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| </pre><pre class="rust"><code><span class="kw">use</span> <span class="kw">super</span>::{<span class="ident">exp</span>, <span class="ident">fabs</span>, <span class="ident">get_high_word</span>, <span class="ident">with_set_low_word</span>}; |
| <span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/s_erf.c */</span> |
| <span class="comment">/* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */</span> |
| <span class="comment">/* double erf(double x) |
| * double erfc(double x) |
| * x |
| * 2 |\ |
| * erf(x) = --------- | exp(-t*t)dt |
| * sqrt(pi) \| |
| * 0 |
| * |
| * erfc(x) = 1-erf(x) |
| * Note that |
| * erf(-x) = -erf(x) |
| * erfc(-x) = 2 - erfc(x) |
| * |
| * Method: |
| * 1. For |x| in [0, 0.84375] |
| * erf(x) = x + x*R(x^2) |
| * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] |
| * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] |
| * where R = P/Q where P is an odd poly of degree 8 and |
| * Q is an odd poly of degree 10. |
| * -57.90 |
| * | R - (erf(x)-x)/x | <= 2 |
| * |
| * |
| * Remark. The formula is derived by noting |
| * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) |
| * and that |
| * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 |
| * is close to one. The interval is chosen because the fix |
| * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is |
| * near 0.6174), and by some experiment, 0.84375 is chosen to |
| * guarantee the error is less than one ulp for erf. |
| * |
| * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and |
| * c = 0.84506291151 rounded to single (24 bits) |
| * erf(x) = sign(x) * (c + P1(s)/Q1(s)) |
| * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 |
| * 1+(c+P1(s)/Q1(s)) if x < 0 |
| * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 |
| * Remark: here we use the taylor series expansion at x=1. |
| * erf(1+s) = erf(1) + s*Poly(s) |
| * = 0.845.. + P1(s)/Q1(s) |
| * That is, we use rational approximation to approximate |
| * erf(1+s) - (c = (single)0.84506291151) |
| * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] |
| * where |
| * P1(s) = degree 6 poly in s |
| * Q1(s) = degree 6 poly in s |
| * |
| * 3. For x in [1.25,1/0.35(~2.857143)], |
| * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) |
| * erf(x) = 1 - erfc(x) |
| * where |
| * R1(z) = degree 7 poly in z, (z=1/x^2) |
| * S1(z) = degree 8 poly in z |
| * |
| * 4. For x in [1/0.35,28] |
| * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 |
| * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0 |
| * = 2.0 - tiny (if x <= -6) |
| * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else |
| * erf(x) = sign(x)*(1.0 - tiny) |
| * where |
| * R2(z) = degree 6 poly in z, (z=1/x^2) |
| * S2(z) = degree 7 poly in z |
| * |
| * Note1: |
| * To compute exp(-x*x-0.5625+R/S), let s be a single |
| * precision number and s := x; then |
| * -x*x = -s*s + (s-x)*(s+x) |
| * exp(-x*x-0.5626+R/S) = |
| * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); |
| * Note2: |
| * Here 4 and 5 make use of the asymptotic series |
| * exp(-x*x) |
| * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) |
| * x*sqrt(pi) |
| * We use rational approximation to approximate |
| * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 |
| * Here is the error bound for R1/S1 and R2/S2 |
| * |R1/S1 - f(x)| < 2**(-62.57) |
| * |R2/S2 - f(x)| < 2**(-61.52) |
| * |
| * 5. For inf > x >= 28 |
| * erf(x) = sign(x) *(1 - tiny) (raise inexact) |
| * erfc(x) = tiny*tiny (raise underflow) if x > 0 |
| * = 2 - tiny if x<0 |
| * |
| * 7. Special case: |
| * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, |
| * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, |
| * erfc/erf(NaN) is NaN |
| */</span> |
| |
| <span class="kw">const</span> <span class="ident">ERX</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">8.45062911510467529297e-01</span>; <span class="comment">/* 0x3FEB0AC1, 0x60000000 */</span> |
| <span class="comment">/* |
| * Coefficients for approximation to erf on [0,0.84375] |
| */</span> |
| <span class="kw">const</span> <span class="ident">EFX8</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.02703333676410069053e+00</span>; <span class="comment">/* 0x3FF06EBA, 0x8214DB69 */</span> |
| <span class="kw">const</span> <span class="ident">PP0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.28379167095512558561e-01</span>; <span class="comment">/* 0x3FC06EBA, 0x8214DB68 */</span> |
| <span class="kw">const</span> <span class="ident">PP1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.25042107247001499370e-01</span>; <span class="comment">/* 0xBFD4CD7D, 0x691CB913 */</span> |
| <span class="kw">const</span> <span class="ident">PP2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.84817495755985104766e-02</span>; <span class="comment">/* 0xBF9D2A51, 0xDBD7194F */</span> |
