| Index: fusl/src/math/j0f.c
|
| diff --git a/fusl/src/math/j0f.c b/fusl/src/math/j0f.c
|
| index 45883dc419e9816bbd0ce31af33619484032ee86..6d926d3ac2109463c893b24be4e344fd95831dfe 100644
|
| --- a/fusl/src/math/j0f.c
|
| +++ b/fusl/src/math/j0f.c
|
| @@ -18,113 +18,108 @@
|
|
|
| static float pzerof(float), qzerof(float);
|
|
|
| -static const float
|
| -invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
|
| -tpi = 6.3661974669e-01; /* 0x3f22f983 */
|
| +static const float invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
|
| + tpi = 6.3661974669e-01; /* 0x3f22f983 */
|
|
|
| -static float common(uint32_t ix, float x, int y0)
|
| -{
|
| - float z,s,c,ss,cc;
|
| - /*
|
| - * 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)
|
| - */
|
| - s = sinf(x);
|
| - c = cosf(x);
|
| - if (y0)
|
| - c = -c;
|
| - 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 (y0)
|
| - ss = -ss;
|
| - cc = pzerof(x)*cc-qzerof(x)*ss;
|
| - }
|
| - }
|
| - return invsqrtpi*cc/sqrtf(x);
|
| +static float common(uint32_t ix, float x, int y0) {
|
| + float z, s, c, ss, cc;
|
| + /*
|
| + * 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)
|
| + */
|
| + s = sinf(x);
|
| + c = cosf(x);
|
| + if (y0)
|
| + c = -c;
|
| + 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 (y0)
|
| + ss = -ss;
|
| + cc = pzerof(x) * cc - qzerof(x) * ss;
|
| + }
|
| + }
|
| + return invsqrtpi * cc / sqrtf(x);
|
| }
|
|
|
| /* R0/S0 on [0, 2.00] */
|
| -static const float
|
| -R02 = 1.5625000000e-02, /* 0x3c800000 */
|
| -R03 = -1.8997929874e-04, /* 0xb947352e */
|
| -R04 = 1.8295404516e-06, /* 0x35f58e88 */
|
| -R05 = -4.6183270541e-09, /* 0xb19eaf3c */
|
| -S01 = 1.5619102865e-02, /* 0x3c7fe744 */
|
| -S02 = 1.1692678527e-04, /* 0x38f53697 */
|
| -S03 = 5.1354652442e-07, /* 0x3509daa6 */
|
| -S04 = 1.1661400734e-09; /* 0x30a045e8 */
|
| +static const float R02 = 1.5625000000e-02, /* 0x3c800000 */
|
| + R03 = -1.8997929874e-04, /* 0xb947352e */
|
| + R04 = 1.8295404516e-06, /* 0x35f58e88 */
|
| + R05 = -4.6183270541e-09, /* 0xb19eaf3c */
|
| + S01 = 1.5619102865e-02, /* 0x3c7fe744 */
|
| + S02 = 1.1692678527e-04, /* 0x38f53697 */
|
| + S03 = 5.1354652442e-07, /* 0x3509daa6 */
|
| + S04 = 1.1661400734e-09; /* 0x30a045e8 */
|
|
|
| -float j0f(float x)
|
| -{
|
| - float z,r,s;
|
| - uint32_t ix;
|
| +float j0f(float x) {
|
| + float z, r, s;
|
| + uint32_t ix;
|
|
|
| - GET_FLOAT_WORD(ix, x);
|
| - ix &= 0x7fffffff;
|
| - if (ix >= 0x7f800000)
|
| - return 1/(x*x);
|
| - x = fabsf(x);
|
| + GET_FLOAT_WORD(ix, x);
|
| + ix &= 0x7fffffff;
|
| + if (ix >= 0x7f800000)
|
| + return 1 / (x * x);
|
| + x = fabsf(x);
|
|
|
| - if (ix >= 0x40000000) { /* |x| >= 2 */
|
| - /* large ulp error near zeros */
|
| - return common(ix, x, 0);
|
| - }
|
| - if (ix >= 0x3a000000) { /* |x| >= 2**-11 */
