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Merge pull request #7339 from amosbird/f10

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Fix preciseExp10
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Alexander Kuzmenkov 2019-10-22 12:00:53 +03:00 committed by GitHub
commit be4618dd05
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3 changed files with 1049 additions and 347 deletions
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1311
dbms/tests/queries/0_stateless/00534_exp10.reference
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3
dbms/tests/queries/0_stateless/00534_exp10.sql
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@ -1 +1,2 @@
SELECT number, exp10(number) FROM system.numbers LIMIT 310;
SELECT number, exp10(number - 500) FROM system.numbers LIMIT 1000;
SELECT exp10(nan);

82
libs/libcommon/src/preciseExp10.c
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@ -171,47 +171,57 @@ obstacle to adoption, that text has been removed.
#include <math.h>
#include <stdint.h>
#include <stdio.h>
double preciseExp10(double x)
{
if (isnan(x)) return NAN;
// ranging between DBL_TRUE_MIN and DBL_MAX. Outsiders are treated as zeros or infinities
static const double p10[]
= {1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1,
1e+1, 1e+2, 1e+3, 1e+4, 1e+5, 1e+6, 1e+7, 1e+8, 1e+9, 1e+10, 1e+11, 1e+12, 1e+13, 1e+14, 1e+15, 1e+16,
1e+17, 1e+18, 1e+19, 1e+20, 1e+21, 1e+22, 1e+23, 1e+24, 1e+25, 1e+26, 1e+27, 1e+28, 1e+29, 1e+30, 1e+31, 1e+32,
1e+33, 1e+34, 1e+35, 1e+36, 1e+37, 1e+38, 1e+39, 1e+40, 1e+41, 1e+42, 1e+43, 1e+44, 1e+45, 1e+46, 1e+47, 1e+48,
1e+49, 1e+50, 1e+51, 1e+52, 1e+53, 1e+54, 1e+55, 1e+56, 1e+57, 1e+58, 1e+59, 1e+60, 1e+61, 1e+62, 1e+63, 1e+64,
1e+65, 1e+66, 1e+67, 1e+68, 1e+69, 1e+70, 1e+71, 1e+72, 1e+73, 1e+74, 1e+75, 1e+76, 1e+77, 1e+78, 1e+79, 1e+80,
1e+81, 1e+82, 1e+83, 1e+84, 1e+85, 1e+86, 1e+87, 1e+88, 1e+89, 1e+90, 1e+91, 1e+92, 1e+93, 1e+94, 1e+95, 1e+96,
1e+97, 1e+98, 1e+99, 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-323, 1e-322, 1e-321, 1e-320, 1e-319, 1e-318, 1e-317, 1e-316, 1e-315, 1e-314, 1e-313, 1e-312, 1e-311, 1e-310, 1e-309, 1e-308, 1e-307,
1e-306, 1e-305, 1e-304, 1e-303, 1e-302, 1e-301, 1e-300, 1e-299, 1e-298, 1e-297, 1e-296, 1e-295, 1e-294, 1e-293, 1e-292, 1e-291, 1e-290,
1e-289, 1e-288, 1e-287, 1e-286, 1e-285, 1e-284, 1e-283, 1e-282, 1e-281, 1e-280, 1e-279, 1e-278, 1e-277, 1e-276, 1e-275, 1e-274, 1e-273,
1e-272, 1e-271, 1e-270, 1e-269, 1e-268, 1e-267, 1e-266, 1e-265, 1e-264, 1e-263, 1e-262, 1e-261, 1e-260, 1e-259, 1e-258, 1e-257, 1e-256,
1e-255, 1e-254, 1e-253, 1e-252, 1e-251, 1e-250, 1e-249, 1e-248, 1e-247, 1e-246, 1e-245, 1e-244, 1e-243, 1e-242, 1e-241, 1e-240, 1e-239,
1e-238, 1e-237, 1e-236, 1e-235, 1e-234, 1e-233, 1e-232, 1e-231, 1e-230, 1e-229, 1e-228, 1e-227, 1e-226, 1e-225, 1e-224, 1e-223, 1e-222,
