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00000000000000000000000 1 0 01111111

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Unformatted text preview: 00000000000000000000 +1 0 01111111 00000000000000000000000 ;1 1 01111111 00000000000000000000000 2;126 0 00000001 00000000000000000000000 2127(2 ; 2;23) 0 11111110 11111111111111111111111 +1 0 11111111 00000000000000000000000 ;1 1 11111111 00000000000000000000000 NaN ? 11111111 Anything but all zeros Denormal ? 00000000 Anything but all zeros { Under ow threshold: 2;126 1:17 10;38 { Over ow threshold: 2127(2 ; 2;23) 2128 3:40 { NaN: not a number { Denormal: un-normalized number (d0 = 0) { u = 2;24 5:96 10;8 2 1038 Floating Point Standards IEEE binary double-precision standard s η − 1023 f 52 bit fraction 1 bit sign 11 bit biased exponent { Represented number: (;1)s2 ;1023(1 + f ) { Under ow threshold: 2;1022 2:23 10;308 { Over ow threshold: 21023(2;2;52) 21024 1:80 10308 { u = 2;53 1:11 10;16 3 Stability Assume that an operation (+ ; = fl(a b) = a b(1 + ) { The relative error is jfl(a b) ; a bj ja bj p ) satis jj u es u (3a) (3b) Analyze the roundo error in computing a dot...
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