feat: add num_bits() function (#570)

## Describe the changes

adding a `num_bits()` function similar to
dcf73a5f96/ff/src/biginteger/mod.rs (L482)

this could be useful for small field optimizations

## Linked Issues

Resolves #

docs/sidebars.js

@@ -191,11 +191,6 @@ module.exports = {
         },
       ]
     },
-    {
-      type: "doc",
-      label: "ZK Containers",
-      id: "ZKContainers",
-    },
     {
       type: "doc",
       label: "Ingonyama Grant program",

examples/c++/msm/README.md

@@ -1,9 +1,5 @@
 # Icicle example: Muli-Scalar Multiplication (MSM)
 
-## Best-Practices
-
-We recommend to run our examples in [ZK-containers](../../ZK-containers.md) to save your time and mental energy.
-
 ## Key-Takeaway
 
 `Icicle` provides CUDA C++ template function `MSM` to accelerate [Multi-Scalar Multiplication](https://github.com/ingonyama-zk/ingopedia/blob/master/src/msm.md).

examples/c++/multiply/README.md

@@ -1,9 +1,5 @@
 # Icicle example: Multiplication
 
-## Best-Practices
-
-We recommend to run our examples in [ZK-containers](../../ZK-containers.md) to save your time and mental energy.
-
 ## Key-Takeaway
 
 `Icicle` accelerates multiplication operation `*` using [Karatsuba algorithm](https://en.wikipedia.org/wiki/Karatsuba_algorithm)

examples/c++/ntt/README.md

@@ -1,9 +1,5 @@
 # Icicle example: Number-Theoretical Transform (NTT)
 
-## Best-Practices
-
-We recommend to run our examples in [ZK-containers](../../ZK-containers.md) to save your time and mental energy.
-
 ## Key-Takeaway
 
 `Icicle` provides CUDA C++ template function NTT for [Number Theoretical Transform](https://github.com/ingonyama-zk/ingopedia/blob/master/src/fft.md), also known as Discrete Fourier Transform.

examples/c++/pedersen-commitment/README.md

@@ -1,9 +1,5 @@
 # ICICLE example: Pedersen Commitment
 
-## Best-Practices
-
-We recommend to run our examples in [ZK-containers](../../ZK-containers.md) to save your time and mental energy.
-
 ## Key-Takeaway
 
 A Pedersen Commitment is a cryptographic primitive to commit to a value or a vector of values while keeping it hidden, yet enabling the committer to reveal the value later. It provides both hiding (the commitment does not reveal any information about the value) and binding properties (once a value is committed, it cannot be changed without detection).

examples/c++/polynomial-api/README.md

@@ -1,9 +1,5 @@
 # ICICLE examples: computations with polynomials
 
-## Best-Practices
-
-We recommend to run our examples in [ZK-containers](../../ZK-containers.md) to save your time and mental energy.
-
 ## Key-Takeaway
 
 Polynomials are crucial for Zero-Knowledge Proofs (ZKPs): they enable efficient representation and verification of computational statements, facilitate privacy-preserving protocols, and support complex mathematical operations essential for constructing and verifying proofs without revealing underlying data. Polynomial API is documented [here](https://dev.ingonyama.com/icicle/polynomials/overview)

examples/c++/poseidon/README.md

@@ -1,9 +1,5 @@
 # Icicle example: build a Merkle tree using Poseidon hash
 
-## Best-Practices
-
-We recommend to run our examples in [ZK-containers](../../ZK-containers.md) to save your time and mental energy.
-
 ## Key-Takeaway
 
 `Icicle` provides CUDA C++ template `poseidon_hash` to accelerate the popular [Poseidon hash function](https://www.poseidon-hash.info/).

examples/rust/msm/README.md

@@ -2,10 +2,6 @@
 
 `ICICLE` provides Rust bindings to CUDA-accelerated C++ implementation of [Multi-Scalar Multiplication](https://github.com/ingonyama-zk/ingopedia/blob/master/src/msm.md).
 
-## Best Practices
-
-In order to save time and setting up prerequisites manually, we recommend running this example in our [ZKContainer](../../ZKContainer.md).
-
 ## Usage
 
 ```rust

examples/rust/ntt/README.md

@@ -4,10 +4,6 @@
 
 `ICICLE` provides Rust bindings to CUDA-accelerated C++ implementation of [Number Theoretic Transform](https://github.com/ingonyama-zk/ingopedia/blob/master/src/fft.md).
 
-## Best Practices
-
-In order to save time and setting up prerequisites manually, we recommend running this example in our [ZKContainer](../../ZKContainer.md).
-
 ## Usage
 
 ```rust

icicle/include/fields/field.cuh

@@ -124,6 +124,19 @@ public:
    */
   static constexpr HOST_DEVICE_INLINE unsigned num_of_reductions() { return CONFIG::num_of_reductions; }
 
+  // count number of bits of the field element without leading zeros.
+  static constexpr HOST_DEVICE_INLINE unsigned num_bits(const Field& x)
+  {
+    size_t size = sizeof(x.limbs_storage.limbs[0]) * 8;
+    unsigned ret = size * TLC;
+    for (unsigned i = TLC; i-- > 0;) {
+      int leading = __clz(x.limbs_storage.limbs[i]);
+      ret -= leading;
+      if (leading != size) { break; }
+    }
+    return ret;
+  }
+
   static constexpr unsigned slack_bits = 32 * TLC - NBITS;
 
   struct Wide {