double
converts inttype integers or booleans into decimal encoding
Syntax
y = double(X)
Arguments
- X
matrix of encoded integers or booleans
- y
matrix of numbers in decimal notation
Description
converts data stored using 1, 2, 4 or 8 bytes integers into
decimal representation on 8 bytes. If X
entries are already double precision floats, nothing is done.
 | double() and iconvert(..,0)
are equivalent and have the same speed. |
| Booleans can also be processed with double().
However, bool2s() does it roughly twice faster. |
 | Since the mantissa of uint64 is encoded on
64 bits while the mantissa of (double precision) decimal
numbers is encoded only on 52 bits, the relative accuracy of
uint64 integers greater than 252
may then be up to
212 ~4000 times better for them
than for "double". As a consequence, applying
double() on int64 or
uint64 integers greater than 252
change their values
and downgrades their accuracy (roundoff errors). Some examples illustrating
such effects are provided herebelow. |
Examples
x = int8([0 12 140]) double(x) // Applying double() rounds off and truncates int64() or uint64() numbers // ---------------------------------------------------------------------- i = int64(2)^52 // 52 bits, as for decimal numbers mantissa i = [i+(0:3:9)' i+(3:30:93)' i+(30:300:930)'] err = i - double(i) // no errors for |integers|<= 2^52 i = int64(2)^53 // 53 bits integers => more accurate than decimal numbers i = [i+(0:3:9)' i+(3:30:93)' i+(30:300:930)'] err = i - double(i) // round-off errors appear i = int64(2)^55 i = [i+(0:3:9)' i+(3:30:93)' i+(30:300:930)'] err = i - double(i) i = int64(2)^62 i = [i+(0:3:9)' i+(3:30:93)' i+(30:300:930)'] err = i - double(i)
--> i = int64(2)^52 // 52 bits, as for decimal numbers mantissa i = 4503599627370496 --> i = [i+(0:3:9)' i+(3:30:93)' i+(30:300:930)'] i = 4503599627370496 4503599627370499 4503599627370526 4503599627370499 4503599627370529 4503599627370826 4503599627370502 4503599627370559 4503599627371126 4503599627370505 4503599627370589 4503599627371426 --> err = i - double(i) // no errors for |integers|<= 2^52 err = 0 0 0 0 0 0 0 0 0 0 0 0 --> i = int64(2)^53 // 53 bits integers => more accurate than decimal numbers i = 9007199254740992 --> i = [i+(0:3:9)' i+(3:30:93)' i+(30:300:930)'] i = 9007199254740992 9007199254740995 9007199254741022 9007199254740995 9007199254741025 9007199254741322 9007199254740998 9007199254741055 9007199254741622 9007199254741001 9007199254741085 9007199254741922 --> err = i - double(i) // round-off errors appear err = 0 -1 0 -1 1 0 0 -1 0 1 1 0 --> i = int64(2)^55 i = 36028797018963968 --> i = [i+(0:3:9)' i+(3:30:93)' i+(30:300:930)'] i = 36028797018963968 36028797018963971 36028797018963998 36028797018963971 36028797018964001 36028797018964298 36028797018963974 36028797018964031 36028797018964598 36028797018963977 36028797018964061 36028797018964898 --> err = i - double(i) err = 0 3 -2 3 1 2 -2 -1 -2 1 -3 2 --> i = int64(2)^62 i = 4611686018427387904 --> i = [i+(0:3:9)' i+(3:30:93)' i+(30:300:930)'] i = 4611686018427387904 4611686018427387907 4611686018427387934 4611686018427387907 4611686018427387937 4611686018427388234 4611686018427387910 4611686018427387967 4611686018427388534 4611686018427387913 4611686018427387997 4611686018427388834 --> err = i - double(i) err = 0 3 30 3 33 330 6 63 -394 9 93 -94
// Comparing speeds of double(), bool2s() and iconvert(,0) on booleans // ------------------------------------------------------------------- b = (rand(1000,1000)<0.5); tic(),for i=1:100, bool2s(b); end, toc() tic(),for i=1:100, double(b); end, toc() tic(),for i=1:100, iconvert(b,0); end, toc()
--> b = (rand(1000,1000)<0.5); --> tic(),for i=1:100, bool2s(b); end, toc() ans = 1.1680533 --> tic(),for i=1:100, double(b); end, toc() ans = 2.9003021 --> tic(),for i=1:100, iconvert(b,0); end, toc() ans = 2.1867567
// Speed comparison between double() and iconvert(..,0) on int32 integers // ---------------------------------------------------------------------- i = int32((rand(1000,1000)-0.5)*1000); tic(),for j=1:100, double(i); end, toc() tic(),for j=1:100, iconvert(i,0); end, toc()
--> i = int32((rand(1000,1000)-0.5)*10000); --> tic(),for j=1:100, double(i); end, toc() ans = 2.2464656 --> tic(),for j=1:100, iconvert(i,0); end, toc() ans = 2.2771408
See also
History
| バージョン | 記述 |
| 6.0 | New int64 and uint64 encoded integers can now be converted. |
| Report an issue | ||
| << clean | Floating point | fix >> |