Line data Source code
1 : /*-------------------------------------------------------------------------
2 : *
3 : * float.c
4 : * Functions for the built-in floating-point types.
5 : *
6 : * Portions Copyright (c) 1996-2025, PostgreSQL Global Development Group
7 : * Portions Copyright (c) 1994, Regents of the University of California
8 : *
9 : *
10 : * IDENTIFICATION
11 : * src/backend/utils/adt/float.c
12 : *
13 : *-------------------------------------------------------------------------
14 : */
15 : #include "postgres.h"
16 :
17 : #include <ctype.h>
18 : #include <float.h>
19 : #include <math.h>
20 : #include <limits.h>
21 :
22 : #include "catalog/pg_type.h"
23 : #include "common/int.h"
24 : #include "common/shortest_dec.h"
25 : #include "libpq/pqformat.h"
26 : #include "utils/array.h"
27 : #include "utils/float.h"
28 : #include "utils/fmgrprotos.h"
29 : #include "utils/sortsupport.h"
30 :
31 :
32 : /*
33 : * Configurable GUC parameter
34 : *
35 : * If >0, use shortest-decimal format for output; this is both the default and
36 : * allows for compatibility with clients that explicitly set a value here to
37 : * get round-trip-accurate results. If 0 or less, then use the old, slow,
38 : * decimal rounding method.
39 : */
40 : int extra_float_digits = 1;
41 :
42 : /* Cached constants for degree-based trig functions */
43 : static bool degree_consts_set = false;
44 : static float8 sin_30 = 0;
45 : static float8 one_minus_cos_60 = 0;
46 : static float8 asin_0_5 = 0;
47 : static float8 acos_0_5 = 0;
48 : static float8 atan_1_0 = 0;
49 : static float8 tan_45 = 0;
50 : static float8 cot_45 = 0;
51 :
52 : /*
53 : * These are intentionally not static; don't "fix" them. They will never
54 : * be referenced by other files, much less changed; but we don't want the
55 : * compiler to know that, else it might try to precompute expressions
56 : * involving them. See comments for init_degree_constants().
57 : *
58 : * The additional extern declarations are to silence
59 : * -Wmissing-variable-declarations.
60 : */
61 : extern float8 degree_c_thirty;
62 : extern float8 degree_c_forty_five;
63 : extern float8 degree_c_sixty;
64 : extern float8 degree_c_one_half;
65 : extern float8 degree_c_one;
66 : float8 degree_c_thirty = 30.0;
67 : float8 degree_c_forty_five = 45.0;
68 : float8 degree_c_sixty = 60.0;
69 : float8 degree_c_one_half = 0.5;
70 : float8 degree_c_one = 1.0;
71 :
72 : /* Local function prototypes */
73 : static double sind_q1(double x);
74 : static double cosd_q1(double x);
75 : static void init_degree_constants(void);
76 :
77 :
78 : /*
79 : * We use these out-of-line ereport() calls to report float overflow,
80 : * underflow, and zero-divide, because following our usual practice of
81 : * repeating them at each call site would lead to a lot of code bloat.
82 : *
83 : * This does mean that you don't get a useful error location indicator.
84 : */
85 : pg_noinline void
86 84 : float_overflow_error(void)
87 : {
88 84 : ereport(ERROR,
89 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
90 : errmsg("value out of range: overflow")));
91 : }
92 :
93 : pg_noinline void
94 30 : float_underflow_error(void)
95 : {
96 30 : ereport(ERROR,
97 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
98 : errmsg("value out of range: underflow")));
99 : }
100 :
101 : pg_noinline void
102 72 : float_zero_divide_error(void)
103 : {
104 72 : ereport(ERROR,
105 : (errcode(ERRCODE_DIVISION_BY_ZERO),
106 : errmsg("division by zero")));
107 : }
108 :
109 :
110 : /*
111 : * Returns -1 if 'val' represents negative infinity, 1 if 'val'
112 : * represents (positive) infinity, and 0 otherwise. On some platforms,
113 : * this is equivalent to the isinf() macro, but not everywhere: C99
114 : * does not specify that isinf() needs to distinguish between positive
115 : * and negative infinity.
116 : */
117 : int
118 0 : is_infinite(double val)
119 : {
120 0 : int inf = isinf(val);
121 :
122 0 : if (inf == 0)
123 0 : return 0;
124 0 : else if (val > 0)
125 0 : return 1;
126 : else
127 0 : return -1;
128 : }
129 :
130 :
131 : /* ========== USER I/O ROUTINES ========== */
132 :
133 :
134 : /*
135 : * float4in - converts "num" to float4
136 : *
137 : * Note that this code now uses strtof(), where it used to use strtod().
138 : *
139 : * The motivation for using strtof() is to avoid a double-rounding problem:
140 : * for certain decimal inputs, if you round the input correctly to a double,
141 : * and then round the double to a float, the result is incorrect in that it
142 : * does not match the result of rounding the decimal value to float directly.
143 : *
144 : * One of the best examples is 7.038531e-26:
145 : *
146 : * 0xAE43FDp-107 = 7.03853069185120912085...e-26
147 : * midpoint 7.03853100000000022281...e-26
148 : * 0xAE43FEp-107 = 7.03853130814879132477...e-26
149 : *
150 : * making 0xAE43FDp-107 the correct float result, but if you do the conversion
151 : * via a double, you get
152 : *
153 : * 0xAE43FD.7FFFFFF8p-107 = 7.03853099999999907487...e-26
154 : * midpoint 7.03853099999999964884...e-26
155 : * 0xAE43FD.80000000p-107 = 7.03853100000000022281...e-26
156 : * 0xAE43FD.80000008p-107 = 7.03853100000000137076...e-26
157 : *
158 : * so the value rounds to the double exactly on the midpoint between the two
159 : * nearest floats, and then rounding again to a float gives the incorrect
160 : * result of 0xAE43FEp-107.
161 : *
162 : */
163 : Datum
164 718788 : float4in(PG_FUNCTION_ARGS)
165 : {
166 718788 : char *num = PG_GETARG_CSTRING(0);
167 :
168 718788 : PG_RETURN_FLOAT4(float4in_internal(num, NULL, "real", num,
169 : fcinfo->context));
170 : }
171 :
172 : /*
173 : * float4in_internal - guts of float4in()
174 : *
175 : * This is exposed for use by functions that want a reasonably
176 : * platform-independent way of inputting floats. The behavior is
177 : * essentially like strtof + ereturn on error.
178 : *
179 : * Uses the same API as float8in_internal below, so most of its
180 : * comments also apply here, except regarding use in geometric types.
181 : */
182 : float4
183 729144 : float4in_internal(char *num, char **endptr_p,
184 : const char *type_name, const char *orig_string,
185 : struct Node *escontext)
186 : {
187 : float val;
188 : char *endptr;
189 :
190 : /*
191 : * endptr points to the first character _after_ the sequence we recognized
192 : * as a valid floating point number. orig_string points to the original
193 : * input string.
194 : */
195 :
196 : /* skip leading whitespace */
197 729354 : while (*num != '\0' && isspace((unsigned char) *num))
198 210 : num++;
199 :
200 : /*
201 : * Check for an empty-string input to begin with, to avoid the vagaries of
202 : * strtod() on different platforms.
203 : */
204 729144 : if (*num == '\0')
205 12 : ereturn(escontext, 0,
206 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
207 : errmsg("invalid input syntax for type %s: \"%s\"",
208 : type_name, orig_string)));
209 :
210 729132 : errno = 0;
211 729132 : val = strtof(num, &endptr);
212 :
213 : /* did we not see anything that looks like a double? */
214 729132 : if (endptr == num || errno != 0)
215 : {
216 136 : int save_errno = errno;
217 :
218 : /*
219 : * C99 requires that strtof() accept NaN, [+-]Infinity, and [+-]Inf,
220 : * but not all platforms support all of these (and some accept them
221 : * but set ERANGE anyway...) Therefore, we check for these inputs
222 : * ourselves if strtof() fails.
223 : *
224 : * Note: C99 also requires hexadecimal input as well as some extended
225 : * forms of NaN, but we consider these forms unportable and don't try
226 : * to support them. You can use 'em if your strtof() takes 'em.
227 : */
228 136 : if (pg_strncasecmp(num, "NaN", 3) == 0)
229 : {
230 0 : val = get_float4_nan();
231 0 : endptr = num + 3;
232 : }
233 136 : else if (pg_strncasecmp(num, "Infinity", 8) == 0)
234 : {
235 0 : val = get_float4_infinity();
236 0 : endptr = num + 8;
237 : }
238 136 : else if (pg_strncasecmp(num, "+Infinity", 9) == 0)
239 : {
240 0 : val = get_float4_infinity();
241 0 : endptr = num + 9;
242 : }
243 136 : else if (pg_strncasecmp(num, "-Infinity", 9) == 0)
244 : {
245 0 : val = -get_float4_infinity();
246 0 : endptr = num + 9;
247 : }
248 136 : else if (pg_strncasecmp(num, "inf", 3) == 0)
249 : {
250 0 : val = get_float4_infinity();
251 0 : endptr = num + 3;
252 : }
253 136 : else if (pg_strncasecmp(num, "+inf", 4) == 0)
254 : {
255 0 : val = get_float4_infinity();
256 0 : endptr = num + 4;
257 : }
258 136 : else if (pg_strncasecmp(num, "-inf", 4) == 0)
259 : {
260 0 : val = -get_float4_infinity();
261 0 : endptr = num + 4;
262 : }
263 136 : else if (save_errno == ERANGE)
264 : {
265 : /*
266 : * Some platforms return ERANGE for denormalized numbers (those
267 : * that are not zero, but are too close to zero to have full
268 : * precision). We'd prefer not to throw error for that, so try to
269 : * detect whether it's a "real" out-of-range condition by checking
270 : * to see if the result is zero or huge.
271 : */
272 72 : if (val == 0.0 ||
273 : #if !defined(HUGE_VALF)
274 : isinf(val)
275 : #else
276 18 : (val >= HUGE_VALF || val <= -HUGE_VALF)
277 : #endif
278 : )
279 : {
280 : /* see comments in float8in_internal for rationale */
281 66 : char *errnumber = pstrdup(num);
282 :
283 66 : errnumber[endptr - num] = '\0';
284 :
285 66 : ereturn(escontext, 0,
286 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
287 : errmsg("\"%s\" is out of range for type real",
288 : errnumber)));
289 : }
290 : }
291 : else
292 64 : ereturn(escontext, 0,
293 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
294 : errmsg("invalid input syntax for type %s: \"%s\"",
295 : type_name, orig_string)));
296 : }
297 :
298 : /* skip trailing whitespace */
299 729200 : while (*endptr != '\0' && isspace((unsigned char) *endptr))
300 198 : endptr++;
301 :
302 : /* report stopping point if wanted, else complain if not end of string */
303 729002 : if (endptr_p)
304 0 : *endptr_p = endptr;
305 729002 : else if (*endptr != '\0')
306 36 : ereturn(escontext, 0,
307 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
308 : errmsg("invalid input syntax for type %s: \"%s\"",
309 : type_name, orig_string)));
310 :
311 728966 : return val;
312 : }
313 :
314 : /*
315 : * float4out - converts a float4 number to a string
316 : * using a standard output format
317 : */
318 : Datum
319 355752 : float4out(PG_FUNCTION_ARGS)
320 : {
321 355752 : float4 num = PG_GETARG_FLOAT4(0);
322 355752 : char *ascii = (char *) palloc(32);
323 355752 : int ndig = FLT_DIG + extra_float_digits;
324 :
325 355752 : if (extra_float_digits > 0)
326 : {
327 342940 : float_to_shortest_decimal_buf(num, ascii);
328 342940 : PG_RETURN_CSTRING(ascii);
329 : }
330 :
331 12812 : (void) pg_strfromd(ascii, 32, ndig, num);
332 12812 : PG_RETURN_CSTRING(ascii);
333 : }
334 :
335 : /*
336 : * float4recv - converts external binary format to float4
337 : */
338 : Datum
339 0 : float4recv(PG_FUNCTION_ARGS)
340 : {
341 0 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
342 :
343 0 : PG_RETURN_FLOAT4(pq_getmsgfloat4(buf));
344 : }
345 :
346 : /*
347 : * float4send - converts float4 to binary format
348 : */
349 : Datum
350 6492 : float4send(PG_FUNCTION_ARGS)
351 : {
352 6492 : float4 num = PG_GETARG_FLOAT4(0);
353 : StringInfoData buf;
354 :
355 6492 : pq_begintypsend(&buf);
356 6492 : pq_sendfloat4(&buf, num);
357 6492 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
358 : }
359 :
360 : /*
361 : * float8in - converts "num" to float8
362 : */
363 : Datum
364 747288 : float8in(PG_FUNCTION_ARGS)
365 : {
366 747288 : char *num = PG_GETARG_CSTRING(0);
367 :
368 747288 : PG_RETURN_FLOAT8(float8in_internal(num, NULL, "double precision", num,
369 : fcinfo->context));
370 : }
371 :
372 : /*
373 : * float8in_internal - guts of float8in()
374 : *
375 : * This is exposed for use by functions that want a reasonably
376 : * platform-independent way of inputting doubles. The behavior is
377 : * essentially like strtod + ereturn on error, but note the following
378 : * differences:
379 : * 1. Both leading and trailing whitespace are skipped.
380 : * 2. If endptr_p is NULL, we report error if there's trailing junk.
381 : * Otherwise, it's up to the caller to complain about trailing junk.
382 : * 3. In event of a syntax error, the report mentions the given type_name
383 : * and prints orig_string as the input; this is meant to support use of
384 : * this function with types such as "box" and "point", where what we are
385 : * parsing here is just a substring of orig_string.
386 : *
387 : * If escontext points to an ErrorSaveContext node, that is filled instead
388 : * of throwing an error; the caller must check SOFT_ERROR_OCCURRED()
389 : * to detect errors.
390 : *
391 : * "num" could validly be declared "const char *", but that results in an
392 : * unreasonable amount of extra casting both here and in callers, so we don't.
393 : */
394 : float8
395 1904864 : float8in_internal(char *num, char **endptr_p,
396 : const char *type_name, const char *orig_string,
397 : struct Node *escontext)
398 : {
399 : double val;
400 : char *endptr;
401 :
402 : /* skip leading whitespace */
403 1906188 : while (*num != '\0' && isspace((unsigned char) *num))
404 1324 : num++;
405 :
406 : /*
407 : * Check for an empty-string input to begin with, to avoid the vagaries of
408 : * strtod() on different platforms.
409 : */
410 1904864 : if (*num == '\0')
411 18 : ereturn(escontext, 0,
412 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
413 : errmsg("invalid input syntax for type %s: \"%s\"",
414 : type_name, orig_string)));
415 :
416 1904846 : errno = 0;
417 1904846 : val = strtod(num, &endptr);
418 :
419 : /* did we not see anything that looks like a double? */
420 1904846 : if (endptr == num || errno != 0)
421 : {
422 270 : int save_errno = errno;
423 :
424 : /*
425 : * C99 requires that strtod() accept NaN, [+-]Infinity, and [+-]Inf,
426 : * but not all platforms support all of these (and some accept them
427 : * but set ERANGE anyway...) Therefore, we check for these inputs
428 : * ourselves if strtod() fails.
429 : *
430 : * Note: C99 also requires hexadecimal input as well as some extended
431 : * forms of NaN, but we consider these forms unportable and don't try
432 : * to support them. You can use 'em if your strtod() takes 'em.
433 : */
434 270 : if (pg_strncasecmp(num, "NaN", 3) == 0)
435 : {
436 0 : val = get_float8_nan();
437 0 : endptr = num + 3;
438 : }
439 270 : else if (pg_strncasecmp(num, "Infinity", 8) == 0)
440 : {
441 0 : val = get_float8_infinity();
442 0 : endptr = num + 8;
443 : }
444 270 : else if (pg_strncasecmp(num, "+Infinity", 9) == 0)
445 : {
446 0 : val = get_float8_infinity();
447 0 : endptr = num + 9;
448 : }
449 270 : else if (pg_strncasecmp(num, "-Infinity", 9) == 0)
450 : {
451 0 : val = -get_float8_infinity();
452 0 : endptr = num + 9;
453 : }
454 270 : else if (pg_strncasecmp(num, "inf", 3) == 0)
455 : {
456 0 : val = get_float8_infinity();
457 0 : endptr = num + 3;
458 : }
459 270 : else if (pg_strncasecmp(num, "+inf", 4) == 0)
460 : {
461 0 : val = get_float8_infinity();
462 0 : endptr = num + 4;
463 : }
464 270 : else if (pg_strncasecmp(num, "-inf", 4) == 0)
465 : {
466 0 : val = -get_float8_infinity();
467 0 : endptr = num + 4;
468 : }
469 270 : else if (save_errno == ERANGE)
470 : {
471 : /*
472 : * Some platforms return ERANGE for denormalized numbers (those
473 : * that are not zero, but are too close to zero to have full
474 : * precision). We'd prefer not to throw error for that, so try to
475 : * detect whether it's a "real" out-of-range condition by checking
476 : * to see if the result is zero or huge.
477 : *
478 : * On error, we intentionally complain about double precision not
479 : * the given type name, and we print only the part of the string
480 : * that is the current number.
481 : */
482 126 : if (val == 0.0 || val >= HUGE_VAL || val <= -HUGE_VAL)
483 : {
484 108 : char *errnumber = pstrdup(num);
485 :
486 108 : errnumber[endptr - num] = '\0';
487 108 : ereturn(escontext, 0,
488 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
489 : errmsg("\"%s\" is out of range for type double precision",
490 : errnumber)));
491 : }
492 : }
493 : else
494 144 : ereturn(escontext, 0,
495 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
496 : errmsg("invalid input syntax for type %s: \"%s\"",
497 : type_name, orig_string)));
498 : }
499 :
500 : /* skip trailing whitespace */
501 1904998 : while (*endptr != '\0' && isspace((unsigned char) *endptr))
502 404 : endptr++;
503 :
504 : /* report stopping point if wanted, else complain if not end of string */
505 1904594 : if (endptr_p)
506 1157378 : *endptr_p = endptr;
507 747216 : else if (*endptr != '\0')
508 42 : ereturn(escontext, 0,
509 : (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
510 : errmsg("invalid input syntax for type %s: \"%s\"",
511 : type_name, orig_string)));
512 :
513 1904552 : return val;
514 : }
515 :
516 :
517 : /*
518 : * float8out - converts float8 number to a string
519 : * using a standard output format
520 : */
521 : Datum
522 1371332 : float8out(PG_FUNCTION_ARGS)
523 : {
524 1371332 : float8 num = PG_GETARG_FLOAT8(0);
525 :
526 1371332 : PG_RETURN_CSTRING(float8out_internal(num));
527 : }
528 :
529 : /*
530 : * float8out_internal - guts of float8out()
531 : *
532 : * This is exposed for use by functions that want a reasonably
533 : * platform-independent way of outputting doubles.
534 : * The result is always palloc'd.
