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Diffstat (limited to 'usr/src/libm/src/Q/hypotl.c')
| -rw-r--r-- | usr/src/libm/src/Q/hypotl.c | 150 |
1 files changed, 150 insertions, 0 deletions
diff --git a/usr/src/libm/src/Q/hypotl.c b/usr/src/libm/src/Q/hypotl.c new file mode 100644 index 0000000..ad7221f --- /dev/null +++ b/usr/src/libm/src/Q/hypotl.c @@ -0,0 +1,150 @@ +/* + * CDDL HEADER START + * + * The contents of this file are subject to the terms of the + * Common Development and Distribution License (the "License"). + * You may not use this file except in compliance with the License. + * + * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE + * or http://www.opensolaris.org/os/licensing. + * See the License for the specific language governing permissions + * and limitations under the License. + * + * When distributing Covered Code, include this CDDL HEADER in each + * file and include the License file at usr/src/OPENSOLARIS.LICENSE. + * If applicable, add the following below this CDDL HEADER, with the + * fields enclosed by brackets "[]" replaced with your own identifying + * information: Portions Copyright [yyyy] [name of copyright owner] + * + * CDDL HEADER END + */ + +/* + * Copyright 2006 Sun Microsystems, Inc. All rights reserved. + * Use is subject to license terms. + */ + +#pragma ident "@(#)hypotl.c 1.11 06/01/31 SMI" + +#pragma weak hypotl = __hypotl + +/* + * long double hypotl(long double x, long double y); + * Method : + * If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has + * error less than 1 ulp. + * So, compute sqrt(x*x+y*y) with some care as follows: + * Assume x>y>0; + * 1. save and set rounding to round-to-nearest + * 2. if x > 2y use + * x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y + * where x1 = x with lower 64 bits cleared, x2 = x-x1; else + * 3. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with + * lower 64 bits chopped, y2 = y-y1. + * + * NOTE: DO NOT remove parenthsis! + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units + * in the last place) + */ + +#include "libm.h" + +extern enum fp_direction_type __swapRD(enum fp_direction_type); + +static const long double zero = 0.0L, one = 1.0L; + +long double +hypotl(long double x, long double y) { + int n0, n1, n2, n3; + long double t1, t2, y1, y2, w; + int *px = (int *) &x, *py = (int *) &y; + int *pt1 = (int *) &t1, *py1 = (int *) &y1; + enum fp_direction_type rd; + int j, k, nx, ny, nz; + + if ((*(int *) &one) != 0) { /* determine word ordering */ + n0 = 0; + n1 = 1; + n2 = 2; + n3 = 3; + } else { + n0 = 3; + n1 = 2; + n2 = 1; + n3 = 0; + } + + px[n0] &= 0x7fffffff; /* clear sign bit of x and y */ + py[n0] &= 0x7fffffff; + k = 0x7fff0000; + nx = px[n0] & k; /* exponent of x and y */ + ny = py[n0] & k; + if (ny > nx) { + w = x; + x = y; + y = w; + nz = ny; + ny = nx; + nx = nz; + } /* force x > y */ + if ((nx - ny) >= 0x00730000) + return (x + y); /* x/y >= 2**116 */ + if (nx < 0x5ff30000 && ny > 0x205b0000) { /* medium x,y */ + /* save and set RD to Rounding to nearest */ + rd = __swapRD(fp_nearest); + w = x - y; + if (w > y) { + pt1[n0] = px[n0]; + pt1[n1] = px[n1]; + pt1[n2] = pt1[n3] = 0; + t2 = x - t1; + x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1))); + } else { + x = x + x; + py1[n0] = py[n0]; + py1[n1] = py[n1]; + py1[n2] = py1[n3] = 0; + y2 = y - y1; + pt1[n0] = px[n0]; + pt1[n1] = px[n1]; + pt1[n2] = pt1[n3] = 0; + t2 = x - t1; + x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x))); + } + if (rd != fp_nearest) + (void) __swapRD(rd); /* restore rounding mode */ + return (x); + } else { + if (nx == k || ny == k) { /* x or y is INF or NaN */ + if (isinfl(x)) + t2 = x; + else if (isinfl(y)) + t2 = y; + else + t2 = x + y; /* invalid if x or y is sNaN */ + return (t2); + } + if (ny == 0) { + if (y == zero || x == zero) + return (x + y); + t1 = scalbnl(one, 16381); + x *= t1; + y *= t1; + return (scalbnl(one, -16381) * hypotl(x, y)); + } + j = nx - 0x3fff0000; + px[n0] -= j; + py[n0] -= j; + pt1[n0] = nx; + pt1[n1] = pt1[n2] = pt1[n3] = 0; + return (t1 * hypotl(x, y)); + } +} |