portedportable, not yet portedexecuted, not portableexecutable, not hit by this run
| 1 | ! This file is part of MOM6, the Modular Ocean Model version 6. | |
| 2 | ! See the LICENSE file for licensing information. | |
| 3 | ! SPDX-License-Identifier: Apache-2.0 | |
| 4 | ||
| 5 | #include "do_concurrent_compat.h" | |
| 6 | ||
| 7 | !> Interfaces to non-domain-oriented communication subroutines, including the | |
| 8 | !! MOM6 reproducing sums facility | |
| 9 | module MOM_coms | |
| 10 | ||
| 11 | use, intrinsic :: iso_fortran_env, only : int64 | |
| 12 | use MOM_coms_infra, only : PE_here, root_PE, num_PEs, set_rootPE, Set_PElist, Get_PElist | |
| 13 | use MOM_coms_infra, only : broadcast, field_chksum, MOM_infra_init, MOM_infra_end | |
| 14 | use MOM_coms_infra, only : sum_across_PEs, max_across_PEs, min_across_PEs | |
| 15 | use MOM_coms_infra, only : all_across_PEs, any_across_PEs | |
| 16 | use MOM_error_handler, only : MOM_error, MOM_mesg, FATAL, WARNING | |
| 17 | use MOM_coms_infra, only : sync_PEs | |
| 18 | ||
| 19 | implicit none ; private | |
| 20 | ||
| 21 | public :: PE_here, root_PE, num_PEs, MOM_infra_init, MOM_infra_end | |
| 22 | public :: sync_PEs | |
| 23 | public :: broadcast, sum_across_PEs, min_across_PEs, max_across_PEs, field_chksum | |
| 24 | public :: all_across_PEs, any_across_PEs | |
| 25 | public :: set_PElist, Get_PElist, Set_rootPE | |
| 26 | public :: reproducing_sum, reproducing_sum_EFP, EFP_sum_across_PEs, EFP_list_sum_across_PEs | |
| 27 | public :: EFP_plus, EFP_minus, EFP_to_real, real_to_EFP, EFP_real_diff | |
| 28 | public :: operator(+), operator(-), assignment(=) | |
| 29 | public :: query_EFP_overflow_error, reset_EFP_overflow_error | |
| 30 | ||
| 31 | integer, parameter :: accum_width = digits(1_int64) | |
| 32 | !< Accumulator width; total available bits for summation (excluding sign bit) | |
| 33 | integer, parameter :: prec_width = 46 | |
| 34 | !< Precision width; total bits for computed results | |
| 35 | integer, parameter :: guard_width = accum_width - prec_width | |
| 36 | !< Number of guard bits reserved for carry overflow | |
| 37 | ||
| 38 | ! A sum of N points does N - 1 additions, which at most adds N - 1 carry bits. | |
| 39 | ! For G guard bits, the maximum value is 2**G - 1. A summation of N values | |
| 40 | ! therefore requires that N - 1 <= 2**G - 1, or simply N <= 2**G. | |
| 41 | ||
| 42 | integer, parameter :: max_summands = 2**guard_width | |
| 43 | !< Maximum number of summable points that can guarantee no carry overflow. | |
| 44 | !! Assumes that guard_bits is less than number of bits in a default integer. | |
| 45 | ||
| 46 | integer(kind=int64), parameter :: prec = (2_int64)**prec_width | |
| 47 | !< EPF upper bound (exclusive). For each EPF bin e(i), 0 <= e(i) < prec. | |
| 48 | ||
| 49 | real, parameter :: r_prec = 2.**prec_width | |
| 50 | !< Real-value of prec [nondim] | |
| 51 | real, parameter :: I_prec = 2.**(-prec_width) | |
| 52 | !< Inverse real-value of prec [nondim] | |
| 53 | ||
| 54 | integer, parameter :: efp_digits = 6 | |
| 55 | !< The number of base `prec` digits used to represent an EFP value. | |
| 56 | real, parameter, dimension(efp_digits) :: & | |
| 57 | pr = [r_prec**2, r_prec, 1., r_prec**(-1), r_prec**(-2), r_prec**(-3)] | |
| 58 | !< An array of the real precision of each of the integers in arbitrary | |
| 59 | !! units [a] | |
| 60 | real, parameter, dimension(efp_digits) :: & | |
| 61 | I_pr = [r_prec**(-2), r_prec**(-1), 1., r_prec, r_prec**2, r_prec**3] | |
| 62 | !< An array of the inverse of the real precision of each of the integers in | |
| 63 | !! arbitrary units [a-1] | |
| 64 | real, parameter :: max_efp_float = pr(1) * real(huge(1_int64)) | |
| 65 | !< The largest float with an EFP representation in arbitrary units [a]. | |
| 66 | !! NOTE: Only the first bin can exceed precision, but is bounded by the | |
| 67 | !! largest signed integer. | |
| 68 | ||
| 69 | !$omp declare target(pr, I_pr) | |
| 70 | ||
| 71 | logical :: overflow_error = .false. | |
| 72 | !< This becomes true if an overflow is encountered. | |
| 73 | logical :: NaN_error = .false. | |
| 74 | !< This becomes true if a NaN is encountered. | |
| 75 | logical :: debug = .false. | |
| 76 | !< Making this true enables debugging output. | |
| 77 | ||
| 78 | ! This module provides interfaces to the non-domain-oriented communication subroutines. | |
| 79 | ||
| 80 | !> Find an accurate and order-invariant sum of a distributed 2d or 3d field, in some cases after | |
| 81 | !! undoing the scaling of the input array and restoring that scaling in the returned value | |
| 82 | interface reproducing_sum | |
| 83 | module procedure reproducing_sum_2d, reproducing_sum_3d | |
| 84 | end interface reproducing_sum | |
| 85 | ||
| 86 | !> Find an accurate and order-invariant sum of a distributed 2d field, returning the result | |
| 87 | !! in the form of an extended fixed point value that can be converted back with EFP_to_real. | |
| 88 | interface reproducing_sum_EFP | |
| 89 | module procedure reproducing_EFP_sum_2d | |
| 90 | end interface reproducing_sum_EFP | |
| 91 | ||
| 92 | !> Sum a value or 1-d array of values across processors, returning the sums in place | |
| 93 | interface EFP_sum_across_PEs | |
| 94 | module procedure EFP_list_sum_across_PEs, EFP_val_sum_across_PEs | |
| 95 | end interface EFP_sum_across_PEs | |
| 96 | ||
| 97 | !> The Extended Fixed Point (EFP) type provides a public interface for doing sums | |
| 98 | !! and taking differences with this type. | |
| 99 | !! | |
| 100 | !! The use of this type is documented in | |
| 101 | !! Hallberg, R. & A. Adcroft, 2014: An Order-invariant Real-to-Integer Conversion Sum. | |
| 102 | !! Parallel Computing, 40(5-6), doi:10.1016/j.parco.2014.04.007. | |
| 103 | type, public :: EFP_type ; private | |
| 104 | integer(kind=int64), dimension(efp_digits) :: v !< The value in this type | |
| 105 | end type EFP_type | |
| 106 | ||
| 107 | !> Add two extended-fixed-point numbers | |
| 108 | interface operator (+) ; module procedure EFP_plus ; end interface | |
| 109 | !> Subtract one extended-fixed-point number from another | |
| 110 | interface operator (-) ; module procedure EFP_minus ; end interface | |
| 111 | !> Copy the value of one extended-fixed-point number into another | |
| 112 | interface assignment(=); module procedure EFP_assign ; end interface | |
| 113 | ||
| 114 | contains | |
| 115 | ||
| 116 | !> This subroutine uses a conversion to an integer representation of real numbers to give an | |
| 117 | !! order-invariant sum of distributed 2-D arrays that reproduces across domain decomposition, with | |
| 118 | !! the result returned as an extended fixed point type that can be converted back to a real number | |