535 : */
536 : char *
537 7497096 : float8out_internal(double num)
538 : {
539 7497096 : char *ascii = (char *) palloc(32);
540 7497096 : int ndig = DBL_DIG + extra_float_digits;
541 :
542 7497096 : if (extra_float_digits > 0)
543 : {
544 7279692 : double_to_shortest_decimal_buf(num, ascii);
545 7279692 : return ascii;
546 : }
547 :
548 217404 : (void) pg_strfromd(ascii, 32, ndig, num);
549 217404 : return ascii;
550 : }
551 :
552 : /*
553 : * float8recv - converts external binary format to float8
554 : */
555 : Datum
556 26 : float8recv(PG_FUNCTION_ARGS)
557 : {
558 26 : StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
559 :
560 26 : PG_RETURN_FLOAT8(pq_getmsgfloat8(buf));
561 : }
562 :
563 : /*
564 : * float8send - converts float8 to binary format
565 : */
566 : Datum
567 5156 : float8send(PG_FUNCTION_ARGS)
568 : {
569 5156 : float8 num = PG_GETARG_FLOAT8(0);
570 : StringInfoData buf;
571 :
572 5156 : pq_begintypsend(&buf);
573 5156 : pq_sendfloat8(&buf, num);
574 5156 : PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
575 : }
576 :
577 :
578 : /* ========== PUBLIC ROUTINES ========== */
579 :
580 :
581 : /*
582 : * ======================
583 : * FLOAT4 BASE OPERATIONS
584 : * ======================
585 : */
586 :
587 : /*
588 : * float4abs - returns |arg1| (absolute value)
589 : */
590 : Datum
591 30 : float4abs(PG_FUNCTION_ARGS)
592 : {
593 30 : float4 arg1 = PG_GETARG_FLOAT4(0);
594 :
595 30 : PG_RETURN_FLOAT4(fabsf(arg1));
596 : }
597 :
598 : /*
599 : * float4um - returns -arg1 (unary minus)
600 : */
601 : Datum
602 16 : float4um(PG_FUNCTION_ARGS)
603 : {
604 16 : float4 arg1 = PG_GETARG_FLOAT4(0);
605 : float4 result;
606 :
607 16 : result = -arg1;
608 16 : PG_RETURN_FLOAT4(result);
609 : }
610 :
611 : Datum
612 0 : float4up(PG_FUNCTION_ARGS)
613 : {
614 0 : float4 arg = PG_GETARG_FLOAT4(0);
615 :
616 0 : PG_RETURN_FLOAT4(arg);
617 : }
618 :
619 : Datum
620 18 : float4larger(PG_FUNCTION_ARGS)
621 : {
622 18 : float4 arg1 = PG_GETARG_FLOAT4(0);
623 18 : float4 arg2 = PG_GETARG_FLOAT4(1);
624 : float4 result;
625 :
626 18 : if (float4_gt(arg1, arg2))
627 6 : result = arg1;
628 : else
629 12 : result = arg2;
630 18 : PG_RETURN_FLOAT4(result);
631 : }
632 :
633 : Datum
634 0 : float4smaller(PG_FUNCTION_ARGS)
635 : {
636 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
637 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
638 : float4 result;
639 :
640 0 : if (float4_lt(arg1, arg2))
641 0 : result = arg1;
642 : else
643 0 : result = arg2;
644 0 : PG_RETURN_FLOAT4(result);
645 : }
646 :
647 : /*
648 : * ======================
649 : * FLOAT8 BASE OPERATIONS
650 : * ======================
651 : */
652 :
653 : /*
654 : * float8abs - returns |arg1| (absolute value)
655 : */
656 : Datum
657 132468 : float8abs(PG_FUNCTION_ARGS)
658 : {
659 132468 : float8 arg1 = PG_GETARG_FLOAT8(0);
660 :
661 132468 : PG_RETURN_FLOAT8(fabs(arg1));
662 : }
663 :
664 :
665 : /*
666 : * float8um - returns -arg1 (unary minus)
667 : */
668 : Datum
669 282 : float8um(PG_FUNCTION_ARGS)
670 : {
671 282 : float8 arg1 = PG_GETARG_FLOAT8(0);
672 : float8 result;
673 :
674 282 : result = -arg1;
675 282 : PG_RETURN_FLOAT8(result);
676 : }
677 :
678 : Datum
679 0 : float8up(PG_FUNCTION_ARGS)
680 : {
681 0 : float8 arg = PG_GETARG_FLOAT8(0);
682 :
683 0 : PG_RETURN_FLOAT8(arg);
684 : }
685 :
686 : Datum
687 12876 : float8larger(PG_FUNCTION_ARGS)
688 : {
689 12876 : float8 arg1 = PG_GETARG_FLOAT8(0);
690 12876 : float8 arg2 = PG_GETARG_FLOAT8(1);
691 : float8 result;
692 :
693 12876 : if (float8_gt(arg1, arg2))
694 12270 : result = arg1;
695 : else
696 606 : result = arg2;
697 12876 : PG_RETURN_FLOAT8(result);
698 : }
699 :
700 : Datum
701 1152 : float8smaller(PG_FUNCTION_ARGS)
702 : {
703 1152 : float8 arg1 = PG_GETARG_FLOAT8(0);
704 1152 : float8 arg2 = PG_GETARG_FLOAT8(1);
705 : float8 result;
706 :
707 1152 : if (float8_lt(arg1, arg2))
708 888 : result = arg1;
709 : else
710 264 : result = arg2;
711 1152 : PG_RETURN_FLOAT8(result);
712 : }
713 :
714 :
715 : /*
716 : * ====================
717 : * ARITHMETIC OPERATORS
718 : * ====================
719 : */
720 :
721 : /*
722 : * float4pl - returns arg1 + arg2
723 : * float4mi - returns arg1 - arg2
724 : * float4mul - returns arg1 * arg2
725 : * float4div - returns arg1 / arg2
726 : */
727 : Datum
728 54 : float4pl(PG_FUNCTION_ARGS)
729 : {
730 54 : float4 arg1 = PG_GETARG_FLOAT4(0);
731 54 : float4 arg2 = PG_GETARG_FLOAT4(1);
732 :
733 54 : PG_RETURN_FLOAT4(float4_pl(arg1, arg2));
734 : }
735 :
736 : Datum
737 18 : float4mi(PG_FUNCTION_ARGS)
738 : {
739 18 : float4 arg1 = PG_GETARG_FLOAT4(0);
740 18 : float4 arg2 = PG_GETARG_FLOAT4(1);
741 :
742 18 : PG_RETURN_FLOAT4(float4_mi(arg1, arg2));
743 : }
744 :
745 : Datum
746 36 : float4mul(PG_FUNCTION_ARGS)
747 : {
748 36 : float4 arg1 = PG_GETARG_FLOAT4(0);
749 36 : float4 arg2 = PG_GETARG_FLOAT4(1);
750 :
751 36 : PG_RETURN_FLOAT4(float4_mul(arg1, arg2));
752 : }
753 :
754 : Datum
755 48 : float4div(PG_FUNCTION_ARGS)
756 : {
757 48 : float4 arg1 = PG_GETARG_FLOAT4(0);
758 48 : float4 arg2 = PG_GETARG_FLOAT4(1);
759 :
760 48 : PG_RETURN_FLOAT4(float4_div(arg1, arg2));
761 : }
762 :
763 : /*
764 : * float8pl - returns arg1 + arg2
765 : * float8mi - returns arg1 - arg2
766 : * float8mul - returns arg1 * arg2
767 : * float8div - returns arg1 / arg2
768 : */
769 : Datum
770 108118 : float8pl(PG_FUNCTION_ARGS)
771 : {
772 108118 : float8 arg1 = PG_GETARG_FLOAT8(0);
773 108118 : float8 arg2 = PG_GETARG_FLOAT8(1);
774 :
775 108118 : PG_RETURN_FLOAT8(float8_pl(arg1, arg2));
776 : }
777 :
778 : Datum
779 12552 : float8mi(PG_FUNCTION_ARGS)
780 : {
781 12552 : float8 arg1 = PG_GETARG_FLOAT8(0);
782 12552 : float8 arg2 = PG_GETARG_FLOAT8(1);
783 :
784 12552 : PG_RETURN_FLOAT8(float8_mi(arg1, arg2));
785 : }
786 :
787 : Datum
788 1866772 : float8mul(PG_FUNCTION_ARGS)
789 : {
790 1866772 : float8 arg1 = PG_GETARG_FLOAT8(0);
791 1866772 : float8 arg2 = PG_GETARG_FLOAT8(1);
792 :
793 1866772 : PG_RETURN_FLOAT8(float8_mul(arg1, arg2));
794 : }
795 :
796 : Datum
797 15268 : float8div(PG_FUNCTION_ARGS)
798 : {
799 15268 : float8 arg1 = PG_GETARG_FLOAT8(0);
800 15268 : float8 arg2 = PG_GETARG_FLOAT8(1);
801 :
802 15268 : PG_RETURN_FLOAT8(float8_div(arg1, arg2));
803 : }
804 :
805 :
806 : /*
807 : * ====================
808 : * COMPARISON OPERATORS
809 : * ====================
810 : */
811 :
812 : /*
813 : * float4{eq,ne,lt,le,gt,ge} - float4/float4 comparison operations
814 : */
815 : int
816 15313384 : float4_cmp_internal(float4 a, float4 b)
817 : {
818 15313384 : if (float4_gt(a, b))
819 383986 : return 1;
820 14929398 : if (float4_lt(a, b))
821 2069574 : return -1;
822 12859824 : return 0;
823 : }
824 :
825 : Datum
826 45004 : float4eq(PG_FUNCTION_ARGS)
827 : {
828 45004 : float4 arg1 = PG_GETARG_FLOAT4(0);
829 45004 : float4 arg2 = PG_GETARG_FLOAT4(1);
830 :
831 45004 : PG_RETURN_BOOL(float4_eq(arg1, arg2));
832 : }
833 :
834 : Datum
835 30 : float4ne(PG_FUNCTION_ARGS)
836 : {
837 30 : float4 arg1 = PG_GETARG_FLOAT4(0);
838 30 : float4 arg2 = PG_GETARG_FLOAT4(1);
839 :
840 30 : PG_RETURN_BOOL(float4_ne(arg1, arg2));
841 : }
842 :
843 : Datum
844 15056 : float4lt(PG_FUNCTION_ARGS)
845 : {
846 15056 : float4 arg1 = PG_GETARG_FLOAT4(0);
847 15056 : float4 arg2 = PG_GETARG_FLOAT4(1);
848 :
849 15056 : PG_RETURN_BOOL(float4_lt(arg1, arg2));
850 : }
851 :
852 : Datum
853 3828 : float4le(PG_FUNCTION_ARGS)
854 : {
855 3828 : float4 arg1 = PG_GETARG_FLOAT4(0);
856 3828 : float4 arg2 = PG_GETARG_FLOAT4(1);
857 :
858 3828 : PG_RETURN_BOOL(float4_le(arg1, arg2));
859 : }
860 :
861 : Datum
862 4732 : float4gt(PG_FUNCTION_ARGS)
863 : {
864 4732 : float4 arg1 = PG_GETARG_FLOAT4(0);
865 4732 : float4 arg2 = PG_GETARG_FLOAT4(1);
866 :
867 4732 : PG_RETURN_BOOL(float4_gt(arg1, arg2));
868 : }
869 :
870 : Datum
871 3828 : float4ge(PG_FUNCTION_ARGS)
872 : {
873 3828 : float4 arg1 = PG_GETARG_FLOAT4(0);
874 3828 : float4 arg2 = PG_GETARG_FLOAT4(1);
875 :
876 3828 : PG_RETURN_BOOL(float4_ge(arg1, arg2));
877 : }
878 :
879 : Datum
880 1895478 : btfloat4cmp(PG_FUNCTION_ARGS)
881 : {
882 1895478 : float4 arg1 = PG_GETARG_FLOAT4(0);
883 1895478 : float4 arg2 = PG_GETARG_FLOAT4(1);
884 :
885 1895478 : PG_RETURN_INT32(float4_cmp_internal(arg1, arg2));
886 : }
887 :
888 : static int
889 13407844 : btfloat4fastcmp(Datum x, Datum y, SortSupport ssup)
890 : {
891 13407844 : float4 arg1 = DatumGetFloat4(x);
892 13407844 : float4 arg2 = DatumGetFloat4(y);
893 :
894 13407844 : return float4_cmp_internal(arg1, arg2);
895 : }
896 :
897 : Datum
898 1308 : btfloat4sortsupport(PG_FUNCTION_ARGS)
899 : {
900 1308 : SortSupport ssup = (SortSupport) PG_GETARG_POINTER(0);
901 :
902 1308 : ssup->comparator = btfloat4fastcmp;
903 1308 : PG_RETURN_VOID();
904 : }
905 :
906 : /*
907 : * float8{eq,ne,lt,le,gt,ge} - float8/float8 comparison operations
908 : */
909 : int
910 25460130 : float8_cmp_internal(float8 a, float8 b)
911 : {
912 25460130 : if (float8_gt(a, b))
913 9466198 : return 1;
914 15993932 : if (float8_lt(a, b))
915 15732380 : return -1;
916 261552 : return 0;
917 : }
918 :
919 : Datum
920 577482 : float8eq(PG_FUNCTION_ARGS)
921 : {
922 577482 : float8 arg1 = PG_GETARG_FLOAT8(0);
923 577482 : float8 arg2 = PG_GETARG_FLOAT8(1);
924 :
925 577482 : PG_RETURN_BOOL(float8_eq(arg1, arg2));
926 : }
927 :
928 : Datum
929 16368 : float8ne(PG_FUNCTION_ARGS)
930 : {
931 16368 : float8 arg1 = PG_GETARG_FLOAT8(0);
932 16368 : float8 arg2 = PG_GETARG_FLOAT8(1);
933 :
934 16368 : PG_RETURN_BOOL(float8_ne(arg1, arg2));
935 : }
936 :
937 : Datum
938 49786 : float8lt(PG_FUNCTION_ARGS)
939 : {
940 49786 : float8 arg1 = PG_GETARG_FLOAT8(0);
941 49786 : float8 arg2 = PG_GETARG_FLOAT8(1);
942 :
943 49786 : PG_RETURN_BOOL(float8_lt(arg1, arg2));
944 : }
945 :
946 : Datum
947 6020 : float8le(PG_FUNCTION_ARGS)
948 : {
949 6020 : float8 arg1 = PG_GETARG_FLOAT8(0);
950 6020 : float8 arg2 = PG_GETARG_FLOAT8(1);
951 :
952 6020 : PG_RETURN_BOOL(float8_le(arg1, arg2));
953 : }
954 :
955 : Datum
956 30936 : float8gt(PG_FUNCTION_ARGS)
957 : {
958 30936 : float8 arg1 = PG_GETARG_FLOAT8(0);
959 30936 : float8 arg2 = PG_GETARG_FLOAT8(1);
960 :
961 30936 : PG_RETURN_BOOL(float8_gt(arg1, arg2));
962 : }
963 :
964 : Datum
965 22744 : float8ge(PG_FUNCTION_ARGS)
966 : {
967 22744 : float8 arg1 = PG_GETARG_FLOAT8(0);
968 22744 : float8 arg2 = PG_GETARG_FLOAT8(1);
969 :
970 22744 : PG_RETURN_BOOL(float8_ge(arg1, arg2));
971 : }
972 :
973 : Datum
974 3150 : btfloat8cmp(PG_FUNCTION_ARGS)
975 : {
976 3150 : float8 arg1 = PG_GETARG_FLOAT8(0);
977 3150 : float8 arg2 = PG_GETARG_FLOAT8(1);
978 :
979 3150 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
980 : }
981 :
982 : static int
983 7758468 : btfloat8fastcmp(Datum x, Datum y, SortSupport ssup)
984 : {
985 7758468 : float8 arg1 = DatumGetFloat8(x);
986 7758468 : float8 arg2 = DatumGetFloat8(y);
987 :
988 7758468 : return float8_cmp_internal(arg1, arg2);
989 : }
990 :
991 : Datum
992 1090 : btfloat8sortsupport(PG_FUNCTION_ARGS)
993 : {
994 1090 : SortSupport ssup = (SortSupport) PG_GETARG_POINTER(0);
995 :
996 1090 : ssup->comparator = btfloat8fastcmp;
997 1090 : PG_RETURN_VOID();
998 : }
999 :
1000 : Datum
1001 0 : btfloat48cmp(PG_FUNCTION_ARGS)
1002 : {
1003 0 : float4 arg1 = PG_GETARG_FLOAT4(0);
1004 0 : float8 arg2 = PG_GETARG_FLOAT8(1);
1005 :
1006 : /* widen float4 to float8 and then compare */
1007 0 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
1008 : }
1009 :
1010 : Datum
1011 0 : btfloat84cmp(PG_FUNCTION_ARGS)
1012 : {
1013 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1014 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
1015 :
1016 : /* widen float4 to float8 and then compare */
1017 0 : PG_RETURN_INT32(float8_cmp_internal(arg1, arg2));
1018 : }
1019 :
1020 : /*
1021 : * in_range support function for float8.
1022 : *
1023 : * Note: we needn't supply a float8_float4 variant, as implicit coercion
1024 : * of the offset value takes care of that scenario just as well.
1025 : */
1026 : Datum
1027 1152 : in_range_float8_float8(PG_FUNCTION_ARGS)
1028 : {
1029 1152 : float8 val = PG_GETARG_FLOAT8(0);
1030 1152 : float8 base = PG_GETARG_FLOAT8(1);
1031 1152 : float8 offset = PG_GETARG_FLOAT8(2);
1032 1152 : bool sub = PG_GETARG_BOOL(3);
1033 1152 : bool less = PG_GETARG_BOOL(4);
1034 : float8 sum;
1035 :
1036 : /*
1037 : * Reject negative or NaN offset. Negative is per spec, and NaN is
1038 : * because appropriate semantics for that seem non-obvious.
1039 : */
1040 1152 : if (isnan(offset) || offset < 0)
1041 6 : ereport(ERROR,
1042 : (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
1043 : errmsg("invalid preceding or following size in window function")));
1044 :
1045 : /*
1046 : * Deal with cases where val and/or base is NaN, following the rule that
1047 : * NaN sorts after non-NaN (cf float8_cmp_internal). The offset cannot
1048 : * affect the conclusion.
1049 : */
1050 1146 : if (isnan(val))
1051 : {
1052 186 : if (isnan(base))
1053 60 : PG_RETURN_BOOL(true); /* NAN = NAN */
1054 : else
1055 126 : PG_RETURN_BOOL(!less); /* NAN > non-NAN */
1056 : }
1057 960 : else if (isnan(base))
1058 : {
1059 126 : PG_RETURN_BOOL(less); /* non-NAN < NAN */
1060 : }
1061 :
1062 : /*
1063 : * Deal with cases where both base and offset are infinite, and computing
1064 : * base +/- offset would produce NaN. This corresponds to a window frame
1065 : * whose boundary infinitely precedes +inf or infinitely follows -inf,
1066 : * which is not well-defined. For consistency with other cases involving
1067 : * infinities, such as the fact that +inf infinitely follows +inf, we
1068 : * choose to assume that +inf infinitely precedes +inf and -inf infinitely
1069 : * follows -inf, and therefore that all finite and infinite values are in
1070 : * such a window frame.
1071 : *
1072 : * offset is known positive, so we need only check the sign of base in
1073 : * this test.
1074 : */
1075 834 : if (isinf(offset) && isinf(base) &&
1076 : (sub ? base > 0 : base < 0))
1077 174 : PG_RETURN_BOOL(true);
1078 :
1079 : /*
1080 : * Otherwise it should be safe to compute base +/- offset. We trust the
1081 : * FPU to cope if an input is +/-inf or the true sum would overflow, and
1082 : * produce a suitably signed infinity, which will compare properly against
1083 : * val whether or not that's infinity.
