Esempio n. 1
0
File: j0f.c Progetto: GregorR/musl
float y0f(float x)
{
	float z,s,c,ss,cc,u,v;
	int32_t hx,ix;

	GET_FLOAT_WORD(hx, x);
	ix = 0x7fffffff & hx;
	/* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
	if (ix >= 0x7f800000)
		return 1.0f/(x+x*x);
	if (ix == 0)
		return -1.0f/0.0f;
	if (hx < 0)
		return 0.0f/0.0f;
	if (ix >= 0x40000000) {  /* |x| >= 2.0 */
		/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
		 * where x0 = x-pi/4
		 *      Better formula:
		 *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
		 *                      =  1/sqrt(2) * (sin(x) + cos(x))
		 *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
		 *                      =  1/sqrt(2) * (sin(x) - cos(x))
		 * To avoid cancellation, use
		 *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
		 * to compute the worse one.
		 */
		s = sinf(x);
		c = cosf(x);
		ss = s-c;
		cc = s+c;
		/*
		 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
		 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
		 */
		if (ix < 0x7f000000) {  /* make sure x+x not overflow */
			z = -cosf(x+x);
			if (s*c < 0.0f)
				cc = z/ss;
			else
				ss = z/cc;
		}
		if (ix > 0x80000000)
			z = (invsqrtpi*ss)/sqrtf(x);
		else {
			u = pzerof(x);
			v = qzerof(x);
			z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
		}
		return z;
	}
	if (ix <= 0x32000000) {  /* x < 2**-27 */
		return u00 + tpi*logf(x);
	}
	z = x*x;
	u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
	v = 1.0f+z*(v01+z*(v02+z*(v03+z*v04)));
	return u/v + tpi*(j0f(x)*logf(x));
}
Esempio n. 2
0
int main()
{
float y;
int i;

for (i = 0; i< 20; i++)
  {
    y = j0f(z[i]);
    printf("%.9e\n", y);
  }
exit(0);
}
Esempio n. 3
0
static void RDFtoRP(const Curve &rdf, int npoints, Curve *rp) {
    const float wstep = 1.f / sqrtf(npoints);
    Curve tmp(rdf);
    for (int i = 0; i < rp->size(); ++i) {
        const float u0 = rp->ToX(i);
        const float u = TWOPI * u0;
        const float wndsize = rdf.x1 * std::min(0.5f, std::max(0.2f, 4.f * u0 * wstep));
        for (int j = 0; j < tmp.size(); ++j) {
            float x = rdf.ToX(j);
            float wnd = BlackmanWindow(x, wndsize);
            tmp[j] = (rdf[j] - 1) * j0f(u*x) * x * wnd;
        }
        (*rp)[i] = fabsf(1.f + TWOPI * Integrate(tmp) * npoints);
    }
}
Esempio n. 4
0
int main(void)
{
	#pragma STDC FENV_ACCESS ON
	float y;
	float d;
	int e, i, err = 0;
	struct f_f *p;

	for (i = 0; i < sizeof t/sizeof *t; i++) {
		p = t + i;

		if (p->r < 0)
			continue;
		fesetround(p->r);
		feclearexcept(FE_ALL_EXCEPT);
		y = j0f(p->x);
		e = fetestexcept(INEXACT|INVALID|DIVBYZERO|UNDERFLOW|OVERFLOW);

		if (!checkexcept(e, p->e, p->r)) {
			printf("%s:%d: bad fp exception: %s j0f(%a)=%a, want %s",
				p->file, p->line, rstr(p->r), p->x, p->y, estr(p->e));
			printf(" got %s\n", estr(e));
			err++;
		}
		d = ulperrf(y, p->y, p->dy);
		if (!checkulp(d, p->r)) {
//			printf("%s:%d: %s j0f(%a) want %a got %a ulperr %.3f = %a + %a\n",
//				p->file, p->line, rstr(p->r), p->x, p->y, y, d, d-p->dy, p->dy);
			err++;
			// TODO: avoid spamming the output
			printf(__FILE__ ": known to be broken near zeros\n");
			break;
		}
	}
	return !!err;
}
Esempio n. 5
0
void
domathf (void)
{
#ifndef NO_FLOAT
  float f1;
  float f2;

  int i1;

