diff options
-rw-r--r-- | include/m_string.h | 4 | ||||
-rw-r--r-- | mysql-test/r/type_float.result | 33 | ||||
-rw-r--r-- | mysql-test/t/type_float.test | 20 | ||||
-rw-r--r-- | sql/field.cc | 151 | ||||
-rw-r--r-- | sql/field.h | 19 | ||||
-rw-r--r-- | sql/init.cc | 13 | ||||
-rw-r--r-- | sql/item_cmpfunc.cc | 2 | ||||
-rw-r--r-- | sql/mysql_priv.h | 2 | ||||
-rw-r--r-- | sql/mysqld.cc | 2 | ||||
-rw-r--r-- | strings/strtod.c | 87 |
10 files changed, 199 insertions, 134 deletions
diff --git a/include/m_string.h b/include/m_string.h index 349084ab21e..773326e9b7d 100644 --- a/include/m_string.h +++ b/include/m_string.h @@ -105,6 +105,10 @@ extern char *stpcpy(char *, const char *); /* For AIX with gcc 2.95.3 */ extern char NEAR _dig_vec_upper[]; extern char NEAR _dig_vec_lower[]; +/* Defined in strtod.c */ +extern const double log_10[310]; +extern const double log_01[310]; + #ifdef BAD_STRING_COMPILER #define strmov(A,B) (memccpy(A,B,0,INT_MAX)-1) #else diff --git a/mysql-test/r/type_float.result b/mysql-test/r/type_float.result index 188963c5bdf..53844d2cfe2 100644 --- a/mysql-test/r/type_float.result +++ b/mysql-test/r/type_float.result @@ -344,3 +344,36 @@ create table t1 (s1 float(0,2)); ERROR 42000: For float(M,D), double(M,D) or decimal(M,D), M must be >= D (column 's1'). create table t1 (s1 float(1,2)); ERROR 42000: For float(M,D), double(M,D) or decimal(M,D), M must be >= D (column 's1'). +create table t1 (f1 double(200, 0)); +insert into t1 values (1e199), (-1e199); +insert into t1 values (1e200), (-1e200); +insert into t1 values (2e200), (-2e200); +Warnings: +Warning 1264 Out of range value adjusted for column 'f1' at row 1 +Warning 1264 Out of range value adjusted for column 'f1' at row 2 +select f1 + 0e0 from t1; +f1 + 0e0 +1e+199 +-1e+199 +1e+200 +-1e+200 +1e+200 +-1e+200 +drop table t1; +create table t1 (f1 float(30, 0)); +insert into t1 values (1e29), (-1e29); +insert into t1 values (1e30), (-1e30); +insert into t1 values (2e30), (-2e30); +Warnings: +Warning 1264 Out of range value adjusted for column 'f1' at row 1 +Warning 1264 Out of range value adjusted for column 'f1' at row 2 +select f1 + 0e0 from t1; +f1 + 0e0 +1.0000000150475e+29 +-1.0000000150475e+29 +1.0000000150475e+30 +-1.0000000150475e+30 +1.0000000150475e+30 +-1.0000000150475e+30 +drop table t1; +End of 5.0 tests diff --git a/mysql-test/t/type_float.test b/mysql-test/t/type_float.test index f790bcf6daa..a55200c8853 100644 --- a/mysql-test/t/type_float.test +++ b/mysql-test/t/type_float.test @@ -222,3 +222,23 @@ drop table t1; create table t1 (s1 float(0,2)); --error 1427 create table t1 (s1 float(1,2)); + +# +# Bug #28121 "INSERT or UPDATE into DOUBLE(200,0) field being truncated to 31 digits" +# + +create table t1 (f1 double(200, 0)); +insert into t1 values (1e199), (-1e199); +insert into t1 values (1e200), (-1e200); +insert into t1 values (2e200), (-2e200); +select f1 + 0e0 from t1; +drop