1084 : */
1085 660 : if (sub)
1086 360 : sum = base - offset;
1087 : else
1088 300 : sum = base + offset;
1089 :
1090 660 : if (less)
1091 258 : PG_RETURN_BOOL(val <= sum);
1092 : else
1093 402 : PG_RETURN_BOOL(val >= sum);
1094 : }
1095 :
1096 : /*
1097 : * in_range support function for float4.
1098 : *
1099 : * We would need a float4_float8 variant in any case, so we supply that and
1100 : * let implicit coercion take care of the float4_float4 case.
1101 : */
1102 : Datum
1103 1152 : in_range_float4_float8(PG_FUNCTION_ARGS)
1104 : {
1105 1152 : float4 val = PG_GETARG_FLOAT4(0);
1106 1152 : float4 base = PG_GETARG_FLOAT4(1);
1107 1152 : float8 offset = PG_GETARG_FLOAT8(2);
1108 1152 : bool sub = PG_GETARG_BOOL(3);
1109 1152 : bool less = PG_GETARG_BOOL(4);
1110 : float8 sum;
1111 :
1112 : /*
1113 : * Reject negative or NaN offset. Negative is per spec, and NaN is
1114 : * because appropriate semantics for that seem non-obvious.
1115 : */
1116 1152 : if (isnan(offset) || offset < 0)
1117 6 : ereport(ERROR,
1118 : (errcode(ERRCODE_INVALID_PRECEDING_OR_FOLLOWING_SIZE),
1119 : errmsg("invalid preceding or following size in window function")));
1120 :
1121 : /*
1122 : * Deal with cases where val and/or base is NaN, following the rule that
1123 : * NaN sorts after non-NaN (cf float8_cmp_internal). The offset cannot
1124 : * affect the conclusion.
1125 : */
1126 1146 : if (isnan(val))
1127 : {
1128 186 : if (isnan(base))
1129 60 : PG_RETURN_BOOL(true); /* NAN = NAN */
1130 : else
1131 126 : PG_RETURN_BOOL(!less); /* NAN > non-NAN */
1132 : }
1133 960 : else if (isnan(base))
1134 : {
1135 126 : PG_RETURN_BOOL(less); /* non-NAN < NAN */
1136 : }
1137 :
1138 : /*
1139 : * Deal with cases where both base and offset are infinite, and computing
1140 : * base +/- offset would produce NaN. This corresponds to a window frame
1141 : * whose boundary infinitely precedes +inf or infinitely follows -inf,
1142 : * which is not well-defined. For consistency with other cases involving
1143 : * infinities, such as the fact that +inf infinitely follows +inf, we
1144 : * choose to assume that +inf infinitely precedes +inf and -inf infinitely
1145 : * follows -inf, and therefore that all finite and infinite values are in
1146 : * such a window frame.
1147 : *
1148 : * offset is known positive, so we need only check the sign of base in
1149 : * this test.
1150 : */
1151 834 : if (isinf(offset) && isinf(base) &&
1152 : (sub ? base > 0 : base < 0))
1153 174 : PG_RETURN_BOOL(true);
1154 :
1155 : /*
1156 : * Otherwise it should be safe to compute base +/- offset. We trust the
1157 : * FPU to cope if an input is +/-inf or the true sum would overflow, and
1158 : * produce a suitably signed infinity, which will compare properly against
1159 : * val whether or not that's infinity.
1160 : */
1161 660 : if (sub)
1162 360 : sum = base - offset;
1163 : else
1164 300 : sum = base + offset;
1165 :
1166 660 : if (less)
1167 258 : PG_RETURN_BOOL(val <= sum);
1168 : else
1169 402 : PG_RETURN_BOOL(val >= sum);
1170 : }
1171 :
1172 :
1173 : /*
1174 : * ===================
1175 : * CONVERSION ROUTINES
1176 : * ===================
1177 : */
1178 :
1179 : /*
1180 : * ftod - converts a float4 number to a float8 number
1181 : */
1182 : Datum
1183 294 : ftod(PG_FUNCTION_ARGS)
1184 : {
1185 294 : float4 num = PG_GETARG_FLOAT4(0);
1186 :
1187 294 : PG_RETURN_FLOAT8((float8) num);
1188 : }
1189 :
1190 :
1191 : /*
1192 : * dtof - converts a float8 number to a float4 number
1193 : */
1194 : Datum
1195 56 : dtof(PG_FUNCTION_ARGS)
1196 : {
1197 56 : float8 num = PG_GETARG_FLOAT8(0);
1198 : float4 result;
1199 :
1200 56 : result = (float4) num;
1201 56 : if (unlikely(isinf(result)) && !isinf(num))
1202 12 : float_overflow_error();
1203 44 : if (unlikely(result == 0.0f) && num != 0.0)
1204 12 : float_underflow_error();
1205 :
1206 32 : PG_RETURN_FLOAT4(result);
1207 : }
1208 :
1209 :
1210 : /*
1211 : * dtoi4 - converts a float8 number to an int4 number
1212 : */
1213 : Datum
1214 1092622 : dtoi4(PG_FUNCTION_ARGS)
1215 : {
1216 1092622 : float8 num = PG_GETARG_FLOAT8(0);
1217 :
1218 : /*
1219 : * Get rid of any fractional part in the input. This is so we don't fail
1220 : * on just-out-of-range values that would round into range. Note
1221 : * assumption that rint() will pass through a NaN or Inf unchanged.
1222 : */
1223 1092622 : num = rint(num);
1224 :
1225 : /* Range check */
1226 1092622 : if (unlikely(isnan(num) || !FLOAT8_FITS_IN_INT32(num)))
1227 24 : ereport(ERROR,
1228 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1229 : errmsg("integer out of range")));
1230 :
1231 1092598 : PG_RETURN_INT32((int32) num);
1232 : }
1233 :
1234 :
1235 : /*
1236 : * dtoi2 - converts a float8 number to an int2 number
1237 : */
1238 : Datum
1239 90 : dtoi2(PG_FUNCTION_ARGS)
1240 : {
1241 90 : float8 num = PG_GETARG_FLOAT8(0);
1242 :
1243 : /*
1244 : * Get rid of any fractional part in the input. This is so we don't fail
1245 : * on just-out-of-range values that would round into range. Note
1246 : * assumption that rint() will pass through a NaN or Inf unchanged.
1247 : */
1248 90 : num = rint(num);
1249 :
1250 : /* Range check */
1251 90 : if (unlikely(isnan(num) || !FLOAT8_FITS_IN_INT16(num)))
1252 12 : ereport(ERROR,
1253 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1254 : errmsg("smallint out of range")));
1255 :
1256 78 : PG_RETURN_INT16((int16) num);
1257 : }
1258 :
1259 :
1260 : /*
1261 : * i4tod - converts an int4 number to a float8 number
1262 : */
1263 : Datum
1264 2324744 : i4tod(PG_FUNCTION_ARGS)
1265 : {
1266 2324744 : int32 num = PG_GETARG_INT32(0);
1267 :
1268 2324744 : PG_RETURN_FLOAT8((float8) num);
1269 : }
1270 :
1271 :
1272 : /*
1273 : * i2tod - converts an int2 number to a float8 number
1274 : */
1275 : Datum
1276 246 : i2tod(PG_FUNCTION_ARGS)
1277 : {
1278 246 : int16 num = PG_GETARG_INT16(0);
1279 :
1280 246 : PG_RETURN_FLOAT8((float8) num);
1281 : }
1282 :
1283 :
1284 : /*
1285 : * ftoi4 - converts a float4 number to an int4 number
1286 : */
1287 : Datum
1288 24 : ftoi4(PG_FUNCTION_ARGS)
1289 : {
1290 24 : float4 num = PG_GETARG_FLOAT4(0);
1291 :
1292 : /*
1293 : * Get rid of any fractional part in the input. This is so we don't fail
1294 : * on just-out-of-range values that would round into range. Note
1295 : * assumption that rint() will pass through a NaN or Inf unchanged.
1296 : */
1297 24 : num = rint(num);
1298 :
1299 : /* Range check */
1300 24 : if (unlikely(isnan(num) || !FLOAT4_FITS_IN_INT32(num)))
1301 12 : ereport(ERROR,
1302 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1303 : errmsg("integer out of range")));
1304 :
1305 12 : PG_RETURN_INT32((int32) num);
1306 : }
1307 :
1308 :
1309 : /*
1310 : * ftoi2 - converts a float4 number to an int2 number
1311 : */
1312 : Datum
1313 24 : ftoi2(PG_FUNCTION_ARGS)
1314 : {
1315 24 : float4 num = PG_GETARG_FLOAT4(0);
1316 :
1317 : /*
1318 : * Get rid of any fractional part in the input. This is so we don't fail
1319 : * on just-out-of-range values that would round into range. Note
1320 : * assumption that rint() will pass through a NaN or Inf unchanged.
1321 : */
1322 24 : num = rint(num);
1323 :
1324 : /* Range check */
1325 24 : if (unlikely(isnan(num) || !FLOAT4_FITS_IN_INT16(num)))
1326 12 : ereport(ERROR,
1327 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1328 : errmsg("smallint out of range")));
1329 :
1330 12 : PG_RETURN_INT16((int16) num);
1331 : }
1332 :
1333 :
1334 : /*
1335 : * i4tof - converts an int4 number to a float4 number
1336 : */
1337 : Datum
1338 486 : i4tof(PG_FUNCTION_ARGS)
1339 : {
1340 486 : int32 num = PG_GETARG_INT32(0);
1341 :
1342 486 : PG_RETURN_FLOAT4((float4) num);
1343 : }
1344 :
1345 :
1346 : /*
1347 : * i2tof - converts an int2 number to a float4 number
1348 : */
1349 : Datum
1350 0 : i2tof(PG_FUNCTION_ARGS)
1351 : {
1352 0 : int16 num = PG_GETARG_INT16(0);
1353 :
1354 0 : PG_RETURN_FLOAT4((float4) num);
1355 : }
1356 :
1357 :
1358 : /*
1359 : * =======================
1360 : * RANDOM FLOAT8 OPERATORS
1361 : * =======================
1362 : */
1363 :
1364 : /*
1365 : * dround - returns ROUND(arg1)
1366 : */
1367 : Datum
1368 1178916 : dround(PG_FUNCTION_ARGS)
1369 : {
1370 1178916 : float8 arg1 = PG_GETARG_FLOAT8(0);
1371 :
1372 1178916 : PG_RETURN_FLOAT8(rint(arg1));
1373 : }
1374 :
1375 : /*
1376 : * dceil - returns the smallest integer greater than or
1377 : * equal to the specified float
1378 : */
1379 : Datum
1380 68460 : dceil(PG_FUNCTION_ARGS)
1381 : {
1382 68460 : float8 arg1 = PG_GETARG_FLOAT8(0);
1383 :
1384 68460 : PG_RETURN_FLOAT8(ceil(arg1));
1385 : }
1386 :
1387 : /*
1388 : * dfloor - returns the largest integer lesser than or
1389 : * equal to the specified float
1390 : */
1391 : Datum
1392 60 : dfloor(PG_FUNCTION_ARGS)
1393 : {
1394 60 : float8 arg1 = PG_GETARG_FLOAT8(0);
1395 :
1396 60 : PG_RETURN_FLOAT8(floor(arg1));
1397 : }
1398 :
1399 : /*
1400 : * dsign - returns -1 if the argument is less than 0, 0
1401 : * if the argument is equal to 0, and 1 if the
1402 : * argument is greater than zero.
1403 : */
1404 : Datum
1405 30 : dsign(PG_FUNCTION_ARGS)
1406 : {
1407 30 : float8 arg1 = PG_GETARG_FLOAT8(0);
1408 : float8 result;
1409 :
1410 30 : if (arg1 > 0)
1411 18 : result = 1.0;
1412 12 : else if (arg1 < 0)
1413 6 : result = -1.0;
1414 : else
1415 6 : result = 0.0;
1416 :
1417 30 : PG_RETURN_FLOAT8(result);
1418 : }
1419 :
1420 : /*
1421 : * dtrunc - returns truncation-towards-zero of arg1,
1422 : * arg1 >= 0 ... the greatest integer less
1423 : * than or equal to arg1
1424 : * arg1 < 0 ... the least integer greater
1425 : * than or equal to arg1
1426 : */
1427 : Datum
1428 36 : dtrunc(PG_FUNCTION_ARGS)
1429 : {
1430 36 : float8 arg1 = PG_GETARG_FLOAT8(0);
1431 : float8 result;
1432 :
1433 36 : if (arg1 >= 0)
1434 30 : result = floor(arg1);
1435 : else
1436 6 : result = -floor(-arg1);
1437 :
1438 36 : PG_RETURN_FLOAT8(result);
1439 : }
1440 :
1441 :
1442 : /*
1443 : * dsqrt - returns square root of arg1
1444 : */
1445 : Datum
1446 4066 : dsqrt(PG_FUNCTION_ARGS)
1447 : {
1448 4066 : float8 arg1 = PG_GETARG_FLOAT8(0);
1449 : float8 result;
1450 :
1451 4066 : if (arg1 < 0)
1452 0 : ereport(ERROR,
1453 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1454 : errmsg("cannot take square root of a negative number")));
1455 :
1456 4066 : result = sqrt(arg1);
1457 4066 : if (unlikely(isinf(result)) && !isinf(arg1))
1458 0 : float_overflow_error();
1459 4066 : if (unlikely(result == 0.0) && arg1 != 0.0)
1460 0 : float_underflow_error();
1461 :
1462 4066 : PG_RETURN_FLOAT8(result);
1463 : }
1464 :
1465 :
1466 : /*
1467 : * dcbrt - returns cube root of arg1
1468 : */
1469 : Datum
1470 36 : dcbrt(PG_FUNCTION_ARGS)
1471 : {
1472 36 : float8 arg1 = PG_GETARG_FLOAT8(0);
1473 : float8 result;
1474 :
1475 36 : result = cbrt(arg1);
1476 36 : if (unlikely(isinf(result)) && !isinf(arg1))
1477 0 : float_overflow_error();
1478 36 : if (unlikely(result == 0.0) && arg1 != 0.0)
1479 0 : float_underflow_error();
1480 :
1481 36 : PG_RETURN_FLOAT8(result);
1482 : }
1483 :
1484 :
1485 : /*
1486 : * dpow - returns pow(arg1,arg2)
1487 : */
1488 : Datum
1489 668 : dpow(PG_FUNCTION_ARGS)
1490 : {
1491 668 : float8 arg1 = PG_GETARG_FLOAT8(0);
1492 668 : float8 arg2 = PG_GETARG_FLOAT8(1);
1493 : float8 result;
1494 :
1495 : /*
1496 : * The POSIX spec says that NaN ^ 0 = 1, and 1 ^ NaN = 1, while all other
1497 : * cases with NaN inputs yield NaN (with no error). Many older platforms
1498 : * get one or more of these cases wrong, so deal with them via explicit
1499 : * logic rather than trusting pow(3).
1500 : */
1501 668 : if (isnan(arg1))
1502 : {
1503 18 : if (isnan(arg2) || arg2 != 0.0)
1504 12 : PG_RETURN_FLOAT8(get_float8_nan());
1505 6 : PG_RETURN_FLOAT8(1.0);
1506 : }
1507 650 : if (isnan(arg2))
1508 : {
1509 18 : if (arg1 != 1.0)
1510 12 : PG_RETURN_FLOAT8(get_float8_nan());
1511 6 : PG_RETURN_FLOAT8(1.0);
1512 : }
1513 :
1514 : /*
1515 : * The SQL spec requires that we emit a particular SQLSTATE error code for
1516 : * certain error conditions. Specifically, we don't return a
1517 : * divide-by-zero error code for 0 ^ -1.
1518 : */
1519 632 : if (arg1 == 0 && arg2 < 0)
1520 6 : ereport(ERROR,
1521 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1522 : errmsg("zero raised to a negative power is undefined")));
1523 626 : if (arg1 < 0 && floor(arg2) != arg2)
1524 6 : ereport(ERROR,
1525 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
1526 : errmsg("a negative number raised to a non-integer power yields a complex result")));
1527 :
1528 : /*
1529 : * We don't trust the platform's pow() to handle infinity cases per POSIX
1530 : * spec either, so deal with those explicitly too. It's easier to handle
1531 : * infinite y first, so that it doesn't matter if x is also infinite.
1532 : */
1533 620 : if (isinf(arg2))
1534 : {
1535 102 : float8 absx = fabs(arg1);
1536 :
1537 102 : if (absx == 1.0)
1538 24 : result = 1.0;
1539 78 : else if (arg2 > 0.0) /* y = +Inf */
1540 : {
1541 42 : if (absx > 1.0)
1542 24 : result = arg2;
1543 : else
1544 18 : result = 0.0;
1545 : }
1546 : else /* y = -Inf */
1547 : {
1548 36 : if (absx > 1.0)
1549 24 : result = 0.0;
1550 : else
1551 12 : result = -arg2;
1552 : }
1553 : }
1554 518 : else if (isinf(arg1))
1555 : {
1556 48 : if (arg2 == 0.0)
1557 12 : result = 1.0;
1558 36 : else if (arg1 > 0.0) /* x = +Inf */
1559 : {
1560 12 : if (arg2 > 0.0)
1561 6 : result = arg1;
1562 : else
1563 6 : result = 0.0;
1564 : }
1565 : else /* x = -Inf */
1566 : {
1567 : /*
1568 : * Per POSIX, the sign of the result depends on whether y is an
1569 : * odd integer. Since x < 0, we already know from the previous
1570 : * domain check that y is an integer. It is odd if y/2 is not
1571 : * also an integer.
1572 : */
1573 24 : float8 halfy = arg2 / 2; /* should be computed exactly */
1574 24 : bool yisoddinteger = (floor(halfy) != halfy);
1575 :
1576 24 : if (arg2 > 0.0)
1577 12 : result = yisoddinteger ? arg1 : -arg1;
1578 : else
1579 12 : result = yisoddinteger ? -0.0 : 0.0;
1580 : }
1581 : }
1582 : else
1583 : {
1584 : /*
1585 : * pow() sets errno on only some platforms, depending on whether it
1586 : * follows _IEEE_, _POSIX_, _XOPEN_, or _SVID_, so we must check both
1587 : * errno and invalid output values. (We can't rely on just the
1588 : * latter, either; some old platforms return a large-but-finite
1589 : * HUGE_VAL when reporting overflow.)
1590 : */
1591 470 : errno = 0;
1592 470 : result = pow(arg1, arg2);
1593 470 : if (errno == EDOM || isnan(result))
1594 : {
1595 : /*
1596 : * We handled all possible domain errors above, so this should be
1597 : * impossible. However, old glibc versions on x86 have a bug that
1598 : * causes them to fail this way for abs(y) greater than 2^63:
1599 : *
1600 : * https://sourceware.org/bugzilla/show_bug.cgi?id=3866
1601 : *
1602 : * Hence, if we get here, assume y is finite but large (large
1603 : * enough to be certainly even). The result should be 0 if x == 0,
1604 : * 1.0 if abs(x) == 1.0, otherwise an overflow or underflow error.
