Template:Order of magnitude/doc

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This is a documentation subpage for Template:Order of magnitude.
It contains usage information, categories and other content or metadata that is not part of the original template.

Usage

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

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