diff options
Diffstat (limited to 'usr/src/lib/libm/common/LD/sincospil.c')
| -rw-r--r-- | usr/src/lib/libm/common/LD/sincospil.c | 208 |
1 files changed, 208 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/LD/sincospil.c b/usr/src/lib/libm/common/LD/sincospil.c new file mode 100644 index 0000000000..59b18fd3dd --- /dev/null +++ b/usr/src/lib/libm/common/LD/sincospil.c @@ -0,0 +1,208 @@ +/* + * 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. + */ + +#pragma weak sincospil = __sincospil + +/* + * 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 "libm_synonyms.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 |