  f1 = acosf(0.0);
  fprintf( stdout, "acosf          : %f\n", f1);

  f1 = acoshf(0.0);
  fprintf( stdout, "acoshf         : %f\n", f1);

  f1 = asinf(1.0);
  fprintf( stdout, "asinf          : %f\n", f1);

  f1 = asinhf(1.0);
  fprintf( stdout, "asinhf         : %f\n", f1);

  f1 = atanf(M_PI_4);
  fprintf( stdout, "atanf          : %f\n", f1);

  f1 = atan2f(2.3, 2.3);
  fprintf( stdout, "atan2f         : %f\n", f1);

  f1 = atanhf(1.0);
  fprintf( stdout, "atanhf         : %f\n", f1);

  f1 = cbrtf(27.0);
  fprintf( stdout, "cbrtf          : %f\n", f1);

  f1 = ceilf(3.5);
  fprintf( stdout, "ceilf          : %f\n", f1);

  f1 = copysignf(3.5, -2.5);
  fprintf( stdout, "copysignf      : %f\n", f1);

  f1 = cosf(M_PI_2);
  fprintf( stdout, "cosf           : %f\n", f1);

  f1 = coshf(M_PI_2);
  fprintf( stdout, "coshf          : %f\n", f1);

  f1 = erff(42.0);
  fprintf( stdout, "erff           : %f\n", f1);

  f1 = erfcf(42.0);
  fprintf( stdout, "erfcf          : %f\n", f1);

  f1 = expf(0.42);
  fprintf( stdout, "expf           : %f\n", f1);

  f1 = exp2f(0.42);
  fprintf( stdout, "exp2f          : %f\n", f1);

  f1 = expm1f(0.00042);
  fprintf( stdout, "expm1f         : %f\n", f1);

  f1 = fabsf(-1.123);
  fprintf( stdout, "fabsf          : %f\n", f1);

  f1 = fdimf(1.123, 2.123);
  fprintf( stdout, "fdimf          : %f\n", f1);

  f1 = floorf(0.5);
  fprintf( stdout, "floorf         : %f\n", f1);
  f1 = floorf(-0.5);
  fprintf( stdout, "floorf         : %f\n", f1);

  f1 = fmaf(2.1, 2.2, 3.01);
  fprintf( stdout, "fmaf           : %f\n", f1);

  f1 = fmaxf(-0.42, 0.42);
  fprintf( stdout, "fmaxf          : %f\n", f1);

  f1 = fminf(-0.42, 0.42);
  fprintf( stdout, "fminf          : %f\n", f1);

  f1 = fmodf(42.0, 3.0);
  fprintf( stdout, "fmodf          : %f\n", f1);

  /* no type-specific variant */
  i1 = fpclassify(1.0);
  fprintf( stdout, "fpclassify     : %d\n", i1);

  f1 = frexpf(42.0, &i1);
  fprintf( stdout, "frexpf         : %f\n", f1);

  f1 = hypotf(42.0, 42.0);
  fprintf( stdout, "hypotf         : %f\n", f1);

  i1 = ilogbf(42.0);
  fprintf( stdout, "ilogbf         : %d\n", i1);

  /* no type-specific variant */
  i1 = isfinite(3.0);
  fprintf( stdout, "isfinite       : %d\n", i1);

  /* no type-specific variant */
  i1 = isgreater(3.0, 3.1);
  fprintf( stdout, "isgreater      : %d\n", i1);

  /* no type-specific variant */
  i1 = isgreaterequal(3.0, 3.1);
  fprintf( stdout, "isgreaterequal : %d\n", i1);

  /* no type-specific variant */
  i1 = isinf(3.0);
  fprintf( stdout, "isinf          : %d\n", i1);

  /* no type-specific variant */
  i1 = isless(3.0, 3.1);
  fprintf( stdout, "isless         : %d\n", i1);

  /* no type-specific variant */
  i1 = islessequal(3.0, 3.1);
  fprintf( stdout, "islessequal    : %d\n", i1);

  /* no type-specific variant */
  i1 = islessgreater(3.0, 3.1);
  fprintf( stdout, "islessgreater  : %d\n", i1);

  /* no type-specific variant */
  i1 = isnan(0.0);
  fprintf( stdout, "isnan          : %d\n", i1);