table t1; + +create table t1 (f1 float(30, 0)); +insert into t1 values (1e29), (-1e29); +insert into t1 values (1e30), (-1e30); +insert into t1 values (2e30), (-2e30); +select f1 + 0e0 from t1; +drop table t1; + +--echo End of 5.0 tests diff --git a/sql/field.cc b/sql/field.cc index 8186659ae89..8989f601b74 100644 --- a/sql/field.cc +++ b/sql/field.cc @@ -3675,56 +3675,9 @@ int Field_float::store(const char *from,uint len,CHARSET_INFO *cs) int Field_float::store(double nr) { - float j; - int error= 0; + int error= truncate(&nr, FLT_MAX); + float j= nr; - if (isnan(nr)) - { - j= 0; - set_null(); - set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); - error= 1; - } - else if (unsigned_flag && nr < 0) - { - j= 0; - set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); - error= 1; - } - else - { - double max_value; - if (dec >= NOT_FIXED_DEC) - { - max_value= FLT_MAX; - } - else - { - uint tmp=min(field_length,array_elements(log_10)-1); - max_value= (log_10[tmp]-1)/log_10[dec]; - /* - The following comparison is needed to not get an overflow if nr - is close to FLT_MAX - */ - if (fabs(nr) < FLT_MAX/10.0e+32) - nr= floor(nr*log_10[dec]+0.5)/log_10[dec]; - } - if (nr < -max_value) - { - j= (float)-max_value; - set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); - error= 1; - } - else if (nr > max_value) - { - j= (float)max_value; - set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); - error= 1; - } - else - j= (float) nr; - } - #ifdef WORDS_BIGENDIAN if (table->s->db_low_byte_first) { @@ -3963,48 +3916,7 @@ int Field_double::store(const char *from,uint len,CHARSET_INFO *cs) int Field_double::store(double nr) { - int error= 0; - - if (isnan(nr)) - { - nr= 0; - set_null(); - set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); - error= 1; - } - else if (unsigned_flag && nr < 0) - { - nr= 0; - set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); - error= 1; - } - else - { - double max_value; - if (not_fixed) - { - max_value= DBL_MAX; - } - else - { - uint tmp=min(field_length,array_elements(log_10)-1); - max_value= (log_10[tmp]-1)/log_10[dec]; - if (fabs(nr) < DBL_MAX/10.0e+32) - nr= floor(nr*log_10[dec]+0.5)/log_10[dec]; - } - if (nr < -max_value) - { - nr= -max_value; - set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); - error= 1; - } - else if (nr > max_value) - { - nr= max_value; - set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); - error= 1; - } - } + int error= truncate(&nr, DBL_MAX); #ifdef WORDS_BIGENDIAN if (table->s->db_low_byte_first) @@ -4023,6 +3935,63 @@ int Field_double::store(longlong nr, bool unsigned_val) return store(unsigned_val ? ulonglong2double((ulonglong) nr) : (double) nr); } +/* + If a field has fixed length, truncate the double argument pointed to by 'nr' + appropriately. + Also ensure that the argument is within [-max_value; max_value] range. +*/ + +int Field_real::truncate(double *nr, double