Numerical analysis textbooks and floating point numbers
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What are some recommended numerical analysis books on floating point numbers? I'd like the book to have the following
In depth coverage on the representation of floating point numbers on modern hardware (the IEEE standard).
How to do arbitrary precision floating point calculations with a reasonably fast modern algorithm.
How to compute the closest 32-bit floating point representation of a dot product and cross product. And do this fast, so no relying on generic arbitrary precision calculations to get the bits of the 32-bit floating point number right.
From what I can infer from doing some searches most books tend to focus on stuff like the runge kutta and not put much emphasis on how to make floating point calculations that are ultra precise.
numerical-methods
asked Jan 24 '12 at 5:12
user782220user782220
39512154
$endgroup$
add a comment |
$begingroup$
What are some recommended numerical analysis books on floating point numbers? I'd like the book to have the following
In depth coverage on the representation of floating point numbers on modern hardware (the IEEE standard).
How to do arbitrary precision floating point calculations with a reasonably fast modern algorithm.
How to compute the closest 32-bit floating point representation of a dot product and cross product. And do this fast, so no relying on generic arbitrary precision calculations to get the bits of the 32-bit floating point number right.
From what I can infer from doing some searches most books tend to focus on stuff like the runge kutta and not put much emphasis on how to make floating point calculations that are ultra precise.
numerical-methods
asked Jan 24 '12 at 5:12
user782220user782220
39512154
$endgroup$
$begingroup$
You could check out the standard, itself: ieeexplore.ieee.org/servlet/opac?punumber=4610933
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– dls
Jan 24 '12 at 5:30
add a comment |
$begingroup$
What are some recommended numerical analysis books on floating point numbers? I'd like the book to have the following
In depth coverage on the representation of floating point numbers on modern hardware (the IEEE standard).
How to do arbitrary precision floating point calculations with a reasonably fast modern algorithm.
How to compute the closest 32-bit floating point representation of a dot product and cross product. And do this fast, so no relying on generic arbitrary precision calculations to get the bits of the 32-bit floating point number right.
From what I can infer from doing some searches most books tend to focus on stuff like the runge kutta and not put much emphasis on how to make floating point calculations that are ultra precise.
numerical-methods
asked Jan 24 '12 at 5:12
user782220user782220
39512154
$endgroup$
What are some recommended numerical analysis books on floating point numbers? I'd like the book to have the following
In depth coverage on the representation of floating point numbers on modern hardware (the IEEE standard).
How to do arbitrary precision floating point calculations with a reasonably fast modern algorithm.
How to compute the closest 32-bit floating point representation of a dot product and cross product. And do this fast, so no relying on generic arbitrary precision calculations to get the bits of the 32-bit floating point number right.
From what I can infer from doing some searches most books tend to focus on stuff like the runge kutta and not put much emphasis on how to make floating point calculations that are ultra precise.
numerical-methods
numerical-methods
asked Jan 24 '12 at 5:12
user782220user782220
39512154
asked Jan 24 '12 at 5:12
user782220user782220
39512154
asked Jan 24 '12 at 5:12
user782220user782220
39512154
asked Jan 24 '12 at 5:12
user782220user782220
39512154
asked Jan 24 '12 at 5:12
user782220user782220
39512154
39512154
$begingroup$
You could check out the standard, itself: ieeexplore.ieee.org/servlet/opac?punumber=4610933
$endgroup$
– dls
Jan 24 '12 at 5:30
add a comment |
$begingroup$
You could check out the standard, itself: ieeexplore.ieee.org/servlet/opac?punumber=4610933
$endgroup$
– dls
Jan 24 '12 at 5:30
$begingroup$
You could check out the standard, itself: ieeexplore.ieee.org/servlet/opac?punumber=4610933
$endgroup$
– dls
Jan 24 '12 at 5:30
$begingroup$
You could check out the standard, itself: ieeexplore.ieee.org/servlet/opac?punumber=4610933
$endgroup$
– dls
Jan 24 '12 at 5:30
add a comment |
2 Answers
2
active
oldest
votes
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You could try the book written by J.M. Muller, N. Brisebarre:
Handbook of Floating Point Arithmetic (amazon.com)
The literature of numerical mathematics concentrates on algorithms for mathematical problems, not on implementation issues of arithmetic operations.
How to compute the closest 32-bit floating point representation of a dot product and cross product.
