# A slightly question about EvalDivide function

**URL:** <https://openfhe.discourse.group/t/a-slightly-question-about-evaldivide-function/1624>\
**Category:** Library Questions\
**Tags:** questions\
**Created:** [October 7, 2024, 1:47pm UTC](https://openfhe.discourse.group/t/a-slightly-question-about-evaldivide-function/1624 "2024-10-07T13:47:05Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![wowblk8](https://avatars.discourse-cdn.com/v4/letter/w/e79b87/32.png) [@wowblk8](https://openfhe.discourse.group/u/wowblk8)\
**Post date:** [October 7, 2024, 1:47pm UTC](https://openfhe.discourse.group/t/a-slightly-question-about-evaldivide-function/1624/1 "2024-10-07T13:47:05Z")

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The first question I’d like to ask is that in cryptocontext.h I see the EvalMult function described as Evaluate approximate division function 1/x where x \>= 1 on a ciphertext using the Chebyshev approximation. But in MWE I used x= -5 to do the calculation without any error and the result was calculated (but incorrectly). Is this allowed behavior or a bug?

The second question is whether I have set this parameter incorrectly and when I change x to 5 the calculation is still incorrect. I don’t think the upper and lower bounds for MWE are set incorrectly. Is the result error because of the degree issue?

Here is a MWE that reproduces the issue:

```c++
int main() {

    uint32_t multDepth = 5;

 
    uint32_t scaleModSize = 58;

    uint32_t batchSize = 8;

    CCParams<CryptoContextCKKSRNS> parameters;
    parameters.SetMultiplicativeDepth(multDepth);
    parameters.SetScalingModSize(scaleModSize);
    parameters.SetBatchSize(batchSize);

    CryptoContext<DCRTPoly> cc = GenCryptoContext(parameters);

    cc->Enable(PKE);
    cc->Enable(KEYSWITCH);
    cc->Enable(LEVELEDSHE);
    cc->Enable(ADVANCEDSHE);
    std::cout << "CKKS scheme is using ring dimension " << cc->GetRingDimension() << std::endl << std::endl;

    auto keys = cc->KeyGen();

    cc->EvalMultKeyGen(keys.secretKey);

    cc->EvalRotateKeyGen(keys.secretKey, {1, -2});
    
    std::vector<double> x1 = {-5};

    Plaintext ptxt1 = cc->MakeCKKSPackedPlaintext(x1);
    // Plaintext ptxt2 = cc->MakeCKKSPackedPlaintext(x2);

    std::cout << "Input x1: " << ptxt1 << std::endl;
    // std::cout << "Input x2: " << ptxt2 << std::endl;

    auto c1 = cc->Encrypt(keys.publicKey, ptxt1);
    // auto c2 = cc->Encrypt(keys.publicKey, ptxt2);

    
    double lowerBound = -10;
    double upperBound = 10;
    // std::complex<double> invalid_coefficient(std::nan(""), 0.0);
    std::vector<double> coefficients = {1e-10, -1.0e-10};
    auto result = cc->EvalDivide(c1, lowerBound, upperBound, 1);

    Plaintext res;

    std::cout.precision(8);

    std::cout << std::endl << "Results of homomorphic computations: " << std::endl;

    cc->Decrypt(keys.secretKey, result, &res);
    res->SetLength(1);
    std::cout << res << std::endl;
    
    return 0;
}

```

I would really appreciate any insights or explanations regarding this behavior.  
Thank you for your help!

Best regards,  
wowblk

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**Author:** ![narger](https://yyz1.discourse-cdn.com/flex031/user_avatar/openfhe.discourse.group/narger/32/420_2.png) [@narger](https://openfhe.discourse.group/u/narger)\
**Post date:** [October 8, 2024, 9:29am UTC](https://openfhe.discourse.group/t/a-slightly-question-about-evaldivide-function/1624/2 "2024-10-08T09:29:36Z")

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Just my 2 cents here: perhaps it is not the right choice to use [-5,5] as the approximation interval since it contains x=0, where 1/x is not defined.

Plus, the fourth argument of EvalDivide is the polynomial degree, which should be set to a larger value, otherwise you are just creating a line.

I refer you to: [https://openfhe.discourse.group/t/how-to-evaluate-approximate-1-x-function-with-high-precision/](https://openfhe.discourse.group/t/how-to-evaluate-approximate-1-x-function-with-high-precision/)

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**Author:** ![ypolyakov](https://yyz1.discourse-cdn.com/flex031/user_avatar/openfhe.discourse.group/ypolyakov/32/47_2.png) [@ypolyakov](https://openfhe.discourse.group/u/ypolyakov)\
**Post date:** [October 10, 2024, 4:34pm UTC](https://openfhe.discourse.group/t/a-slightly-question-about-evaldivide-function/1624/3 "2024-10-10T16:34:42Z")

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Hi @wowblk8,

`EvalDivide` will only work correctly for x\ge1, as written in the documentation. As @narger noted, there is a discontinuity at 0, which complicates the division for the range you are trying to use. The last argument should be much higher than 1 to achieve reasonable precision (when the right range is used).

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**Author:** ![wowblk8](https://avatars.discourse-cdn.com/v4/letter/w/e79b87/32.png) [@wowblk8](https://openfhe.discourse.group/u/wowblk8)\
**Post date:** [October 13, 2024, 11:08am UTC](https://openfhe.discourse.group/t/a-slightly-question-about-evaldivide-function/1624/5 "2024-10-13T11:08:38Z")

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I see. but I tried some experiments with x \<= 0 and lower/upper bound set to the negative scale. Such as I set x = -5 and lower/upper bound to (-1, -5). Then the calculated result is right. On the other hand, I tried the same number but with a positive one. Like x = 5 and lower/upper bound = (1, 5). they come up with the same result but positive one. So I think there is a gap between EvalDivide. EvalDivide function actually can calculate the negative divide equation. So I think the description is wrong or when in situations evaldivide function can’t guarantee OpenFHE library security. Anyways, I think the EvalDivide function is based on the EvalChebyshevSeries function, it should calculate -1…-∞ except 0. If the developer has any concerns about the negative side of the EvalDivide function. I think it should throw an error when the user setting to a negative one（value and lower/upper bound).

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**Author:** ![andreea.alexandru](https://yyz1.discourse-cdn.com/flex031/user_avatar/openfhe.discourse.group/andreea.alexandru/32/378_2.png) [@andreea.alexandru](https://openfhe.discourse.group/u/andreea.alexandru)\
**Post date:** [October 15, 2024, 1:15pm UTC](https://openfhe.discourse.group/t/a-slightly-question-about-evaldivide-function/1624/6 "2024-10-15T13:15:15Z")

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It is indeed normal for the Chebyshev approximation of division to work on intervals [-5, -1] and [1, 5]. The problem is when the interval contains 0, as division is not supported there. I think Yuriy meant |x| \geq 1, not x \geq 1. In theory, it should be |x| \geq \epsilon, but the smaller the \epsilon, the larger the required degree of the approximation.

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**Author:** ![ypolyakov](https://yyz1.discourse-cdn.com/flex031/user_avatar/openfhe.discourse.group/ypolyakov/32/47_2.png) [@ypolyakov](https://openfhe.discourse.group/u/ypolyakov)\
**Post date:** [October 17, 2024, 1:14am UTC](https://openfhe.discourse.group/t/a-slightly-question-about-evaldivide-function/1624/7 "2024-10-17T01:14:11Z")

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@andreea.alexandru Thank you for correcting. Indeed, I meant |x| \ge 1.