Function note

BESSELI is ITK's published polynomial and recurrence, on the x87 unit

FUNC.BESSELI

FN-BESSELI-001: BESSELI is ITK's published polynomial and recurrence, on the x87 unit

Detail for matching Excel's bits · measured · recorded 2026-11-04

BESSELI truncates n to an integer and evaluates the body published in ITK with every operation stored from the x87 unit at precision 64: the I0 and I1 polynomials, and for higher orders Miller backward recurrence from j = 2*(n + int(sqrt(40*n))), rescaling by 1E-10 whenever |q| > 1E10, then normalising by I0(x). The same body in plain binary64 misses by 1 to 4 units in the last place. The published ITK body is itkGaussianOperator.hxx at ITK 311b7060ef39e371f3cd209ec135284ff5fde735 (Apache-2.0).

Call and input routeInputsExcelCorrect valueRecorded in
BESSELI(12.514410892637624, 3.987394155038235)
cell-value2		x: 12.514410892637624
0x40290760dd512b66
n: 3.987394155038235
0x400fe62ee82134c8		21360.000787344507
0x40d4dc000ce65cba		21360.00150112302
0x40d4dc0018982a92		Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture
BESSELI(1.8661547234119729, 7.047660373731416)
cell-value2		x: 1.8661547234119729
0x3ffddbc50e25491c
n: 7.047660373731416
0x401c30cde189f75e		0.0001361367103021099
0x3f21d7fd6fe380e0		0.00013613670961869657
0x3f21d7fd6e62c6a2		Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture
BESSELI(13.469754413420809, 10.617422640816173)
cell-value2		x: 13.469754413420809
0x402af083a685968c
n: 10.617422640816173
0x40253c1ed2043b18		1957.477427686333
0x409e95e8e2cdac05		1957.477488938039
0x409e95e8f2dc3451		Excel 16.0 build 20430, Windows 64-bit, CPU not recorded in this capture

Correct value: mpmath besseli at 800 bits, order the integer part of n, correctly rounded.

Correct value: mpmath besseli at 800 bits, order the integer part of n, correctly rounded.

Correct value: mpmath besseli at 800 bits, order the integer part of n, correctly rounded.

Basis: All 1,318 recorded BESSELI recorded rows match (825 gained, no row lost in the recorded rows).

Evidence and capture sources

Machine-readable note records