1605 : */
1606 0 : if (arg1 == 0.0)
1607 0 : result = 0.0; /* we already verified y is positive */
1608 : else
1609 : {
1610 0 : float8 absx = fabs(arg1);
1611 :
1612 0 : if (absx == 1.0)
1613 0 : result = 1.0;
1614 0 : else if (arg2 >= 0.0 ? (absx > 1.0) : (absx < 1.0))
1615 0 : float_overflow_error();
1616 : else
1617 0 : float_underflow_error();
1618 : }
1619 : }
1620 470 : else if (errno == ERANGE)
1621 : {
1622 6 : if (result != 0.0)
1623 6 : float_overflow_error();
1624 : else
1625 0 : float_underflow_error();
1626 : }
1627 : else
1628 : {
1629 464 : if (unlikely(isinf(result)))
1630 0 : float_overflow_error();
1631 464 : if (unlikely(result == 0.0) && arg1 != 0.0)
1632 0 : float_underflow_error();
1633 : }
1634 : }
1635 :
1636 614 : PG_RETURN_FLOAT8(result);
1637 : }
1638 :
1639 :
1640 : /*
1641 : * dexp - returns the exponential function of arg1
1642 : */
1643 : Datum
1644 54 : dexp(PG_FUNCTION_ARGS)
1645 : {
1646 54 : float8 arg1 = PG_GETARG_FLOAT8(0);
1647 : float8 result;
1648 :
1649 : /*
1650 : * Handle NaN and Inf cases explicitly. This avoids needing to assume
1651 : * that the platform's exp() conforms to POSIX for these cases, and it
1652 : * removes some edge cases for the overflow checks below.
1653 : */
1654 54 : if (isnan(arg1))
1655 6 : result = arg1;
1656 48 : else if (isinf(arg1))
1657 : {
1658 : /* Per POSIX, exp(-Inf) is 0 */
1659 12 : result = (arg1 > 0.0) ? arg1 : 0;
1660 : }
1661 : else
1662 : {
1663 : /*
1664 : * On some platforms, exp() will not set errno but just return Inf or
1665 : * zero to report overflow/underflow; therefore, test both cases.
1666 : */
1667 36 : errno = 0;
1668 36 : result = exp(arg1);
1669 36 : if (unlikely(errno == ERANGE))
1670 : {
1671 6 : if (result != 0.0)
1672 0 : float_overflow_error();
1673 : else
1674 6 : float_underflow_error();
1675 : }
1676 30 : else if (unlikely(isinf(result)))
1677 0 : float_overflow_error();
1678 30 : else if (unlikely(result == 0.0))
1679 0 : float_underflow_error();
1680 : }
1681 :
1682 48 : PG_RETURN_FLOAT8(result);
1683 : }
1684 :
1685 :
1686 : /*
1687 : * dlog1 - returns the natural logarithm of arg1
1688 : */
1689 : Datum
1690 30 : dlog1(PG_FUNCTION_ARGS)
1691 : {
1692 30 : float8 arg1 = PG_GETARG_FLOAT8(0);
1693 : float8 result;
1694 :
1695 : /*
1696 : * Emit particular SQLSTATE error codes for ln(). This is required by the
1697 : * SQL standard.
1698 : */
1699 30 : if (arg1 == 0.0)
1700 6 : ereport(ERROR,
1701 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1702 : errmsg("cannot take logarithm of zero")));
1703 24 : if (arg1 < 0)
1704 6 : ereport(ERROR,
1705 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1706 : errmsg("cannot take logarithm of a negative number")));
1707 :
1708 18 : result = log(arg1);
1709 18 : if (unlikely(isinf(result)) && !isinf(arg1))
1710 0 : float_overflow_error();
1711 18 : if (unlikely(result == 0.0) && arg1 != 1.0)
1712 0 : float_underflow_error();
1713 :
1714 18 : PG_RETURN_FLOAT8(result);
1715 : }
1716 :
1717 :
1718 : /*
1719 : * dlog10 - returns the base 10 logarithm of arg1
1720 : */
1721 : Datum
1722 0 : dlog10(PG_FUNCTION_ARGS)
1723 : {
1724 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1725 : float8 result;
1726 :
1727 : /*
1728 : * Emit particular SQLSTATE error codes for log(). The SQL spec doesn't
1729 : * define log(), but it does define ln(), so it makes sense to emit the
1730 : * same error code for an analogous error condition.
1731 : */
1732 0 : if (arg1 == 0.0)
1733 0 : ereport(ERROR,
1734 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1735 : errmsg("cannot take logarithm of zero")));
1736 0 : if (arg1 < 0)
1737 0 : ereport(ERROR,
1738 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
1739 : errmsg("cannot take logarithm of a negative number")));
1740 :
1741 0 : result = log10(arg1);
1742 0 : if (unlikely(isinf(result)) && !isinf(arg1))
1743 0 : float_overflow_error();
1744 0 : if (unlikely(result == 0.0) && arg1 != 1.0)
1745 0 : float_underflow_error();
1746 :
1747 0 : PG_RETURN_FLOAT8(result);
1748 : }
1749 :
1750 :
1751 : /*
1752 : * dacos - returns the arccos of arg1 (radians)
1753 : */
1754 : Datum
1755 0 : dacos(PG_FUNCTION_ARGS)
1756 : {
1757 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1758 : float8 result;
1759 :
1760 : /* Per the POSIX spec, return NaN if the input is NaN */
1761 0 : if (isnan(arg1))
1762 0 : PG_RETURN_FLOAT8(get_float8_nan());
1763 :
1764 : /*
1765 : * The principal branch of the inverse cosine function maps values in the
1766 : * range [-1, 1] to values in the range [0, Pi], so we should reject any
1767 : * inputs outside that range and the result will always be finite.
1768 : */
1769 0 : if (arg1 < -1.0 || arg1 > 1.0)
1770 0 : ereport(ERROR,
1771 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1772 : errmsg("input is out of range")));
1773 :
1774 0 : result = acos(arg1);
1775 0 : if (unlikely(isinf(result)))
1776 0 : float_overflow_error();
1777 :
1778 0 : PG_RETURN_FLOAT8(result);
1779 : }
1780 :
1781 :
1782 : /*
1783 : * dasin - returns the arcsin of arg1 (radians)
1784 : */
1785 : Datum
1786 110 : dasin(PG_FUNCTION_ARGS)
1787 : {
1788 110 : float8 arg1 = PG_GETARG_FLOAT8(0);
1789 : float8 result;
1790 :
1791 : /* Per the POSIX spec, return NaN if the input is NaN */
1792 110 : if (isnan(arg1))
1793 0 : PG_RETURN_FLOAT8(get_float8_nan());
1794 :
1795 : /*
1796 : * The principal branch of the inverse sine function maps values in the
1797 : * range [-1, 1] to values in the range [-Pi/2, Pi/2], so we should reject
1798 : * any inputs outside that range and the result will always be finite.
1799 : */
1800 110 : if (arg1 < -1.0 || arg1 > 1.0)
1801 0 : ereport(ERROR,
1802 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1803 : errmsg("input is out of range")));
1804 :
1805 110 : result = asin(arg1);
1806 110 : if (unlikely(isinf(result)))
1807 0 : float_overflow_error();
1808 :
1809 110 : PG_RETURN_FLOAT8(result);
1810 : }
1811 :
1812 :
1813 : /*
1814 : * datan - returns the arctan of arg1 (radians)
1815 : */
1816 : Datum
1817 0 : datan(PG_FUNCTION_ARGS)
1818 : {
1819 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1820 : float8 result;
1821 :
1822 : /* Per the POSIX spec, return NaN if the input is NaN */
1823 0 : if (isnan(arg1))
1824 0 : PG_RETURN_FLOAT8(get_float8_nan());
1825 :
1826 : /*
1827 : * The principal branch of the inverse tangent function maps all inputs to
1828 : * values in the range [-Pi/2, Pi/2], so the result should always be
1829 : * finite, even if the input is infinite.
1830 : */
1831 0 : result = atan(arg1);
1832 0 : if (unlikely(isinf(result)))
1833 0 : float_overflow_error();
1834 :
1835 0 : PG_RETURN_FLOAT8(result);
1836 : }
1837 :
1838 :
1839 : /*
1840 : * atan2 - returns the arctan of arg1/arg2 (radians)
1841 : */
1842 : Datum
1843 40 : datan2(PG_FUNCTION_ARGS)
1844 : {
1845 40 : float8 arg1 = PG_GETARG_FLOAT8(0);
1846 40 : float8 arg2 = PG_GETARG_FLOAT8(1);
1847 : float8 result;
1848 :
1849 : /* Per the POSIX spec, return NaN if either input is NaN */
1850 40 : if (isnan(arg1) || isnan(arg2))
1851 0 : PG_RETURN_FLOAT8(get_float8_nan());
1852 :
1853 : /*
1854 : * atan2 maps all inputs to values in the range [-Pi, Pi], so the result
1855 : * should always be finite, even if the inputs are infinite.
1856 : */
1857 40 : result = atan2(arg1, arg2);
1858 40 : if (unlikely(isinf(result)))
1859 0 : float_overflow_error();
1860 :
1861 40 : PG_RETURN_FLOAT8(result);
1862 : }
1863 :
1864 :
1865 : /*
1866 : * dcos - returns the cosine of arg1 (radians)
1867 : */
1868 : Datum
1869 1170 : dcos(PG_FUNCTION_ARGS)
1870 : {
1871 1170 : float8 arg1 = PG_GETARG_FLOAT8(0);
1872 : float8 result;
1873 :
1874 : /* Per the POSIX spec, return NaN if the input is NaN */
1875 1170 : if (isnan(arg1))
1876 0 : PG_RETURN_FLOAT8(get_float8_nan());
1877 :
1878 : /*
1879 : * cos() is periodic and so theoretically can work for all finite inputs,
1880 : * but some implementations may choose to throw error if the input is so
1881 : * large that there are no significant digits in the result. So we should
1882 : * check for errors. POSIX allows an error to be reported either via
1883 : * errno or via fetestexcept(), but currently we only support checking
1884 : * errno. (fetestexcept() is rumored to report underflow unreasonably
1885 : * early on some platforms, so it's not clear that believing it would be a
1886 : * net improvement anyway.)
1887 : *
1888 : * For infinite inputs, POSIX specifies that the trigonometric functions
1889 : * should return a domain error; but we won't notice that unless the
1890 : * platform reports via errno, so also explicitly test for infinite
1891 : * inputs.
1892 : */
1893 1170 : errno = 0;
1894 1170 : result = cos(arg1);
1895 1170 : if (errno != 0 || isinf(arg1))
1896 0 : ereport(ERROR,
1897 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1898 : errmsg("input is out of range")));
1899 1170 : if (unlikely(isinf(result)))
1900 0 : float_overflow_error();
1901 :
1902 1170 : PG_RETURN_FLOAT8(result);
1903 : }
1904 :
1905 :
1906 : /*
1907 : * dcot - returns the cotangent of arg1 (radians)
1908 : */
1909 : Datum
1910 0 : dcot(PG_FUNCTION_ARGS)
1911 : {
1912 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1913 : float8 result;
1914 :
1915 : /* Per the POSIX spec, return NaN if the input is NaN */
1916 0 : if (isnan(arg1))
1917 0 : PG_RETURN_FLOAT8(get_float8_nan());
1918 :
1919 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1920 0 : errno = 0;
1921 0 : result = tan(arg1);
1922 0 : if (errno != 0 || isinf(arg1))
1923 0 : ereport(ERROR,
1924 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1925 : errmsg("input is out of range")));
1926 :
1927 0 : result = 1.0 / result;
1928 : /* Not checking for overflow because cot(0) == Inf */
1929 :
1930 0 : PG_RETURN_FLOAT8(result);
1931 : }
1932 :
1933 :
1934 : /*
1935 : * dsin - returns the sine of arg1 (radians)
1936 : */
1937 : Datum
1938 974 : dsin(PG_FUNCTION_ARGS)
1939 : {
1940 974 : float8 arg1 = PG_GETARG_FLOAT8(0);
1941 : float8 result;
1942 :
1943 : /* Per the POSIX spec, return NaN if the input is NaN */
1944 974 : if (isnan(arg1))
1945 0 : PG_RETURN_FLOAT8(get_float8_nan());
1946 :
1947 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1948 974 : errno = 0;
1949 974 : result = sin(arg1);
1950 974 : if (errno != 0 || isinf(arg1))
1951 0 : ereport(ERROR,
1952 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1953 : errmsg("input is out of range")));
1954 974 : if (unlikely(isinf(result)))
1955 0 : float_overflow_error();
1956 :
1957 974 : PG_RETURN_FLOAT8(result);
1958 : }
1959 :
1960 :
1961 : /*
1962 : * dtan - returns the tangent of arg1 (radians)
1963 : */
1964 : Datum
1965 0 : dtan(PG_FUNCTION_ARGS)
1966 : {
1967 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
1968 : float8 result;
1969 :
1970 : /* Per the POSIX spec, return NaN if the input is NaN */
1971 0 : if (isnan(arg1))
1972 0 : PG_RETURN_FLOAT8(get_float8_nan());
1973 :
1974 : /* Be sure to throw an error if the input is infinite --- see dcos() */
1975 0 : errno = 0;
1976 0 : result = tan(arg1);
1977 0 : if (errno != 0 || isinf(arg1))
1978 0 : ereport(ERROR,
1979 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
1980 : errmsg("input is out of range")));
1981 : /* Not checking for overflow because tan(pi/2) == Inf */
1982 :
1983 0 : PG_RETURN_FLOAT8(result);
1984 : }
1985 :
1986 :
1987 : /* ========== DEGREE-BASED TRIGONOMETRIC FUNCTIONS ========== */
1988 :
1989 :
1990 : /*
1991 : * Initialize the cached constants declared at the head of this file
1992 : * (sin_30 etc). The fact that we need those at all, let alone need this
1993 : * Rube-Goldberg-worthy method of initializing them, is because there are
1994 : * compilers out there that will precompute expressions such as sin(constant)
1995 : * using a sin() function different from what will be used at runtime. If we
1996 : * want exact results, we must ensure that none of the scaling constants used
1997 : * in the degree-based trig functions are computed that way. To do so, we
1998 : * compute them from the variables degree_c_thirty etc, which are also really
1999 : * constants, but the compiler cannot assume that.
2000 : *
2001 : * Other hazards we are trying to forestall with this kluge include the
2002 : * possibility that compilers will rearrange the expressions, or compute
2003 : * some intermediate results in registers wider than a standard double.
2004 : *
2005 : * In the places where we use these constants, the typical pattern is like
2006 : * volatile float8 sin_x = sin(x * RADIANS_PER_DEGREE);
2007 : * return (sin_x / sin_30);
2008 : * where we hope to get a value of exactly 1.0 from the division when x = 30.
2009 : * The volatile temporary variable is needed on machines with wide float
2010 : * registers, to ensure that the result of sin(x) is rounded to double width
2011 : * the same as the value of sin_30 has been. Experimentation with gcc shows
2012 : * that marking the temp variable volatile is necessary to make the store and
2013 : * reload actually happen; hopefully the same trick works for other compilers.
2014 : * (gcc's documentation suggests using the -ffloat-store compiler switch to
2015 : * ensure this, but that is compiler-specific and it also pessimizes code in
2016 : * many places where we don't care about this.)
2017 : */
2018 : static void
2019 6 : init_degree_constants(void)
2020 : {
2021 6 : sin_30 = sin(degree_c_thirty * RADIANS_PER_DEGREE);
2022 6 : one_minus_cos_60 = 1.0 - cos(degree_c_sixty * RADIANS_PER_DEGREE);
2023 6 : asin_0_5 = asin(degree_c_one_half);
2024 6 : acos_0_5 = acos(degree_c_one_half);
2025 6 : atan_1_0 = atan(degree_c_one);
2026 6 : tan_45 = sind_q1(degree_c_forty_five) / cosd_q1(degree_c_forty_five);
2027 6 : cot_45 = cosd_q1(degree_c_forty_five) / sind_q1(degree_c_forty_five);
2028 6 : degree_consts_set = true;
2029 6 : }
2030 :
2031 : #define INIT_DEGREE_CONSTANTS() \
2032 : do { \
2033 : if (!degree_consts_set) \
2034 : init_degree_constants(); \
2035 : } while(0)
2036 :
2037 :
2038 : /*
2039 : * asind_q1 - returns the inverse sine of x in degrees, for x in
2040 : * the range [0, 1]. The result is an angle in the
2041 : * first quadrant --- [0, 90] degrees.
2042 : *
2043 : * For the 3 special case inputs (0, 0.5 and 1), this
2044 : * function will return exact values (0, 30 and 90
2045 : * degrees respectively).
2046 : */
2047 : static double
2048 84 : asind_q1(double x)
2049 : {
2050 : /*
2051 : * Stitch together inverse sine and cosine functions for the ranges [0,
2052 : * 0.5] and (0.5, 1]. Each expression below is guaranteed to return
2053 : * exactly 30 for x=0.5, so the result is a continuous monotonic function
2054 : * over the full range.
2055 : */
2056 84 : if (x <= 0.5)
2057 : {
2058 48 : volatile float8 asin_x = asin(x);
2059 :
2060 48 : return (asin_x / asin_0_5) * 30.0;
2061 : }
2062 : else
2063 : {
2064 36 : volatile float8 acos_x = acos(x);
2065 :
2066 36 : return 90.0 - (acos_x / acos_0_5) * 60.0;
2067 : }
2068 : }
2069 :
2070 :
2071 : /*
2072 : * acosd_q1 - returns the inverse cosine of x in degrees, for x in
2073 : * the range [0, 1]. The result is an angle in the
2074 : * first quadrant --- [0, 90] degrees.
2075 : *
2076 : * For the 3 special case inputs (0, 0.5 and 1), this
2077 : * function will return exact values (0, 60 and 90
2078 : * degrees respectively).
2079 : */
2080 : static double
2081 36 : acosd_q1(double x)
2082 : {
2083 : /*
2084 : * Stitch together inverse sine and cosine functions for the ranges [0,
2085 : * 0.5] and (0.5, 1]. Each expression below is guaranteed to return
2086 : * exactly 60 for x=0.5, so the result is a continuous monotonic function
2087 : * over the full range.
2088 : */
2089 36 : if (x <= 0.5)
2090 : {
2091 24 : volatile float8 asin_x = asin(x);
2092 :
2093 24 : return 90.0 - (asin_x / asin_0_5) * 30.0;
2094 : }
2095 : else
2096 : {
2097 12 : volatile float8 acos_x = acos(x);
2098 :
2099 12 : return (acos_x / acos_0_5) * 60.0;
2100 : }
2101 : }
2102 :
2103 :
2104 : /*
2105 : * dacosd - returns the arccos of arg1 (degrees)
2106 : */
2107 : Datum
2108 60 : dacosd(PG_FUNCTION_ARGS)
2109 : {
2110 60 : float8 arg1 = PG_GETARG_FLOAT8(0);
2111 : float8 result;
2112 :
2113 : /* Per the POSIX spec, return NaN if the input is NaN */
2114 60 : if (isnan(arg1))
2115 0 : PG_RETURN_FLOAT8(get_float8_nan());
2116 :
2117 60 : INIT_DEGREE_CONSTANTS();
2118 :
2119 : /*
2120 : * The principal branch of the inverse cosine function maps values in the
2121 : * range [-1, 1] to values in the range [0, 180], so we should reject any
2122 : * inputs outside that range and the result will always be finite.