|
| - /* up to 4ulp error near 2 */
|
| - z = x*x;
|
| - r = z*(R02+z*(R03+z*(R04+z*R05)));
|
| - s = 1+z*(S01+z*(S02+z*(S03+z*S04)));
|
| - return (1+x/2)*(1-x/2) + z*(r/s);
|
| - }
|
| - if (ix >= 0x21800000) /* |x| >= 2**-60 */
|
| - x = 0.25f*x*x;
|
| - return 1 - x;
|
| + if (ix >= 0x40000000) { /* |x| >= 2 */
|
| + /* large ulp error near zeros */
|
| + return common(ix, x, 0);
|
| + }
|
| + if (ix >= 0x3a000000) { /* |x| >= 2**-11 */
|
| + /* up to 4ulp error near 2 */
|
| + z = x * x;
|
| + r = z * (R02 + z * (R03 + z * (R04 + z * R05)));
|
| + s = 1 + z * (S01 + z * (S02 + z * (S03 + z * S04)));
|
| + return (1 + x / 2) * (1 - x / 2) + z * (r / s);
|
| + }
|
| + if (ix >= 0x21800000) /* |x| >= 2**-60 */
|
| + x = 0.25f * x * x;
|
| + return 1 - x;
|
| }
|
|
|
| -static const float
|
| -u00 = -7.3804296553e-02, /* 0xbd9726b5 */
|
| -u01 = 1.7666645348e-01, /* 0x3e34e80d */
|
| -u02 = -1.3818567619e-02, /* 0xbc626746 */
|
| -u03 = 3.4745343146e-04, /* 0x39b62a69 */
|
| -u04 = -3.8140706238e-06, /* 0xb67ff53c */
|
| -u05 = 1.9559013964e-08, /* 0x32a802ba */
|
| -u06 = -3.9820518410e-11, /* 0xae2f21eb */
|
| -v01 = 1.2730483897e-02, /* 0x3c509385 */
|
| -v02 = 7.6006865129e-05, /* 0x389f65e0 */
|
| -v03 = 2.5915085189e-07, /* 0x348b216c */
|
| -v04 = 4.4111031494e-10; /* 0x2ff280c2 */
|
| +static const float u00 = -7.3804296553e-02, /* 0xbd9726b5 */
|
| + u01 = 1.7666645348e-01, /* 0x3e34e80d */
|
| + u02 = -1.3818567619e-02, /* 0xbc626746 */
|
| + u03 = 3.4745343146e-04, /* 0x39b62a69 */
|
| + u04 = -3.8140706238e-06, /* 0xb67ff53c */
|
| + u05 = 1.9559013964e-08, /* 0x32a802ba */
|
| + u06 = -3.9820518410e-11, /* 0xae2f21eb */
|
| + v01 = 1.2730483897e-02, /* 0x3c509385 */
|
| + v02 = 7.6006865129e-05, /* 0x389f65e0 */
|
| + v03 = 2.5915085189e-07, /* 0x348b216c */
|
| + v04 = 4.4111031494e-10; /* 0x2ff280c2 */
|
|
|
| -float y0f(float x)
|
| -{
|
| - float z,u,v;
|
| - uint32_t ix;
|
| +float y0f(float x) {
|
| + float z, u, v;
|
| + uint32_t ix;
|
|
|
| - 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/x;
|
| - if (ix >= 0x40000000) { /* |x| >= 2.0 */
|
| - /* large ulp error near zeros */
|
| - return common(ix,x,1);
|
| - }
|
| - if (ix >= 0x39000000) { /* x >= 2**-13 */
|
| - /* large ulp error at x ~= 0.89 */
|
| - z = x*x;
|
| - u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
|
| - v = 1+z*(v01+z*(v02+z*(v03+z*v04)));
|
| - return u/v + tpi*(j0f(x)*logf(x));
|
| - }
|
| - return u00 + tpi*logf(x);
|
| + 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 / x;
|
| + if (ix >= 0x40000000) { /* |x| >= 2.0 */
|
| + /* large ulp error near zeros */
|
| + return common(ix, x, 1);
|
| + }
|
| + if (ix >= 0x39000000) { /* x >= 2**-13 */
|
| + /* large ulp error at x ~= 0.89 */
|
| + z = x * x;
|
| + u = u00 +
|