| 119 | !! using EFP_to_real. This technique is described in Hallberg & Adcroft, 2014, Parallel Computing, | |
| 120 | !! doi:10.1016/j.parco.2014.04.007. | |
| 121 | 10 | function reproducing_EFP_sum_2d(array, isr, ier, jsr, jer, overflow_check, err, only_on_PE, unscale) result(EFP_sum) |
| 122 | real, dimension(:,:), intent(in) :: array !< The array to be summed in arbitrary units [a], or in | |
| 123 | !! arbitrary scaled units [A ~> a] if unscale is present | |
| 124 | integer, optional, intent(in) :: isr !< The starting i-index of the sum, noting | |
| 125 | !! that the array indices starts at 1 | |
| 126 | integer, optional, intent(in) :: ier !< The ending i-index of the sum, noting | |
| 127 | !! that the array indices starts at 1 | |
| 128 | integer, optional, intent(in) :: jsr !< The starting j-index of the sum, noting | |
| 129 | !! that the array indices starts at 1 | |
| 130 | integer, optional, intent(in) :: jer !< The ending j-index of the sum, noting | |
| 131 | !! that the array indices starts at 1 | |
| 132 | logical, optional, intent(in) :: overflow_check !< If present and false, disable | |
| 133 | !! checking for overflows in incremental results. | |
| 134 | !! This can speed up calculations if the number | |
| 135 | !! of values being summed is small enough | |
| 136 | integer, optional, intent(out) :: err !< If present, return an error code instead of | |
| 137 | !! triggering any fatal errors directly from | |
| 138 | !! this routine. | |
| 139 | logical, optional, intent(in) :: only_on_PE !< If present and true, do not do the sum | |
| 140 | !! across processors, only reporting the local sum | |
| 141 | real, optional, intent(in) :: unscale !< A factor that is used to undo scaling of array before it is | |
| 142 | !! summed, often to compensate for the scaling in [a A-1 ~> 1] | |
| 143 | type(EFP_type) :: EFP_sum !< The result in extended fixed point format | |
| 144 | ||
| 145 | ! This subroutine uses a conversion to an integer representation | |
| 146 | ! of real numbers to give order-invariant sums that will reproduce | |
| 147 | ! across PE count. This idea comes from R. Hallberg and A. Adcroft. | |
| 148 | ||
| 149 | integer(kind=int64), dimension(efp_digits) :: ints_sum | |
| 150 | integer(kind=int64) :: ival, prec_error | |
| 151 | real :: rs ! The remaining value to add, in arbitrary units [a] | |
| 152 | real :: max_mag_term ! A running maximum magnitude of the values in arbitrary units [a] | |
| 153 | real :: descale ! A local copy of unscale if it is present [a A-1 ~> 1] or 1 | |
| 154 | logical :: over_check, do_sum_across_PEs, do_unscale | |
| 155 | character(len=256) :: mesg | |
| 156 | integer :: i, j, n, is, ie, js, je, sgn | |
| 157 | ||
| 158 | 10 | if (num_PEs() > max_summands) call MOM_error(FATAL, & |
| 159 | "reproducing_sum: Too many processors are being used for the value of "//& | |
| 160 | 0 | "prec. Reduce prec to (2^63-1)/num_PEs.") |
| 161 | ||
| 162 | 10 | prec_error = huge(1_int64) / num_PEs() |
| 163 | ||
| 164 | 10 | is = 1 ; ie = size(array,1) ; js = 1 ; je = size(array,2) |
| 165 | 10 | if (present(isr)) then |
| 166 | 9 | if (isr < is) call MOM_error(FATAL, "Value of isr too small in reproducing_EFP_sum_2d.") |
| 167 | 9 | is = isr |
| 168 | endif | |
| 169 | 10 | if (present(ier)) then |
| 170 | 9 | if (ier > ie) call MOM_error(FATAL, "Value of ier too large in reproducing_EFP_sum_2d.") |
| 171 | 9 | ie = ier |
| 172 | endif | |
| 173 | 10 | if (present(jsr)) then |
| 174 | 9 | if (jsr < js) call MOM_error(FATAL, "Value of jsr too small in reproducing_EFP_sum_2d.") |
| 175 | 9 | js = jsr |
| 176 | endif | |
| 177 | 10 | if (present(jer)) then |
| 178 | 9 | if (jer > je) call MOM_error(FATAL, "Value of jer too large in reproducing_EFP_sum_2d.") |
| 179 | 9 | je = jer |
| 180 | endif | |
| 181 | ||
| 182 | 10 | over_check = .true. ; if (present(overflow_check)) over_check = overflow_check |
| 183 | 10 | do_sum_across_PEs = .true. ; if (present(only_on_PE)) do_sum_across_PEs = .not.only_on_PE |
| 184 | 10 | do_unscale = .false. ; if (present(unscale)) do_unscale = (unscale /= 1.0) |
| 185 | 10 | descale = 1.0 ; if (do_unscale) descale = unscale |
| 186 | ||
| 187 | 10 | overflow_error = .false. ; NaN_error = .false. ; max_mag_term = 0.0 |
| 188 | ||
| 189 | 10 | ints_sum(:) = 0 |
| 190 | 10 | if (over_check) then |
| 191 | call increment_block_ints(array, is, ie, js, je, descale, ints_sum, & | |
| 192 | 10 | max_mag_term, prec_error) |
| 193 | else | |
| 194 | 0 | do j=js,je ; do i=is,ie |
| 195 | 0 | sgn = 1 ; if (array(i,j)<0.0) sgn = -1 |
| 196 | 0 | rs = abs(descale*array(i,j)) |
| 197 | 0 | do n=1,efp_digits |
| 198 | 0 | ival = int(rs*I_pr(n), kind=int64) |
| 199 | 0 | rs = rs - ival*pr(n) |
| 200 | 0 | ints_sum(n) = ints_sum(n) + sgn*ival |
| 201 | enddo | |
| 202 | enddo ; enddo | |
| 203 | 0 | call carry_overflow(ints_sum, prec_error) |
| 204 | endif | |
| 205 | ||
| 206 | 10 | if (present(err)) then |
| 207 | 0 | err = 0 |
| 208 | 0 | if (overflow_error) & |
| 209 | 0 | err = err+2 |
| 210 | 0 | if (NaN_error) & |
| 211 | 0 | err = err+4 |
| 212 | 0 | if (err > 0) then ; do n=1,efp_digits ; ints_sum(n) = 0 ; enddo ; endif |
| 213 | else | |
| 214 | 10 | if (NaN_error) then |
| 215 | 0 | call MOM_error(FATAL, "NaN in input field of reproducing_EFP_sum(_2d).") |
| 216 | endif | |
| 217 | 10 | if (abs(max_mag_term) >= prec_error*pr(1)) then |
| 218 | 0 | write(mesg, '(ES13.5)') max_mag_term |
| 219 | 0 | call MOM_error(FATAL,"Overflow in reproducing_EFP_sum(_2d) conversion of "//trim(mesg)) |
| 220 | endif | |
| 221 | 10 | if (overflow_error) then |
| 222 | 0 | call MOM_error(FATAL, "Overflow in reproducing_EFP_sum(_2d).") |
| 223 | endif | |
| 224 | endif | |
| 225 | ||
| 226 | 10 | if (do_sum_across_PEs) call sum_across_PEs(ints_sum, efp_digits) |
| 227 | ||
| 228 | 10 | call regularize_ints(ints_sum) |
| 229 | ||
| 230 | 70 | EFP_sum%v(:) = ints_sum(:) |
| 231 | ||
| 232 | 10 | end function reproducing_EFP_sum_2d |
| 233 | ||
| 234 | ||
| 235 | !> This subroutine uses a conversion to an integer representation of real numbers to give an | |
| 236 | !! order-invariant sum of distributed 2-D arrays that reproduces across domain decomposition. | |
| 237 | !! This technique is described in Hallberg & Adcroft, 2014, Parallel Computing, | |
| 238 | !! doi:10.1016/j.parco.2014.04.007. | |
| 239 | 1 | function reproducing_sum_2d(array, isr, ier, jsr, jer, EFP_sum, reproducing, & |
| 240 | overflow_check, err, only_on_PE, unscale) result(sum) | |
| 241 | real, dimension(:,:), intent(in) :: array !< The array to be summed in arbitrary units [a], or in | |
| 242 | !! arbitrary scaled units [A ~> a] if unscale is present | |