| <span class="kw">const</span> <span class="ident">PP3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">5.77027029648944159157e-03</span>; <span class="comment">/* 0xBF77A291, 0x236668E4 */</span> |
| <span class="kw">const</span> <span class="ident">PP4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.37630166566501626084e-05</span>; <span class="comment">/* 0xBEF8EAD6, 0x120016AC */</span> |
| <span class="kw">const</span> <span class="ident">QQ1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.97917223959155352819e-01</span>; <span class="comment">/* 0x3FD97779, 0xCDDADC09 */</span> |
| <span class="kw">const</span> <span class="ident">QQ2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.50222499887672944485e-02</span>; <span class="comment">/* 0x3FB0A54C, 0x5536CEBA */</span> |
| <span class="kw">const</span> <span class="ident">QQ3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">5.08130628187576562776e-03</span>; <span class="comment">/* 0x3F74D022, 0xC4D36B0F */</span> |
| <span class="kw">const</span> <span class="ident">QQ4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.32494738004321644526e-04</span>; <span class="comment">/* 0x3F215DC9, 0x221C1A10 */</span> |
| <span class="kw">const</span> <span class="ident">QQ5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.96022827877536812320e-06</span>; <span class="comment">/* 0xBED09C43, 0x42A26120 */</span> |
| <span class="comment">/* |
| * Coefficients for approximation to erf in [0.84375,1.25] |
| */</span> |
| <span class="kw">const</span> <span class="ident">PA0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.36211856075265944077e-03</span>; <span class="comment">/* 0xBF6359B8, 0xBEF77538 */</span> |
| <span class="kw">const</span> <span class="ident">PA1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.14856118683748331666e-01</span>; <span class="comment">/* 0x3FDA8D00, 0xAD92B34D */</span> |
| <span class="kw">const</span> <span class="ident">PA2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">3.72207876035701323847e-01</span>; <span class="comment">/* 0xBFD7D240, 0xFBB8C3F1 */</span> |
| <span class="kw">const</span> <span class="ident">PA3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.18346619901161753674e-01</span>; <span class="comment">/* 0x3FD45FCA, 0x805120E4 */</span> |
| <span class="kw">const</span> <span class="ident">PA4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.10894694282396677476e-01</span>; <span class="comment">/* 0xBFBC6398, 0x3D3E28EC */</span> |
| <span class="kw">const</span> <span class="ident">PA5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.54783043256182359371e-02</span>; <span class="comment">/* 0x3FA22A36, 0x599795EB */</span> |
| <span class="kw">const</span> <span class="ident">PA6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.16637559486879084300e-03</span>; <span class="comment">/* 0xBF61BF38, 0x0A96073F */</span> |
| <span class="kw">const</span> <span class="ident">QA1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.06420880400844228286e-01</span>; <span class="comment">/* 0x3FBB3E66, 0x18EEE323 */</span> |
| <span class="kw">const</span> <span class="ident">QA2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">5.40397917702171048937e-01</span>; <span class="comment">/* 0x3FE14AF0, 0x92EB6F33 */</span> |
| <span class="kw">const</span> <span class="ident">QA3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">7.18286544141962662868e-02</span>; <span class="comment">/* 0x3FB2635C, 0xD99FE9A7 */</span> |
| <span class="kw">const</span> <span class="ident">QA4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.26171219808761642112e-01</span>; <span class="comment">/* 0x3FC02660, 0xE763351F */</span> |
| <span class="kw">const</span> <span class="ident">QA5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.36370839120290507362e-02</span>; <span class="comment">/* 0x3F8BEDC2, 0x6B51DD1C */</span> |
| <span class="kw">const</span> <span class="ident">QA6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.19844998467991074170e-02</span>; <span class="comment">/* 0x3F888B54, 0x5735151D */</span> |
| <span class="comment">/* |
| * Coefficients for approximation to erfc in [1.25,1/0.35] |
| */</span> |
| <span class="kw">const</span> <span class="ident">RA0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">9.86494403484714822705e-03</span>; <span class="comment">/* 0xBF843412, 0x600D6435 */</span> |
| <span class="kw">const</span> <span class="ident">RA1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">6.93858572707181764372e-01</span>; <span class="comment">/* 0xBFE63416, 0xE4BA7360 */</span> |
| <span class="kw">const</span> <span class="ident">RA2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.05586262253232909814e+01</span>; <span class="comment">/* 0xC0251E04, 0x41B0E726 */</span> |