| + z * (u01 + z * (u02 + z * (u03 + z * (u04 + z * (u05 + z * u06)))));
|
| + v = 1 + z * (v01 + z * (v02 + z * (v03 + z * v04)));
|
| + return u / v + tpi * (j0f(x) * logf(x));
|
| + }
|
| + return u00 + tpi * logf(x);
|
| }
|
|
|
| /* The asymptotic expansions of pzero is
|
| @@ -136,88 +131,99 @@ float y0f(float x)
|
| * and
|
| * | pzero(x)-1-R/S | <= 2 ** ( -60.26)
|
| */
|
| -static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
| - 0.0000000000e+00, /* 0x00000000 */
|
| - -7.0312500000e-02, /* 0xbd900000 */
|
| - -8.0816707611e+00, /* 0xc1014e86 */
|
| - -2.5706311035e+02, /* 0xc3808814 */
|
| - -2.4852163086e+03, /* 0xc51b5376 */
|
| - -5.2530439453e+03, /* 0xc5a4285a */
|
| +static const float pR8[6] = {
|
| + /* for x in [inf, 8]=1/[0,0.125] */
|
| + 0.0000000000e+00, /* 0x00000000 */
|
| + -7.0312500000e-02, /* 0xbd900000 */
|
| + -8.0816707611e+00, /* 0xc1014e86 */
|
| + -2.5706311035e+02, /* 0xc3808814 */
|
| + -2.4852163086e+03, /* 0xc51b5376 */
|
| + -5.2530439453e+03, /* 0xc5a4285a */
|
| };
|
| static const float pS8[5] = {
|
| - 1.1653436279e+02, /* 0x42e91198 */
|
| - 3.8337448730e+03, /* 0x456f9beb */
|
| - 4.0597855469e+04, /* 0x471e95db */
|
| - 1.1675296875e+05, /* 0x47e4087c */
|
| - 4.7627726562e+04, /* 0x473a0bba */
|
| + 1.1653436279e+02, /* 0x42e91198 */
|
| + 3.8337448730e+03, /* 0x456f9beb */
|
| + 4.0597855469e+04, /* 0x471e95db */
|
| + 1.1675296875e+05, /* 0x47e4087c */
|
| + 4.7627726562e+04, /* 0x473a0bba */
|
| };
|
| -static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
| - -1.1412546255e-11, /* 0xad48c58a */
|
| - -7.0312492549e-02, /* 0xbd8fffff */
|
| - -4.1596107483e+00, /* 0xc0851b88 */
|
| - -6.7674766541e+01, /* 0xc287597b */
|
| - -3.3123129272e+02, /* 0xc3a59d9b */
|
| - -3.4643338013e+02, /* 0xc3ad3779 */
|
| +static const float pR5[6] = {
|
| + /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
| + -1.1412546255e-11, /* 0xad48c58a */
|
| + -7.0312492549e-02, /* 0xbd8fffff */
|
| + -4.1596107483e+00, /* 0xc0851b88 */
|
| + -6.7674766541e+01, /* 0xc287597b */
|
| + -3.3123129272e+02, /* 0xc3a59d9b */
|
| + -3.4643338013e+02, /* 0xc3ad3779 */
|
| };
|
| static const float pS5[5] = {
|
| - 6.0753936768e+01, /* 0x42730408 */
|
| - 1.0512523193e+03, /* 0x44836813 */
|
| - 5.9789707031e+03, /* 0x45bad7c4 */
|
| - 9.6254453125e+03, /* 0x461665c8 */
|
| - 2.4060581055e+03, /* 0x451660ee */
|
| + 6.0753936768e+01, /* 0x42730408 */
|
| + 1.0512523193e+03, /* 0x44836813 */
|
| + 5.9789707031e+03, /* 0x45bad7c4 */
|
| + 9.6254453125e+03, /* 0x461665c8 */
|
| + 2.4060581055e+03, /* 0x451660ee */
|
| };
|
|
|
| -static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
| - -2.5470459075e-09, /* 0xb12f081b */
|
| - -7.0311963558e-02, /* 0xbd8fffb8 */
|
| - -2.4090321064e+00, /* 0xc01a2d95 */
|
| - -2.1965976715e+01, /* 0xc1afba52 */
