Returning a rational value
A function such as `rat_get_normal(rat x)` computes a normalized rational value by changing its local copy of `x` and returning that value. It does not modify a global object, perform I/O, or retain state between calls. section 10.2.2
A pure function has no effects other than returning a value, and its return value depends only on its parameters. Its interface is therefore the only way it interacts with the rest of the program. section 10.2 section 10.2.2
TAKEAWAY: A function is not pure when it:
- Reads changeable program state outside its arguments. section 10.2.2
- Modifies a global object. section 10.2.2
- Keeps persistent internal state between calls, such as through a local static variable. section 10.2.2
- Performs input or output, for example by calling `printf`. section 10.2.2
Pure functions are easy to understand and optimize: once their parameters are available, execution can be moved, delayed, or performed in parallel, provided the result is ready before use. They suit small tasks but become limited for more complex operations. section 10.2.2
Listing 10.1. A type for computation with rational numbers.
1 #ifndef RATIONALS_H
2 # define RATIONALS_H 1
3 # include <stdbool.h>
4 # include "euclid.h"
5
6 typedef struct rat rat;
7
8 struct rat {
9 bool sign;
10 size_t num;
11 size_t denom;
12 };
13
14 /* Functions that return a value of type rat. */
15 rat rat_get(long long num, unsigned long long denom);
16 rat rat_get_normal(rat x);
17 rat rat_get_extended(rat x, size_t f);
18 rat rat_get_prod(rat x, rat y);
19 rat rat_get_sum(rat x, rat y);
20
21
22 /* Functions that operate on pointers to rat. */
23 void rat_destroy(rat* rp);
24 rat* rat_init(rat* rp,
25 long long num,
26 unsigned long long denom);
27 rat* rat_normalize(rat* rp);
28 rat* rat_extend(rat* rp, size_t f);
29 rat* rat_sumup(rat* rp, rat y);
30 rat* rat_rma(rat* rp, rat x, rat y);
31
32 /* Functions that are implemented as exercises. */
33 /** @brief Print @a x into @a tmp and return tmp. **/
34 char const* rat_print(size_t len, char tmp[len], rat const* x);
35 /** @brief Print @a x normalize and print. **/
36 char const* rat_normalize_print(size_t len, char tmp[len],
37 rat const* x);
38 rat* rat_dotproduct(rat rp[static 1], size_t n,
39 rat const A[n], rat const B[n]);
40
41 #endif
!@%STYLE%@!