  /* no type-specific variant */
  i1 = isnormal(3.0);
  fprintf( stdout, "isnormal       : %d\n", i1);

  /* no type-specific variant */
  f1 = isunordered(1.0, 2.0);
  fprintf( stdout, "isunordered    : %d\n", i1);

  f1 = j0f(1.2);
  fprintf( stdout, "j0f            : %f\n", f1);

  f1 = j1f(1.2);
  fprintf( stdout, "j1f            : %f\n", f1);

  f1 = jnf(2,1.2);
  fprintf( stdout, "jnf            : %f\n", f1);

  f1 = ldexpf(1.2,3);
  fprintf( stdout, "ldexpf         : %f\n", f1);

  f1 = lgammaf(42.0);
  fprintf( stdout, "lgammaf        : %f\n", f1);

  f1 = llrintf(-0.5);
  fprintf( stdout, "llrintf        : %f\n", f1);
  f1 = llrintf(0.5);
  fprintf( stdout, "llrintf        : %f\n", f1);

  f1 = llroundf(-0.5);
  fprintf( stdout, "lroundf        : %f\n", f1);
  f1 = llroundf(0.5);
  fprintf( stdout, "lroundf        : %f\n", f1);

  f1 = logf(42.0);
  fprintf( stdout, "logf           : %f\n", f1);

  f1 = log10f(42.0);
  fprintf( stdout, "log10f         : %f\n", f1);

  f1 = log1pf(42.0);
  fprintf( stdout, "log1pf         : %f\n", f1);

  f1 = log2f(42.0);
  fprintf( stdout, "log2f          : %f\n", f1);

  f1 = logbf(42.0);
  fprintf( stdout, "logbf          : %f\n", f1);

  f1 = lrintf(-0.5);
  fprintf( stdout, "lrintf         : %f\n", f1);
  f1 = lrintf(0.5);
  fprintf( stdout, "lrintf         : %f\n", f1);

  f1 = lroundf(-0.5);
  fprintf( stdout, "lroundf        : %f\n", f1);
  f1 = lroundf(0.5);
  fprintf( stdout, "lroundf        : %f\n", f1);

  f1 = modff(42.0,&f2);
  fprintf( stdout, "lmodff         : %f\n", f1);

  f1 = nanf("");
  fprintf( stdout, "nanf           : %f\n", f1);

  f1 = nearbyintf(1.5);
  fprintf( stdout, "nearbyintf     : %f\n", f1);

  f1 = nextafterf(1.5,2.0);
  fprintf( stdout, "nextafterf     : %f\n", f1);

  f1 = powf(3.01, 2.0);
  fprintf( stdout, "powf           : %f\n", f1);

  f1 = remainderf(3.01,2.0);
  fprintf( stdout, "remainderf     : %f\n", f1);

  f1 = remquof(29.0,3.0,&i1);
  fprintf( stdout, "remquof        : %f\n", f1);

  f1 = rintf(0.5);
  fprintf( stdout, "rintf          : %f\n", f1);
  f1 = rintf(-0.5);
  fprintf( stdout, "rintf          : %f\n", f1);

  f1 = roundf(0.5);
  fprintf( stdout, "roundf         : %f\n", f1);
  f1 = roundf(-0.5);
  fprintf( stdout, "roundf         : %f\n", f1);

  f1 = scalblnf(1.2,3);
  fprintf( stdout, "scalblnf       : %f\n", f1);

  f1 = scalbnf(1.2,3);
  fprintf( stdout, "scalbnf        : %f\n", f1);

  /* no type-specific variant */
  i1 = signbit(1.0);
  fprintf( stdout, "signbit        : %i\n", i1);

  f1 = sinf(M_PI_4);
  fprintf( stdout, "sinf           : %f\n", f1);

  f1 = sinhf(M_PI_4);
  fprintf( stdout, "sinhf          : %f\n", f1);

  f1 = sqrtf(9.0);
  fprintf( stdout, "sqrtf          : %f\n", f1);

  f1 = tanf(M_PI_4);
  fprintf( stdout, "tanf           : %f\n", f1);

  f1 = tanhf(M_PI_4);
  fprintf( stdout, "tanhf          : %f\n", f1);