| <span class="kw">const</span> <span class="ident">RA3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">6.23753324503260060396e+01</span>; <span class="comment">/* 0xC04F300A, 0xE4CBA38D */</span> |
| <span class="kw">const</span> <span class="ident">RA4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.62396669462573470355e+02</span>; <span class="comment">/* 0xC0644CB1, 0x84282266 */</span> |
| <span class="kw">const</span> <span class="ident">RA5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.84605092906711035994e+02</span>; <span class="comment">/* 0xC067135C, 0xEBCCABB2 */</span> |
| <span class="kw">const</span> <span class="ident">RA6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">8.12874355063065934246e+01</span>; <span class="comment">/* 0xC0545265, 0x57E4D2F2 */</span> |
| <span class="kw">const</span> <span class="ident">RA7</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">9.81432934416914548592e+00</span>; <span class="comment">/* 0xC023A0EF, 0xC69AC25C */</span> |
| <span class="kw">const</span> <span class="ident">SA1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.96512716674392571292e+01</span>; <span class="comment">/* 0x4033A6B9, 0xBD707687 */</span> |
| <span class="kw">const</span> <span class="ident">SA2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.37657754143519042600e+02</span>; <span class="comment">/* 0x4061350C, 0x526AE721 */</span> |
| <span class="kw">const</span> <span class="ident">SA3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.34565877475229228821e+02</span>; <span class="comment">/* 0x407B290D, 0xD58A1A71 */</span> |
| <span class="kw">const</span> <span class="ident">SA4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.45387271733267880336e+02</span>; <span class="comment">/* 0x40842B19, 0x21EC2868 */</span> |
| <span class="kw">const</span> <span class="ident">SA5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.29008140027567833386e+02</span>; <span class="comment">/* 0x407AD021, 0x57700314 */</span> |
| <span class="kw">const</span> <span class="ident">SA6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.08635005541779435134e+02</span>; <span class="comment">/* 0x405B28A3, 0xEE48AE2C */</span> |
| <span class="kw">const</span> <span class="ident">SA7</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.57024977031928170135e+00</span>; <span class="comment">/* 0x401A47EF, 0x8E484A93 */</span> |
| <span class="kw">const</span> <span class="ident">SA8</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">6.04244152148580987438e-02</span>; <span class="comment">/* 0xBFAEEFF2, 0xEE749A62 */</span> |
| <span class="comment">/* |
| * Coefficients for approximation to erfc in [1/.35,28] |
| */</span> |
| <span class="kw">const</span> <span class="ident">RB0</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">9.86494292470009928597e-03</span>; <span class="comment">/* 0xBF843412, 0x39E86F4A */</span> |
| <span class="kw">const</span> <span class="ident">RB1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">7.99283237680523006574e-01</span>; <span class="comment">/* 0xBFE993BA, 0x70C285DE */</span> |
| <span class="kw">const</span> <span class="ident">RB2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.77579549177547519889e+01</span>; <span class="comment">/* 0xC031C209, 0x555F995A */</span> |
| <span class="kw">const</span> <span class="ident">RB3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.60636384855821916062e+02</span>; <span class="comment">/* 0xC064145D, 0x43C5ED98 */</span> |
| <span class="kw">const</span> <span class="ident">RB4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">6.37566443368389627722e+02</span>; <span class="comment">/* 0xC083EC88, 0x1375F228 */</span> |
| <span class="kw">const</span> <span class="ident">RB5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">1.02509513161107724954e+03</span>; <span class="comment">/* 0xC0900461, 0x6A2E5992 */</span> |
| <span class="kw">const</span> <span class="ident">RB6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">4.83519191608651397019e+02</span>; <span class="comment">/* 0xC07E384E, 0x9BDC383F */</span> |
| <span class="kw">const</span> <span class="ident">SB1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.03380607434824582924e+01</span>; <span class="comment">/* 0x403E568B, 0x261D5190 */</span> |
| <span class="kw">const</span> <span class="ident">SB2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.25792512996573918826e+02</span>; <span class="comment">/* 0x40745CAE, 0x221B9F0A */</span> |
| <span class="kw">const</span> <span class="ident">SB3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.53672958608443695994e+03</span>; <span class="comment">/* 0x409802EB, 0x189D5118 */</span> |
| <span class="kw">const</span> <span class="ident">SB4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.19985821950859553908e+03</span>; <span class="comment">/* 0x40A8FFB7, 0x688C246A */</span> |
