use super::{exp, fabs, get_high_word, with_set_low_word};

/* origin: FreeBSD /usr/src/lib/msun/src/s_erf.c */

/*

 * ====================================================

 * 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.

 * ====================================================

 */

/* 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

 */

const ERX: f64 = 8.45062911510467529297e-01; /* 0x3FEB0AC1, 0x60000000 */

/*

 * Coefficients for approximation to  erf on [0,0.84375]

 */

const EFX8: f64 = 1.02703333676410069053e+00; /* 0x3FF06EBA, 0x8214DB69 */

const PP0: f64 = 1.28379167095512558561e-01; /* 0x3FC06EBA, 0x8214DB68 */

const PP1: f64 = -3.25042107247001499370e-01; /* 0xBFD4CD7D, 0x691CB913 */

const PP2: f64 = -2.84817495755985104766e-02; /* 0xBF9D2A51, 0xDBD7194F */

const PP3: f64 = -5.77027029648944159157e-03; /* 0xBF77A291, 0x236668E4 */

const PP4: f64 = -2.37630166566501626084e-05; /* 0xBEF8EAD6, 0x120016AC */

const QQ1: f64 = 3.97917223959155352819e-01; /* 0x3FD97779, 0xCDDADC09 */

const QQ2: f64 = 6.50222499887672944485e-02; /* 0x3FB0A54C, 0x5536CEBA */

const QQ3: f64 = 5.08130628187576562776e-03; /* 0x3F74D022, 0xC4D36B0F */

const QQ4: f64 = 1.32494738004321644526e-04; /* 0x3F215DC9, 0x221C1A10 */

const QQ5: f64 = -3.96022827877536812320e-06; /* 0xBED09C43, 0x42A26120 */

/*

 * Coefficients for approximation to  erf  in [0.84375,1.25]

 */

const PA0: f64 = -2.36211856075265944077e-03; /* 0xBF6359B8, 0xBEF77538 */

const PA1: f64 = 4.14856118683748331666e-01; /* 0x3FDA8D00, 0xAD92B34D */

const PA2: f64 = -3.72207876035701323847e-01; /* 0xBFD7D240, 0xFBB8C3F1 */

const PA3: f64 = 3.18346619901161753674e-01; /* 0x3FD45FCA, 0x805120E4 */

const PA4: f64 = -1.10894694282396677476e-01; /* 0xBFBC6398, 0x3D3E28EC */

const PA5: f64 = 3.54783043256182359371e-02; /* 0x3FA22A36, 0x599795EB */

const PA6: f64 = -2.16637559486879084300e-03; /* 0xBF61BF38, 0x0A96073F */

const QA1: f64 = 1.06420880400844228286e-01; /* 0x3FBB3E66, 0x18EEE323 */

const QA2: f64 = 5.40397917702171048937e-01; /* 0x3FE14AF0, 0x92EB6F33 */

const QA3: f64 = 7.18286544141962662868e-02; /* 0x3FB2635C, 0xD99FE9A7 */

const QA4: f64 = 1.26171219808761642112e-01; /* 0x3FC02660, 0xE763351F */

const QA5: f64 = 1.36370839120290507362e-02; /* 0x3F8BEDC2, 0x6B51DD1C */

const QA6: f64 = 1.19844998467991074170e-02; /* 0x3F888B54, 0x5735151D */

/*

 * Coefficients for approximation to  erfc in [1.25,1/0.35]

 */

const RA0: f64 = -9.86494403484714822705e-03; /* 0xBF843412, 0x600D6435 */

const RA1: f64 = -6.93858572707181764372e-01; /* 0xBFE63416, 0xE4BA7360 */

const RA2: f64 = -1.05586262253232909814e+01; /* 0xC0251E04, 0x41B0E726 */

const RA3: f64 = -6.23753324503260060396e+01; /* 0xC04F300A, 0xE4CBA38D */

const RA4: f64 = -1.62396669462573470355e+02; /* 0xC0644CB1, 0x84282266 */

const RA5: f64 = -1.84605092906711035994e+02; /* 0xC067135C, 0xEBCCABB2 */

const RA6: f64 = -8.12874355063065934246e+01; /* 0xC0545265, 0x57E4D2F2 */

const RA7: f64 = -9.81432934416914548592e+00; /* 0xC023A0EF, 0xC69AC25C */

const SA1: f64 = 1.96512716674392571292e+01; /* 0x4033A6B9, 0xBD707687 */

const SA2: f64 = 1.37657754143519042600e+02; /* 0x4061350C, 0x526AE721 */

const SA3: f64 = 4.34565877475229228821e+02; /* 0x407B290D, 0xD58A1A71 */

const SA4: f64 = 6.45387271733267880336e+02; /* 0x40842B19, 0x21EC2868 */

const SA5: f64 = 4.29008140027567833386e+02; /* 0x407AD021, 0x57700314 */

const SA6: f64 = 1.08635005541779435134e+02; /* 0x405B28A3, 0xEE48AE2C */

const SA7: f64 = 6.57024977031928170135e+00; /* 0x401A47EF, 0x8E484A93 */

const SA8: f64 = -6.04244152148580987438e-02; /* 0xBFAEEFF2, 0xEE749A62 */

/*

 * Coefficients for approximation to  erfc in [1/.35,28]