{"css":"{\"css\": \"font-weight: bold;\"}","target":"[[{\"line\":0,\"ch\":1},{\"line\":0,\"ch\":2}],[{\"line\":1,\"ch\":26},{\"line\":1,\"ch\":27}],[{\"line\":9,\"ch\":0},{\"line\":9,\"ch\":1}],[{\"line\":10,\"ch\":0},{\"line\":10,\"ch\":1}],[{\"line\":11,\"ch\":0},{\"line\":11,\"ch\":1}],[{\"line\":12,\"ch\":0},{\"line\":12,\"ch\":1}],[{\"line\":13,\"ch\":0},{\"line\":13,\"ch\":1}],[{\"line\":14,\"ch\":0},{\"line\":14,\"ch\":1}],[{\"line\":15,\"ch\":0},{\"line\":15,\"ch\":1}],[{\"line\":16,\"ch\":0},{\"line\":16,\"ch\":1}],[{\"line\":17,\"ch\":0},{\"line\":17,\"ch\":1}],[{\"line\":18,\"ch\":0},{\"line\":18,\"ch\":1}],[{\"line\":20,\"ch\":1},{\"line\":20,\"ch\":2}],[{\"line\":30,\"ch\":1},{\"line\":30,\"ch\":2}],[{\"line\":37,\"ch\":39},{\"line\":37,\"ch\":40}],[{\"line\":40,\"ch\":1},{\"line\":40,\"ch\":2}],[{\"line\":0,\"ch\":5},{\"line\":0,\"ch\":12}],[{\"line\":1,\"ch\":1},{\"line\":1,\"ch\":2}],[{\"line\":11,\"ch\":1},{\"line\":11,\"ch\":2}],[{\"line\":19,\"ch\":0},{\"line\":19,\"ch\":1}],[{\"line\":20,\"ch\":0},{\"line\":20,\"ch\":1}],[{\"line\":21,\"ch\":0},{\"line\":21,\"ch\":1}],[{\"line\":22,\"ch\":0},{\"line\":22,\"ch\":1}],[{\"line\":23,\"ch\":0},{\"line\":23,\"ch\":1}],[{\"line\":24,\"ch\":0},{\"line\":24,\"ch\":1}],[{\"line\":25,\"ch\":0},{\"line\":25,\"ch\":1}],[{\"line\":26,\"ch\":0},{\"line\":26,\"ch\":1}],[{\"line\":27,\"ch\":0},{\"line\":27,\"ch\":1}],[{\"line\":28,\"ch\":0},{\"line\":28,\"ch\":1}],[{\"line\":31,\"ch\":1},{\"line\":31,\"ch\":2}],[{\"line\":1,\"ch\":5},{\"line\":1,\"ch\":13}],[{\"line\":2,\"ch\":1},{\"line\":2,\"ch\":2}],[{\"line\":12,\"ch\":1},{\"line\":12,\"ch\":2}],[{\"line\":22,\"ch\":1},{\"line\":22,\"ch\":2}],[{\"line\":29,\"ch\":0},{\"line\":29,\"ch\":1}],[{\"line\":30,\"ch\":0},{\"line\":30,\"ch\":1}],[{\"line\":31,\"ch\":0},{\"line\":31,\"ch\":1}],[{\"line\":32,\"ch\":0},{\"line\":32,\"ch\":1}],[{\"line\":33,\"ch\":0},{\"line\":33,\"ch\":1}],[{\"line\":34,\"ch\":0},{\"line\":34,\"ch\":1}],[{\"line\":35,\"ch\":0},{\"line\":35,\"ch\":1}],[{\"line\":36,\"ch\":0},{\"line\":36,\"ch\":1}],[{\"line\":37,\"ch\":0},{\"line\":37,\"ch\":1}],[{\"line\":38,\"ch\":0},{\"line\":38,\"ch\":1}],[{\"line\":2,\"ch\":5},{\"line\":2,\"ch\":14}],[{\"line\":3,\"ch\":5},{\"line\":3,\"ch\":14}],[{\"line\":3,\"ch\":1},{\"line\":3,\"ch\":2}],[{\"line\":13,\"ch\":1},{\"line\":13,\"ch\":2}],[{\"line\":23,\"ch\":1},{\"line\":23,\"ch\":2}],[{\"line\":33,\"ch\":1},{\"line\":33,\"ch\":2}],[{\"line\":39,\"ch\":0},{\"line