哪种算法用于计算 GNU C++ 标准库的指数函数？

Question

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

考虑到有多种算法可以计算初等函数，例如arithmetic-geometric mean iteration algorithm to compute the exponential function and three others shown here；

如果可能的话，您能否说出用于计算 libstdc++ 中指数函数的特定算法？

PS：恐怕我无法确定包含 std::exp 实现的正确 tarball 或理解相关文件内容。

Answer 1

它根本不使用任何复杂的算法。请注意，std::exp 仅针对非常有限数量的类型定义：float、double 和 long double + 任何可转换为 double 的整数类型。这使得无需执行复杂的数学运算。

目前，它使用内置的 __builtin_expf 可以从源代码中验证。这会编译为在我的机器上对 expf 的调用，这是对来自 glibc 的对 libm 的调用。让我们看看我们在他们的 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

中找到了什么

它基本上是浮点数的 3 阶多项式逼近：

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;
}

同样，对于 128 位 long double，这是我现在无法理解的 order 7 approximation and for double they use more complicated algorithm。

哪种算法用于计算 GNU C++ 标准库的指数函数？

Which algorithm is used to compute exponential functions the GNU C++ Standard Library?

c++

gnu

libstdc++

exponentiation