|
| - -5.8079170227e+01, /* 0xc2685112 */
|
| - -3.1447946548e+01, /* 0xc1fb9565 */
|
| +static const float pR3[6] = {
|
| + /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
| + -2.5470459075e-09, /* 0xb12f081b */
|
| + -7.0311963558e-02, /* 0xbd8fffb8 */
|
| + -2.4090321064e+00, /* 0xc01a2d95 */
|
| + -2.1965976715e+01, /* 0xc1afba52 */
|
| + -5.8079170227e+01, /* 0xc2685112 */
|
| + -3.1447946548e+01, /* 0xc1fb9565 */
|
| };
|
| static const float pS3[5] = {
|
| - 3.5856033325e+01, /* 0x420f6c94 */
|
| - 3.6151397705e+02, /* 0x43b4c1ca */
|
| - 1.1936077881e+03, /* 0x44953373 */
|
| - 1.1279968262e+03, /* 0x448cffe6 */
|
| - 1.7358093262e+02, /* 0x432d94b8 */
|
| + 3.5856033325e+01, /* 0x420f6c94 */
|
| + 3.6151397705e+02, /* 0x43b4c1ca */
|
| + 1.1936077881e+03, /* 0x44953373 */
|
| + 1.1279968262e+03, /* 0x448cffe6 */
|
| + 1.7358093262e+02, /* 0x432d94b8 */
|
| };
|
|
|
| -static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
| - -8.8753431271e-08, /* 0xb3be98b7 */
|
| - -7.0303097367e-02, /* 0xbd8ffb12 */
|
| - -1.4507384300e+00, /* 0xbfb9b1cc */
|
| - -7.6356959343e+00, /* 0xc0f4579f */
|
| - -1.1193166733e+01, /* 0xc1331736 */
|
| - -3.2336456776e+00, /* 0xc04ef40d */
|
| +static const float pR2[6] = {
|
| + /* for x in [2.8570,2]=1/[0.3499,0.5] */
|
| + -8.8753431271e-08, /* 0xb3be98b7 */
|
| + -7.0303097367e-02, /* 0xbd8ffb12 */
|
| + -1.4507384300e+00, /* 0xbfb9b1cc */
|
| + -7.6356959343e+00, /* 0xc0f4579f */
|
| + -1.1193166733e+01, /* 0xc1331736 */
|
| + -3.2336456776e+00, /* 0xc04ef40d */
|
| };
|
| static const float pS2[5] = {
|
| - 2.2220300674e+01, /* 0x41b1c32d */
|
| - 1.3620678711e+02, /* 0x430834f0 */
|
| - 2.7047027588e+02, /* 0x43873c32 */
|
| - 1.5387539673e+02, /* 0x4319e01a */
|
| - 1.4657617569e+01, /* 0x416a859a */
|
| + 2.2220300674e+01, /* 0x41b1c32d */
|
| + 1.3620678711e+02, /* 0x430834f0 */
|
| + 2.7047027588e+02, /* 0x43873c32 */
|
| + 1.5387539673e+02, /* 0x4319e01a */
|
| + 1.4657617569e+01, /* 0x416a859a */
|
| };
|
|
|
| -static float pzerof(float x)
|
| -{
|
| - const float *p,*q;
|
| - float_t z,r,s;
|
| - uint32_t ix;
|
| +static float pzerof(float x) {
|
| + const float *p, *q;
|
| + float_t z, r, s;
|
| + 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 /*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]))));
|
| - return 1.0f + r/s;
|
| + 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 /*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]))));
|
| + return 1.0f + r / s;
|
| }
|
|
|
| -
|
| /* For x >= 8, the asymptotic expansions of qzero is
|
| * -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
|
| * We approximate pzero by
|
| @@ -227,88 +233,101 @@ static float pzerof(float x)
|
| * and
|
| * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22)
|
| */
|