\":39,\"ch\":1}],[{\"line\":40,\"ch\":0},{\"line\":40,\"ch\":1}],[{\"line\":2,\"ch\":5},{\"line\":2,\"ch\":14}],[{\"line\":3,\"ch\":5},{\"line\":3,\"ch\":14}],[{\"line\":4,\"ch\":1},{\"line\":4,\"ch\":2}],[{\"line\":14,\"ch\":1},{\"line\":14,\"ch\":2}],[{\"line\":24,\"ch\":1},{\"line\":24,\"ch\":2}],[{\"line\":34,\"ch\":1},{\"line\":34,\"ch\":2}],[{\"line\":5,\"ch\":1},{\"line\":5,\"ch\":2}],[{\"line\":15,\"ch\":1},{\"line\":15,\"ch\":2}],[{\"line\":25,\"ch\":1},{\"line\":25,\"ch\":2}],[{\"line\":35,\"ch\":1},{\"line\":35,\"ch\":2}],[{\"line\":5,\"ch\":5},{\"line\":5,\"ch\":19}],[{\"line\":6,\"ch\":1},{\"line\":6,\"ch\":2}],[{\"line\":16,\"ch\":1},{\"line\":16,\"ch\":2}],[{\"line\":26,\"ch\":1},{\"line\":26,\"ch\":2}],[{\"line\":36,\"ch\":1},{\"line\":36,\"ch\":2}],[{\"line\":7,\"ch\":1},{\"line\":7,\"ch\":2}],[{\"line\":17,\"ch\":1},{\"line\":17,\"ch\":2}],[{\"line\":27,\"ch\":1},{\"line\":27,\"ch\":2}],[{\"line\":37,\"ch\":1},{\"line\":37,\"ch\":2}],[{\"line\":5,\"ch\":13},{\"line\":5,\"ch\":19}],[{\"line\":7,\"ch\":5},{\"line\":7,\"ch\":11}],[{\"line\":8,\"ch\":1},{\"line\":8,\"ch\":2}],[{\"line\":18,\"ch\":1},{\"line\":18,\"ch\":2}],[{\"line\":28,\"ch\":1},{\"line\":28,\"ch\":2}],[{\"line\":38,\"ch\":1},{\"line\":38,\"ch\":2}],[{\"line\":9,\"ch\":0},{\"line\":9,\"ch\":2}],[{\"line\":9,\"ch\":7},{\"line\":9,\"ch\":13}],[{\"line\":10,\"ch\":7},{\"line\":10,\"ch\":13}],[{\"line\":16,\"ch\":33},{\"line\":16,\"ch\":39}],[{\"line\":27,\"ch\":30},{\"line\":27,\"ch\":36}],[{\"line\":33,\"ch\":27},{\"line\":33,\"ch\":33}],[{\"line\":35,\"ch\":37},{\"line\":35,\"ch\":43}],[{\"line\":37,\"ch\":43},{\"line\":37,\"ch\":49}],[{\"line\":10,\"ch\":0},{\"line\":10,\"ch\":2}],[{\"line\":9,\"ch\":7},{\"line\":9,\"ch\":13}],[{\"line\":10,\"ch\":7},{\"line\":10,\"ch\":13}],[{\"line\":16,\"ch\":33},{\"line\":16,\"ch\":39}],[{\"line\":27,\"ch\":30},{\"line\":27,\"ch\":36}],[{\"line\":33,\"ch\":27},{\"line\":33,\"ch\":33}],[{\"line\":35,\"ch\":37},{\"line\":35,\"ch\":43}],[{\"line\":37,\"ch\":43},{\"line\":37,\"ch\":49}],[{\"line\":11,\"ch\":0},{\"line\":11,\"ch\":2}],[{\"line\":12,\"ch\":0},{\"line\":12,\"ch\":2}],[{\"line\":13,\"ch\":0},{\"line\":13,\"ch\":2}],[{\"line\":14,\"ch\":0},{\"line\":14,\"ch\":2}],[{\"line\":14,\"ch\":17},{\"line\":14,\"ch\":26}],[{\"line\":24,\"ch\":19},{\"line\":24,\"ch\":28}],[{\"line\":25,\"ch\":28},{\"line\":25,\"ch\":37}],[{\"line\":14,\"ch\":