Oracle数据类型Number的解析实现
春秋十二月发表于 2020-05-08 04:23:00
存储格式
Oracle Number数据类型是变长的，占0~22字节，不像编程语言中的2/4字节整数或4/8字节浮点数，关于它的存储格式与解析，DSI上有详细的描述，如下所示
符号位/指数字节描述如下
数字字节描述如下
正数或零值的计算
负数值的计算
解析实现
由于Oracle Number的精度高达38位，远超出了基本定长整数或浮点数表达的数值范围，因此解析实际上是大整数/实数的四则运算，为避免造轮子，本文使用了GMP开源库（https://gmplib.org/），用于任意精度的算术运算，操作有符号整数、有理数和浮点数，除了在GMP机器上运行的可用内存所暗示的精度之外，对精度没有实际的限制。解析实现的核心函数是orcl_raw2number
测试用例
测试了123456.789、-123456.789、Oracle Number实际最大最小值、Oracle Number理论最大最小值
Oracle Number数据类型是变长的，占0~22字节，不像编程语言中的2/4字节整数或4/8字节浮点数，关于它的存储格式与解析，DSI上有详细的描述，如下所示
符号位/指数字节描述如下
数字字节描述如下
正数或零值的计算
负数值的计算
解析实现
由于Oracle Number的精度高达38位，远超出了基本定长整数或浮点数表达的数值范围，因此解析实际上是大整数/实数的四则运算，为避免造轮子，本文使用了GMP开源库（https://gmplib.org/），用于任意精度的算术运算，操作有符号整数、有理数和浮点数，除了在GMP机器上运行的可用内存所暗示的精度之外，对精度没有实际的限制。解析实现的核心函数是orcl_raw2number
1 #include <stdio.h>
2 #include <assert.h>
3 #include <gmp.h>
4
5 #define MAX_PREC 256
6
7 static mpf_t s_base100;
8 static mpf_t s_one;
9
10 static void init_mpf_globals()
11 {
12 mpf_init_set_ui(s_base100, 100);
13 mpf_init_set_ui(s_one, 1);
14 }
15
16 static void clear_mpf_globals()
17 {
18 mpf_clear(s_base100);
19 mpf_clear(s_one);
20 }
21
22 static void orcl_raw2number(unsigned char *data, unsigned int len, mpf_t result)
23 {
24 unsigned int sign = *data, digit, i;
25 int exp = sign>=128 ? sign-193 : 62-sign;
26 int exp_val;
27 mpf_t tmp;
28
29 mpf_init2(tmp, MAX_PREC);
30 mpf_init2(result, MAX_PREC);
31
32 if(sign & 0x80){
33 for(i=1; i<len; ++i){
34 digit = data[i] - 1;
35 assert(0<=digit && digit<=99);
36
37 exp_val = exp - i + 1;
38 if(exp_val < 0){
39 mpf_pow_ui(tmp, s_base100, -exp_val);
40 mpf_div(tmp, s_one, tmp);
41 }else
42 mpf_pow_ui(tmp, s_base100, exp_val);
43
44 mpf_mul_ui(tmp, tmp, digit);
45 mpf_add(result, result, tmp);
46 }
47
48 }else{
49 --len; //ignore the last byte
50 for(i=1; i<len; ++i){
51 digit = 101 - data[i];
52 assert(0<=digit && digit<=99);
53
54 exp_val = exp - i + 1;
55 if(exp_val < 0){
56 mpf_pow_ui(tmp, s_base100, -exp_val);
57 mpf_div(tmp, s_one, tmp);
58 }else
59 mpf_pow_ui(tmp, s_base100, exp_val);
60
61 mpf_mul_ui(tmp, tmp, digit);
62 mpf_add(result, result, tmp);
63 }
64
65 mpf_neg(result, result);
66 }
67
68 mpf_clear(tmp);
69 }
2 #include <assert.h>
3 #include <gmp.h>
4
5 #define MAX_PREC 256
6
7 static mpf_t s_base100;
8 static mpf_t s_one;
9
10 static void init_mpf_globals()
11 {
12 mpf_init_set_ui(s_base100, 100);
13 mpf_init_set_ui(s_one, 1);
14 }
15
16 static void clear_mpf_globals()
17 {
18 mpf_clear(s_base100);
19 mpf_clear(s_one);
20 }
21
22 static void orcl_raw2number(unsigned char *data, unsigned int len, mpf_t result)
23 {
24 unsigned int sign = *data, digit, i;
25 int exp = sign>=128 ? sign-193 : 62-sign;
26 int exp_val;
27 mpf_t tmp;
28
29 mpf_init2(tmp, MAX_PREC);
30 mpf_init2(result, MAX_PREC);
31
32 if(sign & 0x80){
33 for(i=1; i<len; ++i){
34 digit = data[i] - 1;
35 assert(0<=digit && digit<=99);
36
37 exp_val = exp - i + 1;
38 if(exp_val < 0){
39 mpf_pow_ui(tmp, s_base100, -exp_val);
40 mpf_div(tmp, s_one, tmp);
41 }else
42 mpf_pow_ui(tmp, s_base100, exp_val);
43
44 mpf_mul_ui(tmp, tmp, digit);
45 mpf_add(result, result, tmp);
46 }
47
48 }else{
49 --len; //ignore the last byte
50 for(i=1; i<len; ++i){
51 digit = 101 - data[i];
52 assert(0<=digit && digit<=99);
53
54 exp_val = exp - i + 1;
55 if(exp_val < 0){
56 mpf_pow_ui(tmp, s_base100, -exp_val);
57 mpf_div(tmp, s_one, tmp);
58 }else
59 mpf_pow_ui(tmp, s_base100, exp_val);
60
61 mpf_mul_ui(tmp, tmp, digit);
62 mpf_add(result, result, tmp);
63 }
64
65 mpf_neg(result, result);
66 }
67
68 mpf_clear(tmp);
69 }
测试用例
测试了123456.789、-123456.789、Oracle Number实际最大最小值、Oracle Number理论最大最小值
1 int main(int argc, char *argv[])
2 {
3 int n = 19;
4 char buf[256];
5 mpf_t r;
6
7 init_mpf_globals();
8
9 //123456.789
10 unsigned char data[] = {0xc3,0xd,0x23,0x39,0x4f,0x5b};
11 orcl_raw2number(data, sizeof(data), r);
