1 /*- 2 * Copyright (c) 2007 Steven G. Kargl 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice unmodified, this list of conditions, and the following 10 * disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 25 */ 26 27 #include <sys/cdefs.h> 28 #if 0 29 __FBSDID("$FreeBSD: head/lib/msun/src/e_sqrtl.c 176720 2008-03-02 01:47:58Z das $"); 30 #endif 31 __RCSID("$NetBSD: e_sqrtl.c,v 1.6 2017/05/06 18:02:52 christos Exp $"); 32 33 #include "namespace.h" 34 #include <machine/ieee.h> 35 #include <float.h> 36 37 #include "math.h" 38 #include "math_private.h" 39 40 #ifdef __HAVE_LONG_DOUBLE 41 42 #define __TEST_FENV 43 #include <fenv.h> 44 45 #ifdef LDBL_IMPLICIT_NBIT 46 #define LDBL_NBIT 0 47 #endif 48 49 #ifdef __HAVE_FENV 50 51 /* Return (x + ulp) for normal positive x. Assumes no overflow. */ 52 static inline long double 53 inc(long double x) 54 { 55 union ieee_ext_u ux = { .extu_ld = x, }; 56 57 if (++ux.extu_fracl == 0) { 58 if (++ux.extu_frach == 0) { 59 ux.extu_exp++; 60 ux.extu_frach |= LDBL_NBIT; 61 } 62 } 63 return (ux.extu_ld); 64 } 65 66 /* Return (x - ulp) for normal positive x. Assumes no underflow. */ 67 static inline long double 68 dec(long double x) 69 { 70 union ieee_ext_u ux = { .extu_ld = x, }; 71 72 if (ux.extu_fracl-- == 0) { 73 if (ux.extu_frach-- == LDBL_NBIT) { 74 ux.extu_exp--; 75 ux.extu_frach |= LDBL_NBIT; 76 } 77 } 78 return (ux.extu_ld); 79 } 80 81 /* 82 * This is slow, but simple and portable. You should use hardware sqrt 83 * if possible. 84 */ 85 86 long double 87 __ieee754_sqrtl(long double x) 88 { 89 union ieee_ext_u ux = { .extu_ld = x, }; 90 int k, r; 91 long double lo, xn; 92 fenv_t env; 93 94 /* If x = NaN, then sqrt(x) = NaN. */ 95 /* If x = Inf, then sqrt(x) = Inf. */ 96 /* If x = -Inf, then sqrt(x) = NaN. */ 97 if (ux.extu_exp == LDBL_MAX_EXP * 2 - 1) 98 return (x * x + x); 99 100 /* If x = +-0, then sqrt(x) = +-0. */ 101 if ((ux.extu_frach | ux.extu_fracl | ux.extu_exp) == 0) 102 return (x); 103 104 /* If x < 0, then raise invalid and return NaN */ 105 if (ux.extu_sign) 106 return ((x - x) / (x - x)); 107 108 feholdexcept(&env); 109 110 if (ux.extu_exp == 0) { 111 /* Adjust subnormal numbers. */ 112 ux.extu_ld *= 0x1.0p514; 113 k = -514; 114 } else { 115 k = 0; 116 } 117 /* 118 * ux.extu_ld is a normal number, so break it into ux.extu_ld = e*2^n where 119 * ux.extu_ld = (2*e)*2^2k for odd n and ux.extu_ld = (4*e)*2^2k for even n. 120 */ 121 if ((ux.extu_exp - EXT_EXP_BIAS) & 1) { /* n is even. */ 122 k += ux.extu_exp - EXT_EXP_BIAS - 1; /* 2k = n - 2. */ 123 ux.extu_exp = EXT_EXP_BIAS + 1; /* ux.extu_ld in [2,4). */ 124 } else { 125 k += ux.extu_exp - EXT_EXP_BIAS; /* 2k = n - 1. */ 126 ux.extu_exp = EXT_EXP_BIAS; /* ux.extu_ld in [1,2). */ 127 } 128 129 /* 130 * Newton's iteration. 131 * Split ux.extu_ld into a high and low part to achieve additional precision. 132 */ 133 xn = sqrt(ux.extu_ld); /* 53-bit estimate of sqrtl(x). */ 134 #if LDBL_MANT_DIG > 100 135 xn = (xn + (ux.extu_ld / xn)) * 0.5; /* 106-bit estimate. */ 136 #endif 137 lo = ux.extu_ld; 138 ux.extu_fracl = 0; /* Zero out lower bits. */ 139 lo = (lo - ux.extu_ld) / xn; /* Low bits divided by xn. */ 140 xn = xn + (ux.extu_ld / xn); /* High portion of estimate. */ 141 ux.extu_ld = xn + lo; /* Combine everything. */ 142 ux.extu_exp += (k >> 1) - 1; 143 144 feclearexcept(FE_INEXACT); 145 r = fegetround(); 146 fesetround(FE_TOWARDZERO); /* Set to round-toward-zero. */ 147 xn = x / ux.extu_ld; /* Chopped quotient (inexact?). */ 148 149 if (!fetestexcept(FE_INEXACT)) { /* Quotient is exact. */ 150 if (xn == ux.extu_ld) { 151 fesetenv(&env); 152 return (ux.extu_ld); 153 } 154 /* Round correctly for inputs like x = y**2 - ulp. */ 155 xn = dec(xn); /* xn = xn - ulp. */ 156 } 157 158 if (r == FE_TONEAREST) { 159 xn = inc(xn); /* xn = xn + ulp. */ 160 } else if (r == FE_UPWARD) { 161 ux.extu_ld = inc(ux.extu_ld); /* ux.extu_ld = ux.extu_ld + ulp. */ 162 xn = inc(xn); /* xn = xn + ulp. */ 163 } 164 ux.extu_ld = ux.extu_ld + xn; /* Chopped sum. */ 165 feupdateenv(&env); /* Restore env and raise inexact */ 166 ux.extu_exp--; 167 return (ux.extu_ld); 168 } 169 170 #else /* !__HAVE_FENV */ 171 172 /* 173 * No fenv support: 174 * poor man's version: just use double 175 */ 176 long double 177 __ieee754_sqrtl(long double x) 178 { 179 return __ieee754_sqrt((double)x); 180 } 181 182 #endif /* __HAVE_FENV */ 183 184 #endif /* __HAVE_LONG_DOUBLE */ 185
Indexes created Mon Sep 22 05:09:51 GMT 2025