 593 * so the Nth input element is not included. 594 */ 595 template<typename _InputIterator, typename _OutputIterator, typename _Tp, 596 typename _BinaryOperation, typename _UnaryOperation> 597 _OutputIterator 598 transform_exclusive_scan(_InputIterator __first, _InputIterator __last, 599 _OutputIterator __result, _Tp __init, 600 _BinaryOperation __binary_op, 601 _UnaryOperation __unary_op) 602 { 603 while (__first != __last) 604 { 605 auto __v = __init; 606 __init = __binary_op(__init, __unary_op(*__first)); 607 ++__first; 608 *__result++ = std::move(__v); 609 } 610 return __result; 611 } 612 613 /** @brief Output the cumulative sum of one range to a second range 614 * 615 * @param __first Start of input range. 616 * @param __last End of input range. 617 * @param __result Start of output range. 618 * @param __binary_op Function to perform summation. 619 * @param __unary_op Function to transform elements of the input range. 620 * @param __init Initial value. 621 * @return The end of the output range. 622 * 623 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 624 * to the output range. Each element of the output range contains the 625 * running total of all earlier elements (and the initial value), 626 * using `__unary_op` to transform the input elements 627 * and using `__binary_op` for summation. 628 * 629 * This function generates an "inclusive" scan, meaning the Nth element 630 * of the output range is the sum of the first N input elements, 631 * so the Nth input element is included. 632 */ 633 template<typename _InputIterator, typename _OutputIterator, 634 typename _BinaryOperation, typename _UnaryOperation, typename _Tp> 635 _OutputIterator 636 transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 637 _OutputIterator __result, 638 _BinaryOperation __binary_op, 639 _UnaryOperation __unary_op, 640 _Tp __init) 641 { 642 for (; __first != __last; ++__first) 643 *__result++ = __init = __binary_op(__init, __unary_op(*__first)); 644 return __result; 645 } 646 647 /** @brief Output the cumulative sum of one range to a second range 648 * 649 * @param __first Start of input range. 650 * @param __last End of input range. 651 * @param __result Start of output range. 652 * @param __binary_op Function to perform summation. 653 * @param __unary_op Function to transform elements of the input range. 654 * @return The end of the output range. 655 * 656 * Write the cumulative sum (aka prefix sum, aka scan) of the input range 657 * to the output range. Each element of the output range contains the 658 * running total of all earlier elements, 659 * using `__unary_op` to transform the input elements 660 * and using `__binary_op` for summation. 661 * 662 * This function generates an "inclusive" scan, meaning the Nth element 663 * of the output range is the sum of the first N input elements, 664 * so the Nth input element is included. 665 */ 666 template<typename _InputIterator, typename _OutputIterator, 667 typename _BinaryOperation, typename _UnaryOperation> 668 _OutputIterator 669 transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 670 _OutputIterator __result, 671 _BinaryOperation __binary_op, 672 _UnaryOperation __unary_op) 673 { 674 if (__first != __last) 675 { 676 auto __init = __unary_op(*__first); 677 *__result++ = __init; 678 ++__first; 679 if (__first != __last) 680 __result = std::transform_inclusive_scan(__first, __last, __result, 681 __binary_op, __unary_op, 682 std::move(__init)); 683 } 684 return __result; 685 } 686 687 /// @} group numeric_ops 688 689_GLIBCXX_END_NAMESPACE_VERSION 690} // namespace std 691 692// Parallel STL algorithms 693# if __PSTL_EXECUTION_POLICIES_DEFINED 694// If <execution> has already been included, pull in implementations 695# include <pstl/glue_numeric_impl.h> 696# else 697// Otherwise just pull in forward declarations 698# include <pstl/glue_numeric_defs.h> 699# define __PSTL_NUMERIC_FORWARD_DECLARED 1 700# endif 701 702// Feature test macro for parallel algorithms 703# define __cpp_lib_parallel_algorithm 201603L 704#endif // C++17 705 706#endif /* _GLIBCXX_NUMERIC */ 707