32},{\"line\":14,\"ch\":50}],[{\"line\":25,\"ch\":19},{\"line\":25,\"ch\":37}],[{\"line\":15,\"ch\":0},{\"line\":15,\"ch\":2}],[{\"line\":16,\"ch\":0},{\"line\":16,\"ch\":2}],[{\"line\":9,\"ch\":7},{\"line\":9,\"ch\":13}],[{\"line\":10,\"ch\":7},{\"line\":10,\"ch\":13}],[{\"line\":16,\"ch\":33},{\"line\":16,\"ch\":39}],[{\"line\":27,\"ch\":30},{\"line\":27,\"ch\":36}],[{\"line\":33,\"ch\":27},{\"line\":33,\"ch\":33}],[{\"line\":35,\"ch\":37},{\"line\":35,\"ch\":43}],[{\"line\":37,\"ch\":43},{\"line\":37,\"ch\":49}],[{\"line\":17,\"ch\":0},{\"line\":17,\"ch\":2}],[{\"line\":18,\"ch\":0},{\"line\":18,\"ch\":2}],[{\"line\":19,\"ch\":0},{\"line\":19,\"ch\":2}],[{\"line\":20,\"ch\":0},{\"line\":20,\"ch\":2}],[{\"line\":21,\"ch\":0},{\"line\":21,\"ch\":2}],[{\"line\":22,\"ch\":0},{\"line\":22,\"ch\":2}],[{\"line\":22,\"ch\":5},{\"line\":22,\"ch\":9}],[{\"line\":23,\"ch\":0},{\"line\":23,\"ch\":2}],[{\"line\":24,\"ch\":0},{\"line\":24,\"ch\":2}],[{\"line\":14,\"ch\":17},{\"line\":14,\"ch\":26}],[{\"line\":24,\"ch\":19},{\"line\":24,\"ch\":28}],[{\"line\":25,\"ch\":28},{\"line\":25,\"ch\":37}],[{\"line\":25,\"ch\":0},{\"line\":25,\"ch\":2}],[{\"line\":14,\"ch\":32},{\"line\":14,\"ch\":50}],[{\"line\":25,\"ch\":19},{\"line\":25,\"ch\":37}],[{\"line\":26,\"ch\":0},{\"line\":26,\"ch\":2}],[{\"line\":27,\"ch\":0},{\"line\":27,\"ch\":2}],[{\"line\":9,\"ch\":7},{\"line\":9,\"ch\":13}],[{\"line\":10,\"ch\":7},{\"line\":10,\"ch\":13}],[{\"line\":16,\"ch\":33},{\"line\":16,\"ch\":39}],[{\"line\":27,\"ch\":30},{\"line\":27,\"ch\":36}],[{\"line\":33,\"ch\":27},{\"line\":33,\"ch\":33}],[{\"line\":35,\"ch\":37},{\"line\":35,\"ch\":43}],[{\"line\":37,\"ch\":43},{\"line\":37,\"ch\":49}],[{\"line\":28,\"ch\":0},{\"line\":28,\"ch\":2}],[{\"line\":29,\"ch\":0},{\"line\":29,\"ch\":2}],[{\"line\":30,\"ch\":0},{\"line\":30,\"ch\":2}],[{\"line\":31,\"ch\":0},{\"line\":31,\"ch\":2}],[{\"line\":32,\"ch\":0},{\"line\":32,\"ch\":2}],[{\"line\":33,\"ch\":0},{\"line\":33,\"ch\":2}],[{\"line\":33,\"ch\":5},{\"line\":33,\"ch\":15}],[{\"line\":35,\"ch\":5},{\"line\":35,\"ch\":15}],[{\"line\":9,\"ch\":7},{\"line\":9,\"ch\":13}],[{\"line\":10,\"ch\":7},{\"line\":10,\"ch\":13}],[{\"line\":16,\"ch\":33},{\"line\":16,\"ch\":39}],[{\"line\":27,\"ch\":30},{\"line\":27,\"ch\":36}],[{\"line\":33,\"ch\":27},{\"line\":33,\"ch\":33}],[{\"line\":35,\"ch\":37},{\"line\":35,\"ch\":43}],[{\"line\":37,\"ch\":43},