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Diffstat (limited to 'usr/src/lib/libm/common/C/sincos.c')
-rw-r--r-- | usr/src/lib/libm/common/C/sincos.c | 368 |
1 files changed, 368 insertions, 0 deletions
diff --git a/usr/src/lib/libm/common/C/sincos.c b/usr/src/lib/libm/common/C/sincos.c new file mode 100644 index 0000000000..461ba30f7f --- /dev/null +++ b/usr/src/lib/libm/common/C/sincos.c @@ -0,0 +1,368 @@ +/* + * 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 2005 Sun Microsystems, Inc. All rights reserved. + * Use is subject to license terms. + */ + +#pragma weak sincos = __sincos + +/* INDENT OFF */ +/* + * sincos(x,s,c) + * Accurate Table look-up algorithm by K.C. Ng, 2000. + * + * 1. Reduce x to x>0 by cos(-x)=cos(x), sin(-x)=-sin(x). + * 2. For 0<= x < 8, let i = (64*x chopped)-10. Let d = x - a[i], where + * a[i] is a double that is close to (i+10.5)/64 (and hence |d|< 10.5/64) + * and such that sin(a[i]) and cos(a[i]) is close to a double (with error + * less than 2**-8 ulp). Then + * + * cos(x) = cos(a[i]+d) = cos(a[i])cos(d) - sin(a[i])*sin(d) + * = TBL_cos_a[i]*(1+QQ1*d^2+QQ2*d^4) - + * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5) + * = TBL_cos_a[i] + (TBL_cos_a[i]*d^2*(QQ1+QQ2*d^2) - + * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5)) + * + * sin(x) = sin(a[i]+d) = sin(a[i])cos(d) + cos(a[i])*sin(d) + * = TBL_sin_a[i]*(1+QQ1*d^2+QQ2*d^4) + + * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5) + * = TBL_sin_a[i] + (TBL_sin_a[i]*d^2*(QQ1+QQ2*d^2) + + * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5)) + * + * Note: for x close to n*pi/2, special treatment is need for either + * sin or cos: + * i in [81, 100] ( pi/2 +-10.5/64 => tiny cos(x) = sin(pi/2-x) + * i in [181,200] ( pi +-10.5/64 => tiny sin(x) = sin(pi-x) + * i in [282,301] ( 3pi/2+-10.5/64 => tiny cos(x) = sin(x-3pi/2) + * i in [382,401] ( 2pi +-10.5/64 => tiny sin(x) = sin(x-2pi) + * i in [483,502] ( 5pi/2+-10.5/64 => tiny cos(x) = sin(5pi/2-x) + * + * 3. For x >= 8.0, use kernel function __rem_pio2 to perform argument + * reduction and call __k_sincos_ to compute sin and cos. + * + * kernel function: + * __rem_pio2 ... argument reduction routine + * __k_sincos_ ... sine and cosine function on [-pi/4,pi/4] + * + * Method. + * Let S and C denote the sin and cos respectively on [-PI/4, +PI/4]. + * 1. Assume the argument x is reduced to y1+y2 = x-k*pi/2 in + * [-pi/2 , +pi/2], and let n = k mod 4. + * 2. Let S=S(y1+y2), C=C(y1+y2). Depending on n, we have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C S/C + * 1 C -S -C/S + * 2 -S -C S/C + * 3 -C S -C/S + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded (less than 1 ulp) + */ + +#include "libm.h" + +static const double sc[] = { +/* ONE = */ 1.0, +/* NONE = */ -1.0, +/* + * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008 + */ +/* PP1 = */ -0.166666666666316558867252052378889521480627858683055567, +/* PP2 = */ .008333315652997472323564894248466758248475374977974017927, +/* + * |(sin(x) - (x+p1*x^3+...