| 243 | integer, optional, intent(in) :: isr !< The starting i-index of the sum, noting | |
| 244 | !! that the array indices starts at 1 | |
| 245 | integer, optional, intent(in) :: ier !< The ending i-index of the sum, noting | |
| 246 | !! that the array indices starts at 1 | |
| 247 | integer, optional, intent(in) :: jsr !< The starting j-index of the sum, noting | |
| 248 | !! that the array indices starts at 1 | |
| 249 | integer, optional, intent(in) :: jer !< The ending j-index of the sum, noting | |
| 250 | !! that the array indices starts at 1 | |
| 251 | type(EFP_type), optional, intent(out) :: EFP_sum !< The result in extended fixed point format | |
| 252 | logical, optional, intent(in) :: reproducing !< If present and false, do the sum | |
| 253 | !! using the naive non-reproducing approach | |
| 254 | logical, optional, intent(in) :: overflow_check !< If present and false, disable | |
| 255 | !! checking for overflows in incremental results. | |
| 256 | !! This can speed up calculations if the number | |
| 257 | !! of values being summed is small enough | |
| 258 | integer, optional, intent(out) :: err !< If present, return an error code instead of | |
| 259 | !! triggering any fatal errors directly from | |
| 260 | !! this routine. | |
| 261 | logical, optional, intent(in) :: only_on_PE !< If present and true, do not do the sum | |
| 262 | !! across processors, only reporting the local sum | |
| 263 | real, optional, intent(in) :: unscale !< A factor that is used to undo scaling of array before it is | |
| 264 | !! summed, often to compensate for the scaling in [a A-1 ~> 1] | |
| 265 | real :: sum !< The sum of the values in array in the same | |
| 266 | !! arbitrary units as array [a] or [A ~> a] | |
| 267 | ||
| 268 | ! Local variables | |
| 269 | integer(kind=int64), dimension(efp_digits) :: ints_sum | |
| 270 | integer(kind=int64) :: prec_error | |
| 271 | real :: rsum(1) ! The running sum, in arbitrary units [a] | |
| 272 | real :: descale ! A local copy of unscale if it is present [a A-1 ~> 1] or 1 | |
| 273 | real :: I_unscale ! The reciprocal of unscale [A a-1 ~> 1] | |
| 274 | logical :: repro, do_sum_across_PEs, do_unscale | |
| 275 | character(len=256) :: mesg | |
| 276 | type(EFP_type) :: EFP_val ! An extended fixed point version of the sum | |
| 277 | integer :: i, j, is, ie, js, je | |
| 278 | ||
| 279 | 1 | if (num_PEs() > max_summands) call MOM_error(FATAL, & |
| 280 | "reproducing_sum: Too many processors are being used for the value of "//& | |
| 281 | 0 | "prec. Reduce prec to (2^63-1)/num_PEs.") |
| 282 | ||
| 283 | 1 | prec_error = huge(1_int64) / num_PEs() |
| 284 | ||
| 285 | 1 | is = 1 ; ie = size(array,1) ; js = 1 ; je = size(array,2) |
| 286 | 1 | if (present(isr)) then |
| 287 | 0 | if (isr < is) call MOM_error(FATAL, "Value of isr too small in reproducing_sum_2d.") |
| 288 | 0 | is = isr |
| 289 | endif | |
| 290 | 1 | if (present(ier)) then |
| 291 | 0 | if (ier > ie) call MOM_error(FATAL, "Value of ier too large in reproducing_sum_2d.") |
| 292 | 0 | ie = ier |
| 293 | endif | |
| 294 | 1 | if (present(jsr)) then |
| 295 | 0 | if (jsr < js) call MOM_error(FATAL, "Value of jsr too small in reproducing_sum_2d.") |
| 296 | 0 | js = jsr |
| 297 | endif | |
| 298 | 1 | if (present(jer)) then |
| 299 | 0 | if (jer > je) call MOM_error(FATAL, "Value of jer too large in reproducing_sum_2d.") |
| 300 | 0 | je = jer |
| 301 | endif | |
| 302 | ||
| 303 | 1 | repro = .true. ; if (present(reproducing)) repro = reproducing |
| 304 | 1 | do_sum_across_PEs = .true. ; if (present(only_on_PE)) do_sum_across_PEs = .not.only_on_PE |
| 305 | 1 | do_unscale = .false. ; if (present(unscale)) do_unscale = (unscale /= 1.0) |
| 306 | 1 | descale = 1.0 ; I_unscale = 1.0 |
| 307 | 1 | if (do_unscale) then |
| 308 | 0 | descale = unscale |
| 309 | 0 | if (abs(unscale) > 0.0) I_unscale = 1.0 / unscale |
| 310 | endif | |
| 311 | ||
| 312 | 1 | if (repro) then |
| 313 | 1 | EFP_val = reproducing_EFP_sum_2d(array, isr, ier, jsr, jer, overflow_check, err, only_on_PE, unscale) |
| 314 | 1 | sum = ints_to_real(EFP_val%v) * I_unscale |
| 315 | 1 | if (present(EFP_sum)) EFP_sum = EFP_val |
| 316 | 1 | if (debug) ints_sum(:) = EFP_sum%v(:) |
| 317 | else | |
| 318 | 0 | rsum(1) = 0.0 |
| 319 | 0 | do j=js,je ; do i=is,ie |
| 320 | 0 | rsum(1) = rsum(1) + descale*array(i,j) |
| 321 | enddo ; enddo | |
| 322 | 0 | if (do_sum_across_PEs) call sum_across_PEs(rsum,1) |
| 323 | 0 | sum = rsum(1) * I_unscale |
| 324 | ||
| 325 | 0 | if (present(err)) then ; err = 0 ; endif |
| 326 | ||
| 327 | 0 | if (debug .or. present(EFP_sum)) then |
| 328 | 0 | overflow_error = .false. |
| 329 | 0 | ints_sum = real_to_ints(sum, prec_error, overflow_error) |
| 330 | 0 | if (overflow_error) then |
| 331 | 0 | if (present(err)) then |
| 332 | 0 | err = err + 2 |
| 333 | else | |
| 334 | 0 | write(mesg, '(ES13.5)') sum |
| 335 | 0 | call MOM_error(FATAL,"Repro_sum_2d: Overflow in real_to_ints conversion of "//trim(mesg)) |
| 336 | endif | |
| 337 | endif | |
| 338 | endif | |
| 339 | 0 | if (present(EFP_sum)) EFP_sum%v(:) = ints_sum(:) |
| 340 | endif | |
| 341 | ||
| 342 | 1 | if (debug) then |
| 343 | 0 | write(mesg,'("2d RS: ", ES24.16, 6 Z17.16)') sum*descale, ints_sum(1:efp_digits) |
| 344 | 0 | call MOM_mesg(mesg, 3) |
| 345 | endif | |
| 346 | ||
| 347 | 1 | end function reproducing_sum_2d |
| 348 | ||
| 349 | !> This subroutine uses a conversion to an integer representation of real numbers to give an | |
| 350 | !! order-invariant sum of distributed 3-D arrays that reproduces across domain decomposition. | |
| 351 | !! This technique is described in Hallberg & Adcroft, 2014, Parallel Computing, | |
| 352 | !! doi:10.1016/j.parco.2014.04.007. | |
| 353 | 6 | function reproducing_sum_3d(array, isr, ier, jsr, jer, sums, EFP_sum, EFP_lay_sums, err, only_on_PE, unscale) & |
| 354 | result(sum) | |
| 355 | real, dimension(:,:,:), intent(in) :: array !< The array to be summed in arbitrary units [a], or in | |
| 356 | !! arbitrary scaled units [A ~> a] if unscale is present | |
| 357 | integer, optional, intent(in) :: isr !< The starting i-index of the sum, noting | |
| 358 | !! that the array indices starts at 1 | |
| 359 | integer, optional, intent(in) :: ier !< The ending i-index of the sum, noting | |
| 360 | !! that the array indices starts at 1 | |
| 361 | integer, optional, intent(in) :: jsr !< The starting j-index of the sum, noting | |
| 362 | !! that the array indices starts at 1 | |
| 363 | integer, optional, intent(in) :: jer !< The ending j-index of the sum, noting | |
| 364 | !! that the array indices starts at 1 | |
| 365 | real, dimension(:), optional, intent(out) :: sums !< The sums by vertical layer in the same | |