| -static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
|
| - 0.0000000000e+00, /* 0x00000000 */
|
| - 7.3242187500e-02, /* 0x3d960000 */
|
| - 1.1768206596e+01, /* 0x413c4a93 */
|
| - 5.5767340088e+02, /* 0x440b6b19 */
|
| - 8.8591972656e+03, /* 0x460a6cca */
|
| - 3.7014625000e+04, /* 0x471096a0 */
|
| +static const float qR8[6] = {
|
| + /* for x in [inf, 8]=1/[0,0.125] */
|
| + 0.0000000000e+00, /* 0x00000000 */
|
| + 7.3242187500e-02, /* 0x3d960000 */
|
| + 1.1768206596e+01, /* 0x413c4a93 */
|
| + 5.5767340088e+02, /* 0x440b6b19 */
|
| + 8.8591972656e+03, /* 0x460a6cca */
|
| + 3.7014625000e+04, /* 0x471096a0 */
|
| };
|
| static const float qS8[6] = {
|
| - 1.6377603149e+02, /* 0x4323c6aa */
|
| - 8.0983447266e+03, /* 0x45fd12c2 */
|
| - 1.4253829688e+05, /* 0x480b3293 */
|
| - 8.0330925000e+05, /* 0x49441ed4 */
|
| - 8.4050156250e+05, /* 0x494d3359 */
|
| - -3.4389928125e+05, /* 0xc8a7eb69 */
|
| + 1.6377603149e+02, /* 0x4323c6aa */
|
| + 8.0983447266e+03, /* 0x45fd12c2 */
|
| + 1.4253829688e+05, /* 0x480b3293 */
|
| + 8.0330925000e+05, /* 0x49441ed4 */
|
| + 8.4050156250e+05, /* 0x494d3359 */
|
| + -3.4389928125e+05, /* 0xc8a7eb69 */
|
| };
|
|
|
| -static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
| - 1.8408595828e-11, /* 0x2da1ec79 */
|
| - 7.3242180049e-02, /* 0x3d95ffff */
|
| - 5.8356351852e+00, /* 0x40babd86 */
|
| - 1.3511157227e+02, /* 0x43071c90 */
|
| - 1.0272437744e+03, /* 0x448067cd */
|
| - 1.9899779053e+03, /* 0x44f8bf4b */
|
| +static const float qR5[6] = {
|
| + /* for x in [8,4.5454]=1/[0.125,0.22001] */
|
| + 1.8408595828e-11, /* 0x2da1ec79 */
|
| + 7.3242180049e-02, /* 0x3d95ffff */
|
| + 5.8356351852e+00, /* 0x40babd86 */
|
| + 1.3511157227e+02, /* 0x43071c90 */
|
| + 1.0272437744e+03, /* 0x448067cd */
|
| + 1.9899779053e+03, /* 0x44f8bf4b */
|
| };
|
| static const float qS5[6] = {
|
| - 8.2776611328e+01, /* 0x42a58da0 */
|
| - 2.0778142090e+03, /* 0x4501dd07 */
|
| - 1.8847289062e+04, /* 0x46933e94 */
|
| - 5.6751113281e+04, /* 0x475daf1d */
|
| - 3.5976753906e+04, /* 0x470c88c1 */
|
| - -5.3543427734e+03, /* 0xc5a752be */
|
| + 8.2776611328e+01, /* 0x42a58da0 */
|
| + 2.0778142090e+03, /* 0x4501dd07 */
|
| + 1.8847289062e+04, /* 0x46933e94 */
|
| + 5.6751113281e+04, /* 0x475daf1d */
|
| + 3.5976753906e+04, /* 0x470c88c1 */
|
| + -5.3543427734e+03, /* 0xc5a752be */
|
| };
|
|
|
| -static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
| - 4.3774099900e-09, /* 0x3196681b */
|
| - 7.3241114616e-02, /* 0x3d95ff70 */
|
| - 3.3442313671e+00, /* 0x405607e3 */
|
| - 4.2621845245e+01, /* 0x422a7cc5 */
|
| - 1.7080809021e+02, /* 0x432acedf */
|
| - 1.6673394775e+02, /* 0x4326bbe4 */
|
| +static const float qR3[6] = {
|
| + /* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
|
| + 4.3774099900e-09, /* 0x3196681b */
|
