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with PCRE_UTF8 support at offset 0 in /web/Sites/BlickinsBuch.de/functions.php on line 241 Warning: preg_replace(): Compilation failed: this version of PCRE is not compiled with PCRE_UTF8 support at offset 0 in /web/Sites/BlickinsBuch.de/functions.php on line 241 Blickinsbuch.de - Handbook of Floating-Point Arithmetic - Jean-Michel Muller, Nicolas Brisebarre, Florent de Dinechin, Claude-Pierre Jeannerod, Lefevre Vincent, Guillaume Melquiond
     Artikel werden geladen

    Handbook of Floating-Point Arithmetic

    Handbook of Floating-Point Arithmetic

    Autoren:

    Verlag:
    Springer Basel AG  Weitere Titel dieses Verlages anzeigen

    Erschienen: Dezember 2009
    Seiten: 572
    Sprache: Englisch
    Preis: 117.69 €
    Illustration: 100 black white illustrations, 100 black white line drawings
    Maße: 264x187x43
    Einband: Gebundene Ausgabe
    ISBN: 9780817647049

    Register

    2Mul, 135,318 2MultFMA, 152 2Sum, 129, 318
    accumulator, 314
    accurate step, 396
    ACL2,471
    addition, 246
    of binary floating-point in hardware, 288
    of binary floating-point in software, 329
    of integers, 274
    of integers in decimal, 275
    of signed zeros, 247
    subnormal handling, 251, 294
    additive range reduction, 378
    Al-Khwarizmi, 167
    algebraic function, 421,424
    algebraic number, 420
    a (smallest normal number), 17,153
    alternate exception-handling attributes, 93,95
    argument reduction, 378
    arithmetic formats, 80
    ARRE (average relative representation error), 30
    attributes, 93
    Babai's algorithm, 528
    Babylonians, 4
    backward error, 186
    bad cases for the TMD, 409
    base, 13
    basic formats, 56, 80
    BCD (binary coded decimal), 83
    Benford's law, 29
    bias, 57, 82, 84,85
    biased exponent, 58-60, 84-86, 245
    big-endian, 61
    binade, 415
    binary 128, 82
    binaryl6, 82
    binary32,16, 82
    binary64, 82
    binding, 109
    bipartite table method, 287
    block floating-point, 313
    Booth recoding, 281
    breakpoint, 21, 406
    Briggs, 375
    Burger and Dybvig conversion algo- rithm, 44
    C programming language, 209
    C++ programming language, 220
    C99, 210
    cancellation, 124,193
    canonical encoding, 83, 85
    carry-ripple adder, 274
    carry-select adder, 279
    carry-skip adder, 276, 277
    catastrophic cancellation, 124, 378
    CENA, 182
    Chebyshev polynomials, 389
    theorem, 391
    dinger conversion algorithms, 46
    close path, 249
    closest vector problem, 525
    Cody, 29
    Cody and Waite reduction algorithm, 379
    cohort, 14, 83, 97, 240
    combination field, 83, 84
    comparisons, 65, 99
    comparison predicates, 65, 99
    CompensatedDotProduct algorithm, 202
    compensated algorithms, 182


    compensated polynomial evaluation, 203
    compensated summation, 192
    component of an expansion, 503
    compound adder, 278, 299
    compression of expansions, 508
    condition numbers, 187
    continued fractions, 382, 521, 522
    contracted expressions, 214
    convergent (continued fractions), 522
    conversion algorithms, 43
    Coq, 472
    CORDIC algorithm, 375
    correctly rounded function, 21, 22
    CRlibm, 381
    CVP, see closest vector problem data dependency, 273
    DblMult, 178
    decimal addition, 275
    decimal arithmetic in hardware, 272
    decimal division, 309
    decimal multiplication, 283
    decimal encoding, 85
    declet, 83
    degree of an algebraic number, 421
    Dekker, 126,135
    Dekker product, 125,135,473
    delay, 273
    denormal number, 15
    directed rounding modes, 22
    division, 262
    SRT algorithms, 308
    by a constant, 312
    by digit recurrence, 263, 306
    in decimal, 309
    in hardware, 305
    division by zero, 25, 67,101
    double-double numbers, 403
    double-word addition, 497
    double-word multiplication, 498
    double precision, 56, 57, 61, 64, 65, 71, 82
    double rounding, 75, 77,114
    DSP (digital signal processing), 297, 316
    dynamic range, 30
    elementary function, 421
    ^max/ 14
    ^min/ 14
    end-around carry adder, 279
    endianness, 61
    Ercegovac, 263
    ErrFma, 176
    Estrin's method, 394
    Euclidean lattice, 446, 524
    exactly rounded function, 21
    exceptions, 25, 66, 74, 95,100, 475
    exclusion lemma, 162, 422, 423
    exclusion zone, 162
    expansion, 503
    Expansion-Sum algorithm, 505
    exponent bias, 85
    extendable precision, 80, 92
    extended formats, 56
    extended precision, 71, 72, 80, 92, 94
    extremal exponents, 14
    faithful arithmetic, 22,131
    faithful result, 22,179,311
    faithful rounding, 22
    far path, 249
    Fast-Expansion-Sum algorithm, 506
    Fast2Sum, 126,127
    <fenv.h>, 210
    field-programmable gate array, 271, 279, 287
    fixed point, 313, 314, 317,477
    FLIP, 321
    <float.h>, 210
    FMA, 51,104, 254, 472
    binary implementation, 259
    decimal, 259
    hardware implementation, 302
    subnormal handling, 258, 305
    FORTRAN, 223
    FPGA, see field-programmable gate array FPGA specific operators, 309
    fraction, 16, 56
    full adder, 275
    fused multiply-add, see FMA
    gamma function, 409 7 notation, 184
    Gappa, 474
    Gay conversion algorithms, 44, 46
    Goldschmidt iteration, 160
    GPGPU (general-purpose graphics pro- cessing units), 108
    GPU (graphical processing unit), 108,271
    graceful underflow, 17
    gradual underflow, 17, 53