| 366 | !! arbitrary units as array [a] or [A ~> a] | |
| 367 | type(EFP_type), optional, intent(out) :: EFP_sum !< The result in extended fixed point format | |
| 368 | type(EFP_type), dimension(:), & | |
| 369 | optional, intent(out) :: EFP_lay_sums !< The sums by vertical layer in EFP format | |
| 370 | integer, optional, intent(out) :: err !< If present, return an error code instead of | |
| 371 | !! triggering any fatal errors directly from | |
| 372 | !! this routine. | |
| 373 | logical, optional, intent(in) :: only_on_PE !< If present and true, do not do the sum | |
| 374 | !! across processors, only reporting the local sum | |
| 375 | real, optional, intent(in) :: unscale !< A factor that is used to undo scaling of array before it is | |
| 376 | !! summed, often to compensate for the scaling in [a A-1 ~> 1] | |
| 377 | real :: sum !< The sum of the values in array in the same | |
| 378 | !! arbitrary units as array [a] or [A ~> a] | |
| 379 | ||
| 380 | ! Local variables | |
| 381 | real :: val ! The real number that is extracted in arbitrary units [a] | |
| 382 | real :: max_mag_term ! A running maximum magnitude of the val's in arbitrary units [a] | |
| 383 | real :: descale ! A local copy of unscale if it is present [a A-1 ~> 1] or 1 | |
| 384 | real :: I_unscale ! The Adcroft reciprocal of unscale [A a-1 ~> 1] | |
| 385 | integer(kind=int64), dimension(efp_digits) :: ints_sum | |
| 386 | 12 | integer(kind=int64), dimension(efp_digits,size(array,3)) :: ints_sums |
| 387 | integer(kind=int64) :: prec_error | |
| 388 | character(len=256) :: mesg | |
| 389 | logical :: do_sum_across_PEs, do_unscale | |
| 390 | integer :: i, j, k, is, ie, js, je, ke, isz, jsz, n | |
| 391 | ||
| 392 | 6 | if (num_PEs() > max_summands) call MOM_error(FATAL, & |
| 393 | "reproducing_sum: Too many processors are being used for the value of "//& | |
| 394 | 0 | "prec. Reduce prec to (2^63-1)/num_PEs.") |
| 395 | ||
| 396 | 6 | prec_error = huge(1_int64) / num_PEs() |
| 397 | 6 | max_mag_term = 0.0 |
| 398 | ||
| 399 | 6 | is = 1 ; ie = size(array,1) ; js = 1 ; je = size(array,2) ; ke = size(array,3) |
| 400 | 6 | if (present(isr)) then |
| 401 | 6 | if (isr < is) call MOM_error(FATAL, "Value of isr too small in reproducing_sum(_3d).") |
| 402 | 6 | is = isr |
| 403 | endif | |
| 404 | 6 | if (present(ier)) then |
| 405 | 6 | if (ier > ie) call MOM_error(FATAL, "Value of ier too large in reproducing_sum(_3d).") |
| 406 | 6 | ie = ier |
| 407 | endif | |
| 408 | 6 | if (present(jsr)) then |
| 409 | 6 | if (jsr < js) call MOM_error(FATAL, "Value of jsr too small in reproducing_sum(_3d).") |
| 410 | 6 | js = jsr |
| 411 | endif | |
| 412 | 6 | if (present(jer)) then |
| 413 | 6 | if (jer > je) call MOM_error(FATAL, "Value of jer too large in reproducing_sum(_3d).") |
| 414 | 6 | je = jer |
| 415 | endif | |
| 416 | 6 | jsz = je+1-js ; isz = ie+1-is |
| 417 | ||
| 418 | 6 | do_sum_across_PEs = .true. ; if (present(only_on_PE)) do_sum_across_PEs = .not.only_on_PE |
| 419 | 6 | do_unscale = .false. ; if (present(unscale)) do_unscale = (unscale /= 1.0) |
| 420 | 6 | descale = 1.0 ; if (do_unscale) descale = unscale |
| 421 | ||
| 422 | 6 | if (present(sums) .or. present(EFP_lay_sums)) then |
| 423 | 6 | if (present(sums)) then ; if (size(sums) < ke) then |
| 424 | 0 | call MOM_error(FATAL, "Sums is smaller than the vertical extent of array in reproducing_sum(_3d).") |
| 425 | endif ; endif | |
| 426 | 6 | if (present(EFP_lay_sums)) then ; if (size(EFP_lay_sums) < ke) then |
| 427 | 0 | call MOM_error(FATAL, "Sums is smaller than the vertical extent of array in reproducing_sum(_3d).") |
| 428 | endif ; endif | |
| 429 | ||
| 430 | 6 | overflow_error = .false. ; NaN_error = .false. ; max_mag_term = 0.0 |
| 431 | ||
| 432 | 944 | ints_sums(:,:) = 0 |
| 433 | 140 | do k=1,ke |
| 434 | call increment_block_ints(array(:,:,k), is, ie, js, je, descale, & | |
| 435 | 140 | ints_sums(:,k), max_mag_term, prec_error) |
| 436 | enddo | |
| 437 | ||
| 438 | 6 | if (present(err)) then |
| 439 | 0 | err = 0 |
| 440 | 0 | if (abs(max_mag_term) >= prec_error*pr(1)) err = err+1 |
| 441 | 0 | if (overflow_error) err = err+2 |
| 442 | 0 | if (NaN_error) err = err+2 |
| 443 | 0 | if (err > 0) then ; do k=1,ke ; do n=1,efp_digits ; ints_sums(n,k) = 0 ; enddo ; enddo ; endif |
| 444 | else | |
| 445 | 6 | if (NaN_error) call MOM_error(FATAL, "NaN in input field of reproducing_sum(_3d).") |
| 446 | 6 | if (abs(max_mag_term) >= prec_error*pr(1)) then |
| 447 | 0 | write(mesg, '(ES13.5)') max_mag_term |
| 448 | 0 | call MOM_error(FATAL,"Overflow in reproducing_sum(_3d) conversion of "//trim(mesg)) |
| 449 | endif | |
| 450 | 6 | if (overflow_error) call MOM_error(FATAL, "Overflow in reproducing_sum(_3d).") |
| 451 | endif | |
| 452 | ||
| 453 | 6 | if (do_sum_across_PEs) call sum_across_PEs(ints_sums(:,1:ke), efp_digits*ke) |
| 454 | ||
| 455 | 6 | sum = 0.0 |
| 456 | 140 | do k=1,ke |
| 457 | 134 | call regularize_ints(ints_sums(:,k)) |
| 458 | 134 | val = ints_to_real(ints_sums(:,k)) |
| 459 | 134 | if (present(sums)) sums(k) = val |
| 460 | 140 | sum = sum + val |
| 461 | enddo | |
| 462 | 6 | if (present(EFP_lay_sums)) then ; do k=1,ke |
| 463 | 0 | EFP_lay_sums(k)%v(:) = ints_sums(:,k) |
| 464 | enddo ; endif | |
| 465 | ||
| 466 | 6 | if (present(EFP_sum)) then |
| 467 | 14 | EFP_sum%v(:) = 0 |
| 468 | 46 | do k=1,ke ; call increment_ints(EFP_sum%v(:), ints_sums(:,k)) ; enddo |
| 469 | endif | |
| 470 | ||
| 471 | 6 | if (debug) then |
| 472 | 0 | do n=1,efp_digits ; ints_sum(n) = 0 ; enddo |
| 473 | 0 | do k=1,ke ; do n=1,efp_digits ; ints_sum(n) = ints_sum(n) + ints_sums(n,k) ; enddo ; enddo |
| 474 | 0 | write(mesg,'("3D RS: ", ES24.16, 6 Z17.16)') sum, ints_sum(1:efp_digits) |
| 475 | 0 | call MOM_mesg(mesg, 3) |
| 476 | endif | |
| 477 | else | |
| 478 | 0 | overflow_error = .false. ; NaN_error = .false. ; max_mag_term = 0.0 |
| 479 | ||
| 480 | 0 | ints_sum(:) = 0 |
| 481 | 0 | do k=1,ke |
| 482 | call increment_block_ints(array(:,:,k), is, ie, js, je, descale, & | |
| 483 | 0 | ints_sum, max_mag_term, prec_error) |
| 484 | enddo | |
| 485 | ||
| 486 | 0 | if (present(err)) then |
| 487 | 0 | err = 0 |
| 488 | 0 | if (abs(max_mag_term) >= prec_error*pr(1)) err = err+1 |
| 489 | 0 | if (overflow_error) err = err+2 |
| 490 | 0 | if (NaN_error) err = err+2 |
| 491 | 0 | if (err > 0) then ; do n=1,efp_digits ; ints_sum(n) = 0 ; enddo ; endif |
| 492 | else | |
| 493 | 0 | if (NaN_error) call MOM_error(FATAL, "NaN in input field of reproducing_sum(_3d).") |
| 494 | 0 | if (abs(max_mag_term) >= prec_error*pr(1)) then |
| 495 | 0 | write(mesg, '(ES13.5)') max_mag_term |