Since these are concatenations of addition and multiplication, I expect that you won't find much about dot and cross products themselves.
edited Jan 12 at 12:23
JB-Franco
3181320
answered Jan 24 '12 at 9:57
Tim van BeekTim van Beek
4,6081521
$endgroup$
2
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There is plenty literature about accurate dot products. See for instance Ogita et al., Accurate sum and dot product. SIAM J. Sci. Comput. 26 (2005), no. 6, 1955–1988 and other papers by S. Rump and collaborators.
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– lhf
Jan 24 '12 at 10:25
$begingroup$
Took a look at the table of contents for "Handbook of Floating Point Arithmetic" and it looks close to what I want.
$endgroup$
– user782220
Jan 24 '12 at 10:27
add a comment |
$begingroup$
Try these books:
Numerical Computing with IEEE Floating Point Arithmetic by Overton
Accuracy and Stability of Numerical Algorithms by Higham
Modern Computer Arithmetic by Brent and Zimmermann
answered Jan 24 '12 at 10:28
lhflhf
166k10171400
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
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active
oldest
votes
$begingroup$
You could try the book written by J.M. Muller, N. Brisebarre:
Handbook of Floating Point Arithmetic (amazon.com)
The literature of numerical mathematics concentrates on algorithms for mathematical problems, not on implementation issues of arithmetic operations.
How to compute the closest 32-bit floating point representation of a dot product and cross product.
Since these are concatenations of addition and multiplication, I expect that you won't find much about dot and cross products themselves.
edited Jan 12 at 12:23
JB-Franco
3181320
answered Jan 24 '12 at 9:57
Tim van BeekTim van Beek
4,6081521
$endgroup$
2
$begingroup$
There is plenty literature about accurate dot products. See for instance Ogita et al., Accurate sum and dot product. SIAM J. Sci. Comput. 26 (2005), no. 6, 1955–1988 and other papers by S. Rump and collaborators.
$endgroup$
– lhf
Jan 24 '12 at 10:25
$begingroup$
Took a look at the table of contents for "Handbook of Floating Point Arithmetic" and it looks close to what I want.
$endgroup$
– user782220
Jan 24 '12 at 10:27
add a comment |
$begingroup$
You could try the book written by J.M. Muller, N. Brisebarre:
Handbook of Floating Point Arithmetic (amazon.com)
The literature of numerical mathematics concentrates on algorithms for mathematical problems, not on implementation issues of arithmetic operations.
How to compute the closest 32-bit floating point representation of a dot product and cross product.
Since these are concatenations of addition and multiplication, I expect that you won't find much about dot and cross products themselves.
edited Jan 12 at 12:23
JB-Franco
3181320
answered Jan 24 '12 at 9:57
Tim van BeekTim van Beek
4,6081521
$endgroup$
2
$begingroup$
There is plenty literature about accurate dot products. See for instance Ogita et al., Accurate sum and dot product. SIAM J. Sci. Comput. 26 (2005), no. 6, 1955–1988 and other papers by S. Rump and collaborators.
$endgroup$
– lhf
Jan 24 '12 at 10:25
$begingroup$
Took a look at the table of contents for "Handbook of Floating Point Arithmetic" and it looks close to what I want.
$endgroup$
– user782220
Jan 24 '12 at 10:27
add a comment |
$begingroup$
You could try the book written by J.M. Muller, N. Brisebarre:
Handbook of Floating Point Arithmetic (amazon.com)
The literature of numerical mathematics concentrates on algorithms for mathematical problems, not on implementation issues of arithmetic operations.
How to compute the closest 32-bit floating point representation of a dot product and cross product.
Since these are concatenations of addition and multiplication, I expect that you won't find much about dot and cross products themselves.
edited Jan 12 at 12:23
JB-Franco
3181320
answered Jan 24 '12 at 9:57
Tim van BeekTim van Beek
4,6081521
$endgroup$
You could try the book written by J.M. Muller, N. Brisebarre:
Handbook of Floating Point Arithmetic (amazon.com)
The literature of numerical mathematics concentrates on algorithms for mathematical problems, not on implementation issues of arithmetic operations.
How to compute the closest 32-bit floating point representation of a dot product and cross product.
