THIS IS PROBABLY WRONG, do NOT use!
With floating point comparing for equality is frought with problems and typically it can only be done approximately. For instance summing a series of calculated numbers will likely not produce the exactly expected results. For instance summing 0.1 10 times should result in a value of 1.0 but it doesn't the value with an f32 is r=1.00000011e+00:
pub fn sum(comptime T: type, start: T, end: T, count: usize) T { var step = (end - start)/@intToFloat(T, count); var r: T = start; var j: usize = 0; while (j < count) : (j += 1) { r += step; } return r; } pub fn testSum() void { var r = sum(f32, 0, 1, 10); warn("r={}\n", r); assert(r != f32(1.0)); } Therefore a notion of approximately equals is needed. Here is a Google search and here was the first hit and seems to have good information.
I took what I've learned so I came up with my own approxEql in zig that uses significant digits to calcuate an allowable max difference that can is then used do determine equality. It "seems" to be working and the code is in approxeql.zig, but I'm have ZERO EXPERTICE so this is probably wrong!!!
Test 1/23 approxEql.nan.inf...OK Test 2/23 approxEql.same...OK Test 3/23 approxEql.0.fepsilon*1...OK Test 4/23 approxEql.0.fepsilon*4...OK Test 5/23 approxEql.0.fepsilon*5...OK Test 6/23 approxEql.0.fepsilon*45...OK Test 7/23 approxEql.0.fepsilon*46...OK Test 8/23 approxEql.0.fepsilon*450...OK Test 9/23 approxEql.0.fepsilon*451...OK Test 10/23 approxEql.sum.near0.f64...OK Test 11/23 approxEql.sum.near0.f32...OK Test 12/23 approxEql.sum.large.f64...OK Test 13/23 approxEql.sum.large.f32...OK Test 14/23 approxEql.sub.near0.f64...OK Test 15/23 approxEql.sub.near0.f32...OK Test 16/23 approxEql.atan32...OK Test 17/23 approxEql.123e12.3.digits...OK Test 18/23 approxEql.123e12.4.digits...OK Test 19/23 approxEql.993e12.3.digits...OK Test 20/23 approxEql.993e12.4.digits...OK Test 21/23 fepsilon.f64...OK Test 22/23 fepsilon.f32...OK Test 23/23 fepsilon.f16...OK All tests passed. $ zig test approxeql.zig Test 1/23 approxEql.nan.inf... approxEql: x=nan y=nan digits=17 both nan result=true approxEql: x=-nan y=-nan digits=17 both nan result=true approxEql: x=inf y=inf digits=17 x == y result=true approxEql: x=-inf y=-inf digits=17 x == y result=true approxEql: x=nan y=0.0e+00 digits=17 abs_diff=nan nan or inf result=false approxEql: x=inf y=0.0e+00 digits=17 abs_diff=inf nan or inf result=false approxEql: x=1.0e+00 y=nan digits=17 abs_diff=nan nan or inf result=false approxEql: x=2.0e+00 y=inf digits=17 abs_diff=inf nan or inf result=false approxEql: x=nan y=nan digits=17 both nan result=true approxEql: x=-nan y=-nan digits=17 both nan result=true approxEql: x=inf y=inf digits=17 x == y result=true approxEql: x=-inf y=-inf digits=17 x == y result=true approxEql: x=nan y=0.0e+00 digits=17 abs_diff=nan nan or inf result=false approxEql: x=inf y=0.0e+00 digits=17 abs_diff=inf nan or inf result=false approxEql: x=1.0e+00 y=nan digits=17 abs_diff=nan nan or inf result=false approxEql: x=2.0e+00 y=inf digits=17 abs_diff=inf nan or inf result=false OK Test 2/23 approxEql.same... approxEql: x=0.0e+00 y=0.0e+00 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=0.0e+00 digits=1 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=2 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=3 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=4 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=5 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=6 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=7 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=8 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=9 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=10 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=11 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=12 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=13 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=14 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=15 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=16 x == y result=true approxEql: x=0.0e+00 y=0.0e+00 digits=17 x == y result=true approxEql: x=1.23e-121 y=1.23e-121 digits=17 x == y result=true approxEql: x=-1.23e-121 y=-1.23e-121 digits=17 x == y result=true approxEql: x=-1.23e+125 y=-1.23e+125 digits=17 x == y result=true approxEql: x=1.23e+125 y=1.23e+125 digits=17 x == y result=true OK Test 3/23 approxEql.0.fepsilon*1... approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=1 abs_diff=2.220446049250313e-16 