diff options
Diffstat (limited to 'vendor/compiler_builtins/libm/src/math/j0f.rs')
| -rw-r--r-- | vendor/compiler_builtins/libm/src/math/j0f.rs | 359 |
1 files changed, 359 insertions, 0 deletions
diff --git a/vendor/compiler_builtins/libm/src/math/j0f.rs b/vendor/compiler_builtins/libm/src/math/j0f.rs new file mode 100644 index 000000000..91c03dbbc --- /dev/null +++ b/vendor/compiler_builtins/libm/src/math/j0f.rs @@ -0,0 +1,359 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.c */ +/* + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +use super::{cosf, fabsf, logf, sinf, sqrtf}; + +const INVSQRTPI: f32 = 5.6418961287e-01; /* 0x3f106ebb */ +const TPI: f32 = 6.3661974669e-01; /* 0x3f22f983 */ + +fn common(ix: u32, x: f32, y0: bool) -> f32 { + let z: f32; + let s: f32; + let mut c: f32; + let mut ss: f32; + let mut cc: f32; + /* + * 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(2.0 * x); + if s * c < 0.0 { + 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] */ +const R02: f32 = 1.5625000000e-02; /* 0x3c800000 */ +const R03: f32 = -1.8997929874e-04; /* 0xb947352e */ +const R04: f32 = 1.8295404516e-06; /* 0x35f58e88 */ +const R05: f32 = -4.6183270541e-09; /* 0xb19eaf3c */ +const S01: f32 = 1.5619102865e-02; /* 0x3c7fe744 */ +const S02: f32 = 1.1692678527e-04; /* 0x38f53697 */ +const S03: f32 = 5.1354652442e-07; /* 0x3509daa6 */ +const S04: f32 = 1.1661400734e-09; /* 0x30a045e8 */ + +pub fn j0f(mut x: f32) -> f32 { + let z: f32; + let r: f32; + let s: f32; + let mut ix: u32; + + ix = x.to_bits(); + ix &= 0x7fffffff; + if ix >= 0x7f800000 { + return 1.0 / (x * x); + } + x = fabsf(x); + + if ix >= 0x40000000 { + /* |x| >= 2 */ + /* large ulp error near zeros */ + return common(ix, x, false); + } + 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 = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * S04))); + return (1.0 + x / 2.0) * (1.0 - x / 2.0) + z * (r / s); + } + if ix >= 0x21800000 { + /* |x| >= 2**-60 */ + x = 0.25 * x * x; + } + return 1.0 - x; +} + +const U00: f32 = -7.3804296553e-02; /* 0xbd9726b5 */ +const U01: f32 = 1.7666645348e-01; /* 0x3e34e80d */ +const U02: f32 = -1.3818567619e-02; /* 0xbc626746 */ +const U03: f32 = 3.4745343146e-04; /* 0x39b62a69 */ +const U04: f32 = -3.8140706238e-06; /* 0xb67ff53c */ +const U05: f32 = 1.9559013964e-08; /* 0x32a802ba */ +const U06: f32 = -3.9820518410e-11; /* 0xae2f21eb */ +const V01: f32 = 1.2730483897e-02; /* 0x3c509385 */ +const V02: f32 = 7.6006865129e-05; /* 0x389f65e0 */ +const V03: f32 = 2.5915085189e-07; /* 0x348b216c */ +const V04: f32 = 4.4111031494e-10; /* 0x2ff280c2 */ + +pub fn y0f(x: f32) -> f32 { + let z: f32; + let u: f32; + let v: f32; + let ix: u32; + + ix = x.to_bits(); + if (ix & 0x7fffffff) == 0 { + return -1.0 / 0.0; + } + if (ix >> 31) != 0 { + return 0.0 / 0.0; + } + if ix >= 0x7f800000 { + return 1.0 / x; + } + if ix >= 0x40000000 { + /* |x| >= 2.0 */ + /* large ulp error near zeros */ + return common(ix, x, true); + } + 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 = 1.0 + 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 + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +const PR8: [f32; 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 */ +]; +const PS8: [f32; 5] = [ + 1.1653436279e+02, /* 0x42e91198 */ + 3.8337448730e+03, /* 0x456f9beb */ + 4.0597855469e+04, /* 0x471e95db */ + 1.1675296875e+05, /* 0x47e4087c */ + 4.7627726562e+04, /* 0x473a0bba */ +]; +const PR5: [f32; 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 */ +]; +const PS5: [f32; 5] = [ + 6.0753936768e+01, /* 0x42730408 */ + 1.0512523193e+03, /* 0x44836813 */ + 5.9789707031e+03, /* 0x45bad7c4 */ + 9.6254453125e+03, /* 0x461665c8 */ + 2.4060581055e+03, /* 0x451660ee */ +]; + +const PR3: [f32; 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 */ +]; +const PS3: [f32; 5] = [ + 3.5856033325e+01, /* 0x420f6c94 */ + 3.6151397705e+02, /* 0x43b4c1ca */ + 1.1936077881e+03, /* 0x44953373 */ + 1.1279968262e+03, /* 0x448cffe6 */ + 1.7358093262e+02, /* 0x432d94b8 */ +]; + +const PR2: [f32; 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 */ +]; +const PS2: [f32; 5] = [ + 2.2220300674e+01, /* 0x41b1c32d */ + 1.3620678711e+02, /* 0x430834f0 */ + 2.7047027588e+02, /* 0x43873c32 */ + 1.5387539673e+02, /* 0x4319e01a */ + 1.4657617569e+01, /* 0x416a859a */ +]; + +fn pzerof(x: f32) -> f32 { + let p: &[f32; 6]; + let q: &[f32; 5]; + let z: f32; + let r: f32; + let s: f32; + let mut ix: u32; + + ix = x.to_bits(); + ix &= 0x7fffffff; + if ix >= 0x41000000 { + p = &PR8; + q = &PS8; + } else if ix >= 0x409173eb { + p = &PR5; + q = &PS5; + } else if ix >= 0x4036d917 { + p = &PR3; + q = &PS3; + } else + /*ix >= 0x40000000*/ + { + p = &PR2; + q = &PS2; + } + z = 1.0 / (x * x); + r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); + s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4])))); + return 1.0 + 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 + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +const QR8: [f32; 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 */ +]; +const QS8: [f32; 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 */ +]; + +const QR5: [f32; 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 */ +]; +const QS5: [f32; 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 */ +]; + +const QR3: [f32; 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 */ +]; +const QS3: [f32; 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 */ +]; + +const QR2: [f32; 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 */ +]; +const QS2: [f32; 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 */ +]; + +fn qzerof(x: f32) -> f32 { + let p: &[f32; 6]; + let q: &[f32; 6]; + let s: f32; + let r: f32; + let z: f32; + let mut ix: u32; + + ix = x.to_bits(); + ix &= 0x7fffffff; + if ix >= 0x41000000 { + p = &QR8; + q = &QS8; + } else if ix >= 0x409173eb { + p = &QR5; + q = &QS5; + } else if ix >= 0x4036d917 { + p = &QR3; + q = &QS3; + } else + /*ix >= 0x40000000*/ + { + p = &QR2; + q = &QS2; + } + z = 1.0 / (x * x); + r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); + s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5]))))); + return (-0.125 + r / s) / x; +} |