| <span class="kw">const</span> <span class="ident">SB5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.55305040643316442583e+03</span>; <span class="comment">/* 0x40A3F219, 0xCEDF3BE6 */</span> |
| <span class="kw">const</span> <span class="ident">SB6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">4.74528541206955367215e+02</span>; <span class="comment">/* 0x407DA874, 0xE79FE763 */</span> |
| <span class="kw">const</span> <span class="ident">SB7</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="op">-</span><span class="number">2.24409524465858183362e+01</span>; <span class="comment">/* 0xC03670E2, 0x42712D62 */</span> |
| |
| <span class="kw">fn</span> <span class="ident">erfc1</span>(<span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">p</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">q</span>: <span class="ident">f64</span>; |
| |
| <span class="ident">s</span> <span class="op">=</span> <span class="ident">fabs</span>(<span class="ident">x</span>) <span class="op">-</span> <span class="number">1.0</span>; |
| <span class="ident">p</span> <span class="op">=</span> <span class="ident">PA0</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">PA1</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">PA2</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">PA3</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">PA4</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">PA5</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">PA6</span>))))); |
| <span class="ident">q</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">QA1</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">QA2</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">QA3</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">QA4</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">QA5</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">QA6</span>))))); |
| |
| <span class="number">1.0</span> <span class="op">-</span> <span class="ident">ERX</span> <span class="op">-</span> <span class="ident">p</span> <span class="op">/</span> <span class="ident">q</span> |
| } |
| |
| <span class="kw">fn</span> <span class="ident">erfc2</span>(<span class="ident">ix</span>: <span class="ident">u32</span>, <span class="kw-2">mut</span> <span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">big_s</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>; |
| |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3ff40000</span> { |
| <span class="comment">/* |x| < 1.25 */</span> |
| <span class="kw">return</span> <span class="ident">erfc1</span>(<span class="ident">x</span>); |
| } |
| |
| <span class="ident">x</span> <span class="op">=</span> <span class="ident">fabs</span>(<span class="ident">x</span>); |
| <span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">/</span> (<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>); |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x4006db6d</span> { |
| <span class="comment">/* |x| < 1/.35 ~ 2.85714 */</span> |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">RA0</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RA1</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RA2</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RA3</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RA4</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RA5</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RA6</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">RA7</span>)))))); |
| <span class="ident">big_s</span> <span class="op">=</span> <span class="number">1.0</span> |
| <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SA1</span> |
| <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SA2</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SA3</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SA4</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SA5</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SA6</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SA7</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">SA8</span>))))))); |
| } <span class="kw">else</span> { |
| <span class="comment">/* |x| > 1/.35 */</span> |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">RB0</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RB1</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RB2</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RB3</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RB4</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">RB5</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">RB6</span>))))); |
| <span class="ident">big_s</span> <span class="op">=</span> |