2123 : */
2124 60 : if (arg1 < -1.0 || arg1 > 1.0)
2125 0 : ereport(ERROR,
2126 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2127 : errmsg("input is out of range")));
2128 :
2129 60 : if (arg1 >= 0.0)
2130 36 : result = acosd_q1(arg1);
2131 : else
2132 24 : result = 90.0 + asind_q1(-arg1);
2133 :
2134 60 : if (unlikely(isinf(result)))
2135 0 : float_overflow_error();
2136 :
2137 60 : PG_RETURN_FLOAT8(result);
2138 : }
2139 :
2140 :
2141 : /*
2142 : * dasind - returns the arcsin of arg1 (degrees)
2143 : */
2144 : Datum
2145 60 : dasind(PG_FUNCTION_ARGS)
2146 : {
2147 60 : float8 arg1 = PG_GETARG_FLOAT8(0);
2148 : float8 result;
2149 :
2150 : /* Per the POSIX spec, return NaN if the input is NaN */
2151 60 : if (isnan(arg1))
2152 0 : PG_RETURN_FLOAT8(get_float8_nan());
2153 :
2154 60 : INIT_DEGREE_CONSTANTS();
2155 :
2156 : /*
2157 : * The principal branch of the inverse sine function maps values in the
2158 : * range [-1, 1] to values in the range [-90, 90], so we should reject any
2159 : * inputs outside that range and the result will always be finite.
2160 : */
2161 60 : if (arg1 < -1.0 || arg1 > 1.0)
2162 0 : ereport(ERROR,
2163 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2164 : errmsg("input is out of range")));
2165 :
2166 60 : if (arg1 >= 0.0)
2167 36 : result = asind_q1(arg1);
2168 : else
2169 24 : result = -asind_q1(-arg1);
2170 :
2171 60 : if (unlikely(isinf(result)))
2172 0 : float_overflow_error();
2173 :
2174 60 : PG_RETURN_FLOAT8(result);
2175 : }
2176 :
2177 :
2178 : /*
2179 : * datand - returns the arctan of arg1 (degrees)
2180 : */
2181 : Datum
2182 60 : datand(PG_FUNCTION_ARGS)
2183 : {
2184 60 : float8 arg1 = PG_GETARG_FLOAT8(0);
2185 : float8 result;
2186 : volatile float8 atan_arg1;
2187 :
2188 : /* Per the POSIX spec, return NaN if the input is NaN */
2189 60 : if (isnan(arg1))
2190 0 : PG_RETURN_FLOAT8(get_float8_nan());
2191 :
2192 60 : INIT_DEGREE_CONSTANTS();
2193 :
2194 : /*
2195 : * The principal branch of the inverse tangent function maps all inputs to
2196 : * values in the range [-90, 90], so the result should always be finite,
2197 : * even if the input is infinite. Additionally, we take care to ensure
2198 : * than when arg1 is 1, the result is exactly 45.
2199 : */
2200 60 : atan_arg1 = atan(arg1);
2201 60 : result = (atan_arg1 / atan_1_0) * 45.0;
2202 :
2203 60 : if (unlikely(isinf(result)))
2204 0 : float_overflow_error();
2205 :
2206 60 : PG_RETURN_FLOAT8(result);
2207 : }
2208 :
2209 :
2210 : /*
2211 : * atan2d - returns the arctan of arg1/arg2 (degrees)
2212 : */
2213 : Datum
2214 60 : datan2d(PG_FUNCTION_ARGS)
2215 : {
2216 60 : float8 arg1 = PG_GETARG_FLOAT8(0);
2217 60 : float8 arg2 = PG_GETARG_FLOAT8(1);
2218 : float8 result;
2219 : volatile float8 atan2_arg1_arg2;
2220 :
2221 : /* Per the POSIX spec, return NaN if either input is NaN */
2222 60 : if (isnan(arg1) || isnan(arg2))
2223 0 : PG_RETURN_FLOAT8(get_float8_nan());
2224 :
2225 60 : INIT_DEGREE_CONSTANTS();
2226 :
2227 : /*
2228 : * atan2d maps all inputs to values in the range [-180, 180], so the
2229 : * result should always be finite, even if the inputs are infinite.
2230 : *
2231 : * Note: this coding assumes that atan(1.0) is a suitable scaling constant
2232 : * to get an exact result from atan2(). This might well fail on us at
2233 : * some point, requiring us to decide exactly what inputs we think we're
2234 : * going to guarantee an exact result for.
2235 : */
2236 60 : atan2_arg1_arg2 = atan2(arg1, arg2);
2237 60 : result = (atan2_arg1_arg2 / atan_1_0) * 45.0;
2238 :
2239 60 : if (unlikely(isinf(result)))
2240 0 : float_overflow_error();
2241 :
2242 60 : PG_RETURN_FLOAT8(result);
2243 : }
2244 :
2245 :
2246 : /*
2247 : * sind_0_to_30 - returns the sine of an angle that lies between 0 and
2248 : * 30 degrees. This will return exactly 0 when x is 0,
2249 : * and exactly 0.5 when x is 30 degrees.
2250 : */
2251 : static double
2252 318 : sind_0_to_30(double x)
2253 : {
2254 318 : volatile float8 sin_x = sin(x * RADIANS_PER_DEGREE);
2255 :
2256 318 : return (sin_x / sin_30) / 2.0;
2257 : }
2258 :
2259 :
2260 : /*
2261 : * cosd_0_to_60 - returns the cosine of an angle that lies between 0
2262 : * and 60 degrees. This will return exactly 1 when x
2263 : * is 0, and exactly 0.5 when x is 60 degrees.
2264 : */
2265 : static double
2266 534 : cosd_0_to_60(double x)
2267 : {
2268 534 : volatile float8 one_minus_cos_x = 1.0 - cos(x * RADIANS_PER_DEGREE);
2269 :
2270 534 : return 1.0 - (one_minus_cos_x / one_minus_cos_60) / 2.0;
2271 : }
2272 :
2273 :
2274 : /*
2275 : * sind_q1 - returns the sine of an angle in the first quadrant
2276 : * (0 to 90 degrees).
2277 : */
2278 : static double
2279 426 : sind_q1(double x)
2280 : {
2281 : /*
2282 : * Stitch together the sine and cosine functions for the ranges [0, 30]
2283 : * and (30, 90]. These guarantee to return exact answers at their
2284 : * endpoints, so the overall result is a continuous monotonic function
2285 : * that gives exact results when x = 0, 30 and 90 degrees.
2286 : */
2287 426 : if (x <= 30.0)
2288 210 : return sind_0_to_30(x);
2289 : else
2290 216 : return cosd_0_to_60(90.0 - x);
2291 : }
2292 :
2293 :
2294 : /*
2295 : * cosd_q1 - returns the cosine of an angle in the first quadrant
2296 : * (0 to 90 degrees).
2297 : */
2298 : static double
2299 426 : cosd_q1(double x)
2300 : {
2301 : /*
2302 : * Stitch together the sine and cosine functions for the ranges [0, 60]
2303 : * and (60, 90]. These guarantee to return exact answers at their
2304 : * endpoints, so the overall result is a continuous monotonic function
2305 : * that gives exact results when x = 0, 60 and 90 degrees.
2306 : */
2307 426 : if (x <= 60.0)
2308 318 : return cosd_0_to_60(x);
2309 : else
2310 108 : return sind_0_to_30(90.0 - x);
2311 : }
2312 :
2313 :
2314 : /*
2315 : * dcosd - returns the cosine of arg1 (degrees)
2316 : */
2317 : Datum
2318 198 : dcosd(PG_FUNCTION_ARGS)
2319 : {
2320 198 : float8 arg1 = PG_GETARG_FLOAT8(0);
2321 : float8 result;
2322 198 : int sign = 1;
2323 :
2324 : /*
2325 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2326 : * if the input is infinite.
2327 : */
2328 198 : if (isnan(arg1))
2329 0 : PG_RETURN_FLOAT8(get_float8_nan());
2330 :
2331 198 : if (isinf(arg1))
2332 0 : ereport(ERROR,
2333 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2334 : errmsg("input is out of range")));
2335 :
2336 198 : INIT_DEGREE_CONSTANTS();
2337 :
2338 : /* Reduce the range of the input to [0,90] degrees */
2339 198 : arg1 = fmod(arg1, 360.0);
2340 :
2341 198 : if (arg1 < 0.0)
2342 : {
2343 : /* cosd(-x) = cosd(x) */
2344 0 : arg1 = -arg1;
2345 : }
2346 :
2347 198 : if (arg1 > 180.0)
2348 : {
2349 : /* cosd(360-x) = cosd(x) */
2350 54 : arg1 = 360.0 - arg1;
2351 : }
2352 :
2353 198 : if (arg1 > 90.0)
2354 : {
2355 : /* cosd(180-x) = -cosd(x) */
2356 54 : arg1 = 180.0 - arg1;
2357 54 : sign = -sign;
2358 : }
2359 :
2360 198 : result = sign * cosd_q1(arg1);
2361 :
2362 198 : if (unlikely(isinf(result)))
2363 0 : float_overflow_error();
2364 :
2365 198 : PG_RETURN_FLOAT8(result);
2366 : }
2367 :
2368 :
2369 : /*
2370 : * dcotd - returns the cotangent of arg1 (degrees)
2371 : */
2372 : Datum
2373 108 : dcotd(PG_FUNCTION_ARGS)
2374 : {
2375 108 : float8 arg1 = PG_GETARG_FLOAT8(0);
2376 : float8 result;
2377 : volatile float8 cot_arg1;
2378 108 : int sign = 1;
2379 :
2380 : /*
2381 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2382 : * if the input is infinite.
2383 : */
2384 108 : if (isnan(arg1))
2385 0 : PG_RETURN_FLOAT8(get_float8_nan());
2386 :
2387 108 : if (isinf(arg1))
2388 0 : ereport(ERROR,
2389 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2390 : errmsg("input is out of range")));
2391 :
2392 108 : INIT_DEGREE_CONSTANTS();
2393 :
2394 : /* Reduce the range of the input to [0,90] degrees */
2395 108 : arg1 = fmod(arg1, 360.0);
2396 :
2397 108 : if (arg1 < 0.0)
2398 : {
2399 : /* cotd(-x) = -cotd(x) */
2400 0 : arg1 = -arg1;
2401 0 : sign = -sign;
2402 : }
2403 :
2404 108 : if (arg1 > 180.0)
2405 : {
2406 : /* cotd(360-x) = -cotd(x) */
2407 36 : arg1 = 360.0 - arg1;
2408 36 : sign = -sign;
2409 : }
2410 :
2411 108 : if (arg1 > 90.0)
2412 : {
2413 : /* cotd(180-x) = -cotd(x) */
2414 36 : arg1 = 180.0 - arg1;
2415 36 : sign = -sign;
2416 : }
2417 :
2418 108 : cot_arg1 = cosd_q1(arg1) / sind_q1(arg1);
2419 108 : result = sign * (cot_arg1 / cot_45);
2420 :
2421 : /*
2422 : * On some machines we get cotd(270) = minus zero, but this isn't always
2423 : * true. For portability, and because the user constituency for this
2424 : * function probably doesn't want minus zero, force it to plain zero.
2425 : */
2426 108 : if (result == 0.0)
2427 24 : result = 0.0;
2428 :
2429 : /* Not checking for overflow because cotd(0) == Inf */
2430 :
2431 108 : PG_RETURN_FLOAT8(result);
2432 : }
2433 :
2434 :
2435 : /*
2436 : * dsind - returns the sine of arg1 (degrees)
2437 : */
2438 : Datum
2439 198 : dsind(PG_FUNCTION_ARGS)
2440 : {
2441 198 : float8 arg1 = PG_GETARG_FLOAT8(0);
2442 : float8 result;
2443 198 : int sign = 1;
2444 :
2445 : /*
2446 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2447 : * if the input is infinite.
2448 : */
2449 198 : if (isnan(arg1))
2450 0 : PG_RETURN_FLOAT8(get_float8_nan());
2451 :
2452 198 : if (isinf(arg1))
2453 0 : ereport(ERROR,
2454 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2455 : errmsg("input is out of range")));
2456 :
2457 198 : INIT_DEGREE_CONSTANTS();
2458 :
2459 : /* Reduce the range of the input to [0,90] degrees */
2460 198 : arg1 = fmod(arg1, 360.0);
2461 :
2462 198 : if (arg1 < 0.0)
2463 : {
2464 : /* sind(-x) = -sind(x) */
2465 0 : arg1 = -arg1;
2466 0 : sign = -sign;
2467 : }
2468 :
2469 198 : if (arg1 > 180.0)
2470 : {
2471 : /* sind(360-x) = -sind(x) */
2472 54 : arg1 = 360.0 - arg1;
2473 54 : sign = -sign;
2474 : }
2475 :
2476 198 : if (arg1 > 90.0)
2477 : {
2478 : /* sind(180-x) = sind(x) */
2479 54 : arg1 = 180.0 - arg1;
2480 : }
2481 :
2482 198 : result = sign * sind_q1(arg1);
2483 :
2484 198 : if (unlikely(isinf(result)))
2485 0 : float_overflow_error();
2486 :
2487 198 : PG_RETURN_FLOAT8(result);
2488 : }
2489 :
2490 :
2491 : /*
2492 : * dtand - returns the tangent of arg1 (degrees)
2493 : */
2494 : Datum
2495 108 : dtand(PG_FUNCTION_ARGS)
2496 : {
2497 108 : float8 arg1 = PG_GETARG_FLOAT8(0);
2498 : float8 result;
2499 : volatile float8 tan_arg1;
2500 108 : int sign = 1;
2501 :
2502 : /*
2503 : * Per the POSIX spec, return NaN if the input is NaN and throw an error
2504 : * if the input is infinite.
2505 : */
2506 108 : if (isnan(arg1))
2507 0 : PG_RETURN_FLOAT8(get_float8_nan());
2508 :
2509 108 : if (isinf(arg1))
2510 0 : ereport(ERROR,
2511 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2512 : errmsg("input is out of range")));
2513 :
2514 108 : INIT_DEGREE_CONSTANTS();
2515 :
2516 : /* Reduce the range of the input to [0,90] degrees */
2517 108 : arg1 = fmod(arg1, 360.0);
2518 :
2519 108 : if (arg1 < 0.0)
2520 : {
2521 : /* tand(-x) = -tand(x) */
2522 0 : arg1 = -arg1;
2523 0 : sign = -sign;
2524 : }
2525 :
2526 108 : if (arg1 > 180.0)
2527 : {
2528 : /* tand(360-x) = -tand(x) */
2529 36 : arg1 = 360.0 - arg1;
2530 36 : sign = -sign;
2531 : }
2532 :
2533 108 : if (arg1 > 90.0)
2534 : {
2535 : /* tand(180-x) = -tand(x) */
2536 36 : arg1 = 180.0 - arg1;
2537 36 : sign = -sign;
2538 : }
2539 :
2540 108 : tan_arg1 = sind_q1(arg1) / cosd_q1(arg1);
2541 108 : result = sign * (tan_arg1 / tan_45);
2542 :
2543 : /*
2544 : * On some machines we get tand(180) = minus zero, but this isn't always
2545 : * true. For portability, and because the user constituency for this
2546 : * function probably doesn't want minus zero, force it to plain zero.
2547 : */
2548 108 : if (result == 0.0)
2549 36 : result = 0.0;
2550 :
2551 : /* Not checking for overflow because tand(90) == Inf */
2552 :
2553 108 : PG_RETURN_FLOAT8(result);
2554 : }
2555 :
2556 :
2557 : /*
2558 : * degrees - returns degrees converted from radians
2559 : */
2560 : Datum
2561 80 : degrees(PG_FUNCTION_ARGS)
2562 : {
2563 80 : float8 arg1 = PG_GETARG_FLOAT8(0);
2564 :
2565 80 : PG_RETURN_FLOAT8(float8_div(arg1, RADIANS_PER_DEGREE));
2566 : }
2567 :
2568 :
2569 : /*
2570 : * dpi - returns the constant PI
2571 : */
2572 : Datum
2573 56 : dpi(PG_FUNCTION_ARGS)
2574 : {
2575 56 : PG_RETURN_FLOAT8(M_PI);
2576 : }
2577 :
2578 :
2579 : /*
2580 : * radians - returns radians converted from degrees
2581 : */
2582 : Datum
2583 1910 : radians(PG_FUNCTION_ARGS)
2584 : {
2585 1910 : float8 arg1 = PG_GETARG_FLOAT8(0);
2586 :
2587 1910 : PG_RETURN_FLOAT8(float8_mul(arg1, RADIANS_PER_DEGREE));
2588 : }
2589 :
2590 :
2591 : /* ========== HYPERBOLIC FUNCTIONS ========== */
2592 :
2593 :
2594 : /*
2595 : * dsinh - returns the hyperbolic sine of arg1
2596 : */
2597 : Datum
2598 24 : dsinh(PG_FUNCTION_ARGS)
2599 : {
2600 24 : float8 arg1 = PG_GETARG_FLOAT8(0);
2601 : float8 result;
2602 :
2603 24 : errno = 0;
2604 24 : result = sinh(arg1);
2605 :
2606 : /*
2607 : * if an ERANGE error occurs, it means there is an overflow. For sinh,
2608 : * the result should be either -infinity or infinity, depending on the
2609 : * sign of arg1.
2610 : */
2611 24 : if (errno == ERANGE)
2612 : {
2613 0 : if (arg1 < 0)
2614 0 : result = -get_float8_infinity();
2615 : else
2616 0 : result = get_float8_infinity();
2617 : }
2618 :
2619 24 : PG_RETURN_FLOAT8(result);
2620 : }
2621 :
2622 :
2623 : /*
2624 : * dcosh - returns the hyperbolic cosine of arg1
2625 : */
2626 : Datum
2627 24 : dcosh(PG_FUNCTION_ARGS)
2628 : {
2629 24 : float8 arg1 = PG_GETARG_FLOAT8(0);
2630 : float8 result;
2631 :
2632 24 : errno = 0;
2633 24 : result = cosh(arg1);
2634 :
2635 : /*
2636 : * if an ERANGE error occurs, it means there is an overflow. As cosh is
2637 : * always positive, it always means the result is positive infinity.
2638 : */
2639 24 : if (errno == ERANGE)
2640 0 : result = get_float8_infinity();
2641 :
2642 24 : if (unlikely(result == 0.0))
2643 0 : float_underflow_error();
2644 :
2645 24 : PG_RETURN_FLOAT8(result);
2646 : }
2647 :
2648 : /*
2649 : * dtanh - returns the hyperbolic tangent of arg1
2650 : */
2651 : Datum
2652 24 : dtanh(PG_FUNCTION_ARGS)
2653 : {
2654 24 : float8 arg1 = PG_GETARG_FLOAT8(0);
2655 : float8 result;
2656 :
2657 : /*
2658 : * For tanh, we don't need an errno check because it never overflows.
2659 : */
2660 24 : result = tanh(arg1);
2661 :
2662 24 : if (unlikely(isinf(result)))
2663 0 : float_overflow_error();
2664 :
2665 24 : PG_RETURN_FLOAT8(result);
2666 : }
2667 :
2668 : /*
2669 : * dasinh - returns the inverse hyperbolic sine of arg1
2670 : */
2671 : Datum
2672 24 : dasinh(PG_FUNCTION_ARGS)
2673 : {
2674 24 : float8 arg1 = PG_GETARG_FLOAT8(0);
2675 : float8 result;
2676 :
2677 : /*
2678 : * For asinh, we don't need an errno check because it never overflows.
