声音变调算法PitchShift(模拟汤姆猫) 附完整C++算法实现代码

上周看到一个变调算法，挺有意思的，原本计划尝试用来润色TTS合成效果的。

实测感觉还需要进一步改进，待有空再思考改进方案。

算法细节原文，移步链接:

http://blogs.zynaptiq.com/bernsee/pitch-shifting-using-the-ft/

C++开源的项目，比较老的一个项目了。

源码下载地址:

http://blogs.zynaptiq.com/bernsee/download/

本人对这份算法源码进行简单的优化调整。

稍微提升了一点性能。

修改后的完整代码:

/****************************************************************************
*
* NAME: smbPitchShift.cpp
* VERSION: 1.2
* HOME URL: http://blogs.zynaptiq.com/bernsee
* KNOWN BUGS: none
*
* SYNOPSIS: Routine for doing pitch shifting while maintaining
* duration using the Short Time Fourier Transform.
*
* DESCRIPTION: The routine takes a pitchShift factor value which is between 0.5
* (one octave down) and 2. (one octave up). A value of exactly 1 does not change
* the pitch. numSampsToProcess tells the routine how many samples in indata[0...
* numSampsToProcess-1] should be pitch shifted and moved to outdata[0 ...
* numSampsToProcess-1]. The two buffers can be identical (ie. it can process the
* data in-place). fftFrameSize defines the FFT frame size used for the
* processing. Typical values are 1024, 2048 and 4096. It may be any value <=
* MAX_FRAME_LENGTH but it MUST be a power of 2. osamp is the STFT
* oversampling factor which also determines the overlap between adjacent STFT
* frames. It should at least be 4 for moderate scaling ratios. A value of 32 is
* recommended for best quality. sampleRate takes the sample rate for the signal
* in unit Hz, ie. 44100 for 44.1 kHz audio. The data passed to the routine in
* indata[] should be in the range [-1.0, 1.0), which is also the output range
* for the data, make sure you scale the data accordingly (for 16bit signed integers
* you would have to divide (and multiply) by 32768).
*
* COPYRIGHT 1999-2015 Stephan M. Bernsee <s.bernsee [AT] zynaptiq [DOT] com>
*
*                         The Wide Open License (WOL)
*
* Permission to use, copy, modify, distribute and sell this software and its
* documentation for any purpose is hereby granted without fee, provided that
* the above copyright notice and this license appear in all source copies.
* THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY OF
* ANY KIND. See http://www.dspguru.com/wol.htm for more information.
*
*****************************************************************************/

#if defined(SMBPITCHSHIFT_BUILD_DLL)
#define SMTPITCHSHIFT_API __declspec(dllexport)
#elif defined(SMPPITCHSHIFT_USE_DLL)
#define SMTPITCHSHIFT_API __declspec(dllimport)
#else
#define SMTPITCHSHIFT_API
#endif

SMTPITCHSHIFT_API void smbPitchShift(float pitchShift, long numSampsToProcess, long fftFrameSize, long osamp, float sampleRate, float *indata, float *outdata);
#define MAX_FRAME_LENGTH 8192

#include <string.h>
#include <math.h>
#include <stdio.h>

#define M_PI 3.14159265358979323846f
#define M_1_PI     0.318309886183790671538f
void smbFft(float *fftBuffer, long fftFrameSize, long sign);
float smbAtan2(float x, float y);

// -----------------------------------------------------------------------------------------------------------------

