Generate a quick checksum for a large array of floats, without using any libraries?

In C (more specifically, C for CUDA), what is the best way to compute a checksum of a large array of floats (say twenty thousand values), that is easy to print with printf, without using any libraries?

I could just sum all of the values in floating precision, but I'm afraid roundoff errors or saturation, or nan/inf values, would make some changes un-detectable.

This is being used to compare values of a variable between runs of the same binary on the same gpu hardware, and this is being used for debugging only, not for security.

To be even more clear, it would be nice if all of the digits of the checksum change (with high probabil开发者_如何学编程ity) when any of the floating point values in the array changes, so that checksums are easy to compare visually.

This is exactly what Cyclic Redundancy Checks are for. Boost has a CRC library, and there are dozens of source code implementations on the web. Probably a 16-bit CRC is best for you, because eyeballing the result is easy. But you might want a 32-bit CRC if you are paranoid about false positives.

If you are using IEEE-754 floats, you can cast the floats to a pointer that is then re-interpreted as an unsigned int pointer and sum them that way in order to avoid any floating point round-off issues. You're basically at that point creating a checksum on the actual bits representing the floating point numbers rather than the floating point values themselves.

So for example:

float array[20] = { /* initialized to some values */ };
unsigned int total = 0;

for (int i=0; i < 20; i++)
{
    float* temp_float_ptr = &array[i];
    unsigned int* temp_uint_ptr = (unsigned int*)temp_float_ptr;
    total += (*temp_uint_ptr);
}

Edit: As mentioned in the comments, this does not create a secure checksum by any means ... it's a very simple form of check-summing, but hopefully it would work for your debugging purposes.

Maybe this is too large for a stackoverflow response, but here's the crc.cu file I hacked together from output of pycrc. It includes a couple of techniques already mentioned in other replies. I trust the crc version the most, but the add and xor versions are convenient when arrays should be full of zeros.

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/*
 * (formerly) file crc.h
 * Functions and types for CRC checks.
 *
 * Generated on Sun May 15 16:28:36 2011,
 * by pycrc v0.7.7, http://www.tty1.net/pycrc/
 * using the configuration:
 *    Width        = 32
 *    Poly         = 0x04c11db7
 *    XorIn        = 0xffffffff
 *    ReflectIn    = True
 *    XorOut       = 0xffffffff
 *    ReflectOut   = True
 *    Algorithm    = table-driven
 *
 * , and then hacked by Drew Wagner to work in CUDA.
 * NOTE: Note, most of this code was generated by the MIT license
 * version of the pycrc.  Accordingly, this derivative work is also
 * licensed under the MIT license.  This license applies ONLY to this file!
 *
 *****************************************************************************/
#ifndef __CRC_CU__
#define __CRC_CU__

/**
 * The definition of the used algorithm.
 *****************************************************************************/
#define CRC_ALGO_TABLE_DRIVEN 1


/**
 * The type of the CRC values.
 *
 * This type must be big enough to contain at least 32 bits.
 *****************************************************************************/
typedef uint32_t crc_t;


/**
 * Calculate the initial crc value.
 *
 * \return     The initial crc value.
 *****************************************************************************/
__device__ crc_t crc_init(void)
{
    return 0xffffffff;
}

/**
 * Calculate the final crc value.
 *
 * \param crc  The current crc value.
 * \return     The final crc value.
 *****************************************************************************/
__device__ crc_t crc_finalize(crc_t crc)
{
    return crc ^ 0xffffffff;
}

/**
 * (formally) file crc.c
 * Functions and types for CRC checks.
 *
 * Generated on Sun May 15 16:28:42 2011,
 * by pycrc v0.7.7, http://www.tty1.net/pycrc/
 * using the configuration:
 *    Width        = 32
 *    Poly         = 0x04c11db7
 *    XorIn        = 0xffffffff
 *    ReflectIn    = True
 *    XorOut       = 0xffffffff
 *    ReflectOut   = True
 *    Algorithm    = table-driven
 *****************************************************************************/