2679 : */
2680 24 : result = asinh(arg1);
2681 :
2682 24 : PG_RETURN_FLOAT8(result);
2683 : }
2684 :
2685 : /*
2686 : * dacosh - returns the inverse hyperbolic cosine of arg1
2687 : */
2688 : Datum
2689 18 : dacosh(PG_FUNCTION_ARGS)
2690 : {
2691 18 : float8 arg1 = PG_GETARG_FLOAT8(0);
2692 : float8 result;
2693 :
2694 : /*
2695 : * acosh is only defined for inputs >= 1.0. By checking this ourselves,
2696 : * we need not worry about checking for an EDOM error, which is a good
2697 : * thing because some implementations will report that for NaN. Otherwise,
2698 : * no error is possible.
2699 : */
2700 18 : if (arg1 < 1.0)
2701 6 : ereport(ERROR,
2702 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2703 : errmsg("input is out of range")));
2704 :
2705 12 : result = acosh(arg1);
2706 :
2707 12 : PG_RETURN_FLOAT8(result);
2708 : }
2709 :
2710 : /*
2711 : * datanh - returns the inverse hyperbolic tangent of arg1
2712 : */
2713 : Datum
2714 24 : datanh(PG_FUNCTION_ARGS)
2715 : {
2716 24 : float8 arg1 = PG_GETARG_FLOAT8(0);
2717 : float8 result;
2718 :
2719 : /*
2720 : * atanh is only defined for inputs between -1 and 1. By checking this
2721 : * ourselves, we need not worry about checking for an EDOM error, which is
2722 : * a good thing because some implementations will report that for NaN.
2723 : */
2724 24 : if (arg1 < -1.0 || arg1 > 1.0)
2725 12 : ereport(ERROR,
2726 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
2727 : errmsg("input is out of range")));
2728 :
2729 : /*
2730 : * Also handle the infinity cases ourselves; this is helpful because old
2731 : * glibc versions may produce the wrong errno for this. All other inputs
2732 : * cannot produce an error.
2733 : */
2734 12 : if (arg1 == -1.0)
2735 0 : result = -get_float8_infinity();
2736 12 : else if (arg1 == 1.0)
2737 0 : result = get_float8_infinity();
2738 : else
2739 12 : result = atanh(arg1);
2740 :
2741 12 : PG_RETURN_FLOAT8(result);
2742 : }
2743 :
2744 :
2745 : /* ========== ERROR FUNCTIONS ========== */
2746 :
2747 :
2748 : /*
2749 : * derf - returns the error function: erf(arg1)
2750 : */
2751 : Datum
2752 6132 : derf(PG_FUNCTION_ARGS)
2753 : {
2754 6132 : float8 arg1 = PG_GETARG_FLOAT8(0);
2755 : float8 result;
2756 :
2757 : /*
2758 : * For erf, we don't need an errno check because it never overflows.
2759 : */
2760 6132 : result = erf(arg1);
2761 :
2762 6132 : if (unlikely(isinf(result)))
2763 0 : float_overflow_error();
2764 :
2765 6132 : PG_RETURN_FLOAT8(result);
2766 : }
2767 :
2768 : /*
2769 : * derfc - returns the complementary error function: 1 - erf(arg1)
2770 : */
2771 : Datum
2772 132 : derfc(PG_FUNCTION_ARGS)
2773 : {
2774 132 : float8 arg1 = PG_GETARG_FLOAT8(0);
2775 : float8 result;
2776 :
2777 : /*
2778 : * For erfc, we don't need an errno check because it never overflows.
2779 : */
2780 132 : result = erfc(arg1);
2781 :
2782 132 : if (unlikely(isinf(result)))
2783 0 : float_overflow_error();
2784 :
2785 132 : PG_RETURN_FLOAT8(result);
2786 : }
2787 :
2788 :
2789 : /* ========== GAMMA FUNCTIONS ========== */
2790 :
2791 :
2792 : /*
2793 : * dgamma - returns the gamma function of arg1
2794 : */
2795 : Datum
2796 78 : dgamma(PG_FUNCTION_ARGS)
2797 : {
2798 78 : float8 arg1 = PG_GETARG_FLOAT8(0);
2799 : float8 result;
2800 :
2801 : /*
2802 : * Handle NaN and Inf cases explicitly. This simplifies the overflow
2803 : * checks on platforms that do not set errno.
2804 : */
2805 78 : if (isnan(arg1))
2806 6 : result = arg1;
2807 72 : else if (isinf(arg1))
2808 : {
2809 : /* Per POSIX, an input of -Inf causes a domain error */
2810 12 : if (arg1 < 0)
2811 : {
2812 6 : float_overflow_error();
2813 : result = get_float8_nan(); /* keep compiler quiet */
2814 : }
2815 : else
2816 6 : result = arg1;
2817 : }
2818 : else
2819 : {
2820 : /*
2821 : * Note: the POSIX/C99 gamma function is called "tgamma", not "gamma".
2822 : *
2823 : * On some platforms, tgamma() will not set errno but just return Inf,
2824 : * NaN, or zero to report overflow/underflow; therefore, test those
2825 : * cases explicitly (note that, like the exponential function, the
2826 : * gamma function has no zeros).
2827 : */
2828 60 : errno = 0;
2829 60 : result = tgamma(arg1);
2830 :
2831 60 : if (errno != 0 || isinf(result) || isnan(result))
2832 : {
2833 24 : if (result != 0.0)
2834 18 : float_overflow_error();
2835 : else
2836 6 : float_underflow_error();
2837 : }
2838 36 : else if (result == 0.0)
2839 0 : float_underflow_error();
2840 : }
2841 :
2842 48 : PG_RETURN_FLOAT8(result);
2843 : }
2844 :
2845 :
2846 : /*
2847 : * dlgamma - natural logarithm of absolute value of gamma of arg1
2848 : */
2849 : Datum
2850 84 : dlgamma(PG_FUNCTION_ARGS)
2851 : {
2852 84 : float8 arg1 = PG_GETARG_FLOAT8(0);
2853 : float8 result;
2854 :
2855 : /*
2856 : * Note: lgamma may not be thread-safe because it may write to a global
2857 : * variable signgam, which may not be thread-local. However, this doesn't
2858 : * matter to us, since we don't use signgam.
2859 : */
2860 84 : errno = 0;
2861 84 : result = lgamma(arg1);
2862 :
2863 : /*
2864 : * If an ERANGE error occurs, it means there was an overflow or a pole
2865 : * error (which happens for zero and negative integer inputs).
2866 : *
2867 : * On some platforms, lgamma() will not set errno but just return infinity
2868 : * to report overflow, but it should never underflow.
2869 : */
2870 84 : if (errno == ERANGE || (isinf(result) && !isinf(arg1)))
2871 18 : float_overflow_error();
2872 :
2873 66 : PG_RETURN_FLOAT8(result);
2874 : }
2875 :
2876 :
2877 :
2878 : /*
2879 : * =========================
2880 : * FLOAT AGGREGATE OPERATORS
2881 : * =========================
2882 : *
2883 : * float8_accum - accumulate for AVG(), variance aggregates, etc.
2884 : * float4_accum - same, but input data is float4
2885 : * float8_avg - produce final result for float AVG()
2886 : * float8_var_samp - produce final result for float VAR_SAMP()
2887 : * float8_var_pop - produce final result for float VAR_POP()
2888 : * float8_stddev_samp - produce final result for float STDDEV_SAMP()
2889 : * float8_stddev_pop - produce final result for float STDDEV_POP()
2890 : *
2891 : * The naive schoolbook implementation of these aggregates works by
2892 : * accumulating sum(X) and sum(X^2). However, this approach suffers from
2893 : * large rounding errors in the final computation of quantities like the
2894 : * population variance (N*sum(X^2) - sum(X)^2) / N^2, since each of the
2895 : * intermediate terms is potentially very large, while the difference is often
2896 : * quite small.
2897 : *
2898 : * Instead we use the Youngs-Cramer algorithm [1] which works by accumulating
2899 : * Sx=sum(X) and Sxx=sum((X-Sx/N)^2), using a numerically stable algorithm to
2900 : * incrementally update those quantities. The final computations of each of
2901 : * the aggregate values is then trivial and gives more accurate results (for
2902 : * example, the population variance is just Sxx/N). This algorithm is also
2903 : * fairly easy to generalize to allow parallel execution without loss of
2904 : * precision (see, for example, [2]). For more details, and a comparison of
2905 : * this with other algorithms, see [3].
2906 : *
2907 : * The transition datatype for all these aggregates is a 3-element array
2908 : * of float8, holding the values N, Sx, Sxx in that order.
2909 : *
2910 : * Note that we represent N as a float to avoid having to build a special
2911 : * datatype. Given a reasonable floating-point implementation, there should
2912 : * be no accuracy loss unless N exceeds 2 ^ 52 or so (by which time the
2913 : * user will have doubtless lost interest anyway...)
2914 : *
2915 : * [1] Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms,
2916 : * E. A. Youngs and E. M. Cramer, Technometrics Vol 13, No 3, August 1971.
2917 : *
2918 : * [2] Updating Formulae and a Pairwise Algorithm for Computing Sample
2919 : * Variances, T. F. Chan, G. H. Golub & R. J. LeVeque, COMPSTAT 1982.
2920 : *
2921 : * [3] Numerically Stable Parallel Computation of (Co-)Variance, Erich
2922 : * Schubert and Michael Gertz, Proceedings of the 30th International
2923 : * Conference on Scientific and Statistical Database Management, 2018.
2924 : */
2925 :
2926 : static float8 *
2927 1492 : check_float8_array(ArrayType *transarray, const char *caller, int n)
2928 : {
2929 : /*
2930 : * We expect the input to be an N-element float array; verify that. We
2931 : * don't need to use deconstruct_array() since the array data is just
2932 : * going to look like a C array of N float8 values.
2933 : */
2934 1492 : if (ARR_NDIM(transarray) != 1 ||
2935 1492 : ARR_DIMS(transarray)[0] != n ||
2936 1492 : ARR_HASNULL(transarray) ||
2937 1492 : ARR_ELEMTYPE(transarray) != FLOAT8OID)
2938 0 : elog(ERROR, "%s: expected %d-element float8 array", caller, n);
2939 1492 : return (float8 *) ARR_DATA_PTR(transarray);
2940 : }
2941 :
2942 : /*
2943 : * float8_combine
2944 : *
2945 : * An aggregate combine function used to combine two 3 fields
2946 : * aggregate transition data into a single transition data.
2947 : * This function is used only in two stage aggregation and
2948 : * shouldn't be called outside aggregate context.
2949 : */
2950 : Datum
2951 18 : float8_combine(PG_FUNCTION_ARGS)
2952 : {
2953 18 : ArrayType *transarray1 = PG_GETARG_ARRAYTYPE_P(0);
2954 18 : ArrayType *transarray2 = PG_GETARG_ARRAYTYPE_P(1);
2955 : float8 *transvalues1;
2956 : float8 *transvalues2;
2957 : float8 N1,
2958 : Sx1,
2959 : Sxx1,
2960 : N2,
2961 : Sx2,
2962 : Sxx2,
2963 : tmp,
2964 : N,
2965 : Sx,
2966 : Sxx;
2967 :
2968 18 : transvalues1 = check_float8_array(transarray1, "float8_combine", 3);
2969 18 : transvalues2 = check_float8_array(transarray2, "float8_combine", 3);
2970 :
2971 18 : N1 = transvalues1[0];
2972 18 : Sx1 = transvalues1[1];
2973 18 : Sxx1 = transvalues1[2];
2974 :
2975 18 : N2 = transvalues2[0];
2976 18 : Sx2 = transvalues2[1];
2977 18 : Sxx2 = transvalues2[2];
2978 :
2979 : /*--------------------
2980 : * The transition values combine using a generalization of the
2981 : * Youngs-Cramer algorithm as follows:
2982 : *
2983 : * N = N1 + N2
2984 : * Sx = Sx1 + Sx2
2985 : * Sxx = Sxx1 + Sxx2 + N1 * N2 * (Sx1/N1 - Sx2/N2)^2 / N;
2986 : *
2987 : * It's worth handling the special cases N1 = 0 and N2 = 0 separately
2988 : * since those cases are trivial, and we then don't need to worry about
2989 : * division-by-zero errors in the general case.
2990 : *--------------------
2991 : */
2992 18 : if (N1 == 0.0)
2993 : {
2994 6 : N = N2;
2995 6 : Sx = Sx2;
2996 6 : Sxx = Sxx2;
2997 : }
2998 12 : else if (N2 == 0.0)
2999 : {
3000 6 : N = N1;
3001 6 : Sx = Sx1;
3002 6 : Sxx = Sxx1;
3003 : }
3004 : else
3005 : {
3006 6 : N = N1 + N2;
3007 6 : Sx = float8_pl(Sx1, Sx2);
3008 6 : tmp = Sx1 / N1 - Sx2 / N2;
3009 6 : Sxx = Sxx1 + Sxx2 + N1 * N2 * tmp * tmp / N;
3010 6 : if (unlikely(isinf(Sxx)) && !isinf(Sxx1) && !isinf(Sxx2))
3011 0 : float_overflow_error();
3012 : }
3013 :
3014 : /*
3015 : * If we're invoked as an aggregate, we can cheat and modify our first
3016 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3017 : * new array with the updated transition data and return it.
3018 : */
3019 18 : if (AggCheckCallContext(fcinfo, NULL))
3020 : {
3021 0 : transvalues1[0] = N;
3022 0 : transvalues1[1] = Sx;
3023 0 : transvalues1[2] = Sxx;
3024 :
3025 0 : PG_RETURN_ARRAYTYPE_P(transarray1);
3026 : }
3027 : else
3028 : {
3029 : Datum transdatums[3];
3030 : ArrayType *result;
3031 :
3032 18 : transdatums[0] = Float8GetDatumFast(N);
3033 18 : transdatums[1] = Float8GetDatumFast(Sx);
3034 18 : transdatums[2] = Float8GetDatumFast(Sxx);
3035 :
3036 18 : result = construct_array_builtin(transdatums, 3, FLOAT8OID);
3037 :
3038 18 : PG_RETURN_ARRAYTYPE_P(result);
3039 : }
3040 : }
3041 :
3042 : Datum
3043 362 : float8_accum(PG_FUNCTION_ARGS)
3044 : {
3045 362 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3046 362 : float8 newval = PG_GETARG_FLOAT8(1);
3047 : float8 *transvalues;
3048 : float8 N,
3049 : Sx,
3050 : Sxx,
3051 : tmp;
3052 :
3053 362 : transvalues = check_float8_array(transarray, "float8_accum", 3);
3054 362 : N = transvalues[0];
3055 362 : Sx = transvalues[1];
3056 362 : Sxx = transvalues[2];
3057 :
3058 : /*
3059 : * Use the Youngs-Cramer algorithm to incorporate the new value into the
3060 : * transition values.
3061 : */
3062 362 : N += 1.0;
3063 362 : Sx += newval;
3064 362 : if (transvalues[0] > 0.0)
3065 : {
3066 264 : tmp = newval * N - Sx;
3067 264 : Sxx += tmp * tmp / (N * transvalues[0]);
3068 :
3069 : /*
3070 : * Overflow check. We only report an overflow error when finite
3071 : * inputs lead to infinite results. Note also that Sxx should be NaN
3072 : * if any of the inputs are infinite, so we intentionally prevent Sxx
3073 : * from becoming infinite.
3074 : */
3075 264 : if (isinf(Sx) || isinf(Sxx))
3076 : {
3077 24 : if (!isinf(transvalues[1]) && !isinf(newval))
3078 0 : float_overflow_error();
3079 :
3080 24 : Sxx = get_float8_nan();
3081 : }
3082 : }
3083 : else
3084 : {
3085 : /*
3086 : * At the first input, we normally can leave Sxx as 0. However, if
3087 : * the first input is Inf or NaN, we'd better force Sxx to NaN;
3088 : * otherwise we will falsely report variance zero when there are no
3089 : * more inputs.
3090 : */
3091 98 : if (isnan(newval) || isinf(newval))
3092 48 : Sxx = get_float8_nan();
3093 : }
3094 :
3095 : /*
3096 : * If we're invoked as an aggregate, we can cheat and modify our first
3097 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3098 : * new array with the updated transition data and return it.
3099 : */
3100 362 : if (AggCheckCallContext(fcinfo, NULL))
3101 : {
3102 356 : transvalues[0] = N;
3103 356 : transvalues[1] = Sx;
3104 356 : transvalues[2] = Sxx;
3105 :
3106 356 : PG_RETURN_ARRAYTYPE_P(transarray);
3107 : }
3108 : else
3109 : {
3110 : Datum transdatums[3];
3111 : ArrayType *result;
3112 :
3113 6 : transdatums[0] = Float8GetDatumFast(N);
3114 6 : transdatums[1] = Float8GetDatumFast(Sx);
3115 6 : transdatums[2] = Float8GetDatumFast(Sxx);
3116 :
3117 6 : result = construct_array_builtin(transdatums, 3, FLOAT8OID);
3118 :
3119 6 : PG_RETURN_ARRAYTYPE_P(result);
3120 : }
3121 : }
3122 :
3123 : Datum
3124 288 : float4_accum(PG_FUNCTION_ARGS)
3125 : {
3126 288 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3127 :
3128 : /* do computations as float8 */
3129 288 : float8 newval = PG_GETARG_FLOAT4(1);
3130 : float8 *transvalues;
3131 : float8 N,
3132 : Sx,
3133 : Sxx,
3134 : tmp;
3135 :
3136 288 : transvalues = check_float8_array(transarray, "float4_accum", 3);
3137 288 : N = transvalues[0];
3138 288 : Sx = transvalues[1];
3139 288 : Sxx = transvalues[2];
3140 :
3141 : /*
3142 : * Use the Youngs-Cramer algorithm to incorporate the new value into the
3143 : * transition values.
3144 : */
3145 288 : N += 1.0;
3146 288 : Sx += newval;
3147 288 : if (transvalues[0] > 0.0)
3148 : {
3149 204 : tmp = newval * N - Sx;
3150 204 : Sxx += tmp * tmp / (N * transvalues[0]);
3151 :
3152 : /*
3153 : * Overflow check. We only report an overflow error when finite
3154 : * inputs lead to infinite results. Note also that Sxx should be NaN
3155 : * if any of the inputs are infinite, so we intentionally prevent Sxx
3156 : * from becoming infinite.
3157 : */
3158 204 : if (isinf(Sx) || isinf(Sxx))
3159 : {
3160 0 : if (!isinf(transvalues[1]) && !isinf(newval))
3161 0 : float_overflow_error();
3162 :
3163 0 : Sxx = get_float8_nan();
3164 : }
3165 : }
3166 : else
3167 : {
3168 : /*
3169 : * At the first input, we normally can leave Sxx as 0. However, if
3170 : * the first input is Inf or NaN, we'd better force Sxx to NaN;
3171 : * otherwise we will falsely report variance zero when there are no
3172 : * more inputs.
3173 : */
3174 84 : if (isnan(newval) || isinf(newval))
3175 24 : Sxx = get_float8_nan();
3176 : }
3177 :
3178 : /*
3179 : * If we're invoked as an aggregate, we can cheat and modify our first
3180 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3181 : * new array with the updated transition data and return it.
