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chore: adds more support math standard
Signed-off-by: slowy07 <[email protected]>
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| // Copyright (c) 2024 arfy slowy - DeRuneLabs | ||
| // | ||
| // Permission is hereby granted, free of charge, to any person obtaining a copy | ||
| // of this software and associated documentation files (the "Software"), to deal | ||
| // in the Software without restriction, including without limitation the rights | ||
| // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | ||
| // copies of the Software, and to permit persons to whom the Software is | ||
| // furnished to do so, subject to the following conditions: | ||
| // | ||
| // The above copyright notice and this permission notice shall be included in all | ||
| // copies or substantial portions of the Software. | ||
| // | ||
| // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | ||
| // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | ||
| // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | ||
| // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | ||
| // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | ||
| // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | ||
| // SOFTWARE. | ||
|
|
||
| // ==================================================== | ||
| // Copyright (c) 2009 The Go Authors. All rights reserved. | ||
| // | ||
| // Redistribution and use in source and binary forms, with or without | ||
| // modification, are permitted provided that the following conditions are | ||
| // met: | ||
| // | ||
| // * Redistributions of source code must retain the above copyright | ||
| // notice, this list of conditions and the following disclaimer. | ||
| // * Redistributions in binary form must reproduce the above | ||
| // copyright notice, this list of conditions and the following disclaimer | ||
| // in the documentation and/or other materials provided with the | ||
| // distribution. | ||
| // * Neither the name of Google Inc. nor the names of its | ||
| // contributors may be used to endorse or promote products derived from | ||
| // this software without specific prior written permission. | ||
| // | ||
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | ||
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | ||
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | ||
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT | ||
| // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | ||
| // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT | ||
| // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | ||
| // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | ||
| // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | ||
| // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | ||
| // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | ||
| // ==================================================== | ||
| // https://github.com/golang/go/blob/go1.19/src/math/log.go and came with this notice. | ||
|
|
||
| // ==================================================== | ||
| // 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. | ||
| // ==================================================== | ||
| // the original C code, the long comment, and the constants | ||
| // below are from FreeBSD's /usr/src/lib/msun/src/e_log.c | ||
| // jane code is a simplified version of C original source code. | ||
| // | ||
| // __ieee754_log(x) | ||
| // Return the logarithm of x | ||
| // | ||
| // Method : | ||
| // 1. Argument Reduction: find k and f such that | ||
| // x = 2**k * (1+f), | ||
| // where sqrt(2)/2 < 1+f < sqrt(2) . | ||
| // | ||
| // 2. Approximation of log(1+f). | ||
| // Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) | ||
| // = 2s + 2/3 s**3 + 2/5 s**5 + ....., | ||
| // = 2s + s*R | ||
| // We use a special Reme algorithm on [0,0.1716] to generate | ||
| // a polynomial of degree 14 to approximate R. The maximum error | ||
| // of this polynomial approximation is bounded by 2**-58.45. In | ||
| // other words, | ||
| // 2 4 6 8 10 12 14 | ||
| // R(z) ~ L1*s +L2*s +L3*s +L4*s +L5*s +L6*s +L7*s | ||
| // (the values of L1 to L7 are listed in the program) and | ||
| // | 2 14 | -58.45 | ||
| // | L1*s +...+L7*s - R(z) | <= 2 | ||
| // | | | ||
| // Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. | ||
| // In order to guarantee error in log below 1ulp, we compute log by | ||
| // log(1+f) = f - s*(f - R) (if f is not too large) | ||
| // log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) | ||
| // | ||
| // 3. Finally, log(x) = k*Ln2 + log(1+f). | ||
| // = k*Ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*Ln2_lo))) | ||
| // Here Ln2 is split into two floating point number: | ||
| // Ln2_hi + Ln2_lo, | ||
| // where n*Ln2_hi is always exact for |n| < 2000. | ||
| // | ||
| // Special cases: | ||
| // log(x) is NaN with signal if x < 0 (including -INF) ; | ||
| // log(+INF) is +INF; log(0) is -INF with signal; | ||
| // log(NaN) is that NaN with no signal. | ||
| // | ||
| // Accuracy: | ||
| // according to an error analysis, the error is always less than | ||