{\"line\":37,\"ch\":49}],[{\"line\":33,\"ch\":5},{\"line\":33,\"ch\":9}],[{\"line\":35,\"ch\":5},{\"line\":35,\"ch\":9}],[{\"line\":33,\"ch\":10},{\"line\":33,\"ch\":15}],[{\"line\":35,\"ch\":10},{\"line\":35,\"ch\":15}],[{\"line\":36,\"ch\":41},{\"line\":36,\"ch\":46}],[{\"line\":38,\"ch\":29},{\"line\":38,\"ch\":34}],[{\"line\":34,\"ch\":0},{\"line\":34,\"ch\":2}],[{\"line\":35,\"ch\":0},{\"line\":35,\"ch\":2}],[{\"line\":33,\"ch\":5},{\"line\":33,\"ch\":15}],[{\"line\":35,\"ch\":5},{\"line\":35,\"ch\":15}],[{\"line\":9,\"ch\":7},{\"line\":9,\"ch\":13}],[{\"line\":10,\"ch\":7},{\"line\":10,\"ch\":13}],[{\"line\":16,\"ch\":33},{\"line\":16,\"ch\":39}],[{\"line\":27,\"ch\":30},{\"line\":27,\"ch\":36}],[{\"line\":33,\"ch\":27},{\"line\":33,\"ch\":33}],[{\"line\":35,\"ch\":37},{\"line\":35,\"ch\":43}],[{\"line\":37,\"ch\":43},{\"line\":37,\"ch\":49}],[{\"line\":33,\"ch\":5},{\"line\":33,\"ch\":9}],[{\"line\":35,\"ch\":5},{\"line\":35,\"ch\":9}],[{\"line\":36,\"ch\":0},{\"line\":36,\"ch\":2}],[{\"line\":33,\"ch\":10},{\"line\":33,\"ch\":15}],[{\"line\":35,\"ch\":10},{\"line\":35,\"ch\":15}],[{\"line\":36,\"ch\":41},{\"line\":36,\"ch\":46}],[{\"line\":38,\"ch\":29},{\"line\":38,\"ch\":34}],[{\"line\":37,\"ch\":0},{\"line\":37,\"ch\":2}],[{\"line\":37,\"ch\":32},{\"line\":37,\"ch\":38}],[{\"line\":9,\"ch\":7},{\"line\":9,\"ch\":13}],[{\"line\":10,\"ch\":7},{\"line\":10,\"ch\":13}],[{\"line\":16,\"ch\":33},{\"line\":16,\"ch\":39}],[{\"line\":27,\"ch\":30},{\"line\":27,\"ch\":36}],[{\"line\":33,\"ch\":27},{\"line\":33,\"ch\":33}],[{\"line\":35,\"ch\":37},{\"line\":35,\"ch\":43}],[{\"line\":37,\"ch\":43},{\"line\":37,\"ch\":49}],[{\"line\":38,\"ch\":0},{\"line\":38,\"ch\":2}],[{\"line\":33,\"ch\":10},{\"line\":33,\"ch\":15}],[{\"line\":35,\"ch\":10},{\"line\":35,\"ch\":15}],[{\"line\":36,\"ch\":41},{\"line\":36,\"ch\":46}],[{\"line\":38,\"ch\":29},{\"line\":38,\"ch\":34}],[{\"line\":33,\"ch\":10},{\"line\":33,\"ch\":15}],[{\"line\":35,\"ch\":10},{\"line\":35,\"ch\":15}],[{\"line\":36,\"ch\":41},{\"line\":36,\"ch\":46}],[{\"line\":38,\"ch\":29},{\"line\":38,\"ch\":34}],[{\"line\":39,\"ch\":0},{\"line\":39,\"ch\":2}],[{\"line\":40,\"ch\":0},{\"line\":40,\"ch\":2}],[{\"line\":40,\"ch\":5},{\"line\":40,\"ch\":11}]]"}
!@%STYLE%@!
Browse the rational-number interface and its value-returning operations to compare pure functions with pointer-based operations. section 10.2.2
