update from main archive 960830
authordrepper <drepper>
Sat, 31 Aug 1996 00:12:34 +0000 (00:12 +0000)
committerdrepper <drepper>
Sat, 31 Aug 1996 00:12:34 +0000 (00:12 +0000)
sysdeps/libm-ieee754/s_cbrtl.c [new file with mode: 0644]

diff --git a/sysdeps/libm-ieee754/s_cbrtl.c b/sysdeps/libm-ieee754/s_cbrtl.c
new file mode 100644 (file)
index 0000000..03ebfe7
--- /dev/null
@@ -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)