summaryrefslogtreecommitdiff
path: root/sysdeps/libm-ieee754
diff options
context:
space:
mode:
Diffstat (limited to 'sysdeps/libm-ieee754')
-rw-r--r--sysdeps/libm-ieee754/s_cbrtl.c123
1 files changed, 123 insertions, 0 deletions
diff --git a/sysdeps/libm-ieee754/s_cbrtl.c b/sysdeps/libm-ieee754/s_cbrtl.c
new file mode 100644
index 0000000000..03ebfe7eb8
--- /dev/null
+++ b/sysdeps/libm-ieee754/s_cbrtl.c
@@ -0,0 +1,123 @@
+/* s_cbrtl.c -- long double version of s_cbrt.c.
+ * Conversion to long double by Ulrich Drepper,
+ * Cygnus Support, drepper@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#if defined(LIBM_SCCS) && !defined(lint)
+static char rcsid[] = "$NetBSD: $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+/* cbrtl(x)
+ * Return cube root of x
+ */
+#ifdef __STDC__
+static const u_int32_t
+#else
+static u_int32_t
+#endif
+ B1_EXP = 10921, /* = Int(B1) */
+ B1_MANT = 0x7bc4b064, /* = Int(1.0-0.03306235651)*2**31 */
+
+ B2_EXP = 10900,
+ B2_MANT = 0x7bc4b064; /* = Int(1.0-0.03306235651)*2**31 */
+
+#ifdef __STDC__
+static const long double
+#else
+static long double
+#endif
+C = 5.42857142857142815906e-01L, /* 19/35 */
+D = -7.05306122448979611050e-01L, /* -864/1225 */
+E = 1.41428571428571436819e+00L, /* 99/70 */
+F = 1.60714285714285720630e+00L, /* 45/28 */
+G = 3.57142857142857150787e-01L; /* 5/14 */
+
+#ifdef __STDC__
+ long double __cbrtl(long double x)
+#else
+ long double __cbrtl(x)
+ long double x;
+#endif
+{
+ int32_t hx;
+ long double r,s,t=0.0,w;
+ u_int32_t sign, se, x0, x1;
+
+ GET_LDOUBLE_WORDS(se,x0,x1,x);
+ sign=se&0x8000; /* sign= sign(x) */
+ se ^= sign;
+ if(se==0x7fff) return(x+x); /* cbrt(NaN,INF) is itself */
+ if((se|x0|x1)==0)
+ return(x); /* cbrt(0) is itself */
+
+ SET_LDOUBLE_EXP(x,se); /* x <- |x| */
+
+/* XXX I don't know whether the numbers for correct are correct. The
+ precalculation is extended from 20 bits to 32 bits. This hopefully
+ gives us the needed bits to get us still along with one iteration
+ step. */
+
+ /* rough cbrt to 5 bits */
+ if(se==0) /* subnormal number */
+ {
+ u_int64_t xxl;
+ u_int32_t set,t0,t1;
+ SET_LDOUBLE_EXP(t,0x4035); /* set t= 2**54 */
+ SET_LDOUBLE_MSW(t,0x80000000);
+ t*=x;
+ GET_LDOUBLE_WORDS(set,t0,t1,t);
+ xxl = ((u_int64_t) set) << 32 | t0;
+ xxl /= 3;
+ xxl += B2_EXP << 16 | B2_MANT;
+ t0 = xxl & 0xffffffffu;
+ set = xxl >> 32;
+ SET_LDOUBLE_WORDS(t,set,t0,t1);
+ }
+ else
+ {
+ u_int64_t xxl = ((u_int64_t) se) << 32 | x0;
+ xxl /= 3;
+ xxl += B1_EXP << 16 | B1_MANT;
+ SET_LDOUBLE_MSW(t,xxl&0xffffffffu);
+ xxl >>= 32;
+ SET_LDOUBLE_EXP(t,xxl);
+ }
+
+
+ /* new cbrt to 23 bits, may be implemented in single precision */
+ r=t*t/x;
+ s=C+r*t;
+ t*=G+F/(s+E+D/s);
+
+ /* chopped to 32 bits and make it larger than cbrt(x) */
+ GET_LDOUBLE_WORDS(se,x0,x1,t);
+ SET_LDOUBLE_WORDS(t,se,x0+1,0);
+
+
+ /* one step newton iteration to 53 bits with error less than 0.667 ulps */
+ s=t*t; /* t*t is exact */
+ r=x/s;
+ w=t+t;
+ r=(r-t)/(w+r); /* r-s is exact */
+ t=t+t*r;
+
+ /* retore the sign bit */
+ GET_LDOUBLE_EXP(se,t);
+ SET_LDOUBLE_EXP(t,se|sign);
+ return(t);
+}
+weak_alias (__cbrtl, cbrtl)