| 496 | 0 | call MOM_error(FATAL,"Overflow in reproducing_sum(_3d) conversion of "//trim(mesg)) |
| 497 | endif | |
| 498 | 0 | if (overflow_error) call MOM_error(FATAL, "Overflow in reproducing_sum(_3d).") |
| 499 | endif | |
| 500 | ||
| 501 | 0 | if (do_sum_across_PEs) call sum_across_PEs(ints_sum, efp_digits) |
| 502 | ||
| 503 | 0 | call regularize_ints(ints_sum) |
| 504 | 0 | sum = ints_to_real(ints_sum) |
| 505 | ||
| 506 | 0 | if (present(EFP_sum)) EFP_sum%v(:) = ints_sum(:) |
| 507 | ||
| 508 | 0 | if (debug) then |
| 509 | 0 | write(mesg,'("3d RS: ", ES24.16, 6 Z17.16)') sum, ints_sum(1:efp_digits) |
| 510 | 0 | call MOM_mesg(mesg, 3) |
| 511 | endif | |
| 512 | endif | |
| 513 | ||
| 514 | 6 | if (do_unscale) then |
| 515 | ! Revise the sum to restore the scaling of input array before it is returned | |
| 516 | 0 | I_unscale = 0.0 ; if (abs(unscale) > 0.0) I_unscale = 1.0 / unscale |
| 517 | 0 | sum = sum * I_unscale |
| 518 | 0 | if (present(sums)) then |
| 519 | 0 | do k=1,ke ; sums(k) = sums(k) * I_unscale ; enddo |
| 520 | endif | |
| 521 | endif | |
| 522 | ||
| 523 | 6 | end function reproducing_sum_3d |
| 524 | ||
| 525 | !> Convert a real number into the array of integers constitute its extended-fixed-point representation | |
| 526 | 9 | function real_to_ints(r, prec_error, overflow) result(ints) |
| 527 | real, intent(in) :: r !< The real number being converted in arbitrary units [a] | |
| 528 | integer(kind=int64), optional, intent(in) :: prec_error !< The PE-count dependent precision of the | |
| 529 | !! integers that is safe from overflows during global | |
| 530 | !! sums. This will be larger than the compile-time | |
| 531 | !! precision parameter, and is used to detect overflows. | |
| 532 | logical, optional, intent(inout) :: overflow !< Returns true if the conversion is being | |
| 533 | !! done on a value that is too large to be represented | |
| 534 | integer(kind=int64), dimension(efp_digits) :: ints | |
| 535 | ||
| 536 | ! This subroutine converts a real number to an equivalent representation | |
| 537 | ! using several long integers. | |
| 538 | ||
| 539 | ! Local variables | |
| 540 | real :: rs ! The remaining value to add, in arbitrary units [a] | |
| 541 | character(len=80) :: mesg | |
| 542 | integer(kind=int64) :: ival, prec_err | |
| 543 | integer :: sgn, i | |
| 544 | ||
| 545 | 9 | prec_err = prec ; if (present(prec_error)) prec_err = prec_error |
| 546 | 63 | ints(:) = 0 |
| 547 | 9 | if ((r >= 1e30) .eqv. (r < 1e30)) then ; NaN_error = .true. ; return ; endif |
| 548 | ||
| 549 | 9 | sgn = 1 ; if (r<0.0) sgn = -1 |
| 550 | 9 | rs = abs(r) |
| 551 | ||
| 552 | 9 | if (present(overflow)) then |
| 553 | 9 | if (.not.(rs < prec_err*pr(1))) overflow = .true. |
| 554 | 9 | if ((r >= 1e30) .eqv. (r < 1e30)) overflow = .true. |
| 555 | 0 | elseif (.not.(rs < prec_err*pr(1))) then |
| 556 | 0 | write(mesg, '(ES13.5)') r |
| 557 | 0 | call MOM_error(FATAL,"Overflow in real_to_ints conversion of "//trim(mesg)) |
| 558 | endif | |
| 559 | ||
| 560 | 63 | do i=1,efp_digits |
| 561 | 54 | ival = int(rs*I_pr(i), kind=int64) |
| 562 | 54 | rs = rs - ival*pr(i) |
| 563 | 63 | ints(i) = sgn*ival |
| 564 | enddo | |
| 565 | ||
| 566 | end function real_to_ints | |
| 567 | ||
| 568 | !> Convert the array of integers that constitute an extended-fixed-point | |
| 569 | !! representation into a real number | |
| 570 | 153 | function ints_to_real(ints) result(r) |
| 571 | integer(kind=int64), dimension(efp_digits), intent(in) :: ints !< The array of EFP integers | |
| 572 | real :: r ! The real number that is extracted in arbitrary units [a] | |
| 573 | ! This subroutine reverses the conversion in real_to_ints. | |
| 574 | ||
| 575 | integer :: i | |
| 576 | ||
| 577 | 153 | r = 0.0 |
| 578 | 1071 | do i=1,efp_digits ; r = r + pr(i)*ints(i) ; enddo |
| 579 | 153 | end function ints_to_real |
| 580 | ||
| 581 | !> Increment an array of integers that constitutes an extended-fixed-point | |
| 582 | !! representation with a another EFP number | |
| 583 | 59 | subroutine increment_ints(int_sum, int2, prec_error) |
| 584 | integer(kind=int64), dimension(efp_digits), intent(inout) :: int_sum !< The array of EFP integers being incremented | |
| 585 | integer(kind=int64), dimension(efp_digits), intent(in) :: int2 !< The array of EFP integers being added | |
| 586 | integer(kind=int64), optional, intent(in) :: prec_error !< The PE-count dependent precision of the | |
| 587 | !! integers that is safe from overflows during global | |
| 588 | !! sums. This will be larger than the compile-time | |
| 589 | !! precision parameter, and is used to detect overflows. | |
| 590 | ||
| 591 | ! This subroutine increments a number with another, both using the integer | |
| 592 | ! representation in real_to_ints. | |
| 593 | integer :: i | |
| 594 | ||
| 595 | 354 | do i=efp_digits,2,-1 |
| 596 | 295 | int_sum(i) = int_sum(i) + int2(i) |
| 597 | ! Carry the local overflow. | |
| 598 | 354 | if (int_sum(i) > prec) then |
| 599 | 40 | int_sum(i) = int_sum(i) - prec |
| 600 | 40 | int_sum(i-1) = int_sum(i-1) + 1 |
| 601 | 255 | elseif (int_sum(i) < -prec) then |
| 602 | 0 | int_sum(i) = int_sum(i) + prec |
| 603 | 0 | int_sum(i-1) = int_sum(i-1) - 1 |
| 604 | endif | |
| 605 | enddo | |
| 606 | 59 | int_sum(1) = int_sum(1) + int2(1) |
| 607 | 59 | if (present(prec_error)) then |
| 608 | 0 | if (abs(int_sum(1)) > prec_error) overflow_error = .true. |
| 609 | else | |
| 610 | 59 | if (abs(int_sum(1)) > prec) overflow_error = .true. |
| 611 | endif | |
| 612 | ||
| 613 | 59 | end subroutine increment_ints |
| 614 | ||
| 615 | ||
| 616 | !> Sum the elements of an array in EFP form and append the result to an | |
| 617 | !! existing EFP array. | |
| 618 | 144 | subroutine increment_block_ints(array, is, ie, js, je, descale, ints_sum, & |
| 619 | max_mag_term, prec_error) | |
| 620 | real, intent(in) :: array(:,:) | |
| 621 | !< The field being added, in arbitrary units [A ~> a] | |
| 622 | integer, intent(in) :: is | |
| 623 | !< Start i-index of the summed domain | |
| 624 | integer, intent(in) :: ie | |
| 625 | !< End i-index of the summed domain | |
| 626 | integer, intent(in) :: js | |
| 627 | !< Start j-index of the summed domain | |
| 628 | integer, intent(in) :: je | |
| 629 | !< End j-index of the summed domain | |
| 630 | real, intent(in) :: descale | |
| 631 | !< Factor to descale array to physical value [a A-1 ~> 1] | |
| 632 | integer(kind=int64), intent(inout) :: ints_sum(efp_digits) | |
| 633 | !< The array of EFP integers being incremented | |
| 634 | real, intent(inout) :: max_mag_term | |
| 635 | !< A running maximum magnitude of the r's, in arbitrary units [a] | |
| 636 | integer(kind=int64), intent(in) :: prec_error | |
