25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You may not use this file except in compliance with the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
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25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * long double hypotl(long double x, long double y);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * error less than 1 ulp.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * So, compute sqrt(x*x+y*y) with some care as follows:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Assume x>y>0;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 1. save and set rounding to round-to-nearest
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 2. if x > 2y use
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * where x1 = x with lower 64 bits cleared, x2 = x-x1; else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * 3. if x <= 2y use
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * lower 64 bits chopped, y2 = y-y1.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * NOTE: DO NOT remove parenthsis!
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Special cases:
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * hypot(x,y) is INF if x or y is +INF or -INF; else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * hypot(x,y) is NAN if x or y is NAN.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * in the last place)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern enum fp_direction_type __swapRD(enum fp_direction_type);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const long double zero = 0.0L, one = 1.0L;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis int *pt1 = (int *) &t1, *py1 = (int *) &y1;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if ((*(int *) &one) != 0) { /* determine word ordering */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis px[n0] &= 0x7fffffff; /* clear sign bit of x and y */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis k = 0x7fff0000;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis nx = px[n0] & k; /* exponent of x and y */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } /* force x > y */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (x + y); /* x/y >= 2**116 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (nx < 0x5ff30000 && ny > 0x205b0000) { /* medium x,y */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis /* save and set RD to Rounding to nearest */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis x = sqrtl(t1 * t1 - (y * (-y) - t2 * (x + t1)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis x = sqrtl(t1 * y1 - (w * (-w) - (t2 * y1 + y2 * x)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (void) __swapRD(rd); /* restore rounding mode */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (nx == k || ny == k) { /* x or y is INF or NaN */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t2 = x + y; /* invalid if x or y is sNaN */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (x + y);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (scalbnl(one, -16381) * hypotl(x, y));