Since these are concatenations of addition and multiplication, I expect that you won't find much about dot and cross products themselves.
edited Jan 12 at 12:23
JB-Franco
3181320
answered Jan 24 '12 at 9:57
Tim van BeekTim van Beek
4,6081521
edited Jan 12 at 12:23
JB-Franco
3181320
edited Jan 12 at 12:23
JB-Franco
3181320
edited Jan 12 at 12:23
JB-Franco
3181320
3181320
answered Jan 24 '12 at 9:57
Tim van BeekTim van Beek
4,6081521
answered Jan 24 '12 at 9:57
Tim van BeekTim van Beek
4,6081521
answered Jan 24 '12 at 9:57
Tim van BeekTim van Beek
4,6081521
4,6081521
2
$begingroup$
There is plenty literature about accurate dot products. See for instance Ogita et al., Accurate sum and dot product. SIAM J. Sci. Comput. 26 (2005), no. 6, 1955–1988 and other papers by S. Rump and collaborators.
$endgroup$
– lhf
Jan 24 '12 at 10:25
$begingroup$
Took a look at the table of contents for "Handbook of Floating Point Arithmetic" and it looks close to what I want.
$endgroup$
– user782220
Jan 24 '12 at 10:27
add a comment |
2
$begingroup$
There is plenty literature about accurate dot products. See for instance Ogita et al., Accurate sum and dot product. SIAM J. Sci. Comput. 26 (2005), no. 6, 1955–1988 and other papers by S. Rump and collaborators.
$endgroup$
– lhf
Jan 24 '12 at 10:25
$begingroup$
Took a look at the table of contents for "Handbook of Floating Point Arithmetic" and it looks close to what I want.
$endgroup$
– user782220
Jan 24 '12 at 10:27
2
2
$begingroup$
There is plenty literature about accurate dot products. See for instance Ogita et al., Accurate sum and dot product. SIAM J. Sci. Comput. 26 (2005), no. 6, 1955–1988 and other papers by S. Rump and collaborators.
$endgroup$
– lhf
Jan 24 '12 at 10:25
$begingroup$
There is plenty literature about accurate dot products. See for instance Ogita et al., Accurate sum and dot product. SIAM J. Sci. Comput. 26 (2005), no. 6, 1955–1988 and other papers by S. Rump and collaborators.
$endgroup$
– lhf
Jan 24 '12 at 10:25
$begingroup$
Took a look at the table of contents for "Handbook of Floating Point Arithmetic" and it looks close to what I want.
$endgroup$
– user782220
Jan 24 '12 at 10:27
$begingroup$
Took a look at the table of contents for "Handbook of Floating Point Arithmetic" and it looks close to what I want.
$endgroup$
– user782220
Jan 24 '12 at 10:27
add a comment |
$begingroup$
Try these books:
Numerical Computing with IEEE Floating Point Arithmetic by Overton
Accuracy and Stability of Numerical Algorithms by Higham
Modern Computer Arithmetic by Brent and Zimmermann
answered Jan 24 '12 at 10:28
lhflhf
166k10171400
$endgroup$
add a comment |
$begingroup$
Try these books:
Numerical Computing with IEEE Floating Point Arithmetic by Overton
Accuracy and Stability of Numerical Algorithms by Higham
Modern Computer Arithmetic by Brent and Zimmermann
answered Jan 24 '12 at 10:28
lhflhf
166k10171400
$endgroup$
add a comment |
$begingroup$
Try these books:
Numerical Computing with IEEE Floating Point Arithmetic by Overton
Accuracy and Stability of Numerical Algorithms by Higham
Modern Computer Arithmetic by Brent and Zimmermann
answered Jan 24 '12 at 10:28
lhflhf
166k10171400
$endgroup$
Try these books:
Numerical Computing with IEEE Floating Point Arithmetic by Overton
Accuracy and Stability of Numerical Algorithms by Higham
Modern Computer Arithmetic by Brent and Zimmermann
answered Jan 24 '12 at 10:28
lhflhf
166k10171400
answered Jan 24 '12 at 10:28
lhflhf
166k10171400
answered Jan 24 '12 at 10:28
lhflhf
166k10171400
answered Jan 24 '12 at 10:28
lhflhf
166k10171400
166k10171400
add a comment |
add a comment |
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$begingroup$
You could check out the standard, itself: ieeexplore.ieee.org/servlet/opac?punumber=4610933
$endgroup$
– dls
Jan 24 '12 at 5:30