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=2 abs_diff=2.220446049250313e-16 max_diff=1.0e-01 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=3 abs_diff=2.220446049250313e-16 max_diff=1.0e-02 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=4 abs_diff=2.220446049250313e-16 max_diff=1.0e-03 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=5 abs_diff=2.220446049250313e-16 max_diff=1.0e-04 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=6 abs_diff=2.220446049250313e-16 max_diff=1.0e-05 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=7 abs_diff=2.220446049250313e-16 max_diff=1.0e-06 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=8 abs_diff=2.220446049250313e-16 max_diff=1.0e-07 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=9 abs_diff=2.220446049250313e-16 max_diff=1.0e-08 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=10 abs_diff=2.220446049250313e-16 max_diff=1.0e-09 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=11 abs_diff=2.220446049250313e-16 max_diff=1.0e-10 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=12 abs_diff=2.220446049250313e-16 max_diff=1.0e-11 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=13 abs_diff=2.220446049250313e-16 max_diff=1.0e-12 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=14 abs_diff=2.220446049250313e-16 max_diff=1.0e-13 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=15 abs_diff=2.220446049250313e-16 max_diff=1.0e-14 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=16 abs_diff=2.220446049250313e-16 max_diff=1.0e-15 close to 0 result=true approxEql: x=0.0e+00 y=2.220446049250313e-16 digits=17 abs_diff=2.220446049250313e-16 max_diff=1.0e-16 scaled_max_diff=2.220446049250313e-33 scaled_epsilon=4.930380657631324e-32 result=false OK Test 4/23 approxEql.0.fepsilon*4... approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=1 abs_diff=8.881784197001253e-16 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=2 abs_diff=8.881784197001253e-16 max_diff=1.0e-01 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=3 abs_diff=8.881784197001253e-16 max_diff=1.0e-02 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=4 abs_diff=8.881784197001253e-16 max_diff=1.0e-03 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=5 abs_diff=8.881784197001253e-16 max_diff=1.0e-04 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=6 abs_diff=8.881784197001253e-16 max_diff=1.0e-05 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=7 abs_diff=8.881784197001253e-16 max_diff=1.0e-06 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=8 abs_diff=8.881784197001253e-16 max_diff=1.0e-07 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=9 abs_diff=8.881784197001253e-16 max_diff=1.0e-08 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=10 abs_diff=8.881784197001253e-16 max_diff=1.0e-09 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=11 abs_diff=8.881784197001253e-16 max_diff=1.0e-10 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=12 abs_diff=8.881784197001253e-16 max_diff=1.0e-11 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=13 abs_diff=8.881784197001253e-16 max_diff=1.0e-12 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=14 abs_diff=8.881784197001253e-16 max_diff=1.0e-13 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=15 abs_diff=8.881784197001253e-16 max_diff=1.0e-14 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=16 abs_diff=8.881784197001253e-16 max_diff=1.0e-15 close to 0 result=true approxEql: x=0.0e+00 y=8.881784197001253e-16 digits=17 abs_diff=8.881784197001253e-16 max_diff=1.0e-16 scaled_max_diff=8.881784197001252e-33 scaled_epsilon=1.9721522630525296e-31 result=false OK Test 5/23 approxEql.0.fepsilon*5... approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=1 abs_diff=1.1102230246251565e-15 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=2 abs_diff=1.1102230246251565e-15 max_diff=1.0e-01 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=3 abs_diff=1.1102230246251565e-15 max_diff=1.0e-02 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=4 abs_diff=1.1102230246251565e-15 max_diff=1.0e-03 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=5 abs_diff=1.1102230246251565e-15 max_diff=1.0e-04 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=6 abs_diff=1.1102230246251565e-15 max_diff=1.0e-05 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=7 abs_diff=1.1102230246251565e-15 max_diff=1.0e-06 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=8 abs_diff=1.1102230246251565e-15 