三角函数的使用

问题

当浮点数很大时，作为三角函数的入参，计算出来的结果会让人大跌眼镜！

X64 Windows平台MSVC2017编译器计算的sin(110000)，上面那个数值明显是不对的

分析

查看sinf函数原型，是通过查表法来实现的，也就说芯片内部不可能维护一个巨大的表格，入参很大会有误差

//! \brief Single-Precision Floating-Point Sine (radians)
//! \param[in] X single precision floating point argument
//! \return the sine of a floating-point argument X (in radians) using table
//! look-up and Taylor series expansion between the look-up table entries.
//!
//! \note 
//! -# This is a standard C math function and requires "math.h" to be 
//! included
//! -# For COFF executables float and double are both single precision
//! 32-bit floating point types, therefore, the double and float variant of 
//! this function may be used interchangeably.
//!
//! <table>
//! <caption id="multi_row">Performance Data</caption>
//! <tr><th>Cycles <th> Comment 
//! <tr><td> 38 <td> Cycle count includes the call and return
//! </table>
//
float32_t sinf (float32_t X);

解决

需要将角度值限制在±2π范围内（理论上说这个范围内的精度是最好的）

// 将角度归一化到[-2π, 2π]范围内
float normalize_angle(float angle)
{
    const float two_pi = 2.0f * PI;
    float normalized = fmodf(angle, two_pi);
    if(normalized < -PI) normalized += two_pi;
    if(normalized > PI) normalized -= two_pi;
    return normalized;
}

调试看归一化后的函数值