static float ponef(float), qonef(float);
static const float
-huge = 1e30,
invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
-tpi = 6.3661974669e-01, /* 0x3f22f983 */
+tpi = 6.3661974669e-01; /* 0x3f22f983 */
+
+static float common(uint32_t ix, float x, int y1, int sign)
+{
+ double z,s,c,ss,cc;
+
+ s = sinf(x);
+ if (y1)
+ s = -s;
+ c = cosf(x);
+ cc = s-c;
+ if (ix < 0x7f000000) {
+ ss = -s-c;
+ z = cosf(2*x);
+ if (s*c > 0)
+ cc = z/ss;
+ else
+ ss = z/cc;
+ if (ix < 0x58800000) {
+ if (y1)
+ ss = -ss;
+ cc = ponef(x)*cc-qonef(x)*ss;
+ }
+ }
+ if (sign)
+ cc = -cc;
+ return invsqrtpi*cc/sqrtf(x);
+}
+
/* R0/S0 on [0,2] */
+static const float
r00 = -6.2500000000e-02, /* 0xbd800000 */
r01 = 1.4070566976e-03, /* 0x3ab86cfd */
r02 = -1.5995563444e-05, /* 0xb7862e36 */
float j1f(float x)
{
- float z,s,c,ss,cc,r,u,v,y;
- int32_t hx,ix;
+ float z,r,s;
+ uint32_t ix;
+ int sign;
- GET_FLOAT_WORD(hx, x);
- ix = hx & 0x7fffffff;
+ GET_FLOAT_WORD(ix, x);
+ sign = ix>>31;
+ ix &= 0x7fffffff;
if (ix >= 0x7f800000)
- return 1.0f/x;
- y = fabsf(x);
- if (ix >= 0x40000000) { /* |x| >= 2.0 */
- s = sinf(y);
- c = cosf(y);
- ss = -s-c;
- cc = s-c;
- if (ix < 0x7f000000) { /* make sure y+y not overflow */
- z = cosf(y+y);
- if (s*c > 0.0f)
- cc = z/ss;
- else
- ss = z/cc;
- }
- /*
- * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
- * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
- */
- if (ix > 0x80000000)
- z = (invsqrtpi*cc)/sqrtf(y);
- else {
- u = ponef(y);
- v = qonef(y);
- z = invsqrtpi*(u*cc-v*ss)/sqrtf(y);
- }
- if (hx < 0)
- return -z;
- return z;
- }
- if (ix < 0x32000000) { /* |x| < 2**-27 */
+ return 1/(x*x);
+ if (ix >= 0x40000000) /* |x| >= 2 */
+ return common(ix, fabsf(x), 0, sign);
+ if (ix >= 0x32000000) { /* |x| >= 2**-27 */
+ z = x*x;
+ r = z*(r00+z*(r01+z*(r02+z*r03)));
+ s = 1+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
+ z = 0.5f + r/s;
+ } else
/* raise inexact if x!=0 */
- if (huge+x > 1.0f)
- return 0.5f*x;
- }
- z = x*x;
- r = z*(r00+z*(r01+z*(r02+z*r03)));
- s = 1.0f+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
- r *= x;
- return 0.5f*x + r/s;
+ z = 0.5f + x;
+ return z*x;
}
static const float U0[5] = {
float y1f(float x)
{
- float z,s,c,ss,cc,u,v;
- int32_t hx,ix;
+ float z,u,v;
+ uint32_t ix;
- GET_FLOAT_WORD(hx, x);
- ix = 0x7fffffff & hx;
- /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
+ GET_FLOAT_WORD(ix, x);
+ if ((ix & 0x7fffffff) == 0)
+ return -1/0.0f;
+ if (ix>>31)
+ return 0/0.0f;
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 */
- s = sinf(x);
- c = cosf(x);
- ss = -s-c;
- cc = s-c;
- 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;
- }
- /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
- * where x0 = x-3pi/4
- * Better formula:
- * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
- * = 1/sqrt(2) * (sin(x) - cos(x))
- * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
- * = -1/sqrt(2) * (cos(x) + sin(x))
- * To avoid cancellation, use
- * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
- * to compute the worse one.
- */
- if (ix > 0x48000000)
- z = (invsqrtpi*ss)/sqrtf(x);
- else {
- u = ponef(x);
- v = qonef(x);
- z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
- }
- return z;
- }
- if (ix <= 0x24800000) /* x < 2**-54 */
+ return 1/x;
+ if (ix >= 0x40000000) /* |x| >= 2.0 */
+ return common(ix,x,1,0);
+ if (ix < 0x32000000) /* x < 2**-27 */
return -tpi/x;
z = x*x;
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
{
const float *p,*q;
float z,r,s;
- int32_t ix;
+ uint32_t ix;
GET_FLOAT_WORD(ix, x);
ix &= 0x7fffffff;
if (ix >= 0x41000000){p = pr8; q = ps8;}
else if (ix >= 0x40f71c58){p = pr5; q = ps5;}
else if (ix >= 0x4036db68){p = pr3; q = ps3;}
- else if (ix >= 0x40000000){p = pr2; q = ps2;}
+ else /*ix >= 0x40000000*/ {p = pr2; q = ps2;}
z = 1.0f/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
{
const float *p,*q;
float s,r,z;
- int32_t ix;
+ uint32_t ix;
GET_FLOAT_WORD(ix, x);
ix &= 0x7fffffff;
if (ix >= 0x40200000){p = qr8; q = qs8;}
else if (ix >= 0x40f71c58){p = qr5; q = qs5;}
else if (ix >= 0x4036db68){p = qr3; q = qs3;}
- else if (ix >= 0x40000000){p = qr2; q = qs2;}
+ else /*ix >= 0x40000000*/ {p = qr2; q = qs2;}
z = 1.0f/(x*x);
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
s = 1.0f+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
projects / musl / blobdiff