| <span class="number">1.0</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SB1</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SB2</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SB3</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SB4</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SB5</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">SB6</span> <span class="op">+</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">SB7</span>)))))); |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">with_set_low_word</span>(<span class="ident">x</span>, <span class="number">0</span>); |
| |
| <span class="ident">exp</span>(<span class="op">-</span><span class="ident">z</span> <span class="op">*</span> <span class="ident">z</span> <span class="op">-</span> <span class="number">0.5625</span>) <span class="op">*</span> <span class="ident">exp</span>((<span class="ident">z</span> <span class="op">-</span> <span class="ident">x</span>) <span class="op">*</span> (<span class="ident">z</span> <span class="op">+</span> <span class="ident">x</span>) <span class="op">+</span> <span class="ident">r</span> <span class="op">/</span> <span class="ident">big_s</span>) <span class="op">/</span> <span class="ident">x</span> |
| } |
| |
| <span class="doccomment">/// Error function (f64)</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Calculates an approximation to the “error function”, which estimates</span> |
| <span class="doccomment">/// the probability that an observation will fall within x standard</span> |
| <span class="doccomment">/// deviations of the mean (assuming a normal distribution).</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">erf</span>(<span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">y</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">sign</span>: <span class="ident">usize</span>; |
| |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">x</span>); |
| <span class="ident">sign</span> <span class="op">=</span> (<span class="ident">ix</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="kw">as</span> <span class="ident">usize</span>; |
| <span class="ident">ix</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x7ff00000</span> { |
| <span class="comment">/* erf(nan)=nan, erf(+-inf)=+-1 */</span> |
| <span class="kw">return</span> <span class="number">1.0</span> <span class="op">-</span> <span class="number">2.0</span> <span class="op">*</span> (<span class="ident">sign</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">+</span> <span class="number">1.0</span> <span class="op">/</span> <span class="ident">x</span>; |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3feb0000</span> { |
| <span class="comment">/* |x| < 0.84375 */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3e300000</span> { |
| <span class="comment">/* |x| < 2**-28 */</span> |
| <span class="comment">/* avoid underflow */</span> |
| <span class="kw">return</span> <span class="number">0.125</span> <span class="op">*</span> (<span class="number">8.0</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">+</span> <span class="ident">EFX8</span> <span class="op">*</span> <span class="ident">x</span>); |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>; |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">PP0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PP1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PP2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PP3</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">PP4</span>))); |
| <span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QQ1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QQ2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QQ3</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QQ4</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">QQ5</span>)))); |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">r</span> <span class="op">/</span> <span class="ident">s</span>; |
| <span class="kw">return</span> <span class="ident">x</span> <span class="op">+</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">y</span>; |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x40180000</span> { |
| <span class="comment">/* 0.84375 <= |x| < 6 */</span> |
| <span class="ident">y</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">-</span> <span class="ident">erfc2</span>(<span class="ident">ix</span>, <span class="ident">x</span>); |
| } <span class="kw">else</span> { |
| <span class="kw">let</span> <span class="ident">x1p_1022</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="number">0x0010000000000000</span>); |
| <span class="ident">y</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">-</span> <span class="ident">x1p_1022</span>; |
| } |
| |
| <span class="kw">if</span> <span class="ident">sign</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="op">-</span><span class="ident">y</span> |
| } <span class="kw">else</span> { |
| <span class="ident">y</span> |
| } |
| } |
| |
| <span class="doccomment">/// Error function (f64)</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Calculates the complementary probability.</span> |
