#include "libm.h"
-static const uint32_t k = 1799; /* constant for reduction */
-static const double kln2 = 1246.97177782734161156; /* k * ln2 */
-
-/*
- * Compute exp(x), scaled to avoid spurious overflow. An exponent is
- * returned separately in 'expt'.
- *
- * Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
- * Output: 2**1023 <= y < 2**1024
- */
-static double __frexp_exp(double x, int *expt)
-{
- double exp_x;
- uint32_t hx;
-
- /*
- * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
- * minimize |exp(kln2) - 2**k|. We also scale the exponent of
- * exp_x to MAX_EXP so that the result can be multiplied by
- * a tiny number without losing accuracy due to denormalization.
- */
- exp_x = exp(x - kln2);
- GET_HIGH_WORD(hx, exp_x);
- *expt = (hx >> 20) - (0x3ff + 1023) + k;
- SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
- return exp_x;
-}
-
/*
- * __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
- * They are intended for large arguments (real part >= ln(DBL_MAX))
- * where care is needed to avoid overflow.
- *
- * The present implementation is narrowly tailored for our hyperbolic and
- * exponential functions. We assume expt is small (0 or -1), and the caller
- * has filtered out very large x, for which overflow would be inevitable.
+ * We use exp(x) = exp(x - kln2) * 2**k,
+ * k is carefully chosen to minimize |exp(kln2) - 2**k|
*/
-double __ldexp_exp(double x, int expt)
-{
- double exp_x, scale;
- int ex_expt;
+static const uint32_t k = 1799;
+static const double kln2 = 1246.97177782734161156;
- exp_x = __frexp_exp(x, &ex_expt);
- expt += ex_expt;
- INSERT_WORDS(scale, (0x3ff + expt) << 20, 0);
- return exp_x * scale;
-}
-
-double complex __ldexp_cexp(double complex z, int expt)
+/* exp(x)/2 when x is huge */
+double __expo2(double x)
{
- double x, y, exp_x, scale1, scale2;
- int ex_expt, half_expt;
-
- x = creal(z);
- y = cimag(z);
- exp_x = __frexp_exp(x, &ex_expt);
- expt += ex_expt;
+ double scale;
+ int n;
/*
- * Arrange so that scale1 * scale2 == 2**expt. We use this to
- * compensate for scalbn being horrendously slow.
+ * efficient scalbn(y, k-1):
+ * 2**(k-1) cannot be represented
+ * so we use that k-1 is even and scale in two steps
*/
- half_expt = expt / 2;
- INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0);
- half_expt = expt - half_expt;
- INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
-
- return cpack(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2);
+ n = (k - 1)/2;
+ INSERT_WORDS(scale, (0x3ff + n) << 20, 0);
+ return exp(x - kln2) * scale * scale;
}