| // 1 ulp (unit in the last place). | ||
| // | ||
| // Constants: | ||
| // The hexadecimal values are the intended ones for the following | ||
| // constants. The decimal values may be used, provided that the | ||
| // compiler will convert from decimal to binary accurately enough | ||
| // to produce the hexadecimal values shown. | ||
|
|
||
| // return natural logarithm of x | ||
| pub fn log(x: f64): f64 { | ||
| const LN2_HI = 6.93147180369123816490e-01 /* 3fe62e42 fee00000 */ | ||
| const LN2_LO = 1.90821492927058770002e-10 /* 3dea39ef 35793c76 */ | ||
| const L1 = 6.666666666666735130e-01 /* 3FE55555 55555593 */ | ||
| const L2 = 3.999999999940941908e-01 /* 3FD99999 9997FA04 */ | ||
| const L3 = 2.857142874366239149e-01 /* 3FD24924 94229359 */ | ||
| const L4 = 2.222219843214978396e-01 /* 3FCC71C5 1D8E78AF */ | ||
| const L5 = 1.818357216161805012e-01 /* 3FC74664 96CB03DE */ | ||
| const L6 = 1.531383769920937332e-01 /* 3FC39A09 D078C69F */ | ||
| const L7 = 1.479819860511658591e-01 /* 3FC2F112 DF3E5244 */ | ||
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||
| match { | ||
| | is_nan(x) | is_inf(x, 1): | ||
| ret x | ||
| | x < 0: | ||
| ret nan() | ||
| | x == 0: | ||
| ret inf(-1) | ||
| } | ||
|
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||
| let (mut f1, mut ki) = frexp(x) | ||
| if f1 < SQRT2 / 2 { | ||
| f1 *= 2 | ||
| ki-- | ||
| } | ||
| let f = f1 - 1 | ||
| let k = f64(ki) | ||
|
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||
| let s = f / (2 + f) | ||
| let s2 = s * s | ||
| let s4 = s2 * s2 | ||
| let t1 = s2 * (L1 * s4 * (L3 + s4 * (L5 * s4 * L7))) | ||
| let t2 = s4 * (L2 + s4*(L4+s4*L6)) | ||
| let R = t1 + t2 | ||
| let hfsq = 0.5 * f * f | ||
| ret k*LN2_HI - ((hfsq - (s*(hfsq+R) + k*LN2_LO)) - f) | ||
| } | ||
|
|
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| // Copyright (c) 2024 arfy slowy - DeRuneLabs | ||
| // | ||
| // Permission is hereby granted, free of charge, to any person obtaining a copy | ||
| // of this software and associated documentation files (the "Software"), to deal | ||
| // in the Software without restriction, including without limitation the rights | ||
| // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | ||
| // copies of the Software, and to permit persons to whom the Software is | ||
| // furnished to do so, subject to the following conditions: | ||
| // | ||
| // The above copyright notice and this permission notice shall be included in all | ||
| // copies or substantial portions of the Software. | ||
| // | ||
| // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | ||
| // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | ||
| // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | ||
| // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | ||
| // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | ||
| // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | ||
| // SOFTWARE. | ||
|
|
||
| // ==================================================== | ||
| // Copyright (c) 2009 The Go Authors. All rights reserved. | ||
| // | ||
| // Redistribution and use in source and binary forms, with or without | ||
| // modification, are permitted provided that the following conditions are | ||
| // met: | ||
| // | ||
| // * Redistributions of source code must retain the above copyright | ||
| // notice, this list of conditions and the following disclaimer. | ||
| // * Redistributions in binary form must reproduce the above | ||
| // copyright notice, this list of conditions and the following disclaimer | ||
| // in the documentation and/or other materials provided with the | ||
| // distribution. | ||
| // * Neither the name of Google Inc. nor the names of its | ||
| // contributors may be used to endorse or promote products derived from | ||
| // this software without specific prior written permission. | ||
| // | ||
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | ||
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | ||
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | ||
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT | ||
| // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | ||
| // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT | ||
| // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | ||
| // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | ||
| // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | ||
| // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | ||
| // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | ||
| // ==================================================== | ||
| // https://github.com/golang/go/blob/go1.19/src/math/log10.go and came with this notice. | ||
|
|
||
| // return the decimal logarithm of x | ||
| pub fn log10(x: f64): f64 { | ||
| ret log(x) * (1 / LN10) | ||
| } | ||
|
|
||
| // return binary logarithm of x | ||
| // special case are the same as for log | ||
| pub fn log2(x: f64): f64 { | ||
| let (frac, exp) = frexp(x) | ||
| if frac == 0.5 { | ||
| ret f64(exp - 1) | ||
| } | ||
| ret log(frac) * (1 / LN2) + f64(exp) | ||
| } |
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