Make use of composed functions and temporaries

[andrjohns]

Description

There are several places throughout the math library where arithmetic is being used in place of the composed functions and constants. There are also places where temporary variables could be used in place of repeated calculations.

An example of this can be seen in: prim/scal/fun/lub_constrain:

  if (x > 0) {
    T exp_minus_x = exp(-x);
    inv_logit_x = 1.0 / (1.0 + exp_minus_x);
    // Prevent x from reaching one unless it really really should.
    if ((x < std::numeric_limits<double>::infinity()) && (inv_logit_x == 1))
      inv_logit_x = 1 - 1e-15;
  } else {
    T exp_x = exp(x);
    inv_logit_x = 1.0 - 1.0 / (1.0 + exp_x);
    // Prevent x from reaching zero unless it really really should.
    if ((x > -std::numeric_limits<double>::infinity()) && (inv_logit_x == 0))
      inv_logit_x = 1e-15;
  }

Which could be updated to:

  T inv_logit_x;
  if (x > 0) {
    inv_logit_x = inv_logit(x);
    // Prevent x from reaching one unless it really really should.
    if ((x < INFTY) && (inv_logit_x == 1))
      inv_logit_x = 1 - 1e-15;
  } else {
    inv_logit_x = inv_logit(x);
    // Prevent x from reaching zero unless it really really should.
    if ((x > NEGATIVE_INFTY) && (inv_logit_x == 0))
      inv_logit_x = 1e-15;
  }

I'll be working through this in my spare time, and will break the PRs into multiple parts. I'll update this issue as I go

• prim
  • scal
    • fun
    • prob
  • mat
    • fun
    • prob
  • arr
    • fun

Current Version:

v2.19.1

[syclik]

Thanks.