    Grow-Expansion algorithm, 505
    Haar condition, 392
    hardness to round, 409
    Harrison, 119
    Heron iteration, 167
    hidden bit convention, 16
    Higham, 190
    HOL Light, 472
    Horner algorithm, 185, 394, 473
    running error bound, 189
    IeeeCC754,116
    IEEE 754-1985 standard, 5, 55, 56
    IEEE 754-2008 standard, 79
    IEEE 854-1987 standard, 6, 70
    ILP (instruction-level parallelism), 328
    implicit bit convention, 16, 29, 30
    inclusion property, 51
    inexact exception, 25, 69, 102, 103, 245, 265, 267
    infinitary, 25
    infinitely precise significand, 15, 21, 407, 422, 423
    insertion summation, 191
    integer multiplication, 281
    integer powers, 177
    integral significand, 14, 16, 83, 86, 422, 423
    interchange formats, 80
    interval arithmetic, 51, 475
    INTLAB, 510
    invalid operation exception, 20, 25, 67, 69, 82,100
    is normal bit, 245, 295, 301, 303, 322
    IteratedProductPower, 178
    iterated products, 37
    Java, 227
    A-fold summation algorithm, 196
    Kahan, 5, 8,17, 32,126,405
    Karatsuba's complex multiplication, 144
    Knuth, 129
    Kulisch, 316
    L2 polynomial approximations, 376
    L°° polynomial approximations, 376
    Lang, 263
    language, 205
    large accumulator, 314
    largest finite number, 16,17, 67,102
    latency, 273
    leading bit convention, 16
    leading-zero anticipation, 286, 291, 295, 303
    leading-zero counter, 284, 289-291, 293, 319
    by monotonic string conversion, 285
    combined with shifter, 286
    tree-based, 285
    least squares polynomial approxima- tions, 376
    left-associativity, 207
    LIA-2, 25
    Lindemann's theorem, 429
    Liouville's theorem, 424
    little-endian, 61
    LLL algorithm, 442, 446, 524
    logarithmic distribution, 29
    logB, 98,101
    look-up table, 279, 287, 311
    LOP (leading one predictor), see leading zero anticipation LSB (least significant bit), 290
    LUT, see look-up table LZA, see leading zero anticipation LZC, see leading zero counter MACHAR, 111
    machine epsilon, 39
    Malcolm, 119
    mantissa, 14
    Markstein, 169
    Mars Climate Orbiter, 8
    <math.h>, 210
    Matula, 40,41
    minimal polynomial, 421
    minimax polynomial approximations, 376
    minimax rational approximations, 376
    modified Booth recoding, 281
    Moller, 129
    monotonic conversion, 64
    MPCHECK, 116
    MRRE (maximum relative representa- tion error), 29
    MSB (most significant bit), 285
    multipartite table method, 287
    multiplication, 251

