src/lib/libm/src/e_sqrtl.c - diff

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Diff for /src/lib/libm/src/e_sqrtl.c between version 1.4.8.1 and 1.4.8.2

-version 1.4.8.1, 2013/11/22 20:15:06
+version 1.4.8.2, 2014/08/20 00:02:18
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+Line 1
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+ /*-
+  * Copyright (c) 2007 Steven G. Kargl
+  * All rights reserved.
+  *
+  * Redistribution and use in source and binary forms, with or without
+  * modification, are permitted provided that the following conditions
+  * are met:
+  * 1. Redistributions of source code must retain the above copyright
+  *    notice unmodified, this list of conditions, and the following
+  *    disclaimer.
+  * 2. Redistributions in binary form must reproduce the above copyright
+  *    notice, this list of conditions and the following disclaimer in the
+  *    documentation and/or other materials provided with the distribution.
+  *
+  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+  */
+ #include <sys/cdefs.h>
+ #if 0
+ __FBSDID("$FreeBSD: head/lib/msun/src/e_sqrtl.c 176720 2008-03-02 01:47:58Z das $");
+ #endif
+ __RCSID("$NetBSD$");
+ #include <machine/ieee.h>
+ #include <float.h>
+ #include "math.h"
+ #include "math_private.h"
+ #ifdef __HAVE_LONG_DOUBLE
+ #ifdef HAVE_FENV_H
+ #include <fenv.h>
+ #endif
+ #ifdef LDBL_IMPLICIT_NBIT
+ #define LDBL_NBIT       0
+ #endif
+ #ifdef HAVE_FENV_H
+ /* Return (x + ulp) for normal positive x. Assumes no overflow. */
+ static inline long double
+ inc(long double x)
+ {
+         union ieee_ext_u ux = { .extu_ld = x, };
+         if (++ux.extu_fracl == 0) {
+                 if (++ux.extu_frach == 0) {
+                         ux.extu_exp++;
+                         ux.extu_frach |= LDBL_NBIT;
+                 }
+         }
+         return (ux.extu_ld);
+ }
+ /* Return (x - ulp) for normal positive x. Assumes no underflow. */
+ static inline long double
+ dec(long double x)
+ {
+         union ieee_ext_u ux = { .extu_ld = x, };
+         if (ux.extu_fracl-- == 0) {
+                 if (ux.extu_frach-- == LDBL_NBIT) {
+                         ux.extu_exp--;
+                         ux.extu_frach |= LDBL_NBIT;
+                 }
+         }
+         return (ux.extu_ld);
+ }
+ /*
+  * This is slow, but simple and portable. You should use hardware sqrt
+  * if possible.
+  */
+ long double
+ __ieee754_sqrtl(long double x)
+ {
+         union ieee_ext_u ux = { .extu_ld = x, };
+         int k, r;
+         long double lo, xn;
+         fenv_t env;
+         /* If x = NaN, then sqrt(x) = NaN. */
+         /* If x = Inf, then sqrt(x) = Inf. */
+         /* If x = -Inf, then sqrt(x) = NaN. */
+         if (ux.extu_exp == LDBL_MAX_EXP * 2 - 1)
+                 return (x * x + x);
+         /* If x = +-0, then sqrt(x) = +-0. */
+         if ((ux.extu_frach | ux.extu_fracl | ux.extu_exp) == 0)
+                 return (x);
+         /* If x < 0, then raise invalid and return NaN */
+         if (ux.extu_sign)
+                 return ((x - x) / (x - x));
+         feholdexcept(&env);
+         if (ux.extu_exp == 0) {
+                 /* Adjust subnormal numbers. */
+                 ux.extu_ld *= 0x1.0p514;
+                 k = -514;
+         } else {
+                 k = 0;
+         }
+         /*
+          * ux.extu_ld is a normal number, so break it into ux.extu_ld = e*2^n where
+          * ux.extu_ld = (2*e)*2^2k for odd n and ux.extu_ld = (4*e)*2^2k for even n.
+          */
+         if ((ux.extu_exp - EXT_EXP_BIAS) & 1) { /* n is even.     */
+                 k += ux.extu_exp - EXT_EXP_BIAS - 1; /* 2k = n - 2.   */
+                 ux.extu_exp = EXT_EXP_BIAS + 1; /* ux.extu_ld in [2,4). */
+         } else {
+                 k += ux.extu_exp - EXT_EXP_BIAS;        /* 2k = n - 1.   */
+                 ux.extu_exp = EXT_EXP_BIAS;     /* ux.extu_ld in [1,2). */
+         }
+         /*
+          * Newton's iteration.
+          * Split ux.extu_ld into a high and low part to achieve additional precision.
+          */
+         xn = sqrt(ux.extu_ld);                  /* 53-bit estimate of sqrtl(x). */
+ #if LDBL_MANT_DIG > 100
+         xn = (xn + (ux.extu_ld / xn)) * 0.5;    /* 106-bit estimate. */
+ #endif
+         lo = ux.extu_ld;
+         ux.extu_fracl = 0;              /* Zero out lower bits. */
+         lo = (lo - ux.extu_ld) / xn;    /* Low bits divided by xn. */
+         xn = xn + (ux.extu_ld / xn);    /* High portion of estimate. */
+         ux.extu_ld = xn + lo;           /* Combine everything. */
+         ux.extu_exp += (k >> 1) - 1;
+         feclearexcept(FE_INEXACT);
+         r = fegetround();
+         fesetround(FE_TOWARDZERO);      /* Set to round-toward-zero. */
+         xn = x / ux.extu_ld;            /* Chopped quotient (inexact?). */
+         if (!fetestexcept(FE_INEXACT)) { /* Quotient is exact. */
+                 if (xn == ux.extu_ld) {
+                         fesetenv(&env);
+                         return (ux.extu_ld);
+                 }
+                 /* Round correctly for inputs like x = y**2 - ulp. */
+                 xn = dec(xn);           /* xn = xn - ulp. */
+         }
+         if (r == FE_TONEAREST) {
+                 xn = inc(xn);           /* xn = xn + ulp. */
+         } else if (r == FE_UPWARD) {
+                 ux.extu_ld = inc(ux.extu_ld);   /* ux.extu_ld = ux.extu_ld + ulp. */
+                 xn = inc(xn);           /* xn  = xn + ulp. */
+         }
+         ux.extu_ld = ux.extu_ld + xn;           /* Chopped sum. */
+         feupdateenv(&env);      /* Restore env and raise inexact */
+         ux.extu_exp--;
+         return (ux.extu_ld);
+ }
+ #else
+ /*
+  * No fenv support:
+  * poor man's version: just use double
+  */
+ long double
+ __ieee754_sqrtl(long double x)
+ {
+         return __ieee754_sqrt((double)x);
+ }
+ #endif
+ #endif

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