/**
 * Static table used for the table_driven implementation.
 *****************************************************************************/
__device__ static const crc_t crc_table[16] = {
    0x00000000, 0x1db71064, 0x3b6e20c8, 0x26d930ac,
    0x76dc4190, 0x6b6b51f4, 0x4db26158, 0x5005713c,
    0xedb88320, 0xf00f9344, 0xd6d6a3e8, 0xcb61b38c,
    0x9b64c2b0, 0x86d3d2d4, 0xa00ae278, 0xbdbdf21c
};

/**
 * Reflect all bits of a \a data word of \a data_len bytes.
 *
 * \param data         The data word to be reflected.
 * \param data_len     The width of \a data expressed in number of bits.
 * \return             The reflected data.
 *****************************************************************************/
__device__ crc_t crc_reflect(crc_t data, size_t data_len)
{
    unsigned int i;
    crc_t ret;

    ret = data & 0x01;
    for (i = 1; i < data_len; i++) {
        data >>= 1;
        ret = (ret << 1) | (data & 0x01);
    }
    return ret;
}

/**
 * Update the crc value with new data.
 *
 * \param crc      The current crc value.
 * \param data     Pointer to a buffer of \a data_len bytes.
 * \param data_len Number of bytes in the \a data buffer.
 * \return         The updated crc value.
 *****************************************************************************/
__device__ crc_t crc_update(crc_t crc, const unsigned char *data, size_t data_len)
{
    unsigned int tbl_idx;

    while (data_len--) {
        tbl_idx = crc ^ (*data >> (0 * 4));
        crc = crc_table[tbl_idx & 0x0f] ^ (crc >> 4);
        tbl_idx = crc ^ (*data >> (1 * 4));
        crc = crc_table[tbl_idx & 0x0f] ^ (crc >> 4);

        data++;
    }
    return crc & 0xffffffff;
}

// Note 1: The xor and add versions below will return 0x00000000 if the vector, or array,
// is all zeros.  This can be convenient, but they will NOT detect if zero values move
// around.  This invariance to changes in order is especially true for the add version.

// Note 2:  Calling these introduces thread synchronization!  Be wary of heisenbugs!

// Note 3: The CRC version is the most principled, but is also slowest, and makes zeros arrays less obvious.

__device__ uint32_t vector_checksum_xor(const float* array, int m, uint32_t prevValue=0x00000000)
{
    __syncthreads();
    if(threadIdx.x==0 && blockIdx.x==0)
    {
        uint32_t sum = prevValue;
        uint32_t * array_ptr = (uint32_t*) array;
        for(int i=0; i<m; i++)
            if(array_ptr[i]!=0x00000000)
                sum ^= array_ptr[i];
        return sum;
    } else { return 0xffffffff;}
    __syncthreads();
}
// Coded for m x n column major arrays with column stride lda
__device__ uint32_t array_checksum_xor(const float* A, int m, int n, int lda, uint32_t prevValue=0x00000000)
{
    uint32_t sum = prevValue;
    __syncthreads();
    if(threadIdx.x==0 && blockIdx.x==0)
    {
        for(int i=0; i<n; i++)
            sum = vector_checksum_xor(&A[i*lda], m, sum);
        return sum;
    } else { return 0xffffffff;}
    __syncthreads();
}
__device__ uint32_t vector_checksum_sum(const float* array, int m, uint32_t prevValue=0x00000000)
{
    __syncthreads();
    if(threadIdx.x==0 && blockIdx.x==0)
    {
        uint32_t sum = prevValue;
        uint32_t * array_ptr = (uint32_t*) array;
        for(int i=0; i<m; i++)
            if(array_ptr[i]!=0x00000000)
                sum += array_ptr[i];
        return sum;
    } else { return 0xffffffff;}
    __syncthreads();
}
// Coded for m x n column major arrays with column stride lda
__device__ uint32_t array_checksum_sum(const float* A, int m, int n, int lda, uint32_t prevValue=0x00000000)
{
    uint32_t sum = prevValue;
    __syncthreads();
    if(threadIdx.x==0 && blockIdx.x==0)
    {
        for(int i=0; i<n; i++)
        {
            sum = vector_checksum_sum(&A[i*lda], m, sum);
        }
        return sum;
    } else { return 0xffffffff;}
    __syncthreads();
}
__device__ uint32_t vector_checksum_crc(const float* array, int m, uint32_t sum=0xffffffff)
{
    __syncthreads();
    if(threadIdx.x==0 && blockIdx.x==0)
    {
        const unsigned char * array_ptr = (const unsigned char*) array;
        sum = crc_update(sum, array_ptr, m*sizeof(float));
        sum = crc_finalize(sum);
        return sum;
    } else { return 0xffffffff;}
    __syncthreads();
}
// Coded for m x n column major arrays with column stride lda
__device__ uint32_t array_checksum_crc(const float* A, int m, int n, int lda, uint32_t sum=0xffffffff)
{
    __syncthreads();
    if(threadIdx.x==0 && blockIdx.x==0)
    {
        for(int i=0; i<n; i++)
        {
            const unsigned char * array_ptr = (const unsigned char*) A;
            sum = crc_update(sum, array_ptr, m*sizeof(float));
        }
        sum = crc_finalize(sum);
        return sum;
    } else { return 0xffffffff;}
    __syncthreads();
}