max_value) +{ + int error= 1; + double res= *nr; + + if (isnan(res)) + { + res= 0; + set_null(); + set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); + goto end; + } + else if (unsigned_flag && res < 0) + { + res= 0; + set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); + goto end; + } + + if (!not_fixed) + { + uint order= field_length - dec; + uint step= array_elements(log_10) - 1; + max_value= 1.0; + for (; order > step; order-= step) + max_value*= log_10[step]; + max_value*= log_10[order]; + max_value-= 1.0 / log_10[dec]; + + double tmp= rint((res - floor(res)) * log_10[dec]) / log_10[dec]; + res= floor(res) + tmp; + } + + if (res < -max_value) + { + res= -max_value; + set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); + } + else if (res > max_value) + { + res= max_value; + set_warning(MYSQL_ERROR::WARN_LEVEL_WARN, ER_WARN_DATA_OUT_OF_RANGE, 1); + } + else + error= 0; + +end: + *nr= res; + return error; +} + int Field_real::store_decimal(const my_decimal *dm) { diff --git a/sql/field.h b/sql/field.h index 78aa12ad200..00854ca11b5 100644 --- a/sql/field.h +++ b/sql/field.h @@ -453,6 +453,7 @@ public: /* base class for float and double and decimal (old one) */ class Field_real :public Field_num { public: + my_bool not_fixed; Field_real(char *ptr_arg, uint32 len_arg, uchar *null_ptr_arg, uchar null_bit_arg, utype unireg_check_arg, @@ -460,12 +461,14 @@ public: struct st_table *table_arg, uint8 dec_arg, bool zero_arg, bool unsigned_arg) :Field_num(ptr_arg, len_arg, null_ptr_arg, null_bit_arg, unireg_check_arg, - field_name_arg, table_arg, dec_arg, zero_arg, unsigned_arg) + field_name_arg, table_arg, dec_arg, zero_arg, unsigned_arg), + not_fixed(dec_arg >= NOT_FIXED_DEC) {} int store_decimal(const my_decimal *); my_decimal *val_decimal(my_decimal *); + int truncate(double *nr, double max_length); uint32 max_display_length() { return field_length; } }; @@ -758,7 +761,6 @@ public: class Field_double :public Field_real { public: - my_bool not_fixed; Field_double(char *ptr_arg, uint32 len_arg, uchar *null_ptr_arg, uchar null_bit_arg, enum utype unireg_check_arg, const char *field_name_arg, @@ -766,21 +768,18 @@ public: uint8 dec_arg,bool zero_arg,bool unsigned_arg) :Field_real(ptr_arg, len_arg, null_ptr_arg, null_bit_arg, unireg_check_arg, field_name_arg, table_arg, - dec_arg, zero_arg, unsigned_arg), - not_fixed(dec_arg >= NOT_FIXED_DEC) + dec_arg, zero_arg, unsigned_arg) {} Field_double(uint32 len_arg, bool maybe_null_arg, const char *field_name_arg, struct st_table *table_arg, uint8 dec_arg) :Field_real((char*) 0, len_arg, maybe_null_arg ? (uchar*) "" : 0, (uint) 0, - NONE, field_name_arg, table_arg, dec_arg, 0, 0), - not_fixed(dec_arg >= NOT_FIXED_DEC) + NONE, field_name_arg, table_arg, dec_arg, 0, 0) {} Field_double(uint32 len_arg, bool maybe_null_arg, const char *field_name_arg, - struct st_table *table_arg, uint8 dec_arg, my_bool