    of binary floating-point in hardware, 296
    by a constant, 311
    by a floating-point constant, 312
    by an arbitrary precision constant, 171, 312
    digit by integer, 280
    in decimal, 283
    of integers, 281
    subnormal handling, 252, 301
    multiplicative range reduction, 378
    NaN (Not a Number), 20, 25, 58, 65, 67, 69, 70, 74, 82, 85, 98, 100, 212, 221, 230, 464
    Nesterenko, 431
    Newton-Raphson iteration, 155, 160, 167, 264, 513
    nonadjacent expansion, 504
    noncanonical encodings, 84
    nonoverlapping expansions, 504
    'P-nonoverlapping, 504 5-nonoverlapping, 504
    nonoverlapping floating-point numbers, 504
    P-nonoverlapping, 504 5-nonoverlapping, 504
    normalized representation, 15
    normal number, 15,16
    normal range, 23
    norm (computation of), 26, 310
    Q (largest finite FP number), 16
    orthogonal polynomials, 389
    Oughtred, 4
    output radix conversion, 43
    overflow, 25, 67,101
    in addition, 248
    parallel adders, 277
    Paranoia, 112,122
    partial carry save, 277
    payload, 98,100
    Payne and Hanek reduction algorithm, 381, 382
    pipeline, 273
    pole, 25
    pow function, 216
    precision, 13
    preferred exponent, 83,240,249,253,259, 265, 267
    preferred width attributes, 93, 95
    prefix tree adders, 278
    Priest, 503
    programming language, 205
    PVS, 472
    quad-word addition, 502
    quad-word renormalization, 500
    quadratic convergence, 156
    quantum, 14,16, 33
    quantum exponent, 14
    quick step, 395
    quiet NaN, 58, 67, 69, 70, 82, 98,100,101, 212, 221
    radix, 13
    radix conversion, 40,43, 246
    range reduction, 151, 378, 379
    RD (round down), see round toward -oo read-only memory, 287
    reconfigurable circuits, see field- programmable gate array RecursiveDotProduct algorithm, 185
    RecursiveSum algorithm, 184
    relative backward error, 186
    relative error, 23, 37
    remainder, 63
    Remez algorithm, 376,391
    reproducibility attributes, 93, 97
    RN , see round to nearest ROM, see read-only memory round bit, 21, 243
    round digit, 243
    rounding, 241
    a value with unbounded exponent range, 241
    in decimal with binary encoding, 246
    by injection, 298
    division, 241
    in binary, 243
    in decimal, 243
    square root, 241, 472
    rounding breakpoint, 21,406
    rounding direction attributes, 20, 93,94
    rounding modes, 20
    roundTiesToAway, 95
    roundTiesToEven, 94, 95

    roundTowardNegative, 94
    roundTowardPositive, 94
    roundTowardZero, 94
    round toward -boo, 20, 52
    round toward -oo, 20, 52
    round toward zero, 21
    round to nearest, 21
    round to nearest even, 21, 62
    RU (round up), see round toward +oc Rump, 12
    running error bounds, 181
    RZ, see round toward zero Scale-Expansion algorithm, 507
    scaleB, 98
    SETUN computer, 5
    Shewchuk, 126,129, 503
    shift-and-add algorithms, 375
    shortest vector problem, 525
    signaling NaN, 58,67,69, 70,82,100,212, 217, 221
    signed infinities, 20
    signed zeros, 20
    significand, 3, 4,13,14,16
    significand alignment, 248
    single precision, 16, 56-58, 61, 64, 65, 71, 82
    slide rule, 4
    SLZ algorithm, 443
    smallest normal number, 16,17
    smallest subnormal number, 17,153
    SoftFloat, 116,321
    square root, 265
    SRT division, 263, 308
    SRTEST, 116
    SSE2, see SSE
    SSE (Streaming SIMD Extension), 53, 76, 106
    standard model of floating-point arith- metic, 183
    status flag, 66
    Steele and White conversion algorithm, 41,44
    Sterbenz's lemma, 122
    sticky bit, 21, 243
    strongly nonoverlapping expansion, 505
    subnormal number, 15-17, 58, 122-124, 128,133,135
    subnormal range, 23
    subtraction, 246
    SVP, see shortest vector problem 6 notation, 184
    table-based methods, 287
    Table Maker's Dilemma, 179,405-407
    tabulated differences, 432
    TestFloat, 116
    three-distance theorem, 437,438
    tie-breaking rule, 21
    Torres y Quevedo, Leonardo, 4
    trailing significand, 16, 56, 59, 60, 81, 82, 84, 85
    transcendental function, 421
    transcendental number, 421,429
    trap, 19, 66-69, 74
    trap handler, 66, 68, 69, 74
    Tuckerman test, 169
    two-length configurations, 438
    TwoMul, 135, 318
    TwoMultFMA, 152
    TwoSum, 129, 318
    UCBTest, 116
    ulp (unit in the last place), 14, 32, 37, 43, 169, 382
    Goldberg definition, 33
    Harrison definition, 32
    underflow, 18, 25, 68,102
    in addition, 248
    unit roundoff, 25, 39,183
    unordered, 65
    unsigned infinity, 20
    value-changing optimization attributes, 93, 96
    Veltkamp splitting, 132,133
    VLIW, 328
    VLSI (very large-scale integration), 270, 271, 287
    Waldschmidt, 431
    weight function, 376
    Weil height, 430
    worst cases for the TMD, 409
    write-read cycle, 41
    YBC 7289, 4

    Z3 computer, 4, 20 Ziv, 407
    zero Zuse, 4, 20
    in the binary interchange formats, 82
    in the decimal interchange formats, 85