3182 : */
3183 288 : if (AggCheckCallContext(fcinfo, NULL))
3184 : {
3185 288 : transvalues[0] = N;
3186 288 : transvalues[1] = Sx;
3187 288 : transvalues[2] = Sxx;
3188 :
3189 288 : PG_RETURN_ARRAYTYPE_P(transarray);
3190 : }
3191 : else
3192 : {
3193 : Datum transdatums[3];
3194 : ArrayType *result;
3195 :
3196 0 : transdatums[0] = Float8GetDatumFast(N);
3197 0 : transdatums[1] = Float8GetDatumFast(Sx);
3198 0 : transdatums[2] = Float8GetDatumFast(Sxx);
3199 :
3200 0 : result = construct_array_builtin(transdatums, 3, FLOAT8OID);
3201 :
3202 0 : PG_RETURN_ARRAYTYPE_P(result);
3203 : }
3204 : }
3205 :
3206 : Datum
3207 62 : float8_avg(PG_FUNCTION_ARGS)
3208 : {
3209 62 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3210 : float8 *transvalues;
3211 : float8 N,
3212 : Sx;
3213 :
3214 62 : transvalues = check_float8_array(transarray, "float8_avg", 3);
3215 62 : N = transvalues[0];
3216 62 : Sx = transvalues[1];
3217 : /* ignore Sxx */
3218 :
3219 : /* SQL defines AVG of no values to be NULL */
3220 62 : if (N == 0.0)
3221 6 : PG_RETURN_NULL();
3222 :
3223 56 : PG_RETURN_FLOAT8(Sx / N);
3224 : }
3225 :
3226 : Datum
3227 84 : float8_var_pop(PG_FUNCTION_ARGS)
3228 : {
3229 84 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3230 : float8 *transvalues;
3231 : float8 N,
3232 : Sxx;
3233 :
3234 84 : transvalues = check_float8_array(transarray, "float8_var_pop", 3);
3235 84 : N = transvalues[0];
3236 : /* ignore Sx */
3237 84 : Sxx = transvalues[2];
3238 :
3239 : /* Population variance is undefined when N is 0, so return NULL */
3240 84 : if (N == 0.0)
3241 0 : PG_RETURN_NULL();
3242 :
3243 : /* Note that Sxx is guaranteed to be non-negative */
3244 :
3245 84 : PG_RETURN_FLOAT8(Sxx / N);
3246 : }
3247 :
3248 : Datum
3249 42 : float8_var_samp(PG_FUNCTION_ARGS)
3250 : {
3251 42 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3252 : float8 *transvalues;
3253 : float8 N,
3254 : Sxx;
3255 :
3256 42 : transvalues = check_float8_array(transarray, "float8_var_samp", 3);
3257 42 : N = transvalues[0];
3258 : /* ignore Sx */
3259 42 : Sxx = transvalues[2];
3260 :
3261 : /* Sample variance is undefined when N is 0 or 1, so return NULL */
3262 42 : if (N <= 1.0)
3263 36 : PG_RETURN_NULL();
3264 :
3265 : /* Note that Sxx is guaranteed to be non-negative */
3266 :
3267 6 : PG_RETURN_FLOAT8(Sxx / (N - 1.0));
3268 : }
3269 :
3270 : Datum
3271 42 : float8_stddev_pop(PG_FUNCTION_ARGS)
3272 : {
3273 42 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3274 : float8 *transvalues;
3275 : float8 N,
3276 : Sxx;
3277 :
3278 42 : transvalues = check_float8_array(transarray, "float8_stddev_pop", 3);
3279 42 : N = transvalues[0];
3280 : /* ignore Sx */
3281 42 : Sxx = transvalues[2];
3282 :
3283 : /* Population stddev is undefined when N is 0, so return NULL */
3284 42 : if (N == 0.0)
3285 0 : PG_RETURN_NULL();
3286 :
3287 : /* Note that Sxx is guaranteed to be non-negative */
3288 :
3289 42 : PG_RETURN_FLOAT8(sqrt(Sxx / N));
3290 : }
3291 :
3292 : Datum
3293 48 : float8_stddev_samp(PG_FUNCTION_ARGS)
3294 : {
3295 48 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3296 : float8 *transvalues;
3297 : float8 N,
3298 : Sxx;
3299 :
3300 48 : transvalues = check_float8_array(transarray, "float8_stddev_samp", 3);
3301 48 : N = transvalues[0];
3302 : /* ignore Sx */
3303 48 : Sxx = transvalues[2];
3304 :
3305 : /* Sample stddev is undefined when N is 0 or 1, so return NULL */
3306 48 : if (N <= 1.0)
3307 36 : PG_RETURN_NULL();
3308 :
3309 : /* Note that Sxx is guaranteed to be non-negative */
3310 :
3311 12 : PG_RETURN_FLOAT8(sqrt(Sxx / (N - 1.0)));
3312 : }
3313 :
3314 : /*
3315 : * =========================
3316 : * SQL2003 BINARY AGGREGATES
3317 : * =========================
3318 : *
3319 : * As with the preceding aggregates, we use the Youngs-Cramer algorithm to
3320 : * reduce rounding errors in the aggregate final functions.
3321 : *
3322 : * The transition datatype for all these aggregates is a 6-element array of
3323 : * float8, holding the values N, Sx=sum(X), Sxx=sum((X-Sx/N)^2), Sy=sum(Y),
3324 : * Syy=sum((Y-Sy/N)^2), Sxy=sum((X-Sx/N)*(Y-Sy/N)) in that order.
3325 : *
3326 : * Note that Y is the first argument to all these aggregates!
3327 : *
3328 : * It might seem attractive to optimize this by having multiple accumulator
3329 : * functions that only calculate the sums actually needed. But on most
3330 : * modern machines, a couple of extra floating-point multiplies will be
3331 : * insignificant compared to the other per-tuple overhead, so I've chosen
3332 : * to minimize code space instead.
3333 : */
3334 :
3335 : Datum
3336 318 : float8_regr_accum(PG_FUNCTION_ARGS)
3337 : {
3338 318 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3339 318 : float8 newvalY = PG_GETARG_FLOAT8(1);
3340 318 : float8 newvalX = PG_GETARG_FLOAT8(2);
3341 : float8 *transvalues;
3342 : float8 N,
3343 : Sx,
3344 : Sxx,
3345 : Sy,
3346 : Syy,
3347 : Sxy,
3348 : tmpX,
3349 : tmpY,
3350 : scale;
3351 :
3352 318 : transvalues = check_float8_array(transarray, "float8_regr_accum", 6);
3353 318 : N = transvalues[0];
3354 318 : Sx = transvalues[1];
3355 318 : Sxx = transvalues[2];
3356 318 : Sy = transvalues[3];
3357 318 : Syy = transvalues[4];
3358 318 : Sxy = transvalues[5];
3359 :
3360 : /*
3361 : * Use the Youngs-Cramer algorithm to incorporate the new values into the
3362 : * transition values.
3363 : */
3364 318 : N += 1.0;
3365 318 : Sx += newvalX;
3366 318 : Sy += newvalY;
3367 318 : if (transvalues[0] > 0.0)
3368 : {
3369 210 : tmpX = newvalX * N - Sx;
3370 210 : tmpY = newvalY * N - Sy;
3371 210 : scale = 1.0 / (N * transvalues[0]);
3372 210 : Sxx += tmpX * tmpX * scale;
3373 210 : Syy += tmpY * tmpY * scale;
3374 210 : Sxy += tmpX * tmpY * scale;
3375 :
3376 : /*
3377 : * Overflow check. We only report an overflow error when finite
3378 : * inputs lead to infinite results. Note also that Sxx, Syy and Sxy
3379 : * should be NaN if any of the relevant inputs are infinite, so we
3380 : * intentionally prevent them from becoming infinite.
3381 : */
3382 210 : if (isinf(Sx) || isinf(Sxx) || isinf(Sy) || isinf(Syy) || isinf(Sxy))
3383 : {
3384 0 : if (((isinf(Sx) || isinf(Sxx)) &&
3385 0 : !isinf(transvalues[1]) && !isinf(newvalX)) ||
3386 0 : ((isinf(Sy) || isinf(Syy)) &&
3387 0 : !isinf(transvalues[3]) && !isinf(newvalY)) ||
3388 0 : (isinf(Sxy) &&
3389 0 : !isinf(transvalues[1]) && !isinf(newvalX) &&
3390 0 : !isinf(transvalues[3]) && !isinf(newvalY)))
3391 0 : float_overflow_error();
3392 :
3393 0 : if (isinf(Sxx))
3394 0 : Sxx = get_float8_nan();
3395 0 : if (isinf(Syy))
3396 0 : Syy = get_float8_nan();
3397 0 : if (isinf(Sxy))
3398 0 : Sxy = get_float8_nan();
3399 : }
3400 : }
3401 : else
3402 : {
3403 : /*
3404 : * At the first input, we normally can leave Sxx et al as 0. However,
3405 : * if the first input is Inf or NaN, we'd better force the dependent
3406 : * sums to NaN; otherwise we will falsely report variance zero when
3407 : * there are no more inputs.
3408 : */
3409 108 : if (isnan(newvalX) || isinf(newvalX))
3410 24 : Sxx = Sxy = get_float8_nan();
3411 108 : if (isnan(newvalY) || isinf(newvalY))
3412 0 : Syy = Sxy = get_float8_nan();
3413 : }
3414 :
3415 : /*
3416 : * If we're invoked as an aggregate, we can cheat and modify our first
3417 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3418 : * new array with the updated transition data and return it.
3419 : */
3420 318 : if (AggCheckCallContext(fcinfo, NULL))
3421 : {
3422 312 : transvalues[0] = N;
3423 312 : transvalues[1] = Sx;
3424 312 : transvalues[2] = Sxx;
3425 312 : transvalues[3] = Sy;
3426 312 : transvalues[4] = Syy;
3427 312 : transvalues[5] = Sxy;
3428 :
3429 312 : PG_RETURN_ARRAYTYPE_P(transarray);
3430 : }
3431 : else
3432 : {
3433 : Datum transdatums[6];
3434 : ArrayType *result;
3435 :
3436 6 : transdatums[0] = Float8GetDatumFast(N);
3437 6 : transdatums[1] = Float8GetDatumFast(Sx);
3438 6 : transdatums[2] = Float8GetDatumFast(Sxx);
3439 6 : transdatums[3] = Float8GetDatumFast(Sy);
3440 6 : transdatums[4] = Float8GetDatumFast(Syy);
3441 6 : transdatums[5] = Float8GetDatumFast(Sxy);
3442 :
3443 6 : result = construct_array_builtin(transdatums, 6, FLOAT8OID);
3444 :
3445 6 : PG_RETURN_ARRAYTYPE_P(result);
3446 : }
3447 : }
3448 :
3449 : /*
3450 : * float8_regr_combine
3451 : *
3452 : * An aggregate combine function used to combine two 6 fields
3453 : * aggregate transition data into a single transition data.
3454 : * This function is used only in two stage aggregation and
3455 : * shouldn't be called outside aggregate context.
3456 : */
3457 : Datum
3458 18 : float8_regr_combine(PG_FUNCTION_ARGS)
3459 : {
3460 18 : ArrayType *transarray1 = PG_GETARG_ARRAYTYPE_P(0);
3461 18 : ArrayType *transarray2 = PG_GETARG_ARRAYTYPE_P(1);
3462 : float8 *transvalues1;
3463 : float8 *transvalues2;
3464 : float8 N1,
3465 : Sx1,
3466 : Sxx1,
3467 : Sy1,
3468 : Syy1,
3469 : Sxy1,
3470 : N2,
3471 : Sx2,
3472 : Sxx2,
3473 : Sy2,
3474 : Syy2,
3475 : Sxy2,
3476 : tmp1,
3477 : tmp2,
3478 : N,
3479 : Sx,
3480 : Sxx,
3481 : Sy,
3482 : Syy,
3483 : Sxy;
3484 :
3485 18 : transvalues1 = check_float8_array(transarray1, "float8_regr_combine", 6);
3486 18 : transvalues2 = check_float8_array(transarray2, "float8_regr_combine", 6);
3487 :
3488 18 : N1 = transvalues1[0];
3489 18 : Sx1 = transvalues1[1];
3490 18 : Sxx1 = transvalues1[2];
3491 18 : Sy1 = transvalues1[3];
3492 18 : Syy1 = transvalues1[4];
3493 18 : Sxy1 = transvalues1[5];
3494 :
3495 18 : N2 = transvalues2[0];
3496 18 : Sx2 = transvalues2[1];
3497 18 : Sxx2 = transvalues2[2];
3498 18 : Sy2 = transvalues2[3];
3499 18 : Syy2 = transvalues2[4];
3500 18 : Sxy2 = transvalues2[5];
3501 :
3502 : /*--------------------
3503 : * The transition values combine using a generalization of the
3504 : * Youngs-Cramer algorithm as follows:
3505 : *
3506 : * N = N1 + N2
3507 : * Sx = Sx1 + Sx2
3508 : * Sxx = Sxx1 + Sxx2 + N1 * N2 * (Sx1/N1 - Sx2/N2)^2 / N
3509 : * Sy = Sy1 + Sy2
3510 : * Syy = Syy1 + Syy2 + N1 * N2 * (Sy1/N1 - Sy2/N2)^2 / N
3511 : * Sxy = Sxy1 + Sxy2 + N1 * N2 * (Sx1/N1 - Sx2/N2) * (Sy1/N1 - Sy2/N2) / N
3512 : *
3513 : * It's worth handling the special cases N1 = 0 and N2 = 0 separately
3514 : * since those cases are trivial, and we then don't need to worry about
3515 : * division-by-zero errors in the general case.
3516 : *--------------------
3517 : */
3518 18 : if (N1 == 0.0)
3519 : {
3520 6 : N = N2;
3521 6 : Sx = Sx2;
3522 6 : Sxx = Sxx2;
3523 6 : Sy = Sy2;
3524 6 : Syy = Syy2;
3525 6 : Sxy = Sxy2;
3526 : }
3527 12 : else if (N2 == 0.0)
3528 : {
3529 6 : N = N1;
3530 6 : Sx = Sx1;
3531 6 : Sxx = Sxx1;
3532 6 : Sy = Sy1;
3533 6 : Syy = Syy1;
3534 6 : Sxy = Sxy1;
3535 : }
3536 : else
3537 : {
3538 6 : N = N1 + N2;
3539 6 : Sx = float8_pl(Sx1, Sx2);
3540 6 : tmp1 = Sx1 / N1 - Sx2 / N2;
3541 6 : Sxx = Sxx1 + Sxx2 + N1 * N2 * tmp1 * tmp1 / N;
3542 6 : if (unlikely(isinf(Sxx)) && !isinf(Sxx1) && !isinf(Sxx2))
3543 0 : float_overflow_error();
3544 6 : Sy = float8_pl(Sy1, Sy2);
3545 6 : tmp2 = Sy1 / N1 - Sy2 / N2;
3546 6 : Syy = Syy1 + Syy2 + N1 * N2 * tmp2 * tmp2 / N;
3547 6 : if (unlikely(isinf(Syy)) && !isinf(Syy1) && !isinf(Syy2))
3548 0 : float_overflow_error();
3549 6 : Sxy = Sxy1 + Sxy2 + N1 * N2 * tmp1 * tmp2 / N;
3550 6 : if (unlikely(isinf(Sxy)) && !isinf(Sxy1) && !isinf(Sxy2))
3551 0 : float_overflow_error();
3552 : }
3553 :
3554 : /*
3555 : * If we're invoked as an aggregate, we can cheat and modify our first
3556 : * parameter in-place to reduce palloc overhead. Otherwise we construct a
3557 : * new array with the updated transition data and return it.
