1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #pragma weak hypotl = __hypotl 31 32 /* 33 * long double hypotl(long double x, long double y); 34 * Method : 35 * If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has 36 * error less than 1 ulp. 37 * So, compute sqrt(x*x+y*y) with some care as follows: 38 * Assume x>y>0; 39 * 1. save and set rounding to round-to-nearest 40 * 2. if x > 2y use 41 * x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y 42 * where x1 = x with lower 64 bits cleared, x2 = x-x1; else 43 * 3. if x <= 2y use 44 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 45 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with 46 * lower 64 bits chopped, y2 = y-y1. 47 * 48 * NOTE: DO NOT remove parenthsis! 49 * 50 * Special cases: 51 * hypot(x,y) is INF if x or y is +INF or -INF; else 52 * hypot(x,y) is NAN if x or y is NAN. 53 * 54 * Accuracy: 55 * hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units 56 * in the last place) 57 */ 58 59 #include "libm.h" 60 #include "longdouble.h" 61 62 extern enum fp_direction_type __swapRD(enum fp_direction_type); 63 64 static const long double zero = 0.0L, one = 1.0L; 65 66 long double 67 hypotl(long double x, long double y) { 68 int n0, n1, n2, n3; 69 long double t1, t2, y1, y2, w; 70 int *px = (int *) &x, *py = (int *) &y; 71 int *pt1 = (int *) &t1, *py1 = (int *) &y1; 72 enum fp_direction_type rd; 73 int j, k, nx, ny, nz; 74 75 if ((*(int *) &one) != 0) { /* determine word ordering */ 76 n0 = 0; 77 n1 = 1; 78 n2 = 2; 79 n3 = 3; 80 } else { 81 n0 = 3; 82 n1 = 2; 83 n2 = 1; 84 n3 = 0; 85 } 86 87 px[n0] &= 0x7fffffff; /* clear sign bit of x and y */ 88 py[n0] &= 0x7fffffff; 89 k = 0x7fff0000; 90 nx = px[n0] & k; /* exponent of x and y */ 91 ny = py[n0] & k; 92 if (ny > nx) { 93 w = x; 94 x = y; 95 y = w; 96 nz = ny; 97 ny = nx; 98 nx = nz; 99 } /* force x > y */ 100 if ((nx - ny) >= 0x00730000) 101 return (x + y); /* x/y >= 2**116 */ 102 if (nx < 0x5ff30000 && ny > 0x205b0000) { /* medium x,y */ 103 /* save and set RD to Rounding to nearest */ 104 rd = __swapRD(fp_nearest); 105 w = x - y; 106 if (w > y) { 107 pt1[n0] = px[n0]; 108 pt1[n1] = px[n1]; 109 pt1[n2] = pt1[n3] = 0; 110 t2 = x - t1; 111 x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1))); 112 } else { 113 x = x + x; 114 py1[n0] = py[n0]; 115 py1[n1] = py[n1]; 116 py1[n2] = py1[n3] = 0; 117 y2 = y - y1; 118 pt1[n0] = px[n0]; 119 pt1[n1] = px[n1]; 120 pt1[n2] = pt1[n3] = 0; 121 t2 = x - t1; 122 x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x))); 123 } 124 if (rd != fp_nearest) 125 (void) __swapRD(rd); /* restore rounding mode */ 126 return (x); 127 } else { 128 if (nx == k || ny == k) { /* x or y is INF or NaN */ 129 if (isinfl(x)) 130 t2 = x; 131 else if (isinfl(y)) 132 t2 = y; 133 else 134 t2 = x + y; /* invalid if x or y is sNaN */ 135 return (t2); 136 } 137 if (ny == 0) { 138 if (y == zero || x == zero) 139 return (x + y); 140 t1 = scalbnl(one, 16381); 141 x *= t1; 142 y *= t1; 143 return (scalbnl(one, -16381) * hypotl(x, y)); 144 } 145 j = nx - 0x3fff0000; 146 px[n0] -= j; 147 py[n0] -= j; 148 pt1[n0] = nx; 149 pt1[n1] = pt1[n2] = pt1[n3] = 0; 150 return (t1 * hypotl(x, y)); 151 } 152 } 153