use __expo2 in sinh and cosh, move __cexp to cmath

[libm] / src / math / __exp.c

diff --git a/src/math/__exp.c b/src/math/__exp.c
index 822efea..ef14e5f 100644 (file)
--- a/src/math/__exp.c
+++ b/src/math/__exp.c
@@ -27,76 +27,25 @@
 
 #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;
-}
-
-// FIXME
-#if 0
-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;
 }
-#endif