#define FAST_MATH_TABLE_SIZE  512

] = {
    0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f,
    0.07356456f, 0.08579731f, 0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f,
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    0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f,
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    0.35989504f, 0.37131719f, 0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f,
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    0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f,
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    0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f,
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    0.40524131f, 0.39399204f, 0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f,
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    -0.82458930f, -0.81758481f, -0.81045720f, -0.80320753f, -0.79583690f,
    -0.78834643f, -0.78073723f, -0.77301045f, -0.76516727f, -0.75720885f,
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    -0.70710678f, -0.69837625f, -0.68954054f, -0.68060100f, -0.67155895f,
    -0.66241578f, -0.65317284f, -0.64383154f, -0.63439328f, -0.62485949f,
    -0.61523159f, -0.60551104f, -0.59569930f, -0.58579786f, -0.57580819f,
    -0.56573181f, -0.55557023f, -0.54532499f, -0.53499762f, -0.52458968f,
    -0.51410274f, -0.50353838f, -0.49289819f, -0.48218377f, -0.47139674f,
    -0.46053871f, -0.44961133f, -0.43861624f, -0.42755509f, -0.41642956f,
    -0.40524131f, -0.39399204f, -0.38268343f, -0.37131719f, -0.35989504f,
    -0.34841868f, -0.33688985f, -0.32531029f, -0.31368174f, -0.30200595f,
    -0.29028468f, -0.27851969f, -0.26671276f, -0.25486566f, -0.24298018f,
    -0.23105811f, -0.21910124f, -0.20711138f, -0.19509032f, -0.18303989f,
    -0.17096189f, -0.15885814f, -0.14673047f, -0.13458071f, -0.12241068f,
    -0.11022221f, -0.09801714f, -0.08579731f, -0.07356456f, -0.06132074f,
    -0.04906767f, -0.03680722f, -0.02454123f, -0.01227154f, -0.00000000f
};

inline float  fastsin(
    float x)
{
    float sinVal, fract, in;                           /* Temporary variables for input, output */
    unsigned short  index;                                        /* Index variable */
    float a, b;                                        /* Two nearest output values */
    int n;
    float findex;

    /* input x is in radians */
    /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
    in = x * 0.159154943092f;

    /* Calculation of floor value of input */
    n = (int)in;

    /* Make negative values towards -infinity */
    if (x < 0.0f)
    {
        n--;
    }

    /* Map input value to [0 1] */
    in = in - (float)n;

    /* Calculation of index of the table */
    findex = (float)FAST_MATH_TABLE_SIZE * in;
    if (findex >= 512.0f) {
        findex -= 512.0f;
    }

    index = ((unsigned short)findex) & 0x1ff;

    /* fractional value calculation */
    fract = findex - (float)index;

    /* Read two nearest values of input value from the sin table */
    a = sinTable_f32[index];
    b = sinTable_f32[index + ];

    /* Linear interpolation process */
    sinVal = (1.0f - fract)*a + fract*b;

    /* Return the output value */
    return (sinVal);
}

inline float  fastcos(
    float x)
{
    float cosVal, fract, in;                   /* Temporary variables for input, output */
    unsigned short index;                                /* Index variable */
    float a, b;                                /* Two nearest output values */
    int n;
    float findex;

    /* input x is in radians */
    /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi, add 0.25 (pi/2) to read sine table */
    in = x * 0.159154943092f + 0.25f;

    /* Calculation of floor value of input */
    n = (int)in;

    /* Make negative values towards -infinity */
    if (in < 0.0f)
    {
        n--;
    }

    /* Map input value to [0 1] */
    in = in - (float)n;

    /* Calculation of index of the table */
    findex = (float)FAST_MATH_TABLE_SIZE * in;
    index = ((unsigned short)findex) & 0x1ff;

    /* fractional value calculation */
    fract = findex - (float)index;

    /* Read two nearest values of input value from the cos table */
    a = sinTable_f32[index];
    b = sinTable_f32[index + ];

    /* Linear interpolation process */
    cosVal = (1.0f - fract)*a + fract*b;

    /* Return the output value */
    return (cosVal);
}

float fastAtan2(float y, float x) {
    //float coeff_1 = PI/4.0f;
    float coeff_1 = 0.785398163f;
    float coeff_2 = 3.0f * coeff_1;
    float abs_y = abs(y) + 0.00000001f;    // kludge to prevent 0/0 condition;
    float angle;
    if (x >= 0.0f) {
        float r = (x - abs_y) / (x + abs_y);
        angle = coeff_1 - coeff_1 * r;
    }
    else {
        float r = (x + abs_y) / (abs_y - x);
        angle = coeff_2 - coeff_1 * r;
    }
    return y < 0.0f ? -angle : angle;
}

float fastSqrt(float v)
{
    int i;
    float x2, y;
    const float threehalfs = 1.5F;