max_diff=1.0e-07 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=9 abs_diff=1.1102230246251565e-15 max_diff=1.0e-08 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=10 abs_diff=1.1102230246251565e-15 max_diff=1.0e-09 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=11 abs_diff=1.1102230246251565e-15 max_diff=1.0e-10 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=12 abs_diff=1.1102230246251565e-15 max_diff=1.0e-11 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=13 abs_diff=1.1102230246251565e-15 max_diff=1.0e-12 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=14 abs_diff=1.1102230246251565e-15 max_diff=1.0e-13 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=15 abs_diff=1.1102230246251565e-15 max_diff=1.0e-14 close to 0 result=true approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=16 abs_diff=1.1102230246251565e-15 max_diff=1.0e-15 scaled_max_diff=1.1102230246251566e-31 scaled_epsilon=2.465190328815662e-31 result=false approxEql: x=0.0e+00 y=1.1102230246251565e-15 digits=17 abs_diff=1.1102230246251565e-15 max_diff=1.0e-16 scaled_max_diff=1.1102230246251567e-32 scaled_epsilon=2.465190328815662e-31 result=false OK Test 6/23 approxEql.0.fepsilon*45... approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=1 abs_diff=9.992007221626409e-15 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=2 abs_diff=9.992007221626409e-15 max_diff=1.0e-01 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=3 abs_diff=9.992007221626409e-15 max_diff=1.0e-02 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=4 abs_diff=9.992007221626409e-15 max_diff=1.0e-03 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=5 abs_diff=9.992007221626409e-15 max_diff=1.0e-04 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=6 abs_diff=9.992007221626409e-15 max_diff=1.0e-05 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=7 abs_diff=9.992007221626409e-15 max_diff=1.0e-06 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=8 abs_diff=9.992007221626409e-15 max_diff=1.0e-07 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=9 abs_diff=9.992007221626409e-15 max_diff=1.0e-08 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=10 abs_diff=9.992007221626409e-15 max_diff=1.0e-09 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=11 abs_diff=9.992007221626409e-15 max_diff=1.0e-10 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=12 abs_diff=9.992007221626409e-15 max_diff=1.0e-11 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=13 abs_diff=9.992007221626409e-15 max_diff=1.0e-12 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=14 abs_diff=9.992007221626409e-15 max_diff=1.0e-13 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=15 abs_diff=9.992007221626409e-15 max_diff=1.0e-14 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=16 abs_diff=9.992007221626409e-15 max_diff=1.0e-15 scaled_max_diff=9.99200722162641e-31 scaled_epsilon=2.2186712959340957e-30 result=false approxEql: x=0.0e+00 y=9.992007221626409e-15 digits=17 abs_diff=9.992007221626409e-15 max_diff=1.0e-16 scaled_max_diff=9.99200722162641e-32 scaled_epsilon=2.2186712959340957e-30 result=false OK Test 7/23 approxEql.0.fepsilon*46... approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=1 abs_diff=1.021405182655144e-14 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=2 abs_diff=1.021405182655144e-14 max_diff=1.0e-01 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=3 abs_diff=1.021405182655144e-14 max_diff=1.0e-02 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=4 abs_diff=1.021405182655144e-14 max_diff=1.0e-03 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=5 abs_diff=1.021405182655144e-14 max_diff=1.0e-04 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=6 abs_diff=1.021405182655144e-14 max_diff=1.0e-05 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=7 abs_diff=1.021405182655144e-14 max_diff=1.0e-06 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=8 abs_diff=1.021405182655144e-14 max_diff=1.0e-07 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=9 abs_diff=1.021405182655144e-14 max_diff=1.0e-08 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=10 abs_diff=1.021405182655144e-14 max_diff=1.0e-09 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=11 abs_diff=1.021405182655144e-14 max_diff=1.0e-10 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=12 abs_diff=1.021405182655144e-14 max_diff=1.0e-11 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=13 abs_diff=1.021405182655144e-14 