diff options
Diffstat (limited to 'lib/msun/src/s_sinpi.c')
| -rw-r--r-- | lib/msun/src/s_sinpi.c | 161 |
1 files changed, 161 insertions, 0 deletions
diff --git a/lib/msun/src/s_sinpi.c b/lib/msun/src/s_sinpi.c new file mode 100644 index 000000000000..8b388de863c3 --- /dev/null +++ b/lib/msun/src/s_sinpi.c @@ -0,0 +1,161 @@ +/*- + * Copyright (c) 2017, 2023 Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/** + * sinpi(x) computes sin(pi*x) without multiplication by pi (almost). First, + * note that sinpi(-x) = -sinpi(x), so the algorithm considers only |x| and + * includes reflection symmetry by considering the sign of x on output. The + * method used depends on the magnitude of x. + * + * 1. For small |x|, sinpi(x) = pi * x where a sloppy threshold is used. The + * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the + * floating-point type and M = 2 to 4. To achieve high accuracy, pi is + * decomposed into high and low parts with the high part containing a + * number of trailing zero bits. x is also split into high and low parts. + * + * 2. For |x| < 1, argument reduction is not required and sinpi(x) is + * computed by calling a kernel that leverages the kernels for sin(x) + * ans cos(x). See k_sinpi.c and k_cospi.c for details. + * + * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where + * |x| = j0 + r with j0 an integer and the remainder r satisfies + * 0 <= r < 1. With the given domain, a simplified inline floor(x) + * is used. Also, note the following identity + * + * sinpi(x) = sin(pi*(j0+r)) + * = sin(pi*j0) * cos(pi*r) + cos(pi*j0) * sin(pi*r) + * = cos(pi*j0) * sin(pi*r) + * = +-sinpi(r) + * + * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1. + * sinpi(r) is then computed via an appropriate kernel. + * + * 4. For |x| >= 0x1p(P-1), |x| is integral and sinpi(x) = copysign(0,x). + * + * 5. Special cases: + * + * sinpi(+-0) = +-0 + * sinpi(+-n) = +-0, for positive integers n. + * sinpi(+-inf) = nan. Raises the "invalid" floating-point exception. + * sinpi(nan) = nan. Raises the "invalid" floating-point exception. + */ + +#include <float.h> +#include "math.h" +#include "math_private.h" + +static const double +pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */ +pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */ + +#include "k_cospi.h" +#include "k_sinpi.h" + +volatile static const double vzero = 0; + +double +sinpi(double x) +{ + double ax, hi, lo, s; + uint32_t hx, ix, j0, lx; + + EXTRACT_WORDS(hx, lx, x); + ix = hx & 0x7fffffff; + INSERT_WORDS(ax, ix, lx); + + if (ix < 0x3ff00000) { /* |x| < 1 */ + if (ix < 0x3fd00000) { /* |x| < 0.25 */ + if (ix < 0x3e200000) { /* |x| < 0x1p-29 */ + if (x == 0) + return (x); + /* + * To avoid issues with subnormal values, + * scale the computation and rescale on + * return. + */ + INSERT_WORDS(hi, hx, 0); + hi *= 0x1p53; + lo = x * 0x1p53 - hi; + s = (pi_lo + pi_hi) * lo + pi_lo * hi + + pi_hi * hi; + return (s * 0x1p-53); + } + + s = __kernel_sinpi(ax); + return ((hx & 0x80000000) ? -s : s); + } + + if (ix < 0x3fe00000) /* |x| < 0.5 */ + s = __kernel_cospi(0.5 - ax); + else if (ix < 0x3fe80000) /* |x| < 0.75 */ + s = __kernel_cospi(ax - 0.5); + else + s = __kernel_sinpi(1 - ax); + return ((hx & 0x80000000) ? -s : s); + } + + if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */ + FFLOOR(x, j0, ix, lx); /* Integer part of ax. */ + ax -= x; + EXTRACT_WORDS(ix, lx, ax); + + if (ix == 0) + s = 0; + else { + if (ix < 0x3fe00000) { /* |x| < 0.5 */ + if (ix < 0x3fd00000) /* |x| < 0.25 */ + s = __kernel_sinpi(ax); + else + s = __kernel_cospi(0.5 - ax); + } else { + if (ix < 0x3fe80000) /* |x| < 0.75 */ + s = __kernel_cospi(ax - 0.5); + else + s = __kernel_sinpi(1 - ax); + } + + if (j0 > 30) + x -= 0x1p30; + j0 = (uint32_t)x; + if (j0 & 1) s = -s; + } + + return ((hx & 0x80000000) ? -s : s); + } + + /* x = +-inf or nan. */ + if (ix >= 0x7ff00000) + return (vzero / vzero); + + /* + * |x| >= 0x1p52 is always an integer, so return +-0. + */ + return (copysign(0, x)); +} + +#if LDBL_MANT_DIG == 53 +__weak_reference(sinpi, sinpil); +#endif |