## Bug #1

### GMT_equal_double and GMT_equal_float fail for values close to zero

Status: | Closed | Start date: | 2012-02-23 | |
---|---|---|---|---|

Priority: | Normal | Due date: | ||

Assignee: | Florian | % Done: | 100% | |

Category: | - | |||

Target version: | - | |||

Affected version: | 5.x-dev | Platform: |

**Description**

Consider this pseudocode example:

float someFloat = 67329.2348f; // arbitrarily chosen

float nextFloat = NearbyFloat(someFloat, 1); // exactly one ULP away from 'someFloat'

float diff = nextFloat - someFloat; // = .0078125000; diff is 1,006,632,960 ULPs away from zero!

Btw, FLT_EPSILON is 872,415,232 ULPs away from zero.

**Related issues**

### History

#### #1 Updated by Florian almost 6 years ago

**Status**changed from*New*to*Resolved***% Done**changed from*0*to*100***Affected version**changed from*all*to*5.x-dev*

Here is another typical catastrophic cancellation:

float degree = 360.0; float lessDegree = nearbyFloat(degree, -1); // = 359.9999695 float diff = degree - lessDegree; // = 0.0000305Now here comes the example why this is dangerous.

#define GMT_CONV_LIMIT 1.0e-8 #define GMT_IS_ZERO(x) (fabs (x) < GMT_CONV_LIMIT) // test if lessDegree ~= degree (very common gmt code): GMT_IS_ZERO (degree - lessDegree) // returns false even though lessDegree is only 1 ULP away from degree!This is probably not what we want. Though, I cheated in this example because I used float instead of double, this example shows that such code can lead to unexpected results. In gmt it worked so far because GMT_CONV_LIMIT is very very large in comparison to DBL_EPSILON. GMT_IS_ZERO---if used in such a way---would also fail for large doubles (10 million or so). Here are some new functions that could be used instead:

/* common_math.c */ * int32_abs Like abs but for int32_t * int64_abs Like abs but for int64_t * floatAlmostEqualUlps Compare 2 floats with ULPs (not safe for values near zero) * doubleAlmostEqualUlps Same as floatAlmostEqualUlps for double * floatAlmostEqualUlpsAndAbs Compare 2 floats with an absolute epsilon check (values near zero), then based on ULPs * doubleAlmostEqualUlpsAndAbs Same as floatAlmostEqualUlpsAndAbs for double * floatAlmostEqual Convenience macro for floatAlmostEqualUlps * doubleAlmostEqual Convenience macro for doubleAlmostEqualUlps * floatAlmostEqualZero Convenience macro for floatAlmostEqualUlpsAndAbs * doubleAlmostEqualZero Convenience macro for doubleAlmostEqualUlpsAndAbsThey are mostly inspired by these C++ functions and don't have the overflow bug #2. *AlmostEqualUlpsAndAbs and *AlmostEqualZero also can handle values close to zero, which GMT_equal_double could not. So instead of

`GMT_IS_ZERO(lon-360.0)`

it is safer to use

`doubleAlmostEqual (lon, 360)`

or if both parameters might be zero

`doubleAlmostEqualZero (lon1, lon2)`

This has been fixed in r9839.

#### #2 Updated by Remko almost 6 years ago

**Status**changed from*Resolved*to*Closed*

#### #3 Updated by Florian about 4 years ago

**Target version**deleted ()*Candidate for next minor release*