Reference · Math

math.log1p

math.log1p(num) -> float

What it does

The natural logarithm of one plus the number, as a float, as Python's math.log1p. For a number close to zero the answer is accurate where math.log(1 + x) is not, since the addition there throws away most of the digits. Its inverse is math.expm1. The number must be above -1.

Examples

print(math.log1p(0), math.log1p(1), math.log1p(math.e - 1))print(math.log1p(1e-10), math.log(1 + 1e-10))

0.0 0.6931471805599453 1.00.00000000009999999999500001 0.0000000001000000082690371

Edge cases

• math.log(1 + 1e-20) is 0.0; math.log1p(1e-20) keeps the value.
• Just above -1 the answer is a large negative number, not an error.
• inf gives inf, NaN gives NaN.
• math.expm1 undoes it: math.expm1(math.log1p(x)) is x.

print(math.log(1 + 1e-20), math.log1p(1e-20))print(math.log1p(-1 + 1e-16))print(math.log1p(math.inf), math.log1p(math.nan))print(math.expm1(math.log1p(0.3)))

0.0 0.00000000000000000001-36.7368005696771inf NaN0.3

Errors

-1 or less is a runtime error (a domain error), not an error value: it stops the request, and ?? does not catch it. A value that is not a number is a runtime error too.

print(math.log1p(-1))

line 1: `math.log1p`: math domain error (-1)

print(math.log1p(-2))

line 1: `math.log1p`: math domain error (-2)

Chaining

A growth rate from a small change: math.log1p of the change is the continuous rate behind it.

let change = 0.0003print(change | math.log1p)print([0, 0.1, 1] | map(math.log1p))

0.00029995500899797546[0.0, 0.09531017980432487, 0.6931471805599453]

See also

math.expm1, math.log, math.exp

Edit this page on GitHub · every example's output was made by running it (tools/refcheck.mjs) · questions on Discord or r/quillo