为大量浮点数生成快速校验和，而不使用任何库？

Question

在 C 语言中（更具体地说，C for CUDA），计算大量浮点数（比如两万个值）的校验和的最佳方法是什么，这很容易用 printf 打印，而不使用任何库？

我可以将所有浮动精度的值相加，但恐怕舍入误差或饱和度或 nan/inf 值会使某些更改无法检测到。

它用于比较同一 GPU 硬件上相同二进制文件运行之间的变量值，并且仅用于调试，而不是用于安全性。

更清楚地说，当数组中的任何浮点值发生变化时，如果校验和的所有数字都发生变化（很有可能），那就太好了，这样校验和就很容易在视觉上进行比较。

Answer 1

这正是循环冗余检查的用途。 Boost有一个CRC库，并且有几十个网络上的源代码实现。 16 位 CRC 可能最适合您，因为观察结果很容易。但如果您担心误报，您可能需要 32 位 CRC。

Answer 2

如果您使用 IEEE-754 浮点数，则可以将浮点数转换为指针，然后将该指针重新解释为无符号 int 指针，并以这种方式求和，以避免任何浮点舍入问题。此时，您基本上是在代表浮点数的实际位而不是浮点值本身上创建校验和。

例如：

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);
}

编辑：正如评论中提到的，这无论如何都不会创建安全校验和......这是一种非常简单的校验和形式，但希望它适用于您的调试目的。

Answer 3

也许这对于 stackoverflow 响应来说太大了，但这是我从 pycrc。它包括其他回复中已经提到的一些技术。我最信任 crc 版本，但是当数组应该全为零时，add 和 xor 版本很方便。

    /*  The MIT License
    Copyright (c) <year> <copyright holders>

    Permission is hereby granted, free of charge, to any person obtaining a copy
    of this software and associated documentation files (the "Software"), to deal
    in the Software without restriction, including without limitation the rights
    to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
    copies of the Software, and to permit persons to whom the Software is
    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in
    all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
    AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
    OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
    THE SOFTWARE.  */

/*
 * (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

Answer 4

适当的 CRC 库可能是您最好的选择，但只是为了潜在的兴趣：您可以使用每个字节（即 *(uint8_t*)& 重新解释）来索引到一个包含 32 位随机数的表中，然后将这些表条目异或在一起。这意味着值中的单个位变化会随机翻转输出中的位。如果不希望拥有与字节数一样多的查找表，则可以通过对已使用的表中的位进行循环移位来获得合理的结果。从概念上讲，它比数学哈希算法简单得多......

Answer 5

编辑：
我相信最好的答案是 TonyK 和 Jason 答案的结合。将 float* 转换为 uint32_t* 后，在缓冲区上使用 32 位 CRC。如果您的编译器提供了 uint32 定义，请获取它，或者根据您的平台自行键入定义（通常在 32 位计算机上为 unsigned long，在 64 位计算机上为 unsigned int。）这是一个 良好的 CRC 解释和实现

Answer 6

如果要在 GPU 上计算校验和，请使用 __int_as_float() 和 __float_as_int() 内在函数将浮点数视为整数。 CUDA 4.0 中包含的 Thrust 库使计算此校验和变得容易 - 这是 minmax Thrust 示例，已移植以执行您正在寻找的操作。

#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;
}