src/math/__sinl.c

   1 /* origin: FreeBSD /usr/src/lib/msun/ld80/k_sinl.c */
   2 /* origin: FreeBSD /usr/src/lib/msun/ld128/k_sinl.c */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
   7  *
   8  * Developed at SunSoft, 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 #include "libm.h"
  16
  17 #if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
  18 #if LDBL_MANT_DIG == 64
  19 /*
  20  * ld80 version of __sin.c.  See __sin.c for most comments.
  21  */
  22 /*
  23  * Domain [-0.7854, 0.7854], range ~[-1.89e-22, 1.915e-22]
  24  * |sin(x)/x - s(x)| < 2**-72.1
  25  *
  26  * See __cosl.c for more details about the polynomial.
  27  */
  28 static const long double
  29 S1 = -0.166666666666666666671L;   /* -0xaaaaaaaaaaaaaaab.0p-66 */
  30 static const double
  31 S2 =  0.0083333333333333332,      /*  0x11111111111111.0p-59 */
  32 S3 = -0.00019841269841269427,     /* -0x1a01a01a019f81.0p-65 */
  33 S4 =  0.0000027557319223597490,   /*  0x171de3a55560f7.0p-71 */
  34 S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */
  35 S6 =  1.6059006598854211e-10,     /*  0x161242b90243b5.0p-85 */
  36 S7 = -7.6429779983024564e-13,     /* -0x1ae42ebd1b2e00.0p-93 */
  37 S8 =  2.6174587166648325e-15;     /*  0x179372ea0b3f64.0p-101 */
  38 #define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*S8))))))
  39 #elif LDBL_MANT_DIG == 113
  40 /*
  41  * ld128 version of __sin.c.  See __sin.c for most comments.
  42  */
  43 /*
  44  * Domain [-0.7854, 0.7854], range ~[-1.53e-37, 1.659e-37]
  45  * |sin(x)/x - s(x)| < 2**-122.1
  46  *
  47  * See __cosl.c for more details about the polynomial.
  48  */
  49 static const long double
  50 S1 = -0.16666666666666666666666666666666666606732416116558L,
  51 S2 =  0.0083333333333333333333333333333331135404851288270047L,
  52 S3 = -0.00019841269841269841269841269839935785325638310428717L,
  53 S4 =  0.27557319223985890652557316053039946268333231205686e-5L,
  54 S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
  55 S6 =  0.16059043836821614596571832194524392581082444805729e-9L,
  56 S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
  57 S8 =  0.28114572543451292625024967174638477283187397621303e-14L;
  58 static const double
  59 S9  = -0.82206352458348947812512122163446202498005154296863e-17,
  60 S10 =  0.19572940011906109418080609928334380560135358385256e-19,
  61 S11 = -0.38680813379701966970673724299207480965452616911420e-22,
  62 S12 =  0.64038150078671872796678569586315881020659912139412e-25;
  63 #define POLY(z) (S2+z*(S3+z*(S4+z*(S5+z*(S6+z*(S7+z*(S8+ \
  64         z*(S9+z*(S10+z*(S11+z*S12))))))))))
  65 #endif
  66
  67 long double __sinl(long double x, long double y, int iy)
  68 {
  69         long double z,r,v;
  70
  71         z = x*x;
  72         v = z*x;
  73         r = POLY(z);
  74         if (iy == 0)
  75                 return x+v*(S1+z*r);
  76         return x-((z*(0.5*y-v*r)-y)-v*S1);
  77 }
  78 #endif