max_diff=1.0e-12 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=14 abs_diff=1.021405182655144e-14 max_diff=1.0e-13 close to 0 result=true approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=15 abs_diff=1.021405182655144e-14 max_diff=1.0e-14 scaled_max_diff=1.0214051826551439e-29 scaled_epsilon=2.267975102510409e-30 result=false approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=16 abs_diff=1.021405182655144e-14 max_diff=1.0e-15 scaled_max_diff=1.0214051826551441e-30 scaled_epsilon=2.267975102510409e-30 result=false approxEql: x=0.0e+00 y=1.021405182655144e-14 digits=17 abs_diff=1.021405182655144e-14 max_diff=1.0e-16 scaled_max_diff=1.021405182655144e-31 scaled_epsilon=2.267975102510409e-30 result=false OK Test 8/23 approxEql.0.fepsilon*450... approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=1 abs_diff=9.992007221626409e-14 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=2 abs_diff=9.992007221626409e-14 max_diff=1.0e-01 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=3 abs_diff=9.992007221626409e-14 max_diff=1.0e-02 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=4 abs_diff=9.992007221626409e-14 max_diff=1.0e-03 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=5 abs_diff=9.992007221626409e-14 max_diff=1.0e-04 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=6 abs_diff=9.992007221626409e-14 max_diff=1.0e-05 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=7 abs_diff=9.992007221626409e-14 max_diff=1.0e-06 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=8 abs_diff=9.992007221626409e-14 max_diff=1.0e-07 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=9 abs_diff=9.992007221626409e-14 max_diff=1.0e-08 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=10 abs_diff=9.992007221626409e-14 max_diff=1.0e-09 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=11 abs_diff=9.992007221626409e-14 max_diff=1.0e-10 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=12 abs_diff=9.992007221626409e-14 max_diff=1.0e-11 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=13 abs_diff=9.992007221626409e-14 max_diff=1.0e-12 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=14 abs_diff=9.992007221626409e-14 max_diff=1.0e-13 close to 0 result=true approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=15 abs_diff=9.992007221626409e-14 max_diff=1.0e-14 scaled_max_diff=9.992007221626409e-29 scaled_epsilon=2.2186712959340957e-29 result=false approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=16 abs_diff=9.992007221626409e-14 max_diff=1.0e-15 scaled_max_diff=9.99200722162641e-30 scaled_epsilon=2.2186712959340957e-29 result=false approxEql: x=0.0e+00 y=9.992007221626409e-14 digits=17 abs_diff=9.992007221626409e-14 max_diff=1.0e-16 scaled_max_diff=9.992007221626408e-31 scaled_epsilon=2.2186712959340957e-29 result=false OK Test 9/23 approxEql.0.fepsilon*451... approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=1 abs_diff=1.0014211682118912e-13 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=2 abs_diff=1.0014211682118912e-13 max_diff=1.0e-01 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=3 abs_diff=1.0014211682118912e-13 max_diff=1.0e-02 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=4 abs_diff=1.0014211682118912e-13 max_diff=1.0e-03 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=5 abs_diff=1.0014211682118912e-13 max_diff=1.0e-04 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=6 abs_diff=1.0014211682118912e-13 max_diff=1.0e-05 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=7 abs_diff=1.0014211682118912e-13 max_diff=1.0e-06 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=8 abs_diff=1.0014211682118912e-13 max_diff=1.0e-07 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=9 abs_diff=1.0014211682118912e-13 max_diff=1.0e-08 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=10 abs_diff=1.0014211682118912e-13 max_diff=1.0e-09 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=11 abs_diff=1.0014211682118912e-13 max_diff=1.0e-10 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=12 abs_diff=1.0014211682118912e-13 max_diff=1.0e-11 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=13 abs_diff=1.0014211682118912e-13 max_diff=1.0e-12 close to 0 result=true approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=14 abs_diff=1.0014211682118912e-13 max_diff=1.0e-13 scaled_max_diff=1.0014211682118914e-27 scaled_epsilon=2.223601676591727e-29 result=false approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=15 