1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 2008, 2010, 2011, 2015, 2016 Free Software Foundation, Inc.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
19 #include "language/expressions/helpers.h"
21 #include <gsl/gsl_roots.h>
22 #include <gsl/gsl_sf.h>
24 #include "language/expressions/private.h"
25 #include "libpspp/assertion.h"
26 #include "libpspp/pool.h"
28 #include "gl/minmax.h"
30 const struct substring empty_string = {NULL, 0};
33 expr_ymd_to_ofs (double year, double month, double day)
41 if (y != year || m != month || d != day)
43 msg (SE, _("One of the arguments to a DATE function is not an integer. "
44 "The result will be system-missing."));
48 ofs = calendar_gregorian_to_offset (y, m, d, settings_get_fmt_settings (),
52 msg (SE, "%s", error);
59 expr_ymd_to_date (double year, double month, double day)
61 double ofs = expr_ymd_to_ofs (year, month, day);
62 return ofs != SYSMIS ? ofs * DAY_S : SYSMIS;
66 expr_wkyr_to_date (double week, double year)
72 msg (SE, _("The week argument to DATE.WKYR is not an integer. "
73 "The result will be system-missing."));
76 else if (w < 1 || w > 53)
78 msg (SE, _("The week argument to DATE.WKYR is outside the acceptable "
80 "The result will be system-missing."));
85 double yr_1_1 = expr_ymd_to_ofs (year, 1, 1);
87 return DAY_S * (yr_1_1 + WEEK_DAY * (w - 1));
94 expr_yrday_to_date (double year, double yday)
100 msg (SE, _("The day argument to DATE.YRDAY is not an integer. "
101 "The result will be system-missing."));
104 else if (yd < 1 || yd > 366)
106 msg (SE, _("The day argument to DATE.YRDAY is outside the acceptable "
107 "range of 1 to 366. "
108 "The result will be system-missing."));
113 double yr_1_1 = expr_ymd_to_ofs (year, 1, 1);
114 if (yr_1_1 != SYSMIS)
115 return DAY_S * (yr_1_1 + yd - 1.);
122 expr_yrmoda (double year, double month, double day)
124 if (year >= 0 && year <= 99)
126 else if (year != (int) year && year > 47516)
128 msg (SE, _("The year argument to YRMODA is greater than 47516. "
129 "The result will be system-missing."));
133 return expr_ymd_to_ofs (year, month, day);
149 /* Stores in *UNIT the unit whose name is NAME.
151 static enum date_unit
152 recognize_unit (struct substring name, enum date_unit *unit)
157 const struct substring name;
159 static const struct unit_name unit_names[] =
161 { DATE_YEARS, SS_LITERAL_INITIALIZER ("years") },
162 { DATE_QUARTERS, SS_LITERAL_INITIALIZER ("quarters") },
163 { DATE_MONTHS, SS_LITERAL_INITIALIZER ("months") },
164 { DATE_WEEKS, SS_LITERAL_INITIALIZER ("weeks") },
165 { DATE_DAYS, SS_LITERAL_INITIALIZER ("days") },
166 { DATE_HOURS, SS_LITERAL_INITIALIZER ("hours") },
167 { DATE_MINUTES, SS_LITERAL_INITIALIZER ("minutes") },
168 { DATE_SECONDS, SS_LITERAL_INITIALIZER ("seconds") },
170 const int unit_name_cnt = sizeof unit_names / sizeof *unit_names;
172 const struct unit_name *un;
174 for (un = unit_names; un < &unit_names[unit_name_cnt]; un++)
175 if (ss_equals_case (un->name, name))
181 msg (SE, _("Unrecognized date unit `%.*s'. "
182 "Valid date units are `%s', `%s', `%s', "
183 "`%s', `%s', `%s', `%s', and `%s'."),
184 (int) ss_length (name), ss_data (name),
185 "years", "quarters", "months",
186 "weeks", "days", "hours", "minutes", "seconds");
191 /* Returns the number of whole years from DATE1 to DATE2,
192 where a year is defined as the same or later month, day, and
195 year_diff (double date1, double date2)
201 assert (date2 >= date1);
202 calendar_offset_to_gregorian (date1 / DAY_S, &y1, &m1, &d1, &yd1);
203 calendar_offset_to_gregorian (date2 / DAY_S, &y2, &m2, &d2, &yd2);
208 int yd1 = 32 * m1 + d1;
209 int yd2 = 32 * m2 + d2;
211 || (yd2 == yd1 && fmod (date2, DAY_S) < fmod (date1, DAY_S)))
217 /* Returns the number of whole months from DATE1 to DATE2,
218 where a month is defined as the same or later day and time of
221 month_diff (double date1, double date2)
227 assert (date2 >= date1);
228 calendar_offset_to_gregorian (date1 / DAY_S, &y1, &m1, &d1, &yd1);
229 calendar_offset_to_gregorian (date2 / DAY_S, &y2, &m2, &d2, &yd2);
231 diff = ((y2 * 12) + m2) - ((y1 * 12) + m1);
234 || (d2 == d1 && fmod (date2, DAY_S) < fmod (date1, DAY_S))))
239 /* Returns the number of whole quarter from DATE1 to DATE2,
240 where a quarter is defined as three months. */
242 quarter_diff (double date1, double date2)
244 return month_diff (date1, date2) / 3;
247 /* Returns the number of seconds in the given UNIT. */
249 date_unit_duration (enum date_unit unit)
273 /* Returns the span from DATE1 to DATE2 in terms of UNIT_NAME. */
275 expr_date_difference (double date1, double date2, struct substring unit_name)
279 if (!recognize_unit (unit_name, &unit))
285 return (date2 >= date1
286 ? year_diff (date1, date2)
287 : -year_diff (date2, date1));
290 return (date2 >= date1
291 ? quarter_diff (date1, date2)
292 : -quarter_diff (date2, date1));
295 return (date2 >= date1
296 ? month_diff (date1, date2)
297 : -month_diff (date2, date1));
304 return trunc ((date2 - date1) / date_unit_duration (unit));
310 /* How to deal with days out of range for a given month. */
313 SUM_ROLLOVER, /* Roll them over to the next month. */
314 SUM_CLOSEST /* Use the last day of the month. */
317 /* Stores in *METHOD the method whose name is NAME.
