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Annotation of src/lib/libm/src/s_tan.c, Revision 1.10

1.1       jtc         1: /* @(#)s_tan.c 5.1 93/09/24 */
                      2: /*
                      3:  * ====================================================
                      4:  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
                      5:  *
                      6:  * Developed at SunPro, a Sun Microsystems, Inc. business.
                      7:  * Permission to use, copy, modify, and distribute this
1.9       simonb      8:  * software is freely granted, provided that this notice
1.1       jtc         9:  * is preserved.
                     10:  * ====================================================
                     11:  */
1.3       jtc        12:
1.8       lukem      13: #include <sys/cdefs.h>
1.6       jtc        14: #if defined(LIBM_SCCS) && !defined(lint)
1.10    ! wiz        15: __RCSID("$NetBSD: s_tan.c,v 1.9 1999/07/02 15:37:43 simonb Exp $");
1.3       jtc        16: #endif
1.1       jtc        17:
                     18: /* tan(x)
                     19:  * Return tangent function of x.
                     20:  *
                     21:  * kernel function:
                     22:  *     __kernel_tan            ... tangent function on [-pi/4,pi/4]
                     23:  *     __ieee754_rem_pio2      ... argument reduction routine
                     24:  *
                     25:  * Method.
1.9       simonb     26:  *      Let S,C and T denote the sin, cos and tan respectively on
                     27:  *     [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
1.1       jtc        28:  *     in [-pi/4 , +pi/4], and let n = k mod 4.
                     29:  *     We have
                     30:  *
                     31:  *          n        sin(x)      cos(x)        tan(x)
                     32:  *     ----------------------------------------------------------
                     33:  *         0          S           C             T
                     34:  *         1          C          -S            -1/T
                     35:  *         2         -S          -C             T
                     36:  *         3         -C           S            -1/T
                     37:  *     ----------------------------------------------------------
                     38:  *
                     39:  * Special cases:
                     40:  *      Let trig be any of sin, cos, or tan.
                     41:  *      trig(+-INF)  is NaN, with signals;
                     42:  *      trig(NaN)    is that NaN;
                     43:  *
                     44:  * Accuracy:
1.9       simonb     45:  *     TRIG(x) returns trig(x) nearly rounded
1.1       jtc        46:  */
                     47:
1.4       jtc        48: #include "math.h"
                     49: #include "math_private.h"
1.1       jtc        50:
1.10    ! wiz        51: double
        !            52: tan(double x)
1.1       jtc        53: {
                     54:        double y[2],z=0.0;
1.5       jtc        55:        int32_t n, ix;
1.1       jtc        56:
                     57:     /* High word of x. */
1.4       jtc        58:        GET_HIGH_WORD(ix,x);
1.1       jtc        59:
                     60:     /* |x| ~< pi/4 */
                     61:        ix &= 0x7fffffff;
                     62:        if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
                     63:
                     64:     /* tan(Inf or NaN) is NaN */
                     65:        else if (ix>=0x7ff00000) return x-x;            /* NaN */
                     66:
                     67:     /* argument reduction needed */
                     68:        else {
                     69:            n = __ieee754_rem_pio2(x,y);
                     70:            return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
                     71:                                                        -1 -- n odd */
                     72:        }
                     73: }

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