abs_diff=1.0014211682118912e-13 max_diff=1.0e-14 scaled_max_diff=1.0014211682118912e-28 scaled_epsilon=2.223601676591727e-29 result=false approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=16 abs_diff=1.0014211682118912e-13 max_diff=1.0e-15 scaled_max_diff=1.0014211682118913e-29 scaled_epsilon=2.223601676591727e-29 result=false approxEql: x=0.0e+00 y=1.0014211682118912e-13 digits=17 abs_diff=1.0014211682118912e-13 max_diff=1.0e-16 scaled_max_diff=1.0014211682118911e-30 scaled_epsilon=2.223601676591727e-29 result=false OK Test 10/23 approxEql.sum.near0.f64... x=1.0e+00 end=9.999999999999062e-01 approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=0 digits == 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=1 abs_diff=9.381384558082573e-14 max_diff=1.0e+00 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=2 abs_diff=9.381384558082573e-14 max_diff=1.0e-01 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=3 abs_diff=9.381384558082573e-14 max_diff=1.0e-02 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=4 abs_diff=9.381384558082573e-14 max_diff=1.0e-03 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=5 abs_diff=9.381384558082573e-14 max_diff=1.0e-04 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=6 abs_diff=9.381384558082573e-14 max_diff=1.0e-05 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=7 abs_diff=9.381384558082573e-14 max_diff=1.0e-06 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=8 abs_diff=9.381384558082573e-14 max_diff=1.0e-07 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=9 abs_diff=9.381384558082573e-14 max_diff=1.0e-08 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=10 abs_diff=9.381384558082573e-14 max_diff=1.0e-09 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=11 abs_diff=9.381384558082573e-14 max_diff=1.0e-10 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=12 abs_diff=9.381384558082573e-14 max_diff=1.0e-11 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=13 abs_diff=9.381384558082573e-14 max_diff=1.0e-12 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=14 abs_diff=9.381384558082573e-14 max_diff=1.0e-13 close to 0 result=true approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=15 abs_diff=9.381384558082573e-14 max_diff=1.0e-14 scaled_max_diff=1.0e-15 scaled_epsilon=2.220446049250313e-16 result=false approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=16 abs_diff=9.381384558082573e-14 max_diff=1.0e-15 scaled_max_diff=1.0000000000000001e-16 scaled_epsilon=2.220446049250313e-16 result=false approxEql: x=1.0e+00 y=9.999999999999062e-01 digits=17 abs_diff=9.381384558082573e-14 max_diff=1.0e-16 scaled_max_diff=9.999999999999999e-18 scaled_epsilon=2.220446049250313e-16 result=false OK Test 11/23 approxEql.sum.near0.f32... x=1.0e+00 end=9.99990701e-01 approxEql: x=1.0e+00 y=9.99990701e-01 digits=0 digits == 0 result=true approxEql: x=1.0e+00 y=9.99990701e-01 digits=1 abs_diff=9.29832458e-06 max_diff=1.0e+00 close to 0 result=true approxEql: x=1.0e+00 y=9.99990701e-01 digits=2 abs_diff=9.29832458e-06 max_diff=1.00000001e-01 close to 0 result=true approxEql: x=1.0e+00 y=9.99990701e-01 digits=3 abs_diff=9.29832458e-06 max_diff=9.99999977e-03 close to 0 result=true approxEql: x=1.0e+00 y=9.99990701e-01 digits=4 abs_diff=9.29832458e-06 max_diff=1.00000004e-03 close to 0 result=true approxEql: x=1.0e+00 y=9.99990701e-01 digits=5 abs_diff=9.29832458e-06 max_diff=9.99999974e-05 close to 0 result=true approxEql: x=1.0e+00 y=9.99990701e-01 digits=6 abs_diff=9.29832458e-06 max_diff=9.99999974e-06 close to 0 result=true approxEql: x=1.0e+00 y=9.99990701e-01 digits=7 abs_diff=9.29832458e-06 max_diff=9.99999997e-07 scaled_max_diff=1.00000001e-07 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=8 abs_diff=9.29832458e-06 max_diff=1.00000001e-07 scaled_max_diff=9.99999993e-09 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=9 abs_diff=9.29832458e-06 max_diff=9.99999993e-09 scaled_max_diff=9.99999971e-10 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=10 abs_diff=9.29832458e-06 max_diff=9.99999971e-10 scaled_max_diff=9.99999943e-11 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=11 abs_diff=9.29832458e-06 max_diff=1.00000001e-10 scaled_max_diff=9.99999996e-12 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=12 abs_diff=9.29832458e-06 max_diff=9.99999996e-12 scaled_max_diff=9.99999996e-13 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=13 abs_diff=9.29832458e-06 max_diff=9.99999996e-13 scaled_max_diff=9.99999982e-14 