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 * hypotl(x,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 32 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 32 bits cleared, 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 61 #if defined(__x86) 62 extern enum fp_direction_type __swap87RD(enum fp_direction_type); 63 64 #define k 0x7fff 65 66 long double 67 hypotl(long double x, long double y) { 68 long double t1, t2, y1, y2, w; 69 int *px = (int *) &x, *py = (int *) &y; 70 int *pt1 = (int *) &t1, *py1 = (int *) &y1; 71 enum fp_direction_type rd; 72 int j, nx, ny, nz; 73 74 px[2] &= 0x7fff; /* clear sign bit and padding bits of x and y */ 75 py[2] &= 0x7fff; 76 nx = px[2]; /* biased exponent of x and y */ 77 ny = py[2]; 78 if (ny > nx) { 79 w = x; 80 x = y; 81 y = w; 82 nz = ny; 83 ny = nx; 84 nx = nz; 85 } /* force nx >= ny */ 86 if (nx - ny >= 66) 87 return (x + y); /* x / y >= 2**65 */ 88 if (nx < 0x5ff3 && ny > 0x205b) { /* medium x,y */ 89 /* save and set RD to Rounding to nearest */ 90 rd = __swap87RD(fp_nearest); 91 w = x - y; 92 if (w > y) { 93 pt1[2] = px[2]; 94 pt1[1] = px[1]; 95 pt1[0] = 0; 96 t2 = x - t1; 97 x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1))); 98 } else { 99 x += x; 100 py1[2] = py[2]; 101 py1[1] = py[1]; 102 py1[0] = 0; 103 y2 = y - y1; 104 pt1[2] = px[2]; 105 pt1[1] = px[1]; 106 pt1[0] = 0; 107 t2 = x - t1; 108 x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x))); 109 } 110 if (rd != fp_nearest) 111 __swap87RD(rd); /* restore rounding mode */ 112 return (x); 113 } else { 114 if (nx == k || ny == k) { /* x or y is INF or NaN */ 115 /* since nx >= ny; nx is always k within this block */ 116 if (px[1] == 0x80000000 && px[0] == 0) 117 return (x); 118 else if (ny == k && py[1] == 0x80000000 && py[0] == 0) 119 return (y); 120 else 121 return (x + y); 122 } 123 if (ny == 0) { 124 if (y == 0.L || x == 0.L) 125 return (x + y); 126 pt1[2] = 0x3fff + 16381; 127 pt1[1] = 0x80000000; 128 pt1[0] = 0; 129 py1[2] = 0x3fff - 16381; 130 py1[1] = 0x80000000; 131 py1[0] = 0; 132 x *= t1; 133 y *= t1; 134 return (y1 * hypotl(x, y)); 135 } 136 j = nx - 0x3fff; 137 px[2] -= j; 138 py[2] -= j; 139 pt1[2] = nx; 140 pt1[1] = 0x80000000; 141 pt1[0] = 0; 142 return (t1 * hypotl(x, y)); 143 } 144 } 145 #endif 146