/* * 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. */ /* * void sincospil(long double x, long double *s, long double *c) * *s = sinl(pi*x); *c = cosl(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 "longdouble.h" #include <sys/isa_defs.h> #define I(q, m) ((int *) &(q))[m] #define U(q, m) ((unsigned *) &(q))[m] #if defined(__i386) || defined(__amd64) #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15))) #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0) #define PREC 64 #define PRECM1 63 #define PRECM2 62 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L; #else #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0) #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1) #define PREC 113 #define PRECM1 112 #define PRECM2 111 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L; #endif static const long double zero = 0.0L, quater = 0.25L, one = 1.0L, pi = 3.141592653589793238462643383279502884197e+0000L, sqrth = 0.707106781186547524400844362104849039284835937688474, tiny = 1.0e-100; void sincospil(long double x, long double *s, long double *c) { long double y, z, t; int hx, n, k; unsigned lx; hx = LDBL_MOST_SIGNIF_I(x); lx = LDBL_LEAST_SIGNIF_U(x); k = ((hx & 0x7fff0000) >> 16) - 0x3fff; if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */ if (k >= 16384) { *s = *c = x - x; } else { if (k >= PREC) { *s = zero; *c = one; } else if (k == PRECM1) { if ((lx & 1) == 0) { *s = zero; *c = one; } else { *s = -zero; *c = -one; } } else { /* k = Prec - 2 */ if ((lx & 1) == 0) { *s = zero; *c = one; } else { *s = one; *c = zero; } if ((lx & 2) != 0) { *s = -*s; *c = -*c; } } } } else if (k < -2) /* |x| < 0.25 */ *s = __k_sincosl(pi * fabsl(x), zero, c); else { /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */ y = 4.0L * fabsl(x); if (k < PRECM2) { z = y + twoPRECM2; n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */ t = z - twoPRECM2; k = 0; if (t == y) k = 1; else if (t > y) { n -= 1; t = quater + (y - t) * quater; } else t = (y - t) * quater; } else { /* k = Prec-3 */ n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */ k = 1; } if (k) { /* x = N/4 */ if ((n & 1) != 0) *s = *c = sqrth + tiny; else if ((n & 2) == 0) { *s = zero; *c = one; } else { *s = one; *c = zero; } if ((n & 4) != 0) *s = -*s; if (((n + 1) & 4) != 0) *c = -*c; } else { if ((n & 1) != 0) t = quater - t; if (((n + (n & 1)) & 2) == 0) *s = __k_sincosl(pi * t, zero, c); else *c = __k_sincosl(pi * t, zero, s); if ((n & 4) != 0) *s = -*s; if (((n + 2) & 4) != 0) *c = -*c; } } if (hx < 0) *s = -*s; } #undef U #undef LDBL_LEAST_SIGNIF_U #undef I #undef LDBL_MOST_SIGNIF_I