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=14 abs_diff=9.29832458e-06 max_diff=1.00000005e-13 scaled_max_diff=1.00000006e-14 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=15 abs_diff=9.29832458e-06 max_diff=9.99999982e-15 scaled_max_diff=1.00000000e-15 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=16 abs_diff=9.29832458e-06 max_diff=1.00000000e-15 scaled_max_diff=1.00000001e-16 scaled_epsilon=1.19209289e-07 result=false approxEql: x=1.0e+00 y=9.99990701e-01 digits=17 abs_diff=9.29832458e-06 max_diff=9.99999950e-17 scaled_max_diff=9.99999983e-18 scaled_epsilon=1.19209289e-07 result=false OK Test 12/23 approxEql.sum.large.f64... x=8.988465674311579e+307 end=8.988465674311085e+307 approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=0 digits == 0 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=1 abs_diff=4.9397047660984315e+294 max_diff=1.0e+00 scaled_max_diff=8.988465674311579e+306 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=2 abs_diff=4.9397047660984315e+294 max_diff=1.0e-01 scaled_max_diff=8.988465674311578e+305 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=3 abs_diff=4.9397047660984315e+294 max_diff=1.0e-02 scaled_max_diff=8.988465674311578e+304 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=4 abs_diff=4.9397047660984315e+294 max_diff=1.0e-03 scaled_max_diff=8.988465674311578e+303 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=5 abs_diff=4.9397047660984315e+294 max_diff=1.0e-04 scaled_max_diff=8.988465674311579e+302 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=6 abs_diff=4.9397047660984315e+294 max_diff=1.0e-05 scaled_max_diff=8.98846567431158e+301 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=7 abs_diff=4.9397047660984315e+294 max_diff=1.0e-06 scaled_max_diff=8.988465674311577e+300 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=8 abs_diff=4.9397047660984315e+294 max_diff=1.0e-07 scaled_max_diff=8.988465674311578e+299 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=9 abs_diff=4.9397047660984315e+294 max_diff=1.0e-08 scaled_max_diff=8.988465674311578e+298 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=10 abs_diff=4.9397047660984315e+294 max_diff=1.0e-09 scaled_max_diff=8.988465674311579e+297 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=11 abs_diff=4.9397047660984315e+294 max_diff=1.0e-10 scaled_max_diff=8.988465674311579e+296 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=12 abs_diff=4.9397047660984315e+294 max_diff=1.0e-11 scaled_max_diff=8.988465674311578e+295 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=13 abs_diff=4.9397047660984315e+294 max_diff=1.0e-12 scaled_max_diff=8.988465674311578e+294 scaled_epsilon=1.9958403095347196e+292 result=true approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=14 abs_diff=4.9397047660984315e+294 max_diff=1.0e-13 scaled_max_diff=8.988465674311578e+293 scaled_epsilon=1.9958403095347196e+292 result=false approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=15 abs_diff=4.9397047660984315e+294 max_diff=1.0e-14 scaled_max_diff=8.988465674311578e+292 scaled_epsilon=1.9958403095347196e+292 result=false approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=16 abs_diff=4.9397047660984315e+294 max_diff=1.0e-15 scaled_max_diff=8.988465674311578e+291 scaled_epsilon=1.9958403095347196e+292 result=false approxEql: x=8.988465674311579e+307 y=8.988465674311085e+307 digits=17 abs_diff=4.9397047660984315e+294 max_diff=1.0e-16 scaled_max_diff=8.988465674311579e+290 scaled_epsilon=1.9958403095347196e+292 result=false OK Test 13/23 approxEql.sum.large.f32... x=1.70141173e+38 end=1.70141102e+38 approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=0 digits == 0 result=true approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=1 abs_diff=7.09884336e+31 max_diff=1.0e+00 scaled_max_diff=1.70141173e+37 scaled_epsilon=2.02824083e+31 result=true approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=2 abs_diff=7.09884336e+31 max_diff=1.00000001e-01 scaled_max_diff=1.70141179e+36 scaled_epsilon=2.02824083e+31 result=true approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=3 abs_diff=7.09884336e+31 max_diff=9.99999977e-03 scaled_max_diff=1.70141171e+35 scaled_epsilon=2.02824083e+31 result=true approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=4 abs_diff=7.09884336e+31 max_diff=1.00000004e-03 scaled_max_diff=1.70141166e+34 scaled_epsilon=2.02824083e+31 result=true approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=5 abs_diff=7.09884336e+31 max_diff=9.99999974e-05 scaled_max_diff=1.70141163e+33 