1e-221, 1e-220, 1e-219, 1e-218, 1e-217, 1e-216, 1e-215, 1e-214, 1e-213, 1e-212, 1e-211, 1e-210, 1e-209, 1e-208, 1e-207, 1e-206, 1e-205,
1e-204, 1e-203, 1e-202, 1e-201, 1e-200, 1e-199, 1e-198, 1e-197, 1e-196, 1e-195, 1e-194, 1e-193, 1e-192, 1e-191, 1e-190, 1e-189, 1e-188,
1e-187, 1e-186, 1e-185, 1e-184, 1e-183, 1e-182, 1e-181, 1e-180, 1e-179, 1e-178, 1e-177, 1e-176, 1e-175, 1e-174, 1e-173, 1e-172, 1e-171,
1e-170, 1e-169, 1e-168, 1e-167, 1e-166, 1e-165, 1e-164, 1e-163, 1e-162, 1e-161, 1e-160, 1e-159, 1e-158, 1e-157, 1e-156, 1e-155, 1e-154,
1e-153, 1e-152, 1e-151, 1e-150, 1e-149, 1e-148, 1e-147, 1e-146, 1e-145, 1e-144, 1e-143, 1e-142, 1e-141, 1e-140, 1e-139, 1e-138, 1e-137,
1e-136, 1e-135, 1e-134, 1e-133, 1e-132, 1e-131, 1e-130, 1e-129, 1e-128, 1e-127, 1e-126, 1e-125, 1e-124, 1e-123, 1e-122, 1e-121, 1e-120,
1e-119, 1e-118, 1e-117, 1e-116, 1e-115, 1e-114, 1e-113, 1e-112, 1e-111, 1e-110, 1e-109, 1e-108, 1e-107, 1e-106, 1e-105, 1e-104, 1e-103,
1e-102, 1e-101, 1e-100, 1e-99, 1e-98, 1e-97, 1e-96, 1e-95, 1e-94, 1e-93, 1e-92, 1e-91, 1e-90, 1e-89, 1e-88, 1e-87, 1e-86,
1e-85, 1e-84, 1e-83, 1e-82, 1e-81, 1e-80, 1e-79, 1e-78, 1e-77, 1e-76, 1e-75, 1e-74, 1e-73, 1e-72, 1e-71, 1e-70, 1e-69,
1e-68, 1e-67, 1e-66, 1e-65, 1e-64, 1e-63, 1e-62, 1e-61, 1e-60, 1e-59, 1e-58, 1e-57, 1e-56, 1e-55, 1e-54, 1e-53, 1e-52,
1e-51, 1e-50, 1e-49, 1e-48, 1e-47, 1e-46, 1e-45, 1e-44, 1e-43, 1e-42, 1e-41, 1e-40, 1e-39, 1e-38, 1e-37, 1e-36, 1e-35,
1e-34, 1e-33, 1e-32, 1e-31, 1e-30, 1e-29, 1e-28, 1e-27, 1e-26, 1e-25, 1e-24, 1e-23, 1e-22, 1e-21, 1e-20, 1e-19, 1e-18,
1e-17, 1e-16, 1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
1e0, 1e+1, 1e+2, 1e+3, 1e+4, 1e+5, 1e+6, 1e+7, 1e+8, 1e+9, 1e+10, 1e+11, 1e+12, 1e+13, 1e+14, 1e+15, 1e+16,
1e+17, 1e+18, 1e+19, 1e+20, 1e+21, 1e+22, 1e+23, 1e+24, 1e+25, 1e+26, 1e+27, 1e+28, 1e+29, 1e+30, 1e+31, 1e+32, 1e+33,
1e+34, 1e+35, 1e+36, 1e+37, 1e+38, 1e+39, 1e+40, 1e+41, 1e+42, 1e+43, 1e+44, 1e+45, 1e+46, 1e+47, 1e+48, 1e+49, 1e+50,
1e+51, 1e+52, 1e+53, 1e+54, 1e+55, 1e+56, 1e+57, 1e+58, 1e+59, 1e+60, 1e+61, 1e+62, 1e+63, 1e+64, 1e+65, 1e+66, 1e+67,
1e+68, 1e+69, 1e+70, 1e+71, 1e+72, 1e+73, 1e+74, 1e+75, 1e+76, 1e+77, 1e+78, 1e+79, 1e+80, 1e+81, 1e+82, 1e+83, 1e+84,
1e+85, 1e+86, 1e+87, 1e+88, 1e+89, 1e+90, 1e+91, 1e+92, 1e+93, 1e+94, 1e+95, 1e+96, 1e+97, 1e+98, 1e+99, 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};
double n, y = modf(x, &n);
if (n > 308)
return x > 0 ? INFINITY : -INFINITY;
if (!y)
return p10[(int)n + 15];
if (n > 308) return INFINITY;
if (n < -323) return 0;
union
{
double f;
uint64_t i;
} u = {n};
if ((u.i >> 52 & 0x7ff) < 0x3ff + 4)
{
y = exp2(3.32192809488736234787031942948939 * y);
return y * p10[(int)n + 15];
}
return pow(10.0, x);
// Using lookup table based formula to get accurate results for integer arguments.
return exp2(3.32192809488736234787031942948939 * y) * p10[(int)n + 323];
}