    x2 = v * 0.5F;
    y = v;
    i = *(int *)&y;
    i = );
    y = *(float *)&i;
    y = y * (threehalfs - (x2 * y * y));
    y = y * (threehalfs - (x2 * y * y));
    y = y * (threehalfs - (x2 * y * y));
    return v*y;
}

void smbPitchShift(float pitchShift, long numSampsToProcess, long fftFrameSize, long osamp, float sampleRate, float *indata, float *outdata)
/*
Routine smbPitchShift(). See top of file for explanation
Purpose: doing pitch shifting while maintaining duration using the Short
Time Fourier Transform.
Author: (c)1999-2015 Stephan M. Bernsee <s.bernsee [AT] zynaptiq [DOT] com>
*/
{

    static float gInFIFO[MAX_FRAME_LENGTH];
    static float gOutFIFO[MAX_FRAME_LENGTH];
     * MAX_FRAME_LENGTH];
     + ];
     + ];
     * MAX_FRAME_LENGTH];
    static float gAnaFreq[MAX_FRAME_LENGTH];
    static float gAnaMagn[MAX_FRAME_LENGTH];
    static float gSynFreq[MAX_FRAME_LENGTH];
    static float gSynMagn[MAX_FRAME_LENGTH];
    static long gRover = false, gInit = false;
    float   phase, tmp, real, imag;

    long i, k, qpd, index;
    float M_2PI = 2.0f*M_PI;
    float W_2PI = M_2PI / fftFrameSize;
    /* set up some handy variables */
    ;
    long stepSize = fftFrameSize / osamp;
    float freqPerBin = sampleRate / (float)fftFrameSize;
    float expct = W_2PI*(float)stepSize;
    float pi_osamp = (M_2PI / osamp);
    float pi_osamp_expct = pi_osamp + expct;
    float pi_osamp_freqPerBin = pi_osamp / freqPerBin;
    float osamp_freqPerBin = osamp* freqPerBin / M_2PI;
    float fft_osamp = 1.0f / (fftFrameSize2*osamp);

    long inFifoLatency = fftFrameSize - stepSize;
    if (gRover == false)
        gRover = inFifoLatency;

    /* initialize our static arrays */
    if (gInit == false) {
        memset(gInFIFO, , MAX_FRAME_LENGTH*sizeof(float));
        memset(gOutFIFO, , MAX_FRAME_LENGTH*sizeof(float));
        memset(gFFTworksp, ,  * MAX_FRAME_LENGTH*sizeof(float));
        memset(gLastPhase, , (MAX_FRAME_LENGTH /  + )*sizeof(float));
        memset(gSumPhase, , (MAX_FRAME_LENGTH /  + )*sizeof(float));
        memset(gOutputAccum, ,  * MAX_FRAME_LENGTH*sizeof(float));
        memset(gAnaFreq, , MAX_FRAME_LENGTH*sizeof(float));
        memset(gAnaMagn, , MAX_FRAME_LENGTH*sizeof(float));
        gInit = true;
    }

    /* main processing loop */
    ; i < numSampsToProcess; i++){

        /* As long as we have not yet collected enough data just read in */
        gInFIFO[gRover] = indata[i];
        outdata[i] = gOutFIFO[gRover - inFifoLatency];
        gRover++;

        /* now we have enough data for processing */
        if (gRover >= fftFrameSize) {
            gRover = inFifoLatency;

            /* do windowing and re,im interleave */
            float * sFFTworksp = gFFTworksp;
            ; k < fftFrameSize; k++) {
                sFFTworksp[] = gInFIFO[k] * (-0.5f*fastcos(W_2PI*k) + 0.5f);
                sFFTworksp[] = 0.0f;
                sFFTworksp += ;
            }
            /* ***************** ANALYSIS ******************* */
            /* do transform */
            smbFft(gFFTworksp, fftFrameSize, -);

            /* this is the analysis step */
            float *pFFTworksp = gFFTworksp;
            ; k <= fftFrameSize2; k++) {
                /* de-interlace FFT buffer */
                real = pFFTworksp[];
                imag = pFFTworksp[];
                /* compute magnitude and phase */
                gAnaMagn[k] = 2.0f*fastSqrt(real*real + imag*imag);
                phase = fastAtan2(imag, real);
                /* compute phase difference */
                /* subtract expected phase difference */
                tmp = (phase - gLastPhase[k]) - (float)k*expct;
                gLastPhase[k] = phase;