scaled_epsilon=2.02824083e+31 result=true approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=6 abs_diff=7.09884336e+31 max_diff=9.99999974e-06 scaled_max_diff=1.70141163e+32 scaled_epsilon=2.02824083e+31 result=true approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=7 abs_diff=7.09884336e+31 max_diff=9.99999997e-07 scaled_max_diff=1.70141161e+31 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=8 abs_diff=7.09884336e+31 max_diff=1.00000001e-07 scaled_max_diff=1.70141167e+30 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=9 abs_diff=7.09884336e+31 max_diff=9.99999993e-09 scaled_max_diff=1.70141159e+29 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=10 abs_diff=7.09884336e+31 max_diff=9.99999971e-10 scaled_max_diff=1.70141162e+28 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=11 abs_diff=7.09884336e+31 max_diff=1.00000001e-10 scaled_max_diff=1.70141168e+27 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=12 abs_diff=7.09884336e+31 max_diff=9.99999996e-12 scaled_max_diff=1.70141164e+26 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=13 abs_diff=7.09884336e+31 max_diff=9.99999996e-13 scaled_max_diff=1.70141168e+25 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=14 abs_diff=7.09884336e+31 max_diff=1.00000005e-13 scaled_max_diff=1.70141180e+24 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=15 abs_diff=7.09884336e+31 max_diff=9.99999982e-15 scaled_max_diff=1.70141166e+23 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=16 abs_diff=7.09884336e+31 max_diff=1.00000000e-15 scaled_max_diff=1.70141163e+22 scaled_epsilon=2.02824083e+31 result=false approxEql: x=1.70141173e+38 y=1.70141102e+38 digits=17 abs_diff=7.09884336e+31 max_diff=9.99999950e-17 scaled_max_diff=1.70141166e+21 scaled_epsilon=2.02824083e+31 result=false OK Test 14/23 approxEql.sub.near0.f64... x=0.0e+00 end=9.381755897326649e-14 approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=1 abs_diff=9.381755897326649e-14 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=2 abs_diff=9.381755897326649e-14 max_diff=1.0e-01 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=3 abs_diff=9.381755897326649e-14 max_diff=1.0e-02 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=4 abs_diff=9.381755897326649e-14 max_diff=1.0e-03 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=5 abs_diff=9.381755897326649e-14 max_diff=1.0e-04 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=6 abs_diff=9.381755897326649e-14 max_diff=1.0e-05 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=7 abs_diff=9.381755897326649e-14 max_diff=1.0e-06 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=8 abs_diff=9.381755897326649e-14 max_diff=1.0e-07 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=9 abs_diff=9.381755897326649e-14 max_diff=1.0e-08 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=10 abs_diff=9.381755897326649e-14 max_diff=1.0e-09 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=11 abs_diff=9.381755897326649e-14 max_diff=1.0e-10 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=12 abs_diff=9.381755897326649e-14 max_diff=1.0e-11 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=13 abs_diff=9.381755897326649e-14 max_diff=1.0e-12 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=14 abs_diff=9.381755897326649e-14 max_diff=1.0e-13 close to 0 result=true approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=15 abs_diff=9.381755897326649e-14 max_diff=1.0e-14 scaled_max_diff=9.38175589732665e-29 scaled_epsilon=2.0831682817249784e-29 result=false approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=16 abs_diff=9.381755897326649e-14 max_diff=1.0e-15 scaled_max_diff=9.38175589732665e-30 scaled_epsilon=2.0831682817249784e-29 result=false approxEql: x=0.0e+00 y=9.381755897326649e-14 digits=17 abs_diff=9.381755897326649e-14 max_diff=1.0e-16 scaled_max_diff=9.38175589732665e-31 scaled_epsilon=2.0831682817249784e-29 result=false OK Test 15/23 approxEql.sub.near0.f32... x=0.0e+00 end=9.32463444e-06 approxEql: x=0.0e+00 y=9.32463444e-06 digits=0 digits == 0 result=true approxEql: x=0.0e+00 y=9.32463444e-06 digits=1 abs_diff=9.32463444e-06 max_diff=1.0e+00 close to 0 result=true approxEql: x=0.0e+00 y=9.32463444e-06 digits=2 abs_diff=9.32463444e-06 max_diff=1.00000001e-01 close to 0 result=true approxEql: x=0.0e+00 y=9.32463444e-06 digits=3 abs_diff=9.32463444e-06 max_diff=9.99999977e-03 close to 0 result=true approxEql: x=0.0e+00 y=9.32463444e-06 digits=4 abs_diff=9.32463444e-06 max_diff=1.00000004e-03 