| 637 | !< The maximum resolvable value for a given number of PEs | |
| 638 | ||
| 639 | integer :: i, j, ib, jb, ibs, ibe, jbs, jbe | |
| 640 | ! Loop indices | |
| 641 | integer :: b | |
| 642 | ! Block counter | |
| 643 | integer :: ni, nj | |
| 644 | ! Array summation domain size along each axis | |
| 645 | integer :: isize_max | |
| 646 | ! Largest block size in i. Typically equal to ni | |
| 647 | integer :: jsize | |
| 648 | ! Number of j-rows per block. | |
| 649 | integer :: nblocks, niblocks, njblocks | |
| 650 | ! Number of total blocks, and number of blocks in i and j | |
| 651 | integer(kind=int64) :: e(efp_digits) | |
| 652 | ! The EPF representation of each array element | |
| 653 | integer(kind=int64) :: block_sum(efp_digits), array_sum(efp_digits) | |
| 654 | ! The cumulant per-block and total array EFP sums | |
| 655 | real :: r, rmag | |
| 656 | ! Local array element value and its magnitude [a] | |
| 657 | real :: max_pos, max_neg, block_max_pos, block_max_neg | |
| 658 | ! Largest positive and negative values (whole array and per-block) used to | |
| 659 | ! find the largest maximum magnitude of array in a thread-safe manner [a] | |
| 660 | integer :: inan, iovf, lnan, lovf | |
| 661 | ! Thread-safe tracking of NaN and overflow state | |
| 662 | integer :: max_sum_count | |
| 663 | ! The total number of local sum operations that ensures no carry overflow | |
| 664 | ||
| 665 | 144 | max_pos = max(0., max_mag_term) |
| 666 | 144 | max_neg = max(0., -max_mag_term) |
| 667 | 144 | inan = 0 ; iovf = 0 |
| 668 | ||
| 669 | ! Reduce the maximum number of summations to account for the cumulant | |
| 670 | ! summations of array_sum and ints_sum. | |
| 671 | 144 | max_sum_count = max_summands - 2 |
| 672 | ||
| 673 | ! Get the compute domain size | |
| 674 | 144 | ni = ie - is + 1 |
| 675 | 144 | nj = je - js + 1 |
| 676 | ||
| 677 | ! Partition in i so that the widest i-slice fits within max_sum_count. | |
| 678 | 144 | niblocks = (ni + max_sum_count - 1) / max_sum_count |
| 679 | ! = ⌈ni / max_sum_count⌉ | |
| 680 | ||
| 681 | ! NOTE: niblocks is typically one, since default max_sum_count is ~130k. | |
| 682 | ||
| 683 | ! For a balanced i-partition, the number of i-points per block is either | |
| 684 | ! ⌊ni / niblocks⌋ or ⌈ni / niblocks⌉. Use the upper bound to find jsize. | |
| 685 | ||
| 686 | 144 | isize_max = (ni + niblocks - 1) / niblocks |
| 687 | ! = ⌈ni / niblocks⌉ | |
| 688 | ||
| 689 | ! Set jsize so that the widest i-slice times the number of j-rows does not | |
| 690 | ! exceed max_sum_count. | |
| 691 | 144 | jsize = max_sum_count / isize_max |
| 692 | ! = ⌊max_sum_count / isize_max⌋ | |
| 693 | ||
| 694 | ! Choose enough j-blocks so that no j-block has more than jsize rows. | |
| 695 | 144 | njblocks = (nj + jsize - 1) / jsize |
| 696 | ! = ⌈nj / jsize⌉ | |
| 697 | ||
| 698 | 144 | nblocks = niblocks * njblocks |
| 699 | ||
| 700 | ! Abort if the number of blocks also exceeds the carry-bit summation limit. | |
| 701 | ! For default settings, this would be over 17 billion points per PE. | |
| 702 | 144 | if (nblocks > max_sum_count) call MOM_error(FATAL, & |
| 703 | "reproducing sum: Number of blocks exceeds summmation carry limit." & | |
| 704 | 0 | ) |
| 705 | ||
| 706 | 144 | array_sum(:) = 0 |
| 707 | ||
| 708 | 432 | do jb=1,njblocks ; do ib=1,niblocks |
| 709 | ! Use evenly distributed blocks, either ⌊n / nblocks⌋ or ⌈n / nblocks⌉. | |
| 710 | 144 | jbs = js + ((jb - 1) * nj) / njblocks |
| 711 | 144 | jbe = js + (jb * nj) / njblocks - 1 |
| 712 | ||
| 713 | 144 | ibs = is + ((ib - 1) * ni) / niblocks |
| 714 | 144 | ibe = is + (ib * ni) / niblocks - 1 |
| 715 | ||
| 716 | 144 | block_sum(:) = 0 |
| 717 | 144 | block_max_pos = 0. |
| 718 | 144 | block_max_neg = 0. |
| 719 | ||
| 720 | ! Compute the sum of each block | |
| 721 | do concurrent (j=jbs:jbe, i=ibs:ibe) & | |
| 722 | DO_LOCALITY(local(r, e, rmag, lnan, lovf)) & | |
| 723 | DO_LOCALITY(reduce(+: block_sum)) & | |
| 724 | 144 | DO_LOCALITY(reduce(max: block_max_pos, block_max_neg, inan, iovf)) |
| 725 | ||
| 726 | ! Convert array(i,j) to EFP form | |
| 727 | 9331200 | r = descale * array(i,j) |
| 728 | 9331200 | call efp_decompose(r, e, rmag, lnan, lovf) |
| 729 | ||
| 730 | ! Verify that the conversion was completed | |
| 731 | 9331200 | inan = max(inan, lnan) |
| 732 | 9331200 | iovf = max(iovf, lovf) |
| 733 | ||
| 734 | 9331200 | if (r >= 0.) then |
| 735 | 9326530 | if (rmag > block_max_pos) block_max_pos = rmag |
| 736 | else | |
| 737 | 4670 | if (rmag > block_max_neg) block_max_neg = rmag |
| 738 | endif | |
| 739 | ||
| 740 | ! Add the EFP result (including potential carry bits) | |
| 741 | 65370384 | block_sum(:) = block_sum(:) + e(:) |
| 742 | enddo ; enddo | |
| 743 | ||
| 744 | 1008 | array_sum(:) = array_sum(:) + block_sum(:) |
| 745 | ||
| 746 | ! Redistribute carry bits across bins | |
| 747 | ! For the final pass (or single pass) this is handled by ints_sum. | |
| 748 | 144 | b = (jb - 1) * niblocks + ib |
| 749 | 144 | if (b < nblocks) call carry_overflow(array_sum, prec_error) |
| 750 | ||
| 751 | ! Update maximum magnitudes | |
| 752 | 144 | max_pos = max(max_pos, block_max_pos) |
| 753 | 288 | max_neg = max(max_neg, block_max_neg) |
| 754 | enddo | |
| 755 | ||
| 756 | ! Finally, apply the cumulant result | |
| 757 | 1008 | ints_sum(:) = ints_sum(:) + array_sum(:) |
| 758 | ||
| 759 | ! Redistribute carry bits to normalize the final result. | |
| 760 | 144 | call carry_overflow(ints_sum, prec_error) |
| 761 | ||
| 762 | ! Extract the maximum value while preserving sign (NOTE: ties to positive) | |
| 763 | 144 | if (max_pos >= max_neg) then |
| 764 | 144 | max_mag_term = max_pos |
| 765 | else | |
| 766 | 0 | max_mag_term = -max_neg |
| 767 | endif | |
| 768 | ||
| 769 | ! Transfer error/warning signals to module flags | |
| 770 | 144 | if (inan /= 0) NaN_error = .true. |
| 771 | 144 | if (iovf /= 0) overflow_error = .true. |
| 772 | 144 | end subroutine increment_block_ints |
| 773 | ||
| 774 | ||
| 775 | !> Decompose one real into its 6 signed EFP bin contributions. NaNs and | |
| 776 | !! overflows are reported by flags, rather than the module-level error | |
| 777 | !! logicals, so that the routine is free of side effects. | |
| 778 | 9331200 | pure subroutine efp_decompose(r, e, rmag, is_nan, is_ovf) |
| 779 | !$omp declare target | |
| 780 | real, intent(in) :: r | |
| 781 | !< The real number being decomposed [a] | |
| 782 | integer(kind=int64), intent(out) :: e(efp_digits) | |
| 783 | !< Signed contribution to EFP bins | |
| 784 | real, intent(out) :: rmag | |
| 785 | !< Equals abs(r), or 0 if r is NaN/Inf [a] | |
| 786 | integer, intent(out) :: is_nan | |