| + 7.3241114616e-02, /* 0x3d95ff70 */
|
| + 3.3442313671e+00, /* 0x405607e3 */
|
| + 4.2621845245e+01, /* 0x422a7cc5 */
|
| + 1.7080809021e+02, /* 0x432acedf */
|
| + 1.6673394775e+02, /* 0x4326bbe4 */
|
| };
|
| static const float qS3[6] = {
|
| - 4.8758872986e+01, /* 0x42430916 */
|
| - 7.0968920898e+02, /* 0x44316c1c */
|
| - 3.7041481934e+03, /* 0x4567825f */
|
| - 6.4604252930e+03, /* 0x45c9e367 */
|
| - 2.5163337402e+03, /* 0x451d4557 */
|
| - -1.4924745178e+02, /* 0xc3153f59 */
|
| + 4.8758872986e+01, /* 0x42430916 */
|
| + 7.0968920898e+02, /* 0x44316c1c */
|
| + 3.7041481934e+03, /* 0x4567825f */
|
| + 6.4604252930e+03, /* 0x45c9e367 */
|
| + 2.5163337402e+03, /* 0x451d4557 */
|
| + -1.4924745178e+02, /* 0xc3153f59 */
|
| };
|
|
|
| -static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
|
| - 1.5044444979e-07, /* 0x342189db */
|
| - 7.3223426938e-02, /* 0x3d95f62a */
|
| - 1.9981917143e+00, /* 0x3fffc4bf */
|
| - 1.4495602608e+01, /* 0x4167edfd */
|
| - 3.1666231155e+01, /* 0x41fd5471 */
|
| - 1.6252708435e+01, /* 0x4182058c */
|
| +static const float qR2[6] = {
|
| + /* for x in [2.8570,2]=1/[0.3499,0.5] */
|
| + 1.5044444979e-07, /* 0x342189db */
|
| + 7.3223426938e-02, /* 0x3d95f62a */
|
| + 1.9981917143e+00, /* 0x3fffc4bf */
|
| + 1.4495602608e+01, /* 0x4167edfd */
|
| + 3.1666231155e+01, /* 0x41fd5471 */
|
| + 1.6252708435e+01, /* 0x4182058c */
|
| };
|
| static const float qS2[6] = {
|
| - 3.0365585327e+01, /* 0x41f2ecb8 */
|
| - 2.6934811401e+02, /* 0x4386ac8f */
|
| - 8.4478375244e+02, /* 0x44533229 */
|
| - 8.8293585205e+02, /* 0x445cbbe5 */
|
| - 2.1266638184e+02, /* 0x4354aa98 */
|
| - -5.3109550476e+00, /* 0xc0a9f358 */
|
| + 3.0365585327e+01, /* 0x41f2ecb8 */
|
| + 2.6934811401e+02, /* 0x4386ac8f */
|
| + 8.4478375244e+02, /* 0x44533229 */
|
| + 8.8293585205e+02, /* 0x445cbbe5 */
|
| + 2.1266638184e+02, /* 0x4354aa98 */
|
| + -5.3109550476e+00, /* 0xc0a9f358 */
|
| };
|
|
|
| -static float qzerof(float x)
|
| -{
|
| - const float *p,*q;
|
| - float_t s,r,z;
|
| - uint32_t ix;
|
| +static float qzerof(float x) {
|
| + const float *p, *q;
|
| + float_t s, r, z;
|
| + uint32_t ix;
|
|
|
| - GET_FLOAT_WORD(ix, x);
|
| - ix &= 0x7fffffff;
|
| - if (ix >= 0x41000000){p = qR8; q = qS8;}
|
| - else if (ix >= 0x40f71c58){p = qR5; q = qS5;}
|
| - else if (ix >= 0x4036db68){p = qR3; q = qS3;}
|
| - 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])))));
|
| - return (-.125f + r/s)/x;
|
| + GET_FLOAT_WORD(ix, x);
|
| + ix &= 0x7fffffff;
|
| + if (ix >= 0x41000000) {
|
| + p = qR8;
|
| + q = qS8;
|
| + } else if (ix >= 0x40f71c58) {
|
| + p = qR5;
|
| + q = qS5;
|
| + } else if (ix >= 0x4036db68) {
|
| + p = qR3;
|
| + q = qS3;
|
| + } 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])))));
|
| + return (-.125f + r / s) / x;
|
| }
|
|
|