在GNU C ++标准库中使用哪种算法计算指数函数? [英] With which algorithm exponential functions are computed in the GNU C++ Standard Library?

问题描述

请考虑 std :: exp 在标题 cmath /w/cpp/numeric"rel =" nofollow noreferrer>数字库.现在，请考虑C ++标准库的实现，例如 libstdc ++ .

Please consider std::exp defined in the header cmath in C++ numerics library. Now, please consider an implementation of the C++ Standard Library, say libstdc++.

考虑有各种算法来计算基本函数，例如算术几何平均迭代算法(用于计算指数函数)和其他三个算法，此处；

Considering there are various algorithms to compute the elementary functions, such as arithmetic-geometric mean iteration algorithm to compute the exponential function and three others shown here;

是否可以在 libstdc ++ 中命名用于计算指数函数的特定算法?

Could you please name the particular algorithm being used to compute the exponential function in libstdc++, if possible?

PS:恐怕我无法查明包含std :: exp实现的正确tarball或理解相关文件的内容.

PS: I could not pinpoint either the correct tarballs containing the std::exp implementation or comprehend the relevant file contents, I'm afraid.

推荐答案

它根本不使用任何复杂的算法.请注意，std::exp仅针对非常有限的几种类型定义:float，double和long double +可转换为double的任何整数类型.这样就不必实施复杂的数学.

It doesn't use any intricate algorithm at all. Note that std::exp is only defined for a very limited number of types: float, double and long double + any Integral type that is castable to double. That makes it not necessary to implement complicated maths.

当前，它使用内置的__builtin_expf，可以从源代码.这将编译为对我计算机上的expf的调用，这是对来自glibc的libm的调用.让我们看看我们在其源代码中找到的内容.当我们搜索expf时，我们发现它在内部调用__ieee754_expf，这是与系统有关的实现. i686和x86_64都只包含一个glibc/sysdeps/ieee754/flt-32/e_expf.c，最终为我们提供了一个实现(为简洁起见，外观

Currently, it uses the builtin __builtin_expf as can be verified from the source code. This compiles to a call to expf on my machine which is a call into libm coming from glibc. Let's see what we find in their source code. When we search for expf we find that this internally calls __ieee754_expf which is a system-dependant implementation. Both i686 and x86_64 just include a glibc/sysdeps/ieee754/flt-32/e_expf.c which finally gives us an implementation (reduced for brevity, the look into the sources

基本上是浮点数的3阶多项式近似值:

It is basically a order 3 polynomial approximation for floats:

static inline uint32_t
top12 (float x)
{
  return asuint (x) >> 20;
}

float
__expf (float x)
{
  uint64_t ki, t;
  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  double_t kd, xd, z, r, r2, y, s;

  xd = (double_t) x;
  // [...] skipping fast under/overflow handling

  /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
  z = InvLn2N * xd;

  /* Round and convert z to int, the result is in [-150*N, 128*N] and
     ideally ties-to-even rule is used, otherwise the magnitude of r
     can be bigger which gives larger approximation error.  */
  kd = roundtoint (z);
  ki = converttoint (z);
  r = z - kd;

  /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
  t = T[ki % N];
  t += ki << (52 - EXP2F_TABLE_BITS);
  s = asdouble (t);
  z = C[0] * r + C[1];
  r2 = r * r;
  y = C[2] * r + 1;
  y = z * r2 + y;
  y = y * s;
  return (float) y;
}

类似地，对于128位long double，它是 7阶近似，对于double，他们使用

Similarly, for 128-bit long double, it's an order 7 approximation and for double they use more complicated algorithm that I can't make sense of right now.

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