sin.c File Reference

Sine function. More...

#include "prim.h"

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Functions
double	sin (double x)
	Sine function. More...

Detailed Description

Sine function.

Definition in file sin.c.

Function Documentation

sin()

double sin

(

double

x

)

Sine function.

Returns

Sine function of x

Kernel function:
__kernel_sin        ... sine function on [-pi/4,pi/4]
__kernel_cos        ... cose function on [-pi/4,pi/4]
__ieee754_rem_pio2  ... argument reduction routine

Method:
Let S,C and T denote the sin, cos and tan respectively on
[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
in [-pi/4 , +pi/4], and let n = k mod 4.

We have

     n        sin(x)      cos(x)        tan(x)
----------------------------------------------------------
     0          S           C             T
     1          C          -S           -1/T
     2         -S          -C             T
     3         -C           S           -1/T
----------------------------------------------------------

Special cases:
Let trig be any of sin, cos, or tan.
trig(+-INF)  is NaN
trig(NaN)    is that NaN

Accuracy:
TRIG(x) returns trig(x) nearly rounded

Definition at line 86 of file sin.c.

References __kernel_cos(), __kernel_sin(), and rempio2().

Referenced by ccos(), ccosh(), ccot(), ccoth(), ccsc(), ccsch(), cexp(), cot(), cpow(), crd(), csc(), csec(), csech(), csin(), csinh(), ctan(), ctanh(), cvc(), cvs(), hcc(), hcv(), RealNumber::Sine(), and ver().

{
    double y[2], z = 0.0;
    int32_t n, ix;

    GET_HIGH_WORD(ix, x);
    ix &= 0x7FFFFFFF;

    // |x| ~< pi/4
    if (ix <= 0x3FE921FB)
    {
        return __kernel_sin(x, z, 0);
    }

    // sin(Inf or NaN) is NaN
    if (ix >= 0x7FF00000)
    {
        return NAN;
    }

    // argument reduction needed
    n = rempio2(x, y);
    switch (n & 3)
    {
    case 0:
        return __kernel_sin(y[0], y[1], 1);
    case 1:
        return __kernel_cos(y[0], y[1]);
    case 2:
        return -__kernel_sin(y[0], y[1], 1);
    default:
        return -__kernel_cos(y[0], y[1]);
    }
}

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