  f1 = tgammaf(2.1);
  fprintf( stdout, "tgammaf        : %f\n", f1);

  f1 = truncf(3.5);
  fprintf( stdout, "truncf         : %f\n", f1);

  f1 = y0f(1.2);
  fprintf( stdout, "y0f            : %f\n", f1);

  f1 = y1f(1.2);
  fprintf( stdout, "y1f            : %f\n", f1);

  f1 = ynf(3,1.2);
  fprintf( stdout, "ynf            : %f\n", f1);
#endif
}
Esempio n. 6
0
int main(int argc, char *argv[])
{
  float x = 0.0;
  if (argv) x = j0f((float) argc);
  return 0;
}
Esempio n. 7
0
TEST(math, j0f) {
  ASSERT_FLOAT_EQ(1.0f, j0f(0.0f));
  ASSERT_FLOAT_EQ(0.76519769f, j0f(1.0f));
}
Esempio n. 8
0
float jnf(int n, float x) {
    uint32_t ix;
    int nm1, sign, i;
    float a, b, temp;

    GET_FLOAT_WORD(ix, x);
    sign = ix >> 31;
    ix &= 0x7fffffff;
    if (ix > 0x7f800000) /* nan */
        return x;

    /* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */
    if (n == 0)
        return j0f(x);
    if (n < 0) {
        nm1 = -(n + 1);
        x = -x;
        sign ^= 1;
    } else
        nm1 = n - 1;
    if (nm1 == 0)
        return j1f(x);

    sign &= n; /* even n: 0, odd n: signbit(x) */
    x = fabsf(x);
    if (ix == 0 || ix == 0x7f800000) /* if x is 0 or inf */
        b = 0.0f;
    else if (nm1 < x) {
        /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
        a = j0f(x);
        b = j1f(x);
        for (i = 0; i < nm1;) {
            i++;
            temp = b;
            b = b * (2.0f * i / x) - a;
            a = temp;
        }
    } else {
        if (ix < 0x35800000) { /* x < 2**-20 */
                               /* x is tiny, return the first Taylor expansion of J(n,x)
                                * J(n,x) = 1/n!*(x/2)^n  - ...
                                */
            if (nm1 > 8)       /* underflow */
                nm1 = 8;
            temp = 0.5f * x;
            b = temp;
            a = 1.0f;
            for (i = 2; i <= nm1 + 1; i++) {
                a *= (float)i; /* a = n! */
                b *= temp;     /* b = (x/2)^n */
            }
            b = b / a;
        } else {
            /* use backward recurrence */
            /*                      x      x^2      x^2
             *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
             *                      2n  - 2(n+1) - 2(n+2)
             *
             *                      1      1        1
             *  (for large x)   =  ----  ------   ------   .....
             *                      2n   2(n+1)   2(n+2)
             *                      -- - ------ - ------ -
             *                       x     x         x
             *
             * Let w = 2n/x and h=2/x, then the above quotient
             * is equal to the continued fraction:
             *                  1
             *      = -----------------------
             *                     1
             *         w - -----------------
             *                        1
             *              w+h - ---------
             *                     w+2h - ...
             *
             * To determine how many terms needed, let
             * Q(0) = w, Q(1) = w(w+h) - 1,
             * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
             * When Q(k) > 1e4      good for single
             * When Q(k) > 1e9      good for double
             * When Q(k) > 1e17     good for quadruple
             */
            /* determine k */
            float t, q0, q1, w, h, z, tmp, nf;
            int k;