12 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
13 printf("result: %s\n", buf);
14 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
15 mpf_clear(r);
16
17 //-123456.789
18 unsigned char data2[] = {0x3c,0x59,0x43,0x2d,0x17,0xb,0x66};
19 orcl_raw2number(data2, sizeof(data2), r);
20 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
21 printf("result: %s\n", buf);
22 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
23 mpf_clear(r);
24
25 //0
26 unsigned char zero[] = {0x80};
27 orcl_raw2number(zero, sizeof(zero), r);
28 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
29 printf("result: %s\n", buf);
30 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
31 mpf_clear(r);
32
33 //test actual max value:9999
9(the number of 9 is 38)
34 unsigned char max_data[] = {0xd3,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64};
35 orcl_raw2number(max_data, sizeof(max_data), r);
36 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
37 printf("result: %s\n", buf);
38 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
39 mpf_clear(r);
40
41 //test actual min value:-99999(the number of 9 is 38)
42 unsigned char min_data[] = {0x2c,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x66};
43 orcl_raw2number(min_data, sizeof(min_data), r);
44 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
45 printf("result: %s\n", buf);
46 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
47 mpf_clear(r);
48
49 clear_mpf_globals();
50
51 //test max oracle number value
52 mpf_init2(r, 256);
53
54 mpf_set_str(r, "1e125", 10);
55 mpf_out_str(NULL, 10, 0, r); printf("\n");
56 gmp_printf("%Ff\n", r);
57
58 //test min oracle number value
59 mpf_set_str(r, "-1e125", 10);
60 mpf_out_str(NULL, 10, 0, r); printf("\n");
61 gmp_printf("%Ff\n", r);
62
63 mpf_clear(r);
64
65 return 0;
66 }
输出如下2 {
3 int n = 19;
4 char buf[256];
5 mpf_t r;
6
7 init_mpf_globals();
8
9 //123456.789
10 unsigned char data[] = {0xc3,0xd,0x23,0x39,0x4f,0x5b};
11 orcl_raw2number(data, sizeof(data), r);
12 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
13 printf("result: %s\n", buf);
14 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
15 mpf_clear(r);
16
17 //-123456.789
18 unsigned char data2[] = {0x3c,0x59,0x43,0x2d,0x17,0xb,0x66};
19 orcl_raw2number(data2, sizeof(data2), r);
20 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
21 printf("result: %s\n", buf);
22 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
23 mpf_clear(r);
24
25 //0
26 unsigned char zero[] = {0x80};
27 orcl_raw2number(zero, sizeof(zero), r);
28 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
29 printf("result: %s\n", buf);
30 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
31 mpf_clear(r);
32
33 //test actual max value:9999
9(the number of 9 is 38)34 unsigned char max_data[] = {0xd3,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64,0x64};
35 orcl_raw2number(max_data, sizeof(max_data), r);
36 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
37 printf("result: %s\n", buf);
38 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
39 mpf_clear(r);
40
41 //test actual min value:-9999
9(the number of 9 is 38)42 unsigned char min_data[] = {0x2c,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x2,0x66};
43 orcl_raw2number(min_data, sizeof(min_data), r);
44 gmp_snprintf(buf, sizeof(buf), "%Ff\n\t%.*Ff(%d digits)", r, n, r, n);
45 printf("result: %s\n", buf);
46 printf("\t"); mpf_out_str(NULL, 10, 0, r); printf("\n");
47 mpf_clear(r);
48
49 clear_mpf_globals();
50
51 //test max oracle number value
52 mpf_init2(r, 256);
53
54 mpf_set_str(r, "1e125", 10);
55 mpf_out_str(NULL, 10, 0, r); printf("\n");
56 gmp_printf("%Ff\n", r);
57
58 //test min oracle number value
59 mpf_set_str(r, "-1e125", 10);
60 mpf_out_str(NULL, 10, 0, r); printf("\n");
61 gmp_printf("%Ff\n", r);
62
63 mpf_clear(r);
64
65 return 0;
66 }