/* * (c) copyright 1988 by the Vrije Universiteit, Amsterdam, The Netherlands. * See the copyright notice in the ACK home directory, in the file "Copyright". * * Author: Ceriel J.H. Jacobs */ /* $Header$ */ #define __NO_DEFS #include static double sinus(x, quadrant) double x; { /* sin(0.5*pi*x) = x * P(x*x)/Q(x*x) for x in [0,1] */ /* Hart & Cheney # 3374 */ static double p[6] = { 0.4857791909822798473837058825e+10, -0.1808816670894030772075877725e+10, 0.1724314784722489597789244188e+09, -0.6351331748520454245913645971e+07, 0.1002087631419532326179108883e+06, -0.5830988897678192576148973679e+03 }; static double q[6] = { 0.3092566379840468199410228418e+10, 0.1202384907680254190870913060e+09, 0.2321427631602460953669856368e+07, 0.2848331644063908832127222835e+05, 0.2287602116741682420054505174e+03, 0.1000000000000000000000000000e+01 }; double xsqr; int t; if (x < 0) { quadrant += 2; x = -x; } if (M_PI_2 - x == M_PI_2) { switch(quadrant) { case 0: case 2: return 0.0; case 1: return 1.0; case 3: return -1.0; } } if (x >= M_2PI) { if (x <= 0x7fffffff) { /* Use extended precision to calculate reduced argument. Split 2pi in 2 parts a1 and a2, of which the first only uses some bits of the mantissa, so that n * a1 is exactly representable, where n is the integer part of x/pi. Here we used 12 bits of the mantissa for a1. Also split x in integer part x1 and fraction part x2. We then compute x-n*2pi as ((x1 - n*a1) + x2) - n*a2. */ #define A1 6.2822265625 #define A2 0.00095874467958647692528676655900576 double n = (long) (x / M_2PI); double x1 = (long) x; double x2 = x - x1; x = x1 - n * A1; x += x2; x -= n * A2; #undef A1 #undef A2 } else { extern double _fif(); double dummy; x = _fif(x/M_2PI, 1.0, &dummy) * M_2PI; } } x /= M_PI_2; t = x; x -= t; quadrant = (quadrant + (int)(t % 4)) % 4; if (quadrant & 01) { x = 1 - x; } if (quadrant > 1) { x = -x; } xsqr = x * x; x = x * POLYNOM5(xsqr, p) / POLYNOM5(xsqr, q); return x; } double _sin(x) double x; { return sinus(x, 0); } double _cos(x) double x; { if (x < 0) x = -x; return sinus(x, 1); }