not_fixed_srg) + struct st_table *table_arg, uint8 dec_arg, my_bool not_fixed_arg) :Field_real((char*) 0, len_arg, maybe_null_arg ? (uchar*) "" : 0, (uint) 0, - NONE, field_name_arg, table_arg, dec_arg, 0, 0), - not_fixed(not_fixed_srg) - {} + NONE, field_name_arg, table_arg, dec_arg, 0, 0) + {not_fixed= not_fixed_arg; } enum_field_types type() const { return FIELD_TYPE_DOUBLE;} enum ha_base_keytype key_type() const { return HA_KEYTYPE_DOUBLE; } int store(const char *to,uint length,CHARSET_INFO *charset); diff --git a/sql/init.cc b/sql/init.cc index ad55a2a8b24..b3b68926683 100644 --- a/sql/init.cc +++ b/sql/init.cc @@ -21,8 +21,6 @@ void unireg_init(ulong options) { - uint i; - double nr; DBUG_ENTER("unireg_init"); MYSYS_PROGRAM_DONT_USE_CURSES(); @@ -39,16 +37,5 @@ void unireg_init(ulong options) VOID(strmov(reg_ext,".frm")); specialflag=SPECIAL_SAME_DB_NAME | options; /* Set options from argv */ - /* Make a tab of powers of 10 */ - for (i=0,nr=1.0; i < array_elements(log_10) ; i++) - { /* It's used by filesort... */ - log_10[i]= nr ; nr*= 10.0; - } - /* Make a tab of powers of 0.1 */ - for (i= 0, nr= 0.1; i < array_elements(log_01); i++) - { - log_01[i]= nr; - nr*= 0.1; - } DBUG_VOID_RETURN; } diff --git a/sql/item_cmpfunc.cc b/sql/item_cmpfunc.cc index 0de9ef3e9ad..59af6f0fec7 100644 --- a/sql/item_cmpfunc.cc +++ b/sql/item_cmpfunc.cc @@ -507,7 +507,7 @@ int Arg_comparator::set_compare_func(Item_bool_func2 *item, Item_result type) { if ((*a)->decimals < NOT_FIXED_DEC && (*b)->decimals < NOT_FIXED_DEC) { - precision= 5 * log_01[max((*a)->decimals, (*b)->decimals)]; + precision= 5 * log_01[max((*a)->decimals, (*b)->decimals) + 1]; if (func == &Arg_comparator::compare_real) func= &Arg_comparator::compare_real_fixed; else if (func == &Arg_comparator::compare_e_real) diff --git a/sql/mysql_priv.h b/sql/mysql_priv.h index 90b1f21afb2..b2a5bc31eb3 100644 --- a/sql/mysql_priv.h +++ b/sql/mysql_priv.h @@ -1269,8 +1269,6 @@ extern char language[FN_REFLEN], reg_ext[FN_EXTLEN]; extern char glob_hostname[FN_REFLEN], mysql_home[FN_REFLEN]; extern char pidfile_name[FN_REFLEN], system_time_zone[30], *opt_init_file; extern char log_error_file[FN_REFLEN], *opt_tc_log_file; -extern double log_10[32]; -extern double log_01[32]; extern ulonglong log_10_int[20]; extern ulonglong keybuff_size; extern ulonglong thd_startup_options; diff --git a/sql/mysqld.cc b/sql/mysqld.cc index 051bad5b310..62086080ee1 100644 --- a/sql/mysqld.cc +++ b/sql/mysqld.cc @@ -434,8 +434,6 @@ ulong slow_launch_threads = 0, sync_binlog_period; ulong expire_logs_days = 0; ulong rpl_recovery_rank=0; -double log_10[32]; /* 10 potences */ -double log_01[32]; time_t server_start_time; char mysql_home[FN_REFLEN], pidfile_name[FN_REFLEN], system_time_zone[30]; diff --git a/strings/strtod.c b/strings/strtod.c index 7196cafb2c9..0ada423f373 100644 --- a/strings/strtod.c +++ b/strings/strtod.c @@ -31,13 +31,74 @@ #define MAX_DBL_EXP 