| 787 | !< Equals 1 if r is a NaN or Inf, else 0 | |
| 788 | integer, intent(out) :: is_ovf | |
| 789 | !< Equals 1 if abs(r) has no EFP representation, else 0 | |
| 790 | ||
| 791 | real :: rs | |
| 792 | ! The remaining value to add, in arbitrary units [a] | |
| 793 | integer(kind=int64) :: ival | |
| 794 | integer :: sgn | |
| 795 | integer :: n | |
| 796 | ||
| 797 | 9331200 | e(:) = 0 |
| 798 | 9331200 | rmag = 0.0 ; is_nan = 0 ; is_ovf = 0 |
| 799 | ||
| 800 | 9331200 | if ((r >= 1e30) .eqv. (r < 1e30)) then |
| 801 | 0 | is_nan = 1 |
| 802 | 0 | return |
| 803 | endif | |
| 804 | ||
| 805 | 9331200 | sgn = 1 |
| 806 | 9331200 | if (r < 0.0) sgn = -1 |
| 807 | ||
| 808 | 9331200 | rs = abs(r) ; rmag = rs |
| 809 | ||
| 810 | ! Abort if the number has no EFP representation | |
| 811 | 9331200 | if (rs > max_efp_float) then |
| 812 | 0 | is_ovf = 1 |
| 813 | 0 | return |
| 814 | endif | |
| 815 | ||
| 816 | 65318400 | do n=1,efp_digits |
| 817 | 55987200 | ival = int(rs * I_pr(n), kind=int64) |
| 818 | 55987200 | rs = rs - ival * pr(n) |
| 819 | 55987200 | e(n) = sgn * ival |
| 820 | enddo | |
| 821 | end subroutine efp_decompose | |
| 822 | ||
| 823 | ||
| 824 | !> This subroutine handles carrying of the overflow. | |
| 825 | 156 | subroutine carry_overflow(int_sum, prec_error) |
| 826 | integer(kind=int64), dimension(efp_digits), intent(inout) :: int_sum !< The array of EFP integers being | |
| 827 | !! modified by carries, but without changing value. | |
| 828 | integer(kind=int64), intent(in) :: prec_error !< The PE-count dependent precision of the | |
| 829 | !! integers that is safe from overflows during global | |
| 830 | !! sums. This will be larger than the compile-time | |
| 831 | !! precision parameter, and is used to detect overflows. | |
| 832 | ||
| 833 | ! This subroutine handles carrying of the overflow. | |
| 834 | integer :: i, num_carry | |
| 835 | ||
| 836 | 936 | do i=efp_digits,2,-1 ; if (abs(int_sum(i)) >= prec) then |
| 837 | 320 | num_carry = int(int_sum(i) * I_prec) |
| 838 | 320 | int_sum(i) = int_sum(i) - num_carry*prec |
| 839 | 320 | int_sum(i-1) = int_sum(i-1) + num_carry |
| 840 | endif ; enddo | |
| 841 | 156 | if (abs(int_sum(1)) > prec_error) then |
| 842 | 0 | overflow_error = .true. |
| 843 | endif | |
| 844 | ||
| 845 | 156 | end subroutine carry_overflow |
| 846 | ||
| 847 | !> This subroutine carries the overflow, and then makes sure that | |
| 848 | !! all integers are of the same sign as the overall value. | |
| 849 | 162 | subroutine regularize_ints(int_sum) |
| 850 | integer(kind=int64), dimension(efp_digits), & | |
| 851 | intent(inout) :: int_sum !< The array of integers being modified to take a | |
| 852 | !! regular form with all integers of the same sign, | |
| 853 | !! but without changing value. | |
| 854 | ||
| 855 | ! This subroutine carries the overflow, and then makes sure that | |
| 856 | ! all integers are of the same sign as the overall value. | |
| 857 | logical :: positive | |
| 858 | integer :: i, num_carry | |
| 859 | ||
| 860 | 972 | do i=efp_digits,2,-1 ; if (abs(int_sum(i)) >= prec) then |
| 861 | 2 | num_carry = int(int_sum(i) * I_prec) |
| 862 | 2 | int_sum(i) = int_sum(i) - num_carry*prec |
| 863 | 2 | int_sum(i-1) = int_sum(i-1) + num_carry |
| 864 | endif ; enddo | |
| 865 | ||
| 866 | ! Determine the sign of the final number. | |
| 867 | 162 | positive = .true. |
| 868 | 526 | do i=1,efp_digits |
| 869 | 526 | if (abs(int_sum(i)) > 0) then |
| 870 | 128 | if (int_sum(i) < 0) positive = .false. |
| 871 | 128 | exit |
| 872 | endif | |
| 873 | enddo | |
| 874 | ||
| 875 | 162 | if (positive) then |
| 876 | 960 | do i=efp_digits,2,-1 ; if (int_sum(i) < 0) then |
| 877 | 4 | int_sum(i) = int_sum(i) + prec |
| 878 | 4 | int_sum(i-1) = int_sum(i-1) - 1 |
| 879 | endif ; enddo | |
| 880 | else | |
| 881 | 12 | do i=efp_digits,2,-1 ; if (int_sum(i) > 0) then |
| 882 | 1 | int_sum(i) = int_sum(i) - prec |
| 883 | 1 | int_sum(i-1) = int_sum(i-1) + 1 |
| 884 | endif ; enddo | |
| 885 | endif | |
| 886 | ||
| 887 | 162 | end subroutine regularize_ints |
| 888 | ||
| 889 | !> Returns the status of the module's error flag | |
| 890 | 0 | function query_EFP_overflow_error() |
| 891 | logical :: query_EFP_overflow_error | |
| 892 | 0 | query_EFP_overflow_error = overflow_error |
| 893 | 0 | end function query_EFP_overflow_error |
| 894 | ||
| 895 | !> Reset the module's error flag to false | |
| 896 | 0 | subroutine reset_EFP_overflow_error() |
| 897 | 0 | overflow_error = .false. |
| 898 | 0 | end subroutine reset_EFP_overflow_error |
| 899 | ||
| 900 | !> Add two extended-fixed-point numbers | |
| 901 | 3 | function EFP_plus(EFP1, EFP2) |
| 902 | type(EFP_type) :: EFP_plus !< The result in extended fixed point format | |
| 903 | type(EFP_type), intent(in) :: EFP1 !< The first extended fixed point number | |
| 904 | type(EFP_type), intent(in) :: EFP2 !< The second extended fixed point number | |
| 905 | ||
| 906 | 3 | EFP_plus = EFP1 |
| 907 | ||
| 908 | 3 | call increment_ints(EFP_plus%v(:), EFP2%v(:)) |
| 909 | 3 | end function EFP_plus |
| 910 | ||
| 911 | !> Subract one extended-fixed-point number from another | |
| 912 | 12 | function EFP_minus(EFP1, EFP2) |
| 913 | type(EFP_type) :: EFP_minus !< The result in extended fixed point format | |
| 914 | type(EFP_type), intent(in) :: EFP1 !< The first extended fixed point number | |
| 915 | type(EFP_type), intent(in) :: EFP2 !< The extended fixed point number being | |
| 916 | !! subtracted from the first extended fixed point number | |
| 917 | integer :: i | |
| 918 | ||
| 919 | 84 | do i=1,efp_digits ; EFP_minus%v(i) = -1*EFP2%v(i) ; enddo |
| 920 | ||
| 921 | 12 | call increment_ints(EFP_minus%v(:), EFP1%v(:)) |
| 922 | 12 | end function EFP_minus |
| 923 | ||
| 924 | !> Copy one extended-fixed-point number into another | |
| 925 | 68 | subroutine EFP_assign(EFP1, EFP2) |
| 926 | type(EFP_type), intent(out) :: EFP1 !< The recipient extended fixed point number | |
| 927 | type(EFP_type), intent(in) :: EFP2 !< The source extended fixed point number | |
| 928 | integer i | |
| 929 | ! This subroutine assigns all components of the extended fixed point type | |
| 930 | ! variable on the RHS (EFP2) to the components of the variable on the LHS | |
| 931 | ! (EFP1). | |
| 932 | ||
| 933 | 476 | do i=1,efp_digits ; EFP1%v(i) = EFP2%v(i) ; enddo |
| 934 | 68 | end subroutine EFP_assign |
| 935 | ||
| 936 | !> Return the real number that an extended-fixed-point number corresponds with | |
| 937 | 18 | function EFP_to_real(EFP1) |
| 938 | type(EFP_type), intent(inout) :: EFP1 !< The extended fixed point number being converted | |
| 939 | real :: EFP_to_real !< The real version of the number in arbitrary units [a] | |
