sysdeps/ieee754/ldbl-96/s_cosl.c

   1 /* s_cosl.c -- long double version of s_cos.c.
   2  */
   3
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunPro, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 #if defined(LIBM_SCCS) && !defined(lint)
  16 static char rcsid[] = "$NetBSD: $";
  17 #endif
  18
  19 /* cosl(x)
  20  * Return cosine function of x.
  21  *
  22  * kernel function:
  23  *      __kernel_sinl           ... sine function on [-pi/4,pi/4]
  24  *      __kernel_cosl           ... cosine function on [-pi/4,pi/4]
  25  *      __ieee754_rem_pio2l     ... argument reduction routine
  26  *
  27  * Method.
  28  *      Let S,C and T denote the sin, cos and tan respectively on
  29  *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
  30  *      in [-pi/4 , +pi/4], and let n = k mod 4.
  31  *      We have
  32  *
  33  *          n        sin(x)      cos(x)        tan(x)
  34  *     ----------------------------------------------------------
  35  *          0          S           C             T
  36  *          1          C          -S            -1/T
  37  *          2         -S          -C             T
  38  *          3         -C           S            -1/T
  39  *     ----------------------------------------------------------
  40  *
  41  * Special cases:
  42  *      Let trig be any of sin, cos, or tan.
  43  *      trig(+-INF)  is NaN, with signals;
  44  *      trig(NaN)    is that NaN;
  45  *
  46  * Accuracy:
  47  *      TRIG(x) returns trig(x) nearly rounded
  48  */
  49
  50 #include <errno.h>
  51 #include <math.h>
  52 #include <math_private.h>
  53 #include <libm-alias-ldouble.h>
  54
  55 long double __cosl(long double x)
  56 {
  57         long double y[2],z=0.0;
  58         int32_t n, se, i0, i1;
  59
  60     /* High word of x. */
  61         GET_LDOUBLE_WORDS(se,i0,i1,x);
  62
  63     /* |x| ~< pi/4 */
  64         se &= 0x7fff;
  65         if(se < 0x3ffe || (se == 0x3ffe && i0 <= 0xc90fdaa2))
  66           return __kernel_cosl(x,z);
  67
  68     /* cos(Inf or NaN) is NaN */
  69         else if (se==0x7fff) {
  70           if (i1 == 0 && i0 == 0x80000000)
  71             __set_errno (EDOM);
  72           return x-x;
  73         }
  74
  75     /* argument reduction needed */
  76         else {
  77             n = __ieee754_rem_pio2l(x,y);
  78             switch(n&3) {
  79                 case 0: return  __kernel_cosl(y[0],y[1]);
  80                 case 1: return -__kernel_sinl(y[0],y[1],1);
  81                 case 2: return -__kernel_cosl(y[0],y[1]);
  82                 default:
  83                         return  __kernel_sinl(y[0],y[1],1);
  84             }
  85         }
  86 }
  87 libm_alias_ldouble (__cos, cos)