308 #define MAX_RESULT_FOR_MAX_EXP 1.7976931348623157 -static double scaler10[] = { - 1.0, 1e10, 1e20, 1e30, 1e40, 1e50, 1e60, 1e70, 1e80, 1e90 -}; -static double scaler1[] = { - 1.0, 10.0, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9 + +const double log_10[] = { + 1e000, 1e001, 1e002, 1e003, 1e004, 1e005, 1e006, 1e007, 1e008, 1e009, + 1e010, 1e011, 1e012, 1e013, 1e014, 1e015, 1e016, 1e017, 1e018, 1e019, + 1e020, 1e021, 1e022, 1e023, 1e024, 1e025, 1e026, 1e027, 1e028, 1e029, + 1e030, 1e031, 1e032, 1e033, 1e034, 1e035, 1e036, 1e037, 1e038, 1e039, + 1e040, 1e041, 1e042, 1e043, 1e044, 1e045, 1e046, 1e047, 1e048, 1e049, + 1e050, 1e051, 1e052, 1e053, 1e054, 1e055, 1e056, 1e057, 1e058, 1e059, + 1e060, 1e061, 1e062, 1e063, 1e064, 1e065, 1e066, 1e067, 1e068, 1e069, + 1e070, 1e071, 1e072, 1e073, 1e074, 1e075, 1e076, 1e077, 1e078, 1e079, + 1e080, 1e081, 1e082, 1e083, 1e084, 1e085, 1e086, 1e087, 1e088, 1e089, + 1e090, 1e091, 1e092, 1e093, 1e094, 1e095, 1e096, 1e097, 1e098, 1e099, + 1e100, 1e101, 1e102, 1e103, 1e104, 1e105, 1e106, 1e107, 1e108, 1e109, + 1e110, 1e111, 1e112, 1e113, 1e114, 1e115, 1e116, 1e117, 1e118, 1e119, + 1e120, 1e121, 1e122, 1e123, 1e124, 1e125, 1e126, 1e127, 1e128, 1e129, + 1e130, 1e131, 1e132, 1e133, 1e134, 1e135, 1e136, 1e137, 1e138, 1e139, + 1e140, 1e141, 1e142, 1e143, 1e144, 1e145, 1e146, 1e147, 1e148, 1e149, + 1e150, 1e151, 1e152, 1e153, 1e154, 1e155, 1e156, 1e157, 1e158, 1e159, + 1e160, 1e161, 1e162, 1e163, 1e164, 1e165, 1e166, 1e167, 1e168, 1e169, + 1e170, 1e171, 1e172, 1e173, 1e174, 1e175, 1e176, 1e177, 1e178, 1e179, + 1e180, 1e181, 1e182, 1e183, 1e184, 1e185, 1e186, 1e187, 1e188, 1e189, + 1e190, 1e191, 1e192, 1e193, 1e194, 1e195, 1e196, 1e197, 1e198, 1e199, + 1e200, 1e201, 1e202, 1e203, 1e204, 1e205, 1e206, 1e207, 1e208, 1e209, + 1e210, 1e211, 1e212, 1e213, 1e214, 1e215, 1e216, 1e217, 1e218, 1e219, + 1e220, 1e221, 1e222, 1e223, 1e224, 1e225, 1e226, 1e227, 1e228, 1e229, + 1e230, 1e231, 1e232, 1e233, 1e234, 1e235, 1e236, 1e237, 1e238, 1e239, + 1e240, 1e241, 1e242, 1e243, 1e244, 1e245, 1e246, 1e247, 1e248, 1e249, + 1e250, 1e251, 1e252, 1e253, 1e254, 1e255, 1e256, 1e257, 1e258, 1e259, + 1e260, 1e261, 1e262, 1e263, 1e264, 1e265, 1e266, 1e267, 1e268, 1e269, + 1e270, 1e271, 1e272, 1e273, 1e274, 1e275, 1e276, 1e277, 1e278, 1e279, + 1e280, 1e281, 1e282, 1e283, 1e284, 1e285, 1e286, 1e287, 1e288, 1e289, + 1e290, 1e291, 1e292, 1e293, 1e294, 1e295, 1e296, 1e297, 1e298, 1e299, + 1e300, 1e301, 1e302, 1e303, 1e304, 1e305, 1e306, 1e307, 1e308, 1e309 }; +const double log_01[] = { + 1e-000,1e-001,1e-002,1e-003,1e-004,1e-005,1e-006,1e-007,1e-008,1e-009, + 1e-010,1e-011,1e-012,1e-013,1e-014,1e-015,1e-016,1e-017,1e-018,1e-019, + 1e-020,1e-021,1e-022,1e-023,1e-024,1e-025,1e-026,1e-027,1e-028,1e-029, + 1e-030,1e-031,1e-032,1e-033,1e-034,1e-035,1e-036,1e-037,1e-038,1e-039, + 1e-040,1e-041,1e-042,1e-043,1e-044,1e-045,1e-046,1e-047,1e-048,1e-049, + 