| <span class="doccomment">/// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid</span> |
| <span class="doccomment">/// the loss of precision that would result from subtracting</span> |
| <span class="doccomment">/// large probabilities (on large `x`) from 1.</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">erfc</span>(<span class="ident">x</span>: <span class="ident">f64</span>) -> <span class="ident">f64</span> { |
| <span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="ident">y</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ix</span>: <span class="ident">u32</span>; |
| <span class="kw">let</span> <span class="ident">sign</span>: <span class="ident">usize</span>; |
| |
| <span class="ident">ix</span> <span class="op">=</span> <span class="ident">get_high_word</span>(<span class="ident">x</span>); |
| <span class="ident">sign</span> <span class="op">=</span> (<span class="ident">ix</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="kw">as</span> <span class="ident">usize</span>; |
| <span class="ident">ix</span> <span class="op">&=</span> <span class="number">0x7fffffff</span>; |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op">></span><span class="op">=</span> <span class="number">0x7ff00000</span> { |
| <span class="comment">/* erfc(nan)=nan, erfc(+-inf)=0,2 */</span> |
| <span class="kw">return</span> <span class="number">2.0</span> <span class="op">*</span> (<span class="ident">sign</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">+</span> <span class="number">1.0</span> <span class="op">/</span> <span class="ident">x</span>; |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3feb0000</span> { |
| <span class="comment">/* |x| < 0.84375 */</span> |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3c700000</span> { |
| <span class="comment">/* |x| < 2**-56 */</span> |
| <span class="kw">return</span> <span class="number">1.0</span> <span class="op">-</span> <span class="ident">x</span>; |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>; |
| <span class="ident">r</span> <span class="op">=</span> <span class="ident">PP0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PP1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PP2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">PP3</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">PP4</span>))); |
| <span class="ident">s</span> <span class="op">=</span> <span class="number">1.0</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QQ1</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QQ2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QQ3</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">QQ4</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">QQ5</span>)))); |
| <span class="ident">y</span> <span class="op">=</span> <span class="ident">r</span> <span class="op">/</span> <span class="ident">s</span>; |
| <span class="kw">if</span> <span class="ident">sign</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> <span class="op">|</span><span class="op">|</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x3fd00000</span> { |
| <span class="comment">/* x < 1/4 */</span> |
| <span class="kw">return</span> <span class="number">1.0</span> <span class="op">-</span> (<span class="ident">x</span> <span class="op">+</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">y</span>); |
| } |
| <span class="kw">return</span> <span class="number">0.5</span> <span class="op">-</span> (<span class="ident">x</span> <span class="op">-</span> <span class="number">0.5</span> <span class="op">+</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">y</span>); |
| } |
| <span class="kw">if</span> <span class="ident">ix</span> <span class="op"><</span> <span class="number">0x403c0000</span> { |
| <span class="comment">/* 0.84375 <= |x| < 28 */</span> |
| <span class="kw">if</span> <span class="ident">sign</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="kw">return</span> <span class="number">2.0</span> <span class="op">-</span> <span class="ident">erfc2</span>(<span class="ident">ix</span>, <span class="ident">x</span>); |
| } <span class="kw">else</span> { |
| <span class="kw">return</span> <span class="ident">erfc2</span>(<span class="ident">ix</span>, <span class="ident">x</span>); |
| } |
| } |
| |
| <span class="kw">let</span> <span class="ident">x1p_1022</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="number">0x0010000000000000</span>); |
| <span class="kw">if</span> <span class="ident">sign</span> <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="number">2.0</span> <span class="op">-</span> <span class="ident">x1p_1022</span> |
| } <span class="kw">else</span> { |
| <span class="ident">x1p_1022</span> <span class="op">*</span> <span class="ident">x1p_1022</span> |
| } |
| } |
| </code></pre></div> |
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