                /* map delta phase into +/- Pi interval */
                qpd = tmp * M_1_PI;
                )
                    qpd += qpd & ;
                else
                    qpd -= qpd & ;
                /* get deviation from bin frequency from the +/- Pi interval */
                /* compute the k-th partials' true frequency */
                /* store magnitude and true frequency in analysis arrays */
                gAnaFreq[k] = (k + (tmp - M_PI*qpd)  * osamp_freqPerBin);
                pFFTworksp += ;
            }

            /* ***************** PROCESSING ******************* */
            /* this does the actual pitch shifting */
            memset(gSynMagn, , fftFrameSize*sizeof(float));
            memset(gSynFreq, , fftFrameSize*sizeof(float));
            ; k <= fftFrameSize2; k++) {
                index = k*pitchShift;
                if (index <= fftFrameSize2) {
                    gSynMagn[index] += gAnaMagn[k];
                    gSynFreq[index] = gAnaFreq[k] * pitchShift;
                }
            }

            /* ***************** SYNTHESIS ******************* */
            /* this is the synthesis step */
            float *tFFTworksp = gFFTworksp;
            ; k <= fftFrameSize2; k++) {
                gSumPhase[k] += pi_osamp_freqPerBin * gSynFreq[k] - pi_osamp_expct*k;
                tFFTworksp[] = gSynMagn[k] * fastcos(gSumPhase[k]);
                tFFTworksp[] = gSynMagn[k] * fastsin(gSumPhase[k]);
                tFFTworksp += ;
            }

            /* zero negative frequencies */
            memset(gFFTworksp + (fftFrameSize + ), ,  * fftFrameSize);
            /* do inverse transform */
            smbFft(gFFTworksp, fftFrameSize, );
            /* do windowing and add to output accumulator */
            float *ppFFTworksp = gFFTworksp;
            ; k < fftFrameSize; k++) {
                gOutputAccum[k] += (-fastcos(W_2PI*k) *ppFFTworksp[] * fft_osamp) + ppFFTworksp[] * fft_osamp;
                ppFFTworksp += ;
            }
            memcpy(gOutFIFO, gOutputAccum, stepSize*sizeof(float));
            /* shift accumulator */
            memmove(gOutputAccum, gOutputAccum + stepSize, fftFrameSize*sizeof(float));
            /* move input FIFO */
            memcpy(gInFIFO, gInFIFO + stepSize, sizeof(float)*inFifoLatency);
        }
    }
}

// -----------------------------------------------------------------------------------------------------------------

void smbFft(float *fftBuffer, long fftFrameSize, long sign)
/*
FFT routine, (C)1996 S.M.Bernsee. Sign = -1 is FFT, 1 is iFFT (inverse)
Fills fftBuffer[0...2*fftFrameSize-1] with the Fourier transform of the
time domain data in fftBuffer[0...2*fftFrameSize-1]. The FFT array takes
and returns the cosine and sine parts in an interleaved manner, ie.
fftBuffer[0] = cosPart[0], fftBuffer[1] = sinPart[0], asf. fftFrameSize
must be a power of 2. It expects a complex input signal (see footnote 2),
ie. when working with 'common' audio signals our input signal has to be
passed as {in[0],0.,in[1],0.,in[2],0.,...} asf. In that case, the transform
of the frequencies of interest is in fftBuffer[0...fftFrameSize].
*/
{
    float wr, wi, arg, *p1, *p2, temp;
    float tr, ti, ur, ui, *p1r, *p1i, *p2r, *p2i;
    long i, bitm, j, le, le2, k;

