/* * 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 2011 Nexenta Systems, Inc. All rights reserved. */ /* * Copyright 2006 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ /* INDENT OFF */ /* * void sincospi(double x, double *s, double *c) * *s = sin(pi*x); *c = cos(pi*x); * * Algorithm, 10/17/2002, K.C. Ng * ------------------------------ * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary). * 1. If y == z, then x is a multiple of pi/4. Return the following values: * --------------------------------------------------- * n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi) * --------------------------------------------------- * 000 0.00 +0 ___ +1 ___ +0 * 001 0.25 +\/0.5 +\/0.5 +1 * 010 0.50 +1 ___ +0 ___ +inf * 011 0.75 +\/0.5 -\/0.5 -1 * 100 1.00 -0 ___ -1 ___ +0 * 101 1.25 -\/0.5 -\/0.5 +1 * 110 1.50 -1 ___ -0 ___ +inf * 111 1.75 -\/0.5 +\/0.5 -1 * --------------------------------------------------- * 2. Otherwise, * --------------------------------------------------- * n t sin(x*pi) cos(x*pi) tan(x*pi) * --------------------------------------------------- * 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t) * 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t) * 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t) * 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t) * 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t) * 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t) * 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t) * 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t) * --------------------------------------------------- * * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0). * This will return a result with error slightly more than one ulp (but less * than 2 ulp). If one wants accurate result, one may break up pi*t in * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo) * instead. */ #include "libm.h" #include "libm_protos.h" #include "libm_macros.h" #include <math.h> #if defined(__SUNPRO_C) #include <sunmath.h> #endif static const double pi = 3.14159265358979323846, /* 400921FB,54442D18 */ sqrth_h = 0.70710678118654757273731092936941422522068023681640625, sqrth_l = -4.8336466567264565185935844299127932213411660131004e-17; /* INDENT ON */ void sincospi(double x, double *s, double *c) { double y, z, t; int n, ix, k; int hx = ((int *)&x)[HIWORD]; unsigned h, lx = ((unsigned *)&x)[LOWORD]; ix = hx & ~0x80000000; n = (ix >> 20) - 0x3ff; if (n >= 51) { /* |x| >= 2**51 */ if (n >= 1024) { #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) *s = *c = ix >= 0x7ff80000 ? x : x - x; /* assumes sparc-like QNaN */ #else *s = *c = x - x; #endif } else { if (n >= 53) { *s = 0.0; *c = 1.0; } else if (n == 52) { if ((lx & 1) == 0) { *s = 0.0; *c = 1.0; } else { *s = -0.0; *c = -1.0; } } else { /* n == 51 */ if ((lx & 1) == 0) { *s = 0.0; *c = 1.0; } else { *s = 1.0; *c = 0.0; } if ((lx & 2) != 0) { *s = -*s; *c = -*c; } } } } else if (n < -2) /* |x| < 0.25 */ *s = __k_sincos(pi * fabs(x), 0.0, c); else { /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */ if (ix < 0x41C00000) { /* |x| < 2**29 */ y = 4.0 * fabs(x); n = (int)y; /* exact */ z = (double)n; k = z == y; t = (y - z) * 0.25; } else { /* 2**29 <= |x| < 2**51 */ y = fabs(x); k = 50 - n; n = lx >> k; h = n << k; ((unsigned *)&z)[LOWORD] = h; ((int *)&z)[HIWORD] = ix; k = h == lx; t = y - z; } if (k) { /* x = N/4 */ if ((n & 1) != 0) { *s = *c = sqrth_h + sqrth_l; } else { if ((n & 2) == 0) { *s = 0.0; *c = 1.0; } else { *s = 1.0; *c = 0.0; } } if ((n & 4) != 0) *s = -*s; if (((n + 1) & 4) != 0) *c = -*c; } else { if ((n & 1) != 0) t = 0.25 - t; if (((n + (n & 1)) & 2) == 0) *s = __k_sincos(pi * t, 0.0, c); else *c = __k_sincos(pi * t, 0.0, s); if ((n & 4) != 0) *s = -*s; if (((n + 2) & 4) != 0) *c = -*c; } } if (hx < 0) *s = -*s; }