+p4*x^9)| + * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125 + * | x | + */ +/* P1 = */ -1.666666666666629669805215138920301589656e-0001, +/* P2 = */ 8.333333332390951295683993455280336376663e-0003, +/* P3 = */ -1.984126237997976692791551778230098403960e-0004, +/* P4 = */ 2.753403624854277237649987622848330351110e-0006, +/* + * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d) + */ +/* QQ1 = */ -0.4999999999975492381842911981948418542742729, +/* QQ2 = */ 0.041666542904352059294545209158357640398771740, +/* Q1 = */ -0.5, +/* Q2 = */ 4.166666666500350703680945520860748617445e-0002, +/* Q3 = */ -1.388888596436972210694266290577848696006e-0003, +/* Q4 = */ 2.478563078858589473679519517892953492192e-0005, +/* PIO2_H = */ 1.570796326794896557999, +/* PIO2_L = */ 6.123233995736765886130e-17, +/* PIO2_L0 = */ 6.123233995727922165564e-17, +/* PIO2_L1 = */ 8.843720566135701120255e-29, +/* PI_H = */ 3.1415926535897931159979634685, +/* PI_L = */ 1.22464679914735317722606593227425e-16, +/* PI_L0 = */ 1.22464679914558443311283879205095e-16, +/* PI_L1 = */ 1.768744113227140223300005233735517376e-28, +/* PI3O2_H = */ 4.712388980384689673997, +/* PI3O2_L = */ 1.836970198721029765839e-16, +/* PI3O2_L0 = */ 1.836970198720396133587e-16, +/* PI3O2_L1 = */ 6.336322524749201142226e-29, +/* PI2_H = */ 6.2831853071795862319959269370, +/* PI2_L = */ 2.44929359829470635445213186454850e-16, +/* PI2_L0 = */ 2.44929359829116886622567758410190e-16, +/* PI2_L1 = */ 3.537488226454280446600010467471034752e-28, +/* PI5O2_H = */ 7.853981633974482789995, +/* PI5O2_L = */ 3.061616997868382943065e-16, +/* PI5O2_L0 = */ 3.061616997861941598865e-16, +/* PI5O2_L1 = */ 6.441344200433640781982e-28, +}; +/* INDENT ON */ + +#define ONE sc[0] +#define PP1 sc[2] +#define PP2 sc[3] +#define P1 sc[4] +#define P2 sc[5] +#define P3 sc[6] +#define P4 sc[7] +#define QQ1 sc[8] +#define QQ2 sc[9] +#define Q1 sc[10] +#define Q2 sc[11] +#define Q3 sc[12] +#define Q4 sc[13] +#define PIO2_H sc[14] +#define PIO2_L sc[15] +#define PIO2_L0 sc[16] +#define PIO2_L1 sc[17] +#define PI_H sc[18] +#define PI_L sc[19] +#define PI_L0 sc[20] +#define PI_L1 sc[21] +#define PI3O2_H sc[22] +#define PI3O2_L sc[23] +#define PI3O2_L0 sc[24] +#define PI3O2_L1 sc[25] +#define PI2_H sc[26] +#define PI2_L sc[27] +#define PI2_L0 sc[28] +#define PI2_L1 sc[29] +#define PI5O2_H sc[30] +#define PI5O2_L sc[31] +#define PI5O2_L0 sc[32] +#define PI5O2_L1 sc[33] +#define PoS(x, z) ((x * z) * (PP1 + z * PP2)) +#define PoL(x, z) ((x * z) * ((P1 + z * P2) + (z * z) * (P3 + z * P4))) + +extern const double _TBL_sincos[], _TBL_sincosx[]; + +void +sincos(double x, double *s, double *c) { + double z, y[2], w, t, v, p, q; + int i, j, n, hx, ix, lx; + + hx = ((int *)&x)[HIWORD]; + lx = ((int *)&x)[LOWORD]; + ix = hx & ~0x80000000; + + if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */ + if (ix < 0x3e400000) { /* |x| < 2**-27 */ + if ((int)x == 0) + *c = ONE; + *s = x; + } else { + z = x * x; + if (ix < 0x3f800000) { /* |x| < 0.008 */ + q = z * (QQ1 + z * QQ2); + p = PoS(x, z); + } else { + q = z * ((Q1 + z * Q2) + (z * z) * + (Q3 + z * Q4)); + p = PoL(x, z); + } + *c = ONE + q; + *s = x + p; + } + return; + } + + n = ix >> 20; + i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n); + j = i - 10; + if (n < 0x402) { /* |x| < 