    ; i <  * fftFrameSize - ; i += ) {
        , j = ; bitm <  * fftFrameSize; bitm <<= ) {
            if (i & bitm) j++;
            j <<= ;
        }
        if (i < j) {
            p1 = fftBuffer + i; p2 = fftBuffer + j;
            temp = *p1; *(p1++) = *p2;
            *(p2++) = temp; temp = *p1;
            *p1 = *p2; *p2 = temp;
        }
    }
    long k_size = (long)(log((float)fftFrameSize) / log(2.0f) + 0.5f);
    , le = ; k < k_size; k++) {

        le <<= ;
        le2 = le >> ;
        ur = 1.0f;
        ui = 0.0f;
        arg = M_PI / (le2 >> );
        wr = fastcos(arg);
        wi = sign*fastsin(arg);
        ; j < le2; j += ) {
            p1r = fftBuffer + j; p1i = p1r + ;
            p2r = p1r + le2; p2i = p2r + ;
             * fftFrameSize; i += le) {
                tr = *p2r * ur - *p2i * ui;
                ti = *p2r * ui + *p2i * ur;
                *p2r = *p1r - tr; *p2i = *p1i - ti;
                *p1r += tr; *p1i += ti;
                p1r += le; p1i += le;
                p2r += le; p2i += le;
            }
            tr = ur*wr - ui*wi;
            ui = ur*wi + ui*wr;
            ur = tr;
        }
    }
}

// -----------------------------------------------------------------------------------------------------------------

/*

12/12/02, smb

PLEASE NOTE:

There have been some reports on domain errors when the atan2() function was used
as in the above code. Usually, a domain error should not interrupt the program flow
(maybe except in Debug mode) but rather be handled "silently" and a global variable
should be set according to this error. However, on some occasions people ran into
this kind of scenario, so a replacement atan2() function is provided here.

If you are experiencing domain errors and your program stops, simply replace all
instances of atan2() with calls to the smbAtan2() function below.

*/

float smbAtan2(float x, float y)
{
    float signx;
    if (x > 0.0f) signx = 1.0f;
    else signx = -1.0f;

    if (x == 0.0f) return 0.0f;
    if (y == 0.0f) return signx * M_PI / 2.0f;

    return fastAtan2(x, y);
}

主要优化处理是:

sin改为fastsin

cos改为fastcos

atan2 改为fastAtan2

sqrt改为fastSqrt

还有其他一些逻辑上的调整。

附上完整示例代码:

#define _CRT_SECURE_NO_WARNINGS
#define _CRT_SECURE_NO_DEPRECATE 1
#define _CRT_NONSTDC_NO_DEPRECATE 1
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <time.h>
#include <iostream>
//采用https://github.com/mackron/dr_libs/blob/master/dr_wav.h 解码
#define DR_WAV_IMPLEMENTATION
#include "dr_wav.h"
//采用http://blogs.zynaptiq.com/bernsee/pitch-shifting-using-the-ft/
#include "smbPitchShift.h"

auto const epoch = clock();
static double now()
{
    return  (clock() - epoch);
};

template <typename FN>
static double bench(const FN &fn)
{
    auto took = -now();
    ;
}

//写wav文件
void wavWrite_float(char* filename, float* buffer, int sampleRate, uint32_t totalSampleCount) {

    FILE* fp = fopen(filename, "wb");
    if (fp == NULL) {
        printf("文件打开失败.\n");
        return;
    }
    //修正写入的buffer长度
    totalSampleCount *= sizeof(float);
    ;
    int FORMAT_PCM = DR_WAVE_FORMAT_IEEE_FLOAT;
    ;
    ] = { 'R', 'I', 'F', 'F' };
    uint32_t long_number =  + totalSampleCount;
    fwrite(text, , , fp);
    fwrite(&long_number, , , fp);
    text[] = 'W';
    text[] = 'A';
    text[] = 'V';
    text[] = 'E';
    fwrite(text, , , fp);
    text[] = 'f';
    text[] = 'm';
    text[] = 't';
    text[] = ' ';
    fwrite(text, , , fp);

