1 files changed, 128 insertions, 0 deletions
diff --git a/libm/ldouble/unityl.c b/libm/ldouble/unityl.c
new file mode 100644
index 000000000..10670ce3a
--- /dev/null
+++ b/libm/ldouble/unityl.c
@@ -0,0 +1,128 @@
+/*							unityl.c
+ *
+ * Relative error approximations for function arguments near
+ * unity.
+ *
+ *    log1p(x) = log(1+x)
+ *    expm1(x) = exp(x) - 1
+ *    cosm1(x) = cos(x) - 1
+ *
+ */
+
+
+/* log1p(x) = log(1 + x)
+ *                      Relative error:
+ * arithmetic   domain     # trials      peak         rms
+ *    IEEE      0.5, 2      30000       1.4e-19     4.1e-20
+ *
+ */
+
+#include <math.h>
+/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 2.32e-20
+ */
+static long double LP[] = {
+ 4.5270000862445199635215E-5L,
+ 4.9854102823193375972212E-1L,
+ 6.5787325942061044846969E0L,
+ 2.9911919328553073277375E1L,
+ 6.0949667980987787057556E1L,
+ 5.7112963590585538103336E1L,
+ 2.0039553499201281259648E1L,
+};
+static long double LQ[] = {
+/* 1.0000000000000000000000E0L,*/
+ 1.5062909083469192043167E1L,
+ 8.3047565967967209469434E1L,
+ 2.2176239823732856465394E2L,
+ 3.0909872225312059774938E2L,
+ 2.1642788614495947685003E2L,
+ 6.0118660497603843919306E1L,
+};
+
+#define SQRTH 0.70710678118654752440L
+#define SQRT2 1.41421356237309504880L
+#ifdef ANSIPROT
+extern long double logl ( long double );
+extern long double expl ( long double );
+extern long double cosl ( long double );
+extern long double polevll ( long double, void *, int );
+extern long double p1evll ( long double,  void *, int );
+#else
+long double logl(), expl(), cosl(), polevll(), p1evll();
+#endif
+
+long double log1pl(x)
+long double x;
+{
+long double z;
+
+z = 1.0L + x;
+if( (z < SQRTH) || (z > SQRT2) )
+	return( logl(z) );
+z = x*x;
+z = -0.5L * z + x * ( z * polevll( x, LP, 6 ) / p1evll( x, LQ, 6 ) );
+return (x + z);
+}
+
+
+
+/* expm1(x) = exp(x) - 1  */
+
+/*  e^x =  1 + 2x P(x^2)/( Q(x^2) - P(x^2) )
+ * -0.5 <= x <= 0.5
+ */
+
+static long double EP[3] = {
+ 1.2617719307481059087798E-4L,
+ 3.0299440770744196129956E-2L,
+ 9.9999999999999999991025E-1L,
+};
+static long double EQ[4] = {
+ 3.0019850513866445504159E-6L,
+ 2.5244834034968410419224E-3L,
+ 2.2726554820815502876593E-1L,
+ 2.0000000000000000000897E0L,
+};
+
+long double expm1l(x)
+long double x;
+{
+long double r, xx;
+
+if( (x < -0.5L) || (x > 0.5L) )
+	return( expl(x) - 1.0L );
+xx = x * x;
+r = x * polevll( xx, EP, 2 );
+r = r/( polevll( xx, EQ, 3 ) - r );
+return (r + r);
+}
+
+
+
+/* cosm1(x) = cos(x) - 1  */
+
+static long double coscof[7] = {
+ 4.7377507964246204691685E-14L,
+-1.1470284843425359765671E-11L,
+ 2.0876754287081521758361E-9L,
+-2.7557319214999787979814E-7L,
+ 2.4801587301570552304991E-5L,
+-1.3888888888888872993737E-3L,
+ 4.1666666666666666609054E-2L,
+};
+
+extern long double PIO4L;
+
+long double cosm1l(x)
+long double x;
+{
+long double xx;
+
+if( (x < -PIO4L) || (x > PIO4L) )
+	return( cosl(x) - 1.0L );
+xx = x * x;
+xx = -0.5L*xx + xx * xx * polevll( xx, coscof, 6 );
+return xx;
+}