8 */ + x = fabs(x); + v = x - _TBL_sincosx[j]; + t = v * v; + w = _TBL_sincos[(j<<1)]; + z = _TBL_sincos[(j<<1)+1]; + p = v + PoS(v, t); + q = t * (QQ1 + t * QQ2); + if ((((j - 81) ^ (j - 101)) | + ((j - 282) ^ (j - 302)) | + ((j - 483) ^ (j - 503)) | + ((j - 181) ^ (j - 201)) | + ((j - 382) ^ (j - 402))) < 0) { + if (j <= 101) { + /* near pi/2, cos(x) = sin(pi/2-x) */ + t = w * q + z * p; + *s = (hx >= 0)? w + t : -w - t; + p = PIO2_H - x; + i = ix - 0x3ff921fb; + x = p + PIO2_L; + if ((i | ((lx - 0x54442D00) & + 0xffffff00)) == 0) { + /* very close to pi/2 */ + x = p + PIO2_L0; + *c = x + PIO2_L1; + } else { + z = x * x; + if (((ix - 0x3ff92000) >> 12) == 0) { + /* |pi/2-x|<2**-8 */ + w = PIO2_L + PoS(x, z); + } else { + w = PIO2_L + PoL(x, z); + } + *c = p + w; + } + } else if (j <= 201) { + /* near pi, sin(x) = sin(pi-x) */ + *c = z - (w * p - z * q); + p = PI_H - x; + i = ix - 0x400921fb; + x = p + PI_L; + if ((i | ((lx - 0x54442D00) & + 0xffffff00)) == 0) { + /* very close to pi */ + x = p + PI_L0; + *s = (hx >= 0)? x + PI_L1 : + -(x + PI_L1); + } else { + z = x * x; + if (((ix - 0x40092000) >> 11) == 0) { + /* |pi-x|<2**-8 */ + w = PI_L + PoS(x, z); + } else { + w = PI_L + PoL(x, z); + } + *s = (hx >= 0)? p + w : -p - w; + } + } else if (j <= 302) { + /* near 3/2pi, cos(x)=sin(x-3/2pi) */ + t = w * q + z * p; + *s = (hx >= 0)? w + t : -w - t; + p = x - PI3O2_H; + i = ix - 0x4012D97C; + x = p - PI3O2_L; + if ((i | ((lx - 0x7f332100) & + 0xffffff00)) == 0) { + /* very close to 3/2pi */ + x = p - PI3O2_L0; + *c = x - PI3O2_L1; + } else { + z = x * x; + if (((ix - 0x4012D800) >> 9) == 0) { + /* |3/2pi-x|<2**-8 */ + w = PoS(x, z) - PI3O2_L; + } else { + w = PoL(x, z) - PI3O2_L; + } + *c = p + w; + } + } else if (j <= 402) { + /* near 2pi, sin(x)=sin(x-2pi) */ + *c = z - (w * p - z * q); + p = x - PI2_H; + i = ix - 0x401921fb; + x = p - PI2_L; + if ((i | ((lx - 0x54442D00) & + 0xffffff00)) == 0) { + /* very close to 2pi */ + x = p - PI2_L0; + *s = (hx >= 0)? x - PI2_L1 : + -(x - PI2_L1); + } else { + z = x * x; + if (((ix - 0x40192000) >> 10) == 0) { + /* |x-2pi|<2**-8 */ + w = PoS(x, z) - PI2_L; + } else { + w = PoL(x, z) - PI2_L; + } + *s = (hx >= 0)? p + w : -p - w; + } + } else { + /* near 5pi/2, cos(x) = sin(5pi/2-x) */ + t = w * q + z * p; + *s = (hx >= 0)? w + t : -w - t; + p = PI5O2_H - x; + i = ix - 0x401F6A7A; + x = p + PI5O2_L; + if ((i | ((lx - 0x29553800) & + 0xffffff00)) == 0) { + /* very close to pi/2 */ + x = p + PI5O2_L0; + *c = x + PI5O2_L1; + } else { + z = x * x; + if (((ix - 0x401F6A7A) >> 7) == 0) { + /* |5pi/2-x|<2**-8 */ + w = PI5O2_L + PoS(x, z); + } else { + w = PI5O2_L + PoL(x, z); + } + *c = p + w; + } + } + } else { + *c = z - (w * p - z * q); + t = w * q + z * p; + *s = (hx >= 0)? w + t : -w - t; + } + return; + } + + if (ix >= 0x7ff00000) { + *s = *c = x / x; + return; + } + + /* argument reduction needed */ + n = __rem_pio2(x, y); + switch (n & 3) { + case 0: + *s = __k_sincos(y[0], y[1], c); + break; + case 1: + *c = -__k_sincos(y[0], y[1], s); + break; + case 2: + *s = -__k_sincos(y[0], y[1], c); + *c = -*c; + break; + default: + *c = __k_sincos(y[0], y[1], s); + *s = -*s; + } +} |