    long_number = ;
    fwrite(&long_number, , , fp);
    int16_t short_number = FORMAT_PCM;//默认音频格式
    fwrite(&short_number, , , fp);
    short_number = ; // 音频通道数
    fwrite(&short_number, , , fp);
    long_number = sampleRate; // 采样率
    fwrite(&long_number, , , fp);
    long_number = sampleRate * nbyte; // 比特率
    fwrite(&long_number, , , fp);
    short_number = nbyte; // 块对齐
    fwrite(&short_number, , , fp);
    short_number = nbit; // 采样精度
    fwrite(&short_number, , , fp);
    ] = { 'd', 'a', 't', 'a' };
    fwrite(data, , , fp);
    long_number = totalSampleCount;
    fwrite(&long_number, , , fp);
    fwrite(buffer, totalSampleCount, , fp);
    fclose(fp);
}
//读取wav文件
float* wavRead_float(char* filename, uint32_t* sampleRate, uint64_t    *totalSampleCount) {

    unsigned int channels;
    float* buffer = drwav_open_and_read_file_f32(filename, &channels, sampleRate, totalSampleCount);
    if (buffer == NULL) {
        printf("读取wav文件失败.");
    }
    //仅仅处理单通道音频
    )
    {
        drwav_free(buffer);
        buffer = NULL;
        *sampleRate = ;
        *totalSampleCount = ;
    }
    return buffer;
}

//分割路径函数
void splitpath(const char* path, char* drv, char* dir, char* name, char* ext)
{
    const char* end;
    const char* p;
    const char* s;
    ] && path[] == ':') {
        if (drv) {
            *drv++ = *path++;
            *drv++ = *path++;
            *drv = '\0';
        }
    }
    else if (drv)
        *drv = '\0';
    for (end = path; *end && *end != ':';)
        end++;
    for (p = end; p > path && *--p != '\\' && *p != '/';)
        if (*p == '.') {
            end = p;
            break;
        }
    if (ext)
        for (s = end; (*ext = *s++);)
            ext++;
    for (p = end; p > path;)
        if (*--p == '\\' || *p == '/') {
            p++;
            break;
        }
    if (name) {
        for (s = p; s < end;)
            *name++ = *s++;
        *name = '\0';
    }
    if (dir) {
        for (s = path; s < p;)
            *dir++ = *s++;
        *dir = '\0';
    }
}

int main(int argc, char* argv[])
{
    std::cout << "Audio Processing " << std::endl;
    std::cout << "博客:http://tntmonks.cnblogs.com/" << std::endl;
    std::cout << "支持解析单通道wav格式的变调处理." << std::endl;

    ) ;
    ];

    //音频采样率
    uint32_t sampleRate = ;
    //总音频采样数
    uint64_t totalSampleCount = ;
    float* wavBuffer = NULL;
    double nLoadTime = bench([&]
    {
        wavBuffer = wavRead_float(in_file, &sampleRate, &totalSampleCount);
    });
    std::cout << ) << " 毫秒" << std::endl;

    //如果加载成功
    if (wavBuffer != NULL)
    {
        ;                            // 向上移动8个半音
        float pitchShift = pow(2.0f, semitones / 12.0f);    //将半音转换为因子
        printf("pitchShift:%f", pitchShift);
        double nProcessTime = bench([&]
        {
            smbPitchShift(pitchShift, totalSampleCount, , , sampleRate, wavBuffer, wavBuffer);
        });
        std::cout << ) << " 毫秒" << std::endl;
    }
    //保存结果
    double nSaveTime = bench([&]
    {
        ];
        ];
        ];
        ];
        ];
        splitpath(in_file, drive, dir, fname, ext);
        sprintf(out_file, "%s%s%s_out%s", drive, dir, fname, ext);
        wavWrite_float(out_file, wavBuffer, sampleRate, totalSampleCount);
    });
    std::cout << ) << " 毫秒" << std::endl;
    if (wavBuffer)
    {
        free(wavBuffer);
    }
    getchar();
    std::cout << "按任意键退出程序 \n" << std::endl;
    ;
}

示例具体流程为：

加载wav(拖放wav文件到可执行文件上)->变调处理->保存wav

并对 加载，处理，保存 这3个环节都进行了耗时计算并输出。

其中主要的参数是 float semitones = 8，数值越高音调越高。

参数为8时，变调出来的声音有点像汤姆猫。

注：示例代码仅支持处理单通道音频，多通道稍做改动即可支持。

若有其他相关问题或者需求也可以邮件联系俺探讨。

邮箱地址是: 
gaozhihan@vip.qq.com

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