3558 : */
3559 18 : if (AggCheckCallContext(fcinfo, NULL))
3560 : {
3561 0 : transvalues1[0] = N;
3562 0 : transvalues1[1] = Sx;
3563 0 : transvalues1[2] = Sxx;
3564 0 : transvalues1[3] = Sy;
3565 0 : transvalues1[4] = Syy;
3566 0 : transvalues1[5] = Sxy;
3567 :
3568 0 : PG_RETURN_ARRAYTYPE_P(transarray1);
3569 : }
3570 : else
3571 : {
3572 : Datum transdatums[6];
3573 : ArrayType *result;
3574 :
3575 18 : transdatums[0] = Float8GetDatumFast(N);
3576 18 : transdatums[1] = Float8GetDatumFast(Sx);
3577 18 : transdatums[2] = Float8GetDatumFast(Sxx);
3578 18 : transdatums[3] = Float8GetDatumFast(Sy);
3579 18 : transdatums[4] = Float8GetDatumFast(Syy);
3580 18 : transdatums[5] = Float8GetDatumFast(Sxy);
3581 :
3582 18 : result = construct_array_builtin(transdatums, 6, FLOAT8OID);
3583 :
3584 18 : PG_RETURN_ARRAYTYPE_P(result);
3585 : }
3586 : }
3587 :
3588 :
3589 : Datum
3590 30 : float8_regr_sxx(PG_FUNCTION_ARGS)
3591 : {
3592 30 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3593 : float8 *transvalues;
3594 : float8 N,
3595 : Sxx;
3596 :
3597 30 : transvalues = check_float8_array(transarray, "float8_regr_sxx", 6);
3598 30 : N = transvalues[0];
3599 30 : Sxx = transvalues[2];
3600 :
3601 : /* if N is 0 we should return NULL */
3602 30 : if (N < 1.0)
3603 0 : PG_RETURN_NULL();
3604 :
3605 : /* Note that Sxx is guaranteed to be non-negative */
3606 :
3607 30 : PG_RETURN_FLOAT8(Sxx);
3608 : }
3609 :
3610 : Datum
3611 30 : float8_regr_syy(PG_FUNCTION_ARGS)
3612 : {
3613 30 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3614 : float8 *transvalues;
3615 : float8 N,
3616 : Syy;
3617 :
3618 30 : transvalues = check_float8_array(transarray, "float8_regr_syy", 6);
3619 30 : N = transvalues[0];
3620 30 : Syy = transvalues[4];
3621 :
3622 : /* if N is 0 we should return NULL */
3623 30 : if (N < 1.0)
3624 0 : PG_RETURN_NULL();
3625 :
3626 : /* Note that Syy is guaranteed to be non-negative */
3627 :
3628 30 : PG_RETURN_FLOAT8(Syy);
3629 : }
3630 :
3631 : Datum
3632 30 : float8_regr_sxy(PG_FUNCTION_ARGS)
3633 : {
3634 30 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3635 : float8 *transvalues;
3636 : float8 N,
3637 : Sxy;
3638 :
3639 30 : transvalues = check_float8_array(transarray, "float8_regr_sxy", 6);
3640 30 : N = transvalues[0];
3641 30 : Sxy = transvalues[5];
3642 :
3643 : /* if N is 0 we should return NULL */
3644 30 : if (N < 1.0)
3645 0 : PG_RETURN_NULL();
3646 :
3647 : /* A negative result is valid here */
3648 :
3649 30 : PG_RETURN_FLOAT8(Sxy);
3650 : }
3651 :
3652 : Datum
3653 6 : float8_regr_avgx(PG_FUNCTION_ARGS)
3654 : {
3655 6 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3656 : float8 *transvalues;
3657 : float8 N,
3658 : Sx;
3659 :
3660 6 : transvalues = check_float8_array(transarray, "float8_regr_avgx", 6);
3661 6 : N = transvalues[0];
3662 6 : Sx = transvalues[1];
3663 :
3664 : /* if N is 0 we should return NULL */
3665 6 : if (N < 1.0)
3666 0 : PG_RETURN_NULL();
3667 :
3668 6 : PG_RETURN_FLOAT8(Sx / N);
3669 : }
3670 :
3671 : Datum
3672 6 : float8_regr_avgy(PG_FUNCTION_ARGS)
3673 : {
3674 6 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3675 : float8 *transvalues;
3676 : float8 N,
3677 : Sy;
3678 :
3679 6 : transvalues = check_float8_array(transarray, "float8_regr_avgy", 6);
3680 6 : N = transvalues[0];
3681 6 : Sy = transvalues[3];
3682 :
3683 : /* if N is 0 we should return NULL */
3684 6 : if (N < 1.0)
3685 0 : PG_RETURN_NULL();
3686 :
3687 6 : PG_RETURN_FLOAT8(Sy / N);
3688 : }
3689 :
3690 : Datum
3691 24 : float8_covar_pop(PG_FUNCTION_ARGS)
3692 : {
3693 24 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3694 : float8 *transvalues;
3695 : float8 N,
3696 : Sxy;
3697 :
3698 24 : transvalues = check_float8_array(transarray, "float8_covar_pop", 6);
3699 24 : N = transvalues[0];
3700 24 : Sxy = transvalues[5];
3701 :
3702 : /* if N is 0 we should return NULL */
3703 24 : if (N < 1.0)
3704 0 : PG_RETURN_NULL();
3705 :
3706 24 : PG_RETURN_FLOAT8(Sxy / N);
3707 : }
3708 :
3709 : Datum
3710 24 : float8_covar_samp(PG_FUNCTION_ARGS)
3711 : {
3712 24 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3713 : float8 *transvalues;
3714 : float8 N,
3715 : Sxy;
3716 :
3717 24 : transvalues = check_float8_array(transarray, "float8_covar_samp", 6);
3718 24 : N = transvalues[0];
3719 24 : Sxy = transvalues[5];
3720 :
3721 : /* if N is <= 1 we should return NULL */
3722 24 : if (N < 2.0)
3723 18 : PG_RETURN_NULL();
3724 :
3725 6 : PG_RETURN_FLOAT8(Sxy / (N - 1.0));
3726 : }
3727 :
3728 : Datum
3729 6 : float8_corr(PG_FUNCTION_ARGS)
3730 : {
3731 6 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3732 : float8 *transvalues;
3733 : float8 N,
3734 : Sxx,
3735 : Syy,
3736 : Sxy;
3737 :
3738 6 : transvalues = check_float8_array(transarray, "float8_corr", 6);
3739 6 : N = transvalues[0];
3740 6 : Sxx = transvalues[2];
3741 6 : Syy = transvalues[4];
3742 6 : Sxy = transvalues[5];
3743 :
3744 : /* if N is 0 we should return NULL */
3745 6 : if (N < 1.0)
3746 0 : PG_RETURN_NULL();
3747 :
3748 : /* Note that Sxx and Syy are guaranteed to be non-negative */
3749 :
3750 : /* per spec, return NULL for horizontal and vertical lines */
3751 6 : if (Sxx == 0 || Syy == 0)
3752 0 : PG_RETURN_NULL();
3753 :
3754 6 : PG_RETURN_FLOAT8(Sxy / sqrt(Sxx * Syy));
3755 : }
3756 :
3757 : Datum
3758 6 : float8_regr_r2(PG_FUNCTION_ARGS)
3759 : {
3760 6 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3761 : float8 *transvalues;
3762 : float8 N,
3763 : Sxx,
3764 : Syy,
3765 : Sxy;
3766 :
3767 6 : transvalues = check_float8_array(transarray, "float8_regr_r2", 6);
3768 6 : N = transvalues[0];
3769 6 : Sxx = transvalues[2];
3770 6 : Syy = transvalues[4];
3771 6 : Sxy = transvalues[5];
3772 :
3773 : /* if N is 0 we should return NULL */
3774 6 : if (N < 1.0)
3775 0 : PG_RETURN_NULL();
3776 :
3777 : /* Note that Sxx and Syy are guaranteed to be non-negative */
3778 :
3779 : /* per spec, return NULL for a vertical line */
3780 6 : if (Sxx == 0)
3781 0 : PG_RETURN_NULL();
3782 :
3783 : /* per spec, return 1.0 for a horizontal line */
3784 6 : if (Syy == 0)
3785 0 : PG_RETURN_FLOAT8(1.0);
3786 :
3787 6 : PG_RETURN_FLOAT8((Sxy * Sxy) / (Sxx * Syy));
3788 : }
3789 :
3790 : Datum
3791 6 : float8_regr_slope(PG_FUNCTION_ARGS)
3792 : {
3793 6 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3794 : float8 *transvalues;
3795 : float8 N,
3796 : Sxx,
3797 : Sxy;
3798 :
3799 6 : transvalues = check_float8_array(transarray, "float8_regr_slope", 6);
3800 6 : N = transvalues[0];
3801 6 : Sxx = transvalues[2];
3802 6 : Sxy = transvalues[5];
3803 :
3804 : /* if N is 0 we should return NULL */
3805 6 : if (N < 1.0)
3806 0 : PG_RETURN_NULL();
3807 :
3808 : /* Note that Sxx is guaranteed to be non-negative */
3809 :
3810 : /* per spec, return NULL for a vertical line */
3811 6 : if (Sxx == 0)
3812 0 : PG_RETURN_NULL();
3813 :
3814 6 : PG_RETURN_FLOAT8(Sxy / Sxx);
3815 : }
3816 :
3817 : Datum
3818 6 : float8_regr_intercept(PG_FUNCTION_ARGS)
3819 : {
3820 6 : ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
3821 : float8 *transvalues;
3822 : float8 N,
3823 : Sx,
3824 : Sxx,
3825 : Sy,
3826 : Sxy;
3827 :
3828 6 : transvalues = check_float8_array(transarray, "float8_regr_intercept", 6);
3829 6 : N = transvalues[0];
3830 6 : Sx = transvalues[1];
3831 6 : Sxx = transvalues[2];
3832 6 : Sy = transvalues[3];
3833 6 : Sxy = transvalues[5];
3834 :
3835 : /* if N is 0 we should return NULL */
3836 6 : if (N < 1.0)
3837 0 : PG_RETURN_NULL();
3838 :
3839 : /* Note that Sxx is guaranteed to be non-negative */
3840 :
3841 : /* per spec, return NULL for a vertical line */
3842 6 : if (Sxx == 0)
3843 0 : PG_RETURN_NULL();
3844 :
3845 6 : PG_RETURN_FLOAT8((Sy - Sx * Sxy / Sxx) / N);
3846 : }
3847 :
3848 :
3849 : /*
3850 : * ====================================
3851 : * MIXED-PRECISION ARITHMETIC OPERATORS
3852 : * ====================================
3853 : */
3854 :
3855 : /*
3856 : * float48pl - returns arg1 + arg2
3857 : * float48mi - returns arg1 - arg2
3858 : * float48mul - returns arg1 * arg2
3859 : * float48div - returns arg1 / arg2
3860 : */
3861 : Datum
3862 24 : float48pl(PG_FUNCTION_ARGS)
3863 : {
3864 24 : float4 arg1 = PG_GETARG_FLOAT4(0);
3865 24 : float8 arg2 = PG_GETARG_FLOAT8(1);
3866 :
3867 24 : PG_RETURN_FLOAT8(float8_pl((float8) arg1, arg2));
3868 : }
3869 :
3870 : Datum
3871 6 : float48mi(PG_FUNCTION_ARGS)
3872 : {
3873 6 : float4 arg1 = PG_GETARG_FLOAT4(0);
3874 6 : float8 arg2 = PG_GETARG_FLOAT8(1);
3875 :
3876 6 : PG_RETURN_FLOAT8(float8_mi((float8) arg1, arg2));
3877 : }
3878 :
3879 : Datum
3880 8 : float48mul(PG_FUNCTION_ARGS)
3881 : {
3882 8 : float4 arg1 = PG_GETARG_FLOAT4(0);
3883 8 : float8 arg2 = PG_GETARG_FLOAT8(1);
3884 :
3885 8 : PG_RETURN_FLOAT8(float8_mul((float8) arg1, arg2));
3886 : }
3887 :
3888 : Datum
3889 6 : float48div(PG_FUNCTION_ARGS)
3890 : {
3891 6 : float4 arg1 = PG_GETARG_FLOAT4(0);
3892 6 : float8 arg2 = PG_GETARG_FLOAT8(1);
3893 :
3894 6 : PG_RETURN_FLOAT8(float8_div((float8) arg1, arg2));
3895 : }
3896 :
3897 : /*
3898 : * float84pl - returns arg1 + arg2
3899 : * float84mi - returns arg1 - arg2
3900 : * float84mul - returns arg1 * arg2
3901 : * float84div - returns arg1 / arg2
3902 : */
3903 : Datum
3904 12 : float84pl(PG_FUNCTION_ARGS)
3905 : {
3906 12 : float8 arg1 = PG_GETARG_FLOAT8(0);
3907 12 : float4 arg2 = PG_GETARG_FLOAT4(1);
3908 :
3909 12 : PG_RETURN_FLOAT8(float8_pl(arg1, (float8) arg2));
3910 : }
3911 :
3912 : Datum
3913 0 : float84mi(PG_FUNCTION_ARGS)
3914 : {
3915 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
3916 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
3917 :
3918 0 : PG_RETURN_FLOAT8(float8_mi(arg1, (float8) arg2));
3919 : }
3920 :
3921 : Datum
3922 0 : float84mul(PG_FUNCTION_ARGS)
3923 : {
3924 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
3925 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
3926 :
3927 0 : PG_RETURN_FLOAT8(float8_mul(arg1, (float8) arg2));
3928 : }
3929 :
3930 : Datum
3931 6 : float84div(PG_FUNCTION_ARGS)
3932 : {
3933 6 : float8 arg1 = PG_GETARG_FLOAT8(0);
3934 6 : float4 arg2 = PG_GETARG_FLOAT4(1);
3935 :
3936 6 : PG_RETURN_FLOAT8(float8_div(arg1, (float8) arg2));
3937 : }
3938 :
3939 : /*
3940 : * ====================
3941 : * COMPARISON OPERATORS
3942 : * ====================
3943 : */
3944 :
3945 : /*
3946 : * float48{eq,ne,lt,le,gt,ge} - float4/float8 comparison operations
3947 : */
3948 : Datum
3949 2996 : float48eq(PG_FUNCTION_ARGS)
3950 : {
3951 2996 : float4 arg1 = PG_GETARG_FLOAT4(0);
3952 2996 : float8 arg2 = PG_GETARG_FLOAT8(1);
3953 :
3954 2996 : PG_RETURN_BOOL(float8_eq((float8) arg1, arg2));
3955 : }
3956 :
3957 : Datum
3958 20088 : float48ne(PG_FUNCTION_ARGS)
3959 : {
3960 20088 : float4 arg1 = PG_GETARG_FLOAT4(0);
3961 20088 : float8 arg2 = PG_GETARG_FLOAT8(1);
3962 :
3963 20088 : PG_RETURN_BOOL(float8_ne((float8) arg1, arg2));
3964 : }
3965 :
3966 : Datum
3967 4268 : float48lt(PG_FUNCTION_ARGS)
3968 : {
3969 4268 : float4 arg1 = PG_GETARG_FLOAT4(0);
3970 4268 : float8 arg2 = PG_GETARG_FLOAT8(1);
3971 :
3972 4268 : PG_RETURN_BOOL(float8_lt((float8) arg1, arg2));
3973 : }
3974 :
3975 : Datum
3976 26348 : float48le(PG_FUNCTION_ARGS)
3977 : {
3978 26348 : float4 arg1 = PG_GETARG_FLOAT4(0);
3979 26348 : float8 arg2 = PG_GETARG_FLOAT8(1);
3980 :
3981 26348 : PG_RETURN_BOOL(float8_le((float8) arg1, arg2));
3982 : }
3983 :
3984 : Datum
3985 4492 : float48gt(PG_FUNCTION_ARGS)
3986 : {
3987 4492 : float4 arg1 = PG_GETARG_FLOAT4(0);
3988 4492 : float8 arg2 = PG_GETARG_FLOAT8(1);
3989 :
3990 4492 : PG_RETURN_BOOL(float8_gt((float8) arg1, arg2));
3991 : }
3992 :
3993 : Datum
3994 4892 : float48ge(PG_FUNCTION_ARGS)
3995 : {
3996 4892 : float4 arg1 = PG_GETARG_FLOAT4(0);
3997 4892 : float8 arg2 = PG_GETARG_FLOAT8(1);
3998 :
3999 4892 : PG_RETURN_BOOL(float8_ge((float8) arg1, arg2));
4000 : }
4001 :
4002 : /*
4003 : * float84{eq,ne,lt,le,gt,ge} - float8/float4 comparison operations
4004 : */
4005 : Datum
4006 1812 : float84eq(PG_FUNCTION_ARGS)
4007 : {
4008 1812 : float8 arg1 = PG_GETARG_FLOAT8(0);
4009 1812 : float4 arg2 = PG_GETARG_FLOAT4(1);
4010 :
4011 1812 : PG_RETURN_BOOL(float8_eq(arg1, (float8) arg2));
4012 : }
4013 :
4014 : Datum
4015 0 : float84ne(PG_FUNCTION_ARGS)
4016 : {
4017 0 : float8 arg1 = PG_GETARG_FLOAT8(0);
4018 0 : float4 arg2 = PG_GETARG_FLOAT4(1);
4019 :
4020 0 : PG_RETURN_BOOL(float8_ne(arg1, (float8) arg2));
4021 : }
4022 :
4023 : Datum
4024 3198 : float84lt(PG_FUNCTION_ARGS)
4025 : {
4026 3198 : float8 arg1 = PG_GETARG_FLOAT8(0);
4027 3198 : float4 arg2 = PG_GETARG_FLOAT4(1);
4028 :
4029 3198 : PG_RETURN_BOOL(float8_lt(arg1, (float8) arg2));
4030 : }
4031 :
4032 : Datum
4033 3798 : float84le(PG_FUNCTION_ARGS)
4034 : {
4035 3798 : float8 arg1 = PG_GETARG_FLOAT8(0);
4036 3798 : float4 arg2 = PG_GETARG_FLOAT4(1);
4037 :
4038 3798 : PG_RETURN_BOOL(float8_le(arg1, (float8) arg2));
4039 : }
4040 :
4041 : Datum
4042 3198 : float84gt(PG_FUNCTION_ARGS)
4043 : {
4044 3198 : float8 arg1 = PG_GETARG_FLOAT8(0);
4045 3198 : float4 arg2 = PG_GETARG_FLOAT4(1);
4046 :
4047 3198 : PG_RETURN_BOOL(float8_gt(arg1, (float8) arg2));
4048 : }
4049 :
4050 : Datum
4051 3204 : float84ge(PG_FUNCTION_ARGS)
4052 : {
4053 3204 : float8 arg1 = PG_GETARG_FLOAT8(0);
4054 3204 : float4 arg2 = PG_GETARG_FLOAT4(1);
4055 :
4056 3204 : PG_RETURN_BOOL(float8_ge(arg1, (float8) arg2));
4057 : }
4058 :
4059 : /*
4060 : * Implements the float8 version of the width_bucket() function
4061 : * defined by SQL2003. See also width_bucket_numeric().
4062 : *
4063 : * 'bound1' and 'bound2' are the lower and upper bounds of the
4064 : * histogram's range, respectively. 'count' is the number of buckets
4065 : * in the histogram. width_bucket() returns an integer indicating the
4066 : * bucket number that 'operand' belongs to in an equiwidth histogram
4067 : * with the specified characteristics. An operand smaller than the
4068 : * lower bound is assigned to bucket 0. An operand greater than or equal
4069 : * to the upper bound is assigned to an additional bucket (with number
4070 : * count+1). We don't allow "NaN" for any of the float8 inputs, and we
4071 : * don't allow either of the histogram bounds to be +/- infinity.
4072 : */
4073 : Datum
4074 864 : width_bucket_float8(PG_FUNCTION_ARGS)
4075 : {
4076 864 : float8 operand = PG_GETARG_FLOAT8(0);
4077 864 : float8 bound1 = PG_GETARG_FLOAT8(1);
4078 864 : float8 bound2 = PG_GETARG_FLOAT8(2);
4079 864 : int32 count = PG_GETARG_INT32(3);
4080 : int32 result;
4081 :
4082 864 : if (count <= 0)
4083 12 : ereport(ERROR,
4084 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4085 : errmsg("count must be greater than zero")));
4086 :
4087 852 : if (isnan(operand) || isnan(bound1) || isnan(bound2))
4088 6 : ereport(ERROR,
4089 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4090 : errmsg("operand, lower bound, and upper bound cannot be NaN")));
4091 :
4092 : /* Note that we allow "operand" to be infinite */
4093 846 : if (isinf(bound1) || isinf(bound2))
4094 18 : ereport(ERROR,
4095 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4096 : errmsg("lower and upper bounds must be finite")));
4097 :
4098 828 : if (bound1 < bound2)
4099 : {
4100 594 : if (operand < bound1)
4101 114 : result = 0;
4102 480 : else if (operand >= bound2)
4103 : {
4104 120 : if (pg_add_s32_overflow(count, 1, &result))
4105 6 : ereport(ERROR,
4106 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
4107 : errmsg("integer out of range")));
4108 : }
4109 : else
4110 : {
4111 360 : if (!isinf(bound2 - bound1))
4112 : {
4113 : /* The quotient is surely in [0,1], so this can't overflow */
4114 342 : result = count * ((operand - bound1) / (bound2 - bound1));
4115 : }
4116 : else
4117 : {
4118 : /*
4119 : * We get here if bound2 - bound1 overflows DBL_MAX. Since
4120 : * both bounds are finite, their difference can't exceed twice
4121 : * DBL_MAX; so we can perform the computation without overflow
4122 : * by dividing all the inputs by 2. That should be exact too,
4123 : * except in the case where a very small operand underflows to
4124 : * zero, which would have negligible impact on the result
4125 : * given such large bounds.
4126 : */
4127 18 : result = count * ((operand / 2 - bound1 / 2) / (bound2 / 2 - bound1 / 2));
4128 : }
4129 : /* The quotient could round to 1.0, which would be a lie */
4130 360 : if (result >= count)
4131 6 : result = count - 1;
4132 : /* Having done that, we can add 1 without fear of overflow */
4133 360 : result++;
4134 : }
4135 : }
4136 234 : else if (bound1 > bound2)
4137 : {
4138 228 : if (operand > bound1)
4139 12 : result = 0;
4140 216 : else if (operand <= bound2)
4141 : {
4142 30 : if (pg_add_s32_overflow(count, 1, &result))
4143 6 : ereport(ERROR,
4144 : (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
4145 : errmsg("integer out of range")));
4146 : }
4147 : else
4148 : {
4149 186 : if (!isinf(bound1 - bound2))
4150 168 : result = count * ((bound1 - operand) / (bound1 - bound2));
4151 : else
4152 18 : result = count * ((bound1 / 2 - operand / 2) / (bound1 / 2 - bound2 / 2));
4153 186 : if (result >= count)
4154 6 : result = count - 1;
4155 186 : result++;
4156 : }
4157 : }
4158 : else
4159 : {
4160 6 : ereport(ERROR,
4161 : (errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
4162 : errmsg("lower bound cannot equal upper bound")));
4163 : result = 0; /* keep the compiler quiet */
4164 : }
4165 :
4166 810 : PG_RETURN_INT32(result);
4167 : }
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