close to 0 result=true approxEql: x=0.0e+00 y=9.32463444e-06 digits=5 abs_diff=9.32463444e-06 max_diff=9.99999974e-05 close to 0 result=true approxEql: x=0.0e+00 y=9.32463444e-06 digits=6 abs_diff=9.32463444e-06 max_diff=9.99999974e-06 close to 0 result=true approxEql: x=0.0e+00 y=9.32463444e-06 digits=7 abs_diff=9.32463444e-06 max_diff=9.99999997e-07 scaled_max_diff=9.32463524e-13 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=8 abs_diff=9.32463444e-06 max_diff=1.00000001e-07 scaled_max_diff=9.32463402e-14 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=9 abs_diff=9.32463444e-06 max_diff=9.99999993e-09 scaled_max_diff=9.32463504e-15 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=10 abs_diff=9.32463444e-06 max_diff=9.99999971e-10 scaled_max_diff=9.32463419e-16 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=11 abs_diff=9.32463444e-06 max_diff=1.00000001e-10 scaled_max_diff=9.32463432e-17 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=12 abs_diff=9.32463444e-06 max_diff=9.99999996e-12 scaled_max_diff=9.32463416e-18 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=13 abs_diff=9.32463444e-06 max_diff=9.99999996e-13 scaled_max_diff=9.32463437e-19 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=14 abs_diff=9.32463444e-06 max_diff=1.00000005e-13 scaled_max_diff=9.32463514e-20 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=15 abs_diff=9.32463444e-06 max_diff=9.99999982e-15 scaled_max_diff=9.32463417e-21 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=16 abs_diff=9.32463444e-06 max_diff=1.00000000e-15 scaled_max_diff=9.32463377e-22 scaled_epsilon=1.11158304e-12 result=false approxEql: x=0.0e+00 y=9.32463444e-06 digits=17 abs_diff=9.32463444e-06 max_diff=9.99999950e-17 scaled_max_diff=9.32463377e-23 scaled_epsilon=1.11158304e-12 result=false OK Test 16/23 approxEql.atan32... atan(f64(0.2))=1.9739555984988078e-01 atan(f32(0.2))=1.97395563e-01 approxEql: x=1.97395563e-01 y=1.97395995e-01 digits=7 abs_diff=4.32133674e-07 max_diff=9.99999997e-07 close to 0 result=true approxEql: x=-1.97395563e-01 y=-1.97395995e-01 digits=7 abs_diff=4.32133674e-07 max_diff=9.99999997e-07 close to 0 result=true approxEql: x=3.30783039e-01 y=3.30783009e-01 digits=7 abs_diff=2.98023223e-08 max_diff=9.99999997e-07 close to 0 result=true approxEql: x=7.28544652e-01 y=7.28545010e-01 digits=7 abs_diff=3.57627868e-07 max_diff=9.99999997e-07 close to 0 result=true approxEql: x=9.82793748e-01 y=9.82793986e-01 digits=7 abs_diff=2.38418579e-07 max_diff=9.99999997e-07 close to 0 result=true OK Test 17/23 approxEql.123e12.3.digits... approxEql: x=1.21999997e+14 y=1.23000003e+14 digits=3 abs_diff=1.00000595e+12 max_diff=9.99999977e-03 scaled_max_diff=1.22999996e+11 scaled_epsilon=1.4662743e+07 result=false approxEql: x=1.23000003e+14 y=1.23000003e+14 digits=3 x == y result=true approxEql: x=1.24000000e+14 y=1.23000003e+14 digits=3 abs_diff=9.99997571e+11 max_diff=9.99999977e-03 scaled_max_diff=1.23999993e+11 scaled_epsilon=1.4781952e+07 result=false OK Test 18/23 approxEql.123e12.4.digits... approxEql: x=1.22900002e+14 y=1.23000003e+14 digits=4 abs_diff=1.00000595e+11 max_diff=1.00000004e-03 scaled_max_diff=1.23000012e+10 scaled_epsilon=1.4662743e+07 result=false approxEql: x=1.23000003e+14 y=1.23000003e+14 digits=4 x == y result=true approxEql: x=1.23100003e+14 y=1.23000003e+14 digits=4 abs_diff=1.00000595e+11 max_diff=1.00000004e-03 scaled_max_diff=1.23100016e+10 scaled_epsilon=1.4674664e+07 result=false OK Test 19/23 approxEql.993e12.3.digits... approxEql: x=9.92000006e+14 y=9.92999995e+14 digits=3 abs_diff=9.99989182e+11 max_diff=9.99999977e-03 scaled_max_diff=9.93000030e+11 scaled_epsilon=1.18374824e+08 result=false approxEql: x=9.92999995e+14 y=9.92999995e+14 digits=3 x == y result=true approxEql: x=9.93999984e+14 y=9.92999995e+14 digits=3 abs_diff=9.99989182e+11 max_diff=9.99999977e-03 scaled_max_diff=9.93999912e+11 scaled_epsilon=1.18494032e+08 result=false OK Test 20/23 approxEql.993e12.4.digits... approxEql: x=9.92900003e+14 y=9.92999995e+14 digits=4 abs_diff=9.99922073e+10 max_diff=1.00000004e-03 scaled_max_diff=9.92999997e+10 scaled_epsilon=1.18374824e+08 result=false approxEql: x=9.92999995e+14 y=9.92999995e+14 digits=4 x == y result=true approxEql: x=9.93099987e+14 y=9.92999995e+14 digits=4 abs_diff=9.99922073e+10 max_diff=1.00000004e-03 scaled_max_diff=9.93100021e+10 scaled_epsilon=1.18386744e+08 result=false OK Test 21/23 fepsilon.f64...OK Test 22/23 fepsilon.f32...OK Test 23/23 fepsilon.f16...OK All tests passed.