- exponent = - exponent;
- }
- }
- else
- {
- /* Implementation contributed by Bruno Haible. */
-
- /* Since the exponent is an 'int', it fits in 64 bits. Therefore the
- loops are executed no more than 64 times. */
- DOUBLE pow2[64]; /* pow2[i] = 2^2^i */
- DOUBLE powh[64]; /* powh[i] = 2^-2^i */
- int i;
-
- exponent = 0;
- if (x >= L_(1.0))
- {
- /* A positive exponent. */
- DOUBLE pow2_i; /* = pow2[i] */
- DOUBLE powh_i; /* = powh[i] */
-
- /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
- x * 2^exponent = argument, x >= 1.0. */
- for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
- ;
- i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
- {
- if (x >= pow2_i)
- {
- exponent += (1 << i);
- x *= powh_i;
- }
- else
- break;
-
- pow2[i] = pow2_i;
- powh[i] = powh_i;
- }
- /* Avoid making x too small, as it could become a denormalized
- number and thus lose precision. */
- while (i > 0 && x < pow2[i - 1])
- {
- i--;
- powh_i = powh[i];
- }
- exponent += (1 << i);
- x *= powh_i;
- /* Here 2^-2^i <= x < 1.0. */
- }
- else
- {
- /* A negative or zero exponent. */
- DOUBLE pow2_i; /* = pow2[i] */
- DOUBLE powh_i; /* = powh[i] */
-
- /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i,
- x * 2^exponent = argument, x < 1.0. */
- for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5);
- ;
- i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i)
- {
- if (x < powh_i)
- {
- exponent -= (1 << i);
- x *= pow2_i;
- }
- else
- break;
-
- pow2[i] = pow2_i;
- powh[i] = powh_i;
- }
- /* Here 2^-2^i <= x < 1.0. */
- }
-
- /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0. */
- while (i > 0)
- {
- i--;
- if (x < powh[i])
- {
- exponent -= (1 << i);
- x *= pow2[i];
- }
- }
- /* Here 0.5 <= x < 1.0. */
- }
-
- *exp = exponent;
- return (sign < 0 ? - x : x);