            nf = nm1 + 1.0f;
            w = 2 * nf / x;
            h = 2 / x;
            z = w + h;
            q0 = w;
            q1 = w * z - 1.0f;
            k = 1;
            while (q1 < 1.0e4f) {
                k += 1;
                z += h;
                tmp = z * q1 - q0;
                q0 = q1;
                q1 = tmp;
            }
            for (t = 0.0f, i = k; i >= 0; i--)
                t = 1.0f / (2 * (i + nf) / x - t);
            a = t;
            b = 1.0f;
            /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
             *  Hence, if n*(log(2n/x)) > ...
             *  single 8.8722839355e+01
             *  double 7.09782712893383973096e+02
             *  long double 1.1356523406294143949491931077970765006170e+04
             *  then recurrent value may overflow and the result is
             *  likely underflow to zero
             */
            tmp = nf * logf(fabsf(w));
            if (tmp < 88.721679688f) {
                for (i = nm1; i > 0; i--) {
                    temp = b;
                    b = 2.0f * i * b / x - a;
                    a = temp;
                }
            } else {
                for (i = nm1; i > 0; i--) {
                    temp = b;
                    b = 2.0f * i * b / x - a;
                    a = temp;
                    /* scale b to avoid spurious overflow */
                    if (b > 0x1p60f) {
                        a /= b;
                        t /= b;
                        b = 1.0f;
                    }
                }
            }
            z = j0f(x);
            w = j1f(x);
            if (fabsf(z) >= fabsf(w))
                b = t * z / b;
            else
                b = t * w / a;
        }
    }
    return sign ? -b : b;
}
Esempio n. 9
0
__global__ void FloatMathPrecise() {
    int iX;
    float fX, fY;

    acosf(1.0f);
    acoshf(1.0f);
    asinf(0.0f);
    asinhf(0.0f);
    atan2f(0.0f, 1.0f);
    atanf(0.0f);
    atanhf(0.0f);
    cbrtf(0.0f);
    fX = ceilf(0.0f);
    fX = copysignf(1.0f, -2.0f);
    cosf(0.0f);
    coshf(0.0f);
    cospif(0.0f);
    cyl_bessel_i0f(0.0f);
    cyl_bessel_i1f(0.0f);
    erfcf(0.0f);
    erfcinvf(2.0f);
    erfcxf(0.0f);
    erff(0.0f);
    erfinvf(1.0f);
    exp10f(0.0f);
    exp2f(0.0f);
    expf(0.0f);
    expm1f(0.0f);
    fX = fabsf(1.0f);
    fdimf(1.0f, 0.0f);
    fdividef(0.0f, 1.0f);
    fX = floorf(0.0f);
    fmaf(1.0f, 2.0f, 3.0f);
    fX = fmaxf(0.0f, 0.0f);
    fX = fminf(0.0f, 0.0f);
    fmodf(0.0f, 1.0f);
    frexpf(0.0f, &iX);
    hypotf(1.0f, 0.0f);
    ilogbf(1.0f);
    isfinite(0.0f);
    fX = isinf(0.0f);
    fX = isnan(0.0f);
    j0f(0.0f);
    j1f(0.0f);
    jnf(-1.0f, 1.0f);
    ldexpf(0.0f, 0);
    lgammaf(1.0f);
    llrintf(0.0f);
    llroundf(0.0f);
    log10f(1.0f);
    log1pf(-1.0f);
    log2f(1.0f);
    logbf(1.0f);
    logf(1.0f);
    lrintf(0.0f);
    lroundf(0.0f);
    modff(0.0f, &fX);
    fX = nanf("1");
    fX = nearbyintf(0.0f);
    nextafterf(0.0f, 0.0f);
    norm3df(1.0f, 0.0f, 0.0f);
    norm4df(1.0f, 0.0f, 0.0f, 0.0f);
    normcdff(0.0f);
    normcdfinvf(1.0f);
    fX = 1.0f;
    normf(1, &fX);
    powf(1.0f, 0.0f);
    rcbrtf(1.0f);
    remainderf(2.0f, 1.0f);
    remquof(1.0f, 2.0f, &iX);
    rhypotf(0.0f, 1.0f);
    fY = rintf(1.0f);
    rnorm3df(0.0f, 0.0f, 1.0f);
    rnorm4df(0.0f, 0.0f, 0.0f, 1.0f);
    fX = 1.0f;
    rnormf(1, &fX);
    fY = roundf(0.0f);
    rsqrtf(1.0f);
    scalblnf(0.0f, 1);
    scalbnf(0.0f, 1);
    signbit(1.0f);
    sincosf(0.0f, &fX, &fY);
    sincospif(0.0f, &fX, &fY);
    sinf(0.0f);
    sinhf(0.0f);
    sinpif(0.0f);
    sqrtf(0.0f);
    tanf(0.0f);
    tanhf(0.0f);
    tgammaf(2.0f);
    fY = truncf(0.0f);
    y0f(1.0f);
    y1f(1.0f);
    ynf(1, 1.0f);
}