1e-050,1e-051,1e-052,1e-053,1e-054,1e-055,1e-056,1e-057,1e-058,1e-059, + 1e-060,1e-061,1e-062,1e-063,1e-064,1e-065,1e-066,1e-067,1e-068,1e-069, + 1e-070,1e-071,1e-072,1e-073,1e-074,1e-075,1e-076,1e-077,1e-078,1e-079, + 1e-080,1e-081,1e-082,1e-083,1e-084,1e-085,1e-086,1e-087,1e-088,1e-089, + 1e-090,1e-091,1e-092,1e-093,1e-094,1e-095,1e-096,1e-097,1e-098,1e-099, + 1e-100,1e-101,1e-102,1e-103,1e-104,1e-105,1e-106,1e-107,1e-108,1e-109, + 1e-110,1e-111,1e-112,1e-113,1e-114,1e-115,1e-116,1e-117,1e-118,1e-119, + 1e-120,1e-121,1e-122,1e-123,1e-124,1e-125,1e-126,1e-127,1e-128,1e-129, + 1e-130,1e-131,1e-132,1e-133,1e-134,1e-135,1e-136,1e-137,1e-138,1e-139, + 1e-140,1e-141,1e-142,1e-143,1e-144,1e-145,1e-146,1e-147,1e-148,1e-149, + 1e-150,1e-151,1e-152,1e-153,1e-154,1e-155,1e-156,1e-157,1e-158,1e-159, + 1e-160,1e-161,1e-162,1e-163,1e-164,1e-165,1e-166,1e-167,1e-168,1e-169, + 1e-170,1e-171,1e-172,1e-173,1e-174,1e-175,1e-176,1e-177,1e-178,1e-179, + 1e-180,1e-181,1e-182,1e-183,1e-184,1e-185,1e-186,1e-187,1e-188,1e-189, + 1e-190,1e-191,1e-192,1e-193,1e-194,1e-195,1e-196,1e-197,1e-198,1e-199, + 1e-200,1e-201,1e-202,1e-203,1e-204,1e-205,1e-206,1e-207,1e-208,1e-209, + 1e-210,1e-211,1e-212,1e-213,1e-214,1e-215,1e-216,1e-217,1e-218,1e-219, + 1e-220,1e-221,1e-222,1e-223,1e-224,1e-225,1e-226,1e-227,1e-228,1e-229, + 1e-230,1e-231,1e-232,1e-233,1e-234,1e-235,1e-236,1e-237,1e-238,1e-239, + 1e-240,1e-241,1e-242,1e-243,1e-244,1e-245,1e-246,1e-247,1e-248,1e-249, + 1e-250,1e-251,1e-252,1e-253,1e-254,1e-255,1e-256,1e-257,1e-258,1e-259, + 1e-260,1e-261,1e-262,1e-263,1e-264,1e-265,1e-266,1e-267,1e-268,1e-269, + 1e-270,1e-271,1e-272,1e-273,1e-274,1e-275,1e-276,1e-277,1e-278,1e-279, + 1e-280,1e-281,1e-282,1e-283,1e-284,1e-285,1e-286,1e-287,1e-288,1e-289, + 1e-290,1e-291,1e-292,1e-293,1e-294,1e-295,1e-296,1e-297,1e-298,1e-299, + 1e-300,1e-301,1e-302,1e-303,1e-304,1e-305,1e-306,1e-307,1e-308,1e-309 +}; /* Convert string to double (string doesn't have to be null terminated) @@ -57,7 +118,7 @@ double my_strtod(const char *str, char **end_ptr, int *error) { double result= 0.0; uint negative= 0, ndigits, dec_digits= 0, neg_exp= 0; - int exponent= 0, digits_after_dec_point= 0, tmp_exp; + int exponent= 0, digits_after_dec_point= 0, tmp_exp, step; const char *old_str, *end= *end_ptr, *start_of_number; char next_char; my_bool overflow=0; @@ -178,17 +239,13 @@ double my_strtod(const char *str, char **end_ptr, int *error) { exponent= -exponent; neg_exp= 1; /* neg_exp was 0 before */ + step= array_elements(log_01) - 1; } - while (exponent >= 100) - { - result= neg_exp ? result/1.0e100 : result*1.0e100; - exponent-= 100; - } - scaler= scaler10[exponent/10]*scaler1[exponent%10]; - if (neg_exp) - result/= scaler; else - result*= scaler; + step= array_elements(log_10) - 1; + for (; exponent > step; exponent-= step) + result*= neg_exp ? log_01[step] : log_10[step]; + result*= neg_exp ? log_01[exponent] : log_10[exponent]; } done: |