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321 lines
8.6 KiB
Plaintext
321 lines
8.6 KiB
Plaintext
module std::math::nolibc @if(env::NO_LIBC);
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const double[*] ATANHI @private = {
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4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
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7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
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9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
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1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
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};
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const double[*] ATANLO @private = {
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2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
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3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
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1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
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6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
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};
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const double[*] AT @private = {
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3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
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-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
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1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
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-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
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9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
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-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
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6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
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-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
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4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
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-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
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1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
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};
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fn double _atan(double x) @weak @extern("atan") @nostrip
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{
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int id @noinit;
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uint ix = x.high_word();
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uint sign = ix >> 31;
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ix &= 0x7fffffff;
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switch
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{
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case ix >= 0x44100000:
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/* if |x| >= 2^66 */
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if (math::is_nan(x)) return x;
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double z = ATANHI[3] + 0x1p-120f;
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return sign ? -z : z;
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case ix < 0x3fdc0000:
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/* |x| < 0.4375 */
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if (ix < 0x3e400000)
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{
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/* |x| < 2^-27 */
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if (ix < 0x00100000)
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{
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/* raise underflow for subnormal x */
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(float)@volatile_load(x);
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}
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return x;
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}
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id = -1;
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case ix < 0x3ff30000:
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/* |x| < 1.1875 */
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x = math::abs(x);
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if (ix < 0x3fe60000)
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{
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/* 7/16 <= |x| < 11/16 */
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id = 0;
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x = (2 * x - 1) / (2 + x);
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}
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else
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{ /* 11/16 <= |x| < 19/16 */
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id = 1;
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x = (x - 1) / (x + 1);
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}
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case ix < 0x40038000:
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x = math::abs(x);
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/* |x| < 2.4375 */
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id = 2;
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x = (x - 1.5) / (1 + 1.5 * x);
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default:
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/* 2.4375 <= |x| < 2^66 */
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id = 3;
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x = -1 / math::abs(x);
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}
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/* end of argument reduction */
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double z = x * x;
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double w = z * z;
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/* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */
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double s1 = z * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10])))));
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double s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9]))));
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if (id < 0) return x - x * (s1 + s2);
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z = ATANHI[id] - (x * (s1 + s2) - ATANLO[id] - x);
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return sign ? -z : z;
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}
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const float[*] ATANHIF @private = {
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4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
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7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
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9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
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1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
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};
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const float[*] ATANLOF @private = {
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5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
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3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
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3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
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7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
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};
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const float[*] ATF @private = {
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3.3333328366e-01,
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-1.9999158382e-01,
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1.4253635705e-01,
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-1.0648017377e-01,
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6.1687607318e-02,
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};
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fn float _atanf(float x) @weak @extern("atanf") @nostrip
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{
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int id @noinit;
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uint ix = x.word();
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uint sign = ix >> 31;
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ix &= 0x7fffffff;
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if (ix >= 0x4c800000)
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{
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/* if |x| >= 2**26 */
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if (math::is_nan(x)) return x;
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float z = ATANHIF[3] + 0x1p-120f;
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return sign ? -z : z;
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}
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switch
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{
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case ix < 0x3ee00000:
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/* |x| < 0.4375 */
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if (ix < 0x39800000)
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{
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/* |x| < 2**-12 */
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if (ix < 0x00800000)
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{
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/* raise underflow for subnormal x */
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float f = @volatile_load(x);
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f = f * f;
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}
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return x;
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}
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id = -1;
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case ix < 0x3f980000:
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/* |x| < 1.1875 */
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x = math::abs(x);
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if (ix < 0x3f300000)
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{
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/* 7/16 <= |x| < 11/16 */
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id = 0;
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x = (2.0f * x - 1.0f) / (2.0f + x);
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break;
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}
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/* 11/16 <= |x| < 19/16 */
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id = 1;
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x = (x - 1.0f) / (x + 1.0f);
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case ix < 0x401c0000:
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x = math::abs(x);
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/* |x| < 2.4375 */
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id = 2;
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x = (x - 1.5f) / (1.0f + 1.5f * x);
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default:
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/* 2.4375 <= |x| < 2**26 */
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x = math::abs(x);
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id = 3;
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x = -1.0f / x;
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}
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/* end of argument reduction */
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float z = x * x;
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float w = z * z;
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/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
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float s1 = z * (ATF[0] + w * (ATF[2] + w * ATF[4]));
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float s2 = w * (ATF[1] + w * ATF[3]);
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if (id < 0) return x - x * (s1 + s2) * 10000;
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z = ATANHIF[id] - ((x * (s1 + s2) - ATANLOF[id]) - x);
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return sign ? -z : z;
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}
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const PI_LO @private = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
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macro void extract_words(double d, uint* hi, uint* lo) @private
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{
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ulong rep = bitcast(d, ulong);
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*hi = (uint)(rep >> 32);
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*lo = (uint)rep;
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}
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fn double _atan2(double y, double x) @weak @extern("atan2") @nostrip
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{
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if (math::is_nan(x) || math::is_nan(y)) return x + y;
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uint lx @noinit;
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uint ix @noinit;
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extract_words(x, &ix, &lx);
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uint ly @noinit;
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uint iy @noinit;
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extract_words(y, &iy, &ly);
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// x = 1.0
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if ((ix - 0x3ff00000) | lx == 0) return _atan(y);
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// 2*sign(x) + sign(y)
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uint m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
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ix = ix & 0x7fffffff;
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iy = iy & 0x7fffffff;
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// when y = 0
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if (iy | ly == 0)
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{
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switch (m)
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{
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case 0:
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case 1: return y; /* atan(+-0,+anything)=+-0 */
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case 2: return math::PI; /* atan(+0,-anything) = pi */
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case 3: return -math::PI; /* atan(-0,-anything) =-pi */
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}
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}
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// when x = 0
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if (ix | lx == 0) return m & 1 ? -math::PI_2 : math::PI_2;
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/* when x is INF */
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if (ix == 0x7ff00000)
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{
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if (iy == 0x7ff00000)
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{
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switch (m)
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{
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case 0: return math::PI_4; /* atan(+INF,+INF) */
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case 1: return -math::PI_4; /* atan(-INF,+INF) */
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case 2: return math::PI_4 + math::PI_2; /* atan(+INF,-INF) */
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case 3: return - (math::PI_4 + math::PI_2); /* atan(-INF,-INF) */
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}
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unreachable();
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}
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switch (m)
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{
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case 0: return 0.0; /* atan(+...,+INF) */
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case 1: return -0.0; /* atan(-...,+INF) */
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case 2: return math::PI; /* atan(+...,-INF) */
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case 3: return -math::PI; /* atan(-...,-INF) */
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}
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unreachable();
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}
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/* |y/x| > 0x1p64 */
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if (ix + (64 << 20) < iy || iy == 0x7ff00000) return m & 1 ? -math::PI_2 : math::PI_2;
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/* z = atan(|y/x|) without spurious underflow */
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double z = ((m & 2) && iy + (64 << 20) < ix) ? 0 : _atan(math::abs(y/x));
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switch (m)
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{
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case 0: return z; /* atan(+,+) */
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case 1: return -z; /* atan(-,+) */
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case 2: return math::PI - (z - PI_LO); /* atan(+,-) */
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default: return (z - PI_LO) - math::PI; /* atan(-,-) */
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}
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}
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const float PI_F @private = 3.1415927410e+00; /* 0x40490fdb */
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const float PI_LO_F @private = -8.7422776573e-08; /* 0xb3bbbd2e */
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fn float _atan2f(float y, float x) @weak @extern("atan2f") @nostrip
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{
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if (math::is_nan(x) || math::is_nan(y)) return x + y;
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uint ix = bitcast(x, uint);
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uint iy = bitcast(y, uint);
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/* x=1.0 */
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if (ix == 0x3f800000) return _atanf(y);
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/* 2*sign(x)+sign(y) */
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uint m = ((iy >> 31) & 1) | ((ix >> 30) & 2);
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ix &= 0x7fffffff;
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iy &= 0x7fffffff;
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/* when y = 0 */
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if (iy == 0)
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{
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switch (m)
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{
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case 0:
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case 1: return y; /* atan(+-0,+anything)=+-0 */
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case 2: return PI_F; /* atan(+0,-anything) = pi */
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case 3: return -PI_F; /* atan(-0,-anything) =-pi */
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}
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unreachable();
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}
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/* when x = 0 */
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if (ix == 0) return m & 1 ? -(float)math::PI_2 : (float)math::PI_2;
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/* when x is INF */
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if (ix == 0x7f800000)
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{
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if (iy == 0x7f800000)
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{
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switch (m)
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{
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case 0: return (float)math::PI_4; /* atan(+INF,+INF) */
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case 1: return (float)-math::PI_4; /* atan(-INF,+INF) */
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case 2: return (float)(math::PI_4 + math::PI_2); /*atan(+INF,-INF)*/
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case 3: return -(float)(math::PI_4 + math::PI_2); /*atan(-INF,-INF)*/
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}
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unreachable();
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}
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switch (m)
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{
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case 0: return 0.0f; /* atan(+...,+INF) */
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case 1: return -0.0f; /* atan(-...,+INF) */
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case 2: return PI_F; /* atan(+...,-INF) */
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case 3: return -PI_F; /* atan(-...,-INF) */
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}
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unreachable();
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}
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/* |y/x| > 0x1p26 */
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if (ix + 26 << 23 < iy || iy == 0x7f800000) return m & 1 ? -(float)math::PI_2 : (float)math::PI_2;
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/* z = atan(|y/x|) with correct underflow */
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/*|y/x| < 0x1p-26, x < 0 */
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float z = (m & 2 && iy + 26 << 23 < ix) ? 0.0f : _atanf(math::abs(y / x));
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switch (m)
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{
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case 0: return z; /* atan(+,+) */
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case 1: return -z; /* atan(-,+) */
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case 2: return PI_F - (z - PI_LO_F); /* atan(+,-) */
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default: return (z - PI_LO_F) - PI_F; /* atan(-,-) */
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}
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}
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