320 recognize_method (struct substring method_name, enum date_sum_method *method)
322 if (ss_equals_case (method_name, ss_cstr ("closest")))
324 *method = SUM_CLOSEST;
327 else if (ss_equals_case (method_name, ss_cstr ("rollover")))
329 *method = SUM_ROLLOVER;
334 msg (SE, _("Invalid DATESUM method. "
335 "Valid choices are `%s' and `%s'."), "closest", "rollover");
340 /* Returns DATE advanced by the given number of MONTHS, with
341 day-of-month overflow resolved using METHOD. */
343 add_months (double date, int months, enum date_sum_method method)
349 calendar_offset_to_gregorian (date / DAY_S, &y, &m, &d, &yd);
362 assert (m >= 1 && m <= 12);
364 if (method == SUM_CLOSEST && d > calendar_days_in_month (y, m))
365 d = calendar_days_in_month (y, m);
367 output = calendar_gregorian_to_offset (y, m, d, settings_get_fmt_settings (),
369 if (output != SYSMIS)
370 output = (output * DAY_S) + fmod (date, DAY_S);
373 msg (SE, "%s", error);
379 /* Returns DATE advanced by the given QUANTITY of units given in
380 UNIT_NAME, with day-of-month overflow resolved using
383 expr_date_sum (double date, double quantity, struct substring unit_name,
384 struct substring method_name)
387 enum date_sum_method method;
389 if (!recognize_unit (unit_name, &unit)
390 || !recognize_method (method_name, &method))
396 return add_months (date, trunc (quantity) * 12, method);
399 return add_months (date, trunc (quantity) * 3, method);
402 return add_months (date, trunc (quantity), method);
409 return date + quantity * date_unit_duration (unit);
416 compare_string_3way (const struct substring *a, const struct substring *b)
420 for (i = 0; i < a->length && i < b->length; i++)
421 if (a->string[i] != b->string[i])
422 return a->string[i] < b->string[i] ? -1 : 1;
423 for (; i < a->length; i++)
424 if (a->string[i] != ' ')
426 for (; i < b->length; i++)
427 if (b->string[i] != ' ')
433 count_valid (double *d, size_t d_cnt)
439 for (i = 0; i < d_cnt; i++)
440 valid_cnt += is_valid (d[i]);
445 alloc_string (struct expression *e, size_t length)
449 s.string = pool_alloc (e->eval_pool, length);
454 copy_string (struct expression *e, const char *old, size_t length)
456 struct substring s = alloc_string (e, length);
457 memcpy (s.string, old, length);
461 /* Returns the noncentral beta cumulative distribution function
462 value for the given arguments.
464 FIXME: The accuracy of this function is not entirely
465 satisfactory. We only match the example values given in AS
466 310 to the first 5 significant digits. */
468 ncdf_beta (double x, double a, double b, double lambda)
472 if (x <= 0. || x >= 1. || a <= 0. || b <= 0. || lambda <= 0.)
478 /* Algorithm AS 226. */
479 double x0, a0, beta, temp, gx, q, ax, sumq, sum;
480 double err_max = 2 * DBL_EPSILON;
485 x0 = floor (c - 5.0 * sqrt (c));
489 beta = (gsl_sf_lngamma (a0)
491 - gsl_sf_lngamma (a0 + b));
492 temp = gsl_sf_beta_inc (a0, b, x);
493 gx = exp (a0 * log (x) + b * log (1. - x) - beta - log (a0));
495 q = exp (-c + x0 * log (c)) - gsl_sf_lngamma (x0 + 1.);
507 gx = x * (a + b + iter - 1.) * gx / (a + iter);
513 err_bound = (temp - gx) * sumq;
515 while (iter < iter_max && err_bound > err_max);
521 /* Algorithm AS 310. */
523 int iter, iter_lower, iter_upper, iter1, iter2, j;
524 double t, q, r, psum, beta, s1, gx, fx, temp, ftemp, t0, s0, sum, s;
526 double err_max = 2 * DBL_EPSILON;
532 iter_lower = m - 5. * m_sqrt;
533 iter_upper = m + 5. * m_sqrt;
535 t = -c + m * log (c) - gsl_sf_lngamma (m + 1.);
539 beta = (gsl_sf_lngamma (a + m)
541 - gsl_sf_lngamma (a + m + b));
542 s1 = (a + m) * log (x) + b * log (1. - x) - log (a + m) - beta;
544 ftemp = temp = gsl_sf_beta_inc (a + m, b, x);
549 while (iter1 >= iter_lower && q >= err_max)
553 gx = (a + iter1) / (x * (a + b + iter1 - 1.)) * gx;
560 t0 = (gsl_sf_lngamma (a + b)
561 - gsl_sf_lngamma (a + 1.)