#endif

A proper CRC library is probably your best bet, but just for potential interest: rather than XORing the bits in your values, you can use each byte (i.e. an *(uint8_t*)& reinterpretation) to index into a table of say 32-bit random numbers, then XOR those table entries together. This means a single bit of variation in a value randomly flips bits in the output. If it's undesirable to have as many lookup tables as there could be bytes, you can get reasonable results doing a circular shift on the bits in an already-used table. It's a lot simpler conceptually than mathematical hashing algos....

EDITED:
I believe the best answer is the combination of TonyK's and Jason's answers. Use a 32 bit CRC on the buffer, after casting the float* to a uint32_t*. Get the uint32 definition from if your compiler supplies it, or typedef it yourself based on your platform (usually unsigned long on 32-bit machines, unsigned int on 64 bit machines.) Here is a good CRC explanation and implementation

If you want to compute the checksum on the GPU, use the __int_as_float() and __float_as_int() intrinsics to treat the floats-as-ints. The Thrust library included with CUDA 4.0 makes computing this checksum easy - here is the minmax Thrust example, ported to do what you are looking for.

#include <thrust/device_vector.h>
#include <thrust/host_vector.h>
#include <thrust/transform_reduce.h>
#include <thrust/functional.h>
#include <thrust/extrema.h>


// sumAsInt contains a float, but implements a binary
// operator that adds them as if they were ints.
template <typename T>
struct sumAsInt
{
    T val;
};

// sumAsInt_unary_op is a functor that initializes a sumAsInt
// with a given value T.
template <typename T>
struct sumAsInt_unary_op : public thrust::unary_function<T,T>
{
    __host__ __device__
        sumAsInt<T> operator()(const T& x) const {
            sumAsInt<T> result;
            result.val = x;
            return result;
        }
};

// sumAsInt_binary_op is a functor that accepts two sumAsInt 
// structs and returns a new sumAsInt that contains the
// sum of the two floats, as if they were integers.
template <typename T>
struct sumAsInt_binary_op : public thrust::binary_function<T,T,T>
{
    __host__ __device__
        sumAsInt<T> operator()(const sumAsInt<T>& x, const sumAsInt<T>& y) const {
            sumAsInt<T> result;
            result.val = __int_as_float(__float_as_int(x.val)+__float_as_int(y.val));
            return result;
        }
};


int main(void)
{
    // initialize host array
    float x[7] = {-1, 2, 7, -3, -4, 5};

    int sum = 0;
    for ( int i = 0; i < sizeof(x)/sizeof(x[0]); i++ ) {
        sum += *((int *) (&x[i]));
    }
    printf( "CPU sum: %d\n", sum );

    // transfer to device
    thrust::device_vector<float> d_x(x, x + 7);

    // setup arguments
    sumAsInt_unary_op<float>  unary_op;
    sumAsInt_binary_op<float> binary_op;
    sumAsInt<float> init = unary_op(0.0f/*d_x[0]*/);  // initialize with first element

    // compute sum-as-int
    sumAsInt<float> result = thrust::transform_reduce(d_x.begin(), d_x.end(), unary_op, init, binary_op);

    printf( "GPU sum: %d\n", *((int *) (&result.val)) );

//    std::cout << result.val << std::endl;

    return 0;
}