Template:Order of magnitude

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Tests the precision of (internal) compensation offsets of Log10 rounding errors

(incomplete series, missing more exact estimates for each value between -308 and +308)

  • 1.0E+000: OrderOfMagnitude=0; MagRate=1: Offset Estim=-0.000E-99, Exact=0
  • 1.0E+001: OrderOfMagnitude=1; MagRate=1: Offset Estim=-5.550E-17, Exact=0
    1.0E-001: OrderOfMagnitude=-1; MagRate=1: Offset Estim=-3.330E-16, Exact=-3.3306690738755E-16
  • 1.0E+002: OrderOfMagnitude=2; MagRate=1: Offset Estim=-1.000E-16, Exact=0
    1.0E-002: OrderOfMagnitude=-2; MagRate=1: Offset Estim=-6.661E-16, Exact=-6.6613381477509E-16
  • 1.0E+010: OrderOfMagnitude=10; MagRate=1: Offset Estim=-1.000E-16, Exact=0
    1.0E-010: OrderOfMagnitude=-10; MagRate=1: Offset Estim=-8.000E-16, Exact=0
  • 1.0E+020: OrderOfMagnitude=20; MagRate=1: Offset Estim=-1.000E-16, Exact=0
    1.0E-020: OrderOfMagnitude=-20; MagRate=1: Offset Estim=-1.000E-16, Exact=0
  • 1.0E+050: OrderOfMagnitude=50; MagRate=1: Offset Estim=-1.000E-16, Exact=0
  • 1.0E+075: OrderOfMagnitude=75; MagRate=1: Offset Estim=+7.106E-15, Exact=7.105427357601E-15
  • 1.0E+080: OrderOfMagnitude=80; MagRate=1: Offset Estim=-1.000E-15, Exact=0
  • 1.0E+099: OrderOfMagnitude=99; MagRate=1: Offset Estim=+7.106E-15, Exact=7.105427357601E-15
  • 1.0E+100: OrderOfMagnitude=100; MagRate=1: Offset Estim=-1.000E-15, Exact=0
  • 1.0E+200: OrderOfMagnitude=200; MagRate=1: Offset Estim=-1.000E-15, Exact=0
  • 1.0E+250: OrderOfMagnitude=250; MagRate=1: Offset Estim=+1.422E-14, Exact=1.4210854715202E-14
    1.0E-250: OrderOfMagnitude=-250; MagRate=1: Offset Estim=-4.263E-14, Exact=-4.2632564145606E-14
  • 1.0E+300: OrderOfMagnitude=300; MagRate=1: Offset Estim=+2.843E-14, Exact=2.8421709430404E-14
    1.0E-300: OrderOfMagnitude=-300; MagRate=1: Offset Estim=-8.256E-14, Exact=-8.5265128291212E-14
  • 1.0E+301: OrderOfMagnitude=301; MagRate=1: Offset Estim=+2.843E-14, Exact=2.8421709430404E-14
    1.0E-301: OrderOfMagnitude=-301; MagRate=1: Offset Estim=-8.256E-14, Exact=-8.5265128291212E-14
  • 1.0E+302: OrderOfMagnitude=302; MagRate=1: Offset Estim=+2.843E-14, Exact=2.8421709430404E-14
    1.0E-302: OrderOfMagnitude=-302; MagRate=1: Offset Estim=-8.256E-14, Exact=-8.5265128291212E-14
  • 1.0E+303: OrderOfMagnitude=303; MagRate=1: Offset Estim=+2.843E-14, Exact=2.8421709430404E-14
    1.0E-303: OrderOfMagnitude=-303; MagRate=1: Offset Estim=-8.256E-14, Exact=-8.5265128291212E-14
  • 1.0E+304: OrderOfMagnitude=304; MagRate=1: Offset Estim=+0.000E-14, Exact=0
    1.0E-304: OrderOfMagnitude=-304; MagRate=1: Offset Estim=-0.000E-14, Exact=0
  • 1.0E+305: OrderOfMagnitude=305; MagRate=1: Offset Estim=+0.000E-14, Exact=0
    1.0E-305: OrderOfMagnitude=-305; MagRate=1: Offset Estim=-0.000E-14, Exact=0
  • 1.0E+306: OrderOfMagnitude=306; MagRate=1: Offset Estim=+0.000E-14, Exact=0
    1.0E-306: OrderOfMagnitude=-306; MagRate=1: Offset Estim=-0.000E-14, Exact=0
  • 1.0E+307: OrderOfMagnitude=307; MagRate=1: Offset Estim=+0.000E-14, Exact=0
    1.0E-307: OrderOfMagnitude=-307; MagRate=1: Offset Estim=-0.000E-14, Exact=0
  • 1.0E+308: OrderOfMagnitude=308; MagRate=1: Offset Estim=+0.000E-14, Exact=0
    1.0E-308: OrderOfMagnitude=-308; MagRate=1: Offset Estim=-0.000E-14, Exact=0

Maximum (before infinite)

  • 1.75E+308: OrderOfMagnitude=308; MagRate=1

Check denormals (near zero with reduced precision in mantissa)

  • 1.0E-309: OrderOfMagnitude=-309; MagRate=1
  • 1.0E-310: OrderOfMagnitude=-310; MagRate=1
  • 1.0E-311: OrderOfMagnitude=-311; MagRate=1
  • 1.0E-312: OrderOfMagnitude=-313; MagRate=9.9999999998518 : error (bad estimate of rounding error)
  • 1.0E-313: OrderOfMagnitude=-313; MagRate=1
  • 1.0E-314: OrderOfMagnitude=-315; MagRate=10.000000014822 : error (bad estimate of rounding error)
  • 1.0E-315: OrderOfMagnitude=-316; MagRate=10.00000014822 : error (bad estimate of rounding error)
  • 1.0E-316: OrderOfMagnitude=-317; MagRate=9.9999975296723 : error (bad estimate of rounding error)
  • 1.0E-317: OrderOfMagnitude=-317; MagRate=1
  • 1.0E-318: OrderOfMagnitude=-319; MagRate=10.000098814229 : error (bad estimate of rounding error)
  • 1.0E-319: OrderOfMagnitude=-320; MagRate=10 : error (bad estimate of rounding error)
  • 1.0E-320: OrderOfMagnitude=-321; MagRate=10.019801980198 : error (bad estimate of rounding error)
  • 1.0E-321: OrderOfMagnitude=-322; MagRate=10.1 : error (bad estimate of rounding error)
  • 1.0E-322: OrderOfMagnitude=-323; MagRate=10 : error (bad estimate of rounding error)

Minimum positive denormal (above zero)

  • 1.25000000000001E-323: OrderOfMagnitude=-323; MagRate=1
  • 1.25E-323: OrderOfMagnitude=-324; MagRate=Division by zero.

See also