562 - gsl_sf_lngamma (b));
563 s0 = a * log (x) + b * log (1. - x);
566 for (j = 0; j < iter1; j++)
569 s += exp (t0 + s0 + j * log (x));
570 t1 = log (a + b + j) - log (a + 1. + j) + t0;
574 err_bound = (1. - gsl_sf_gamma_inc_P (iter1, c)) * (temp + s);
581 double ebd = err_bound + (1. - psum) * temp;
582 if (ebd < err_max || iter >= iter_upper)
590 gx = x * (a + b + iter2 - 1.) / (a + iter2) * gx;
599 cdf_bvnor (double x0, double x1, double r)
601 double z = pow2 (x0) - 2. * r * x0 * x1 + pow2 (x1);
602 return exp (-z / (2. * (1 - r * r))) * (2. * M_PI * sqrt (1 - r * r));
606 idf_fdist (double P, double df1, double df2)
608 double temp = gsl_cdf_beta_Pinv (P, df1 / 2, df2 / 2);
609 return temp * df2 / ((1. - temp) * df1);
613 * Mathlib : A C Library of Special Functions
614 * Copyright (C) 1998 Ross Ihaka
615 * Copyright (C) 2000 The R Development Core Team
617 * This program is free software; you can redistribute it and/or
619 * it under the terms of the GNU General Public License as
621 * the Free Software Foundation; either version 2 of the
623 * (at your option) any later version.
625 * This program is distributed in the hope that it will be
627 * but WITHOUT ANY WARRANTY; without even the implied warranty
629 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
630 * GNU General Public License for more details.
632 * You should have received a copy of the GNU General Public
634 * along with this program; if not, write to the Free Software
635 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
639 /* Returns the density of the noncentral beta distribution with
640 noncentrality parameter LAMBDA. */
642 npdf_beta (double x, double a, double b, double lambda)
644 if (lambda < 0. || a <= 0. || b <= 0.)
646 else if (lambda == 0.)
647 return gsl_ran_beta_pdf (x, a, b);
650 double max_error = 2 * DBL_EPSILON;
652 double term = gsl_ran_beta_pdf (x, a, b);
653 double lambda2 = 0.5 * lambda;
654 double weight = exp (-lambda2);
655 double sum = weight * term;
656 double psum = weight;
658 for (k = 1; k <= max_iter && 1 - psum < max_error; k++) {
659 weight *= lambda2 / k;
660 term *= x * (a + b) / a;
661 sum += weight * term;
670 round__ (double x, double mult, double fuzzbits, double adjustment)
673 fuzzbits = settings_get_fuzzbits ();
674 adjustment += exp2 (fuzzbits - DBL_MANT_DIG);
677 x = x >= 0. ? floor (x + adjustment) : -floor (-x + adjustment);
682 round_nearest (double x, double mult, double fuzzbits)
684 return round__ (x, mult, fuzzbits, .5);
688 round_zero (double x, double mult, double fuzzbits)
690 return round__ (x, mult, fuzzbits, 0);
694 replace_string (struct expression *e,
695 struct substring haystack,
696 struct substring needle,
697 struct substring replacement,
701 || haystack.length < needle.length
706 struct substring result = alloc_string (e, MAX_STRING);
710 while (i <= haystack.length - needle.length)
711 if (!memcmp (&haystack.string[i], needle.string, needle.length))
713 size_t copy_len = MIN (replacement.length, MAX_STRING - result.length);
714 memcpy (&result.string[result.length], replacement.string, copy_len);
715 result.length += copy_len;
723 if (result.length < MAX_STRING)
724 result.string[result.length++] = haystack.string[i];
727 while (i < haystack.length && result.length < MAX_STRING)
728 result.string[result.length++] = haystack.string[i++];
734 compare_doubles (const void *a_, const void *b_)
736 const double *ap = a_;
737 const double *bp = b_;
741 /* Sort SYSMIS to the end. */
749 median (double *a, size_t n)
751 /* Sort the array in-place, sorting SYSMIS to the end. */
752 qsort (a, n, sizeof *a, compare_doubles);
755 n = count_valid (a, n);
759 : (a[n / 2 - 1] + a[n / 2]) / 2.0);