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 #if defined(ELFOBJ) 31 #pragma weak hypotl = __hypotl 32 #endif 33 34 /* 35 * hypotl(x,y) 36 * Method : 37 * If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has 38 * error less than 1 ulp. 39 * So, compute sqrt(x*x+y*y) with some care as follows: 40 * Assume x>y>0; 41 * 1. save and set rounding to round-to-nearest 42 * 2. if x > 2y use 43 * x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y 44 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 45 * 3. if x <= 2y use 46 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 47 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with 48 * lower 32 bits cleared, y2 = y-y1. 49 * 50 * NOTE: DO NOT remove parenthsis! 51 * 52 * Special cases: 53 * hypot(x,y) is INF if x or y is +INF or -INF; else 54 * hypot(x,y) is NAN if x or y is NAN. 55 * 56 * Accuracy: 57 * hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units 58 * in the last place) 59 */ 60 61 #include "libm.h" 62 63 #if defined(__x86) 64 extern enum fp_direction_type __swap87RD(enum fp_direction_type); 65 66 #define k 0x7fff 67 68 long double 69 hypotl(long double x, long double y) { 70 long double t1, t2, y1, y2, w; 71 int *px = (int *) &x, *py = (int *) &y; 72 int *pt1 = (int *) &t1, *py1 = (int *) &y1; 73 enum fp_direction_type rd; 74 int j, nx, ny, nz; 75 76 px[2] &= 0x7fff; /* clear sign bit and padding bits of x and y */ 77 py[2] &= 0x7fff; 78 nx = px[2]; /* biased exponent of x and y */ 79 ny = py[2]; 80 if (ny > nx) { 81 w = x; 82 x = y; 83 y = w; 84 nz = ny; 85 ny = nx; 86 nx = nz; 87 } /* force nx >= ny */ 88 if (nx - ny >= 66) 89 return (x + y); /* x / y >= 2**65 */ 90 if (nx < 0x5ff3 && ny > 0x205b) { /* medium x,y */ 91 /* save and set RD to Rounding to nearest */ 92 rd = __swap87RD(fp_nearest); 93 w = x - y; 94 if (w > y) { 95 pt1[2] = px[2]; 96 pt1[1] = px[1]; 97 pt1[0] = 0; 98 t2 = x - t1; 99 x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1))); 100 } else { 101 x += x; 102 py1[2] = py[2]; 103 py1[1] = py[1]; 104 py1[0] = 0; 105 y2 = y - y1; 106 pt1[2] = px[2]; 107 pt1[1] = px[1]; 108 pt1[0] = 0; 109 t2 = x - t1; 110 x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x))); 111 } 112 if (rd != fp_nearest) 113 __swap87RD(rd); /* restore rounding mode */ 114 return (x); 115 } else { 116 if (nx == k || ny == k) { /* x or y is INF or NaN */ 117 /* since nx >= ny; nx is always k within this block */ 118 if (px[1] == 0x80000000 && px[0] == 0) 119 return (x); 120 else if (ny == k && py[1] == 0x80000000 && py[0] == 0) 121 return (y); 122 else 123 return (x + y); 124 } 125 if (ny == 0) { 126 if (y == 0.L || x == 0.L) 127 return (x + y); 128 pt1[2] = 0x3fff + 16381; 129 pt1[1] = 0x80000000; 130 pt1[0] = 0; 131 py1[2] = 0x3fff - 16381; 132 py1[1] = 0x80000000; 133 py1[0] = 0; 134 x *= t1; 135 y *= t1; 136 return (y1 * hypotl(x, y)); 137 } 138 j = nx - 0x3fff; 139 px[2] -= j; 140 py[2] -= j; 141 pt1[2] = nx; 142 pt1[1] = 0x80000000; 143 pt1[0] = 0; 144 return (t1 * hypotl(x, y)); 145 } 146 } 147 #endif 148