| 940 | ||
| 941 | 18 | call regularize_ints(EFP1%v) |
| 942 | 18 | EFP_to_real = ints_to_real(EFP1%v) |
| 943 | 18 | end function EFP_to_real |
| 944 | ||
| 945 | !> Take the difference between two extended-fixed-point numbers (EFP1 - EFP2) | |
| 946 | !! and return the result as a real number | |
| 947 | 0 | function EFP_real_diff(EFP1, EFP2) |
| 948 | type(EFP_type), intent(in) :: EFP1 !< The first extended fixed point number | |
| 949 | type(EFP_type), intent(in) :: EFP2 !< The extended fixed point number being | |
| 950 | !! subtracted from the first extended fixed point number | |
| 951 | real :: EFP_real_diff !< The real result in arbitrary units [a] | |
| 952 | ||
| 953 | type(EFP_type) :: EFP_diff | |
| 954 | ||
| 955 | 0 | EFP_diff = EFP1 - EFP2 |
| 956 | 0 | EFP_real_diff = EFP_to_real(EFP_diff) |
| 957 | ||
| 958 | 0 | end function EFP_real_diff |
| 959 | ||
| 960 | !> Return the extended-fixed-point number that a real number corresponds with | |
| 961 | 9 | function real_to_EFP(val, overflow) |
| 962 | real, intent(in) :: val !< The real number being converted in arbitrary units [a] | |
| 963 | logical, optional, intent(inout) :: overflow !< Returns true if the conversion is being | |
| 964 | !! done on a value that is too large to be represented | |
| 965 | type(EFP_type) :: real_to_EFP | |
| 966 | ||
| 967 | logical :: over | |
| 968 | character(len=80) :: mesg | |
| 969 | ||
| 970 | 9 | if (present(overflow)) then |
| 971 | 0 | real_to_EFP%v(:) = real_to_ints(val, overflow=overflow) |
| 972 | else | |
| 973 | 9 | over = .false. |
| 974 | 63 | real_to_EFP%v(:) = real_to_ints(val, overflow=over) |
| 975 | 9 | if (over) then |
| 976 | 0 | write(mesg, '(ES13.5)') val |
| 977 | 0 | call MOM_error(FATAL,"Overflow in real_to_EFP conversion of "//trim(mesg)) |
| 978 | endif | |
| 979 | endif | |
| 980 | ||
| 981 | 9 | end function real_to_EFP |
| 982 | ||
| 983 | !> This subroutine does a sum across PEs of a list of EFP variables, | |
| 984 | !! returning the sums in place, with all overflows carried. | |
| 985 | 4 | subroutine EFP_list_sum_across_PEs(EFPs, nval, errors) |
| 986 | type(EFP_type), dimension(:), & | |
| 987 | intent(inout) :: EFPs !< The list of extended fixed point numbers | |
| 988 | !! being summed across PEs. | |
| 989 | integer, intent(in) :: nval !< The number of values being summed. | |
| 990 | logical, dimension(:), & | |
| 991 | optional, intent(out) :: errors !< A list of error flags for each sum | |
| 992 | ||
| 993 | ! This subroutine does a sum across PEs of a list of EFP variables, | |
| 994 | ! returning the sums in place, with all overflows carried. | |
| 995 | ||
| 996 | 8 | integer(kind=int64), dimension(efp_digits,nval) :: ints |
| 997 | integer(kind=int64) :: prec_error | |
| 998 | logical :: error_found | |
| 999 | character(len=256) :: mesg | |
| 1000 | integer :: i, n | |
| 1001 | ||
| 1002 | 4 | if (num_PEs() > max_summands) call MOM_error(FATAL, & |
| 1003 | "reproducing_sum: Too many processors are being used for the value of "//& | |
| 1004 | 0 | "prec. Reduce prec to (2^63-1)/num_PEs.") |
| 1005 | ||
| 1006 | 4 | prec_error = huge(1_int64) / num_PEs() |
| 1007 | ||
| 1008 | ! overflow_error is an overflow error flag for the whole module. | |
| 1009 | 4 | overflow_error = .false. ; error_found = .false. |
| 1010 | ||
| 1011 | 88 | do i=1,nval ; do n=1,efp_digits ; ints(n,i) = EFPs(i)%v(n) ; enddo ; enddo |
| 1012 | ||
| 1013 | 4 | call sum_across_PEs(ints(:,:), efp_digits*nval) |
| 1014 | ||
| 1015 | 4 | if (present(errors)) errors(:) = .false. |
| 1016 | 16 | do i=1,nval |
| 1017 | 12 | overflow_error = .false. |
| 1018 | 12 | call carry_overflow(ints(:,i), prec_error) |
| 1019 | 84 | do n=1,efp_digits ; EFPs(i)%v(n) = ints(n,i) ; enddo |
| 1020 | 12 | if (present(errors)) errors(i) = overflow_error |
| 1021 | 12 | if (overflow_error) then |
| 1022 | write (mesg,'("EFP_list_sum_across_PEs error at ",i0," val was ",ES12.6, ", prec_error = ",ES12.6)') & | |
| 1023 | 0 | i, EFP_to_real(EFPs(i)), real(prec_error) |
| 1024 | 0 | call MOM_error(WARNING, mesg) |
| 1025 | endif | |
| 1026 | 16 | error_found = error_found .or. overflow_error |
| 1027 | enddo | |
| 1028 | 4 | if (error_found .and. .not.(present(errors))) then |
| 1029 | 0 | call MOM_error(FATAL, "Overflow in EFP_list_sum_across_PEs.") |
| 1030 | endif | |
| 1031 | ||
| 1032 | 4 | end subroutine EFP_list_sum_across_PEs |
| 1033 | ||
| 1034 | !> This subroutine does a sum across PEs of an EFP variable, | |
| 1035 | !! returning the sums in place, with all overflows carried. | |
| 1036 | 0 | subroutine EFP_val_sum_across_PEs(EFP, error) |
| 1037 | type(EFP_type), intent(inout) :: EFP !< The extended fixed point numbers | |
| 1038 | !! being summed across PEs. | |
| 1039 | logical, optional, intent(out) :: error !< An error flag for this sum | |
| 1040 | ||
| 1041 | ! This subroutine does a sum across PEs of a list of EFP variables, | |
| 1042 | ! returning the sums in place, with all overflows carried. | |
| 1043 | ||
| 1044 | integer(kind=int64), dimension(efp_digits) :: ints | |
| 1045 | integer(kind=int64) :: prec_error | |
| 1046 | logical :: error_found | |
| 1047 | character(len=256) :: mesg | |
| 1048 | integer :: n | |
| 1049 | ||
| 1050 | 0 | if (num_PEs() > max_summands) call MOM_error(FATAL, & |
| 1051 | "reproducing_sum: Too many processors are being used for the value of "//& | |
| 1052 | 0 | "prec. Reduce prec to (2^63-1)/num_PEs.") |
| 1053 | ||
| 1054 | 0 | prec_error = huge(1_int64) / num_PEs() |
| 1055 | ||
| 1056 | ! overflow_error is an overflow error flag for the whole module. | |
| 1057 | 0 | overflow_error = .false. ; error_found = .false. |
| 1058 | ||
| 1059 | 0 | do n=1,efp_digits ; ints(n) = EFP%v(n) ; enddo |
| 1060 | ||
| 1061 | 0 | call sum_across_PEs(ints(:), efp_digits) |
| 1062 | ||
| 1063 | 0 | if (present(error)) error = .false. |
| 1064 | ||
| 1065 | 0 | overflow_error = .false. |
| 1066 | 0 | call carry_overflow(ints(:), prec_error) |
| 1067 | 0 | do n=1,efp_digits ; EFP%v(n) = ints(n) ; enddo |
| 1068 | 0 | if (present(error)) error = overflow_error |
| 1069 | 0 | if (overflow_error) then |
| 1070 | write (mesg,'("EFP_val_sum_across_PEs error val was ",ES12.6, ", prec_error = ",ES12.6)') & | |
| 1071 | 0 | EFP_to_real(EFP), real(prec_error) |
| 1072 | 0 | call MOM_error(WARNING, mesg) |
| 1073 | endif | |
| 1074 | 0 | error_found = error_found .or. overflow_error |
| 1075 | ||
| 1076 | 0 | if (error_found .and. .not.(present(error))) then |
| 1077 | 0 | call MOM_error(FATAL, "Overflow in EFP_val_sum_across_PEs.") |
| 1078 | endif | |
| 1079 | ||
| 1080 | 0 | end subroutine EFP_val_sum_across_PEs |
| 1081 | ||
| 1082 | 0 | end module MOM_coms |