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gnasher729
gnasher729
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For ieee754 floating point numbers (the most common) we have abs(f(r) - r) <= c with a rather small c as long as r is in the range of normalised numbers. For tiny numbers (denormalised) it behaves like fixed point.

You get better bounds if you assume that $2^k <= x < 2 \cdot 2^k$ with an error <= $c \ cdot 2^k$$c \cdot 2^k$, especially if x is slightly smaller than some power of two - you can often improve the precision of an algorithm if you can arrange things so intermediate results are slightly smaller than powers of two.

For ieee754 floating point numbers (the most common) we have abs(f(r) - r) <= c with a rather small c as long as r is in the range of normalised numbers. For tiny numbers (denormalised) it behaves like fixed point.

You get better bounds if you assume that $2^k <= x < 2 \cdot 2^k$ with an error <= $c \ cdot 2^k$, especially if x is slightly smaller than some power of two - you can often improve the precision of an algorithm if you can arrange things so intermediate results are slightly smaller than powers of two.

For ieee754 floating point numbers (the most common) we have abs(f(r) - r) <= c with a rather small c as long as r is in the range of normalised numbers. For tiny numbers (denormalised) it behaves like fixed point.

You get better bounds if you assume that $2^k <= x < 2 \cdot 2^k$ with an error <= $c \cdot 2^k$, especially if x is slightly smaller than some power of two - you can often improve the precision of an algorithm if you can arrange things so intermediate results are slightly smaller than powers of two.

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gnasher729
gnasher729
  • 31.6k
  • 35
  • 55

For ieee754 floating point numbers (the most common) we have abs(f(r) - r) <= c with a rather small c as long as r is in the range of normalised numbers. For tiny numbers (denormalised) it behaves like fixed point.

You get better bounds if you assume that $2^k <= x < 2 \cdot 2^k$ with an error <= $c \ cdot 2^k$, especially if x is slightly smaller than some power of two - you can often improve the precision of an algorithm if you can arrange things so intermediate results are slightly smaller than powers of two.