 */

const RB0: f64 = -9.86494292470009928597e-03; /* 0xBF843412, 0x39E86F4A */

const RB1: f64 = -7.99283237680523006574e-01; /* 0xBFE993BA, 0x70C285DE */

const RB2: f64 = -1.77579549177547519889e+01; /* 0xC031C209, 0x555F995A */

const RB3: f64 = -1.60636384855821916062e+02; /* 0xC064145D, 0x43C5ED98 */

const RB4: f64 = -6.37566443368389627722e+02; /* 0xC083EC88, 0x1375F228 */

const RB5: f64 = -1.02509513161107724954e+03; /* 0xC0900461, 0x6A2E5992 */

const RB6: f64 = -4.83519191608651397019e+02; /* 0xC07E384E, 0x9BDC383F */

const SB1: f64 = 3.03380607434824582924e+01; /* 0x403E568B, 0x261D5190 */

const SB2: f64 = 3.25792512996573918826e+02; /* 0x40745CAE, 0x221B9F0A */

const SB3: f64 = 1.53672958608443695994e+03; /* 0x409802EB, 0x189D5118 */

const SB4: f64 = 3.19985821950859553908e+03; /* 0x40A8FFB7, 0x688C246A */

const SB5: f64 = 2.55305040643316442583e+03; /* 0x40A3F219, 0xCEDF3BE6 */

const SB6: f64 = 4.74528541206955367215e+02; /* 0x407DA874, 0xE79FE763 */

const SB7: f64 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */

fn erfc1(x: f64) -> f64 {

    let s: f64;

    let p: f64;

    let q: f64;

    s = fabs(x) - 1.0;

    p = PA0 + s * (PA1 + s * (PA2 + s * (PA3 + s * (PA4 + s * (PA5 + s * PA6)))));

    q = 1.0 + s * (QA1 + s * (QA2 + s * (QA3 + s * (QA4 + s * (QA5 + s * QA6)))));

    1.0 - ERX - p / q

}

fn erfc2(ix: u32, mut x: f64) -> f64 {

    let s: f64;

    let r: f64;

    let big_s: f64;

    let z: f64;

    if ix < 0x3ff40000 {

        /* |x| < 1.25 */

        return erfc1(x);

    }

    x = fabs(x);

    s = 1.0 / (x * x);

    if ix < 0x4006db6d {

        /* |x| < 1/.35 ~ 2.85714 */

        r = RA0 + s * (RA1 + s * (RA2 + s * (RA3 + s * (RA4 + s * (RA5 + s * (RA6 + s * RA7))))));

        big_s = 1.0

            + s * (SA1

                + s * (SA2 + s * (SA3 + s * (SA4 + s * (SA5 + s * (SA6 + s * (SA7 + s * SA8)))))));

    } else {

        /* |x| > 1/.35 */

        r = RB0 + s * (RB1 + s * (RB2 + s * (RB3 + s * (RB4 + s * (RB5 + s * RB6)))));

        big_s =

            1.0 + s * (SB1 + s * (SB2 + s * (SB3 + s * (SB4 + s * (SB5 + s * (SB6 + s * SB7))))));

    }

    z = with_set_low_word(x, 0);

    exp(-z * z - 0.5625) * exp((z - x) * (z + x) + r / big_s) / x

}

/// Error function (f64)

///

/// Calculates an approximation to the “error function”, which estimates

/// the probability that an observation will fall within x standard

/// deviations of the mean (assuming a normal distribution).

#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]

pub fn erf(x: f64) -> f64 {

    let r: f64;

    let s: f64;

    let z: f64;

    let y: f64;

    let mut ix: u32;

    let sign: usize;

    ix = get_high_word(x);

    sign = (ix >> 31) as usize;

    ix &= 0x7fffffff;

    if ix >= 0x7ff00000 {

        /* erf(nan)=nan, erf(+-inf)=+-1 */

        return 1.0 - 2.0 * (sign as f64) + 1.0 / x;

    }

    if ix < 0x3feb0000 {

        /* |x| < 0.84375 */

        if ix < 0x3e300000 {

            /* |x| < 2**-28 */

            /* avoid underflow */

            return 0.125 * (8.0 * x + EFX8 * x);

        }

        z = x * x;

        r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));

        s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));

        y = r / s;

        return x + x * y;

    }

    if ix < 0x40180000 {

        /* 0.84375 <= |x| < 6 */

        y = 1.0 - erfc2(ix, x);

    } else {

        let x1p_1022 = f64::from_bits(0x0010000000000000);

        y = 1.0 - x1p_1022;

    }

    if sign != 0 { -y } else { y }

}

/// Complementary error function (f64)

///

/// Calculates the complementary probability.

/// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid

/// the loss of precision that would result from subtracting

/// large probabilities (on large `x`) from 1.

pub fn erfc(x: f64) -> f64 {

    let r: f64;

    let s: f64;

    let z: f64;

    let y: f64;

    let mut ix: u32;

    let sign: usize;

    ix = get_high_word(x);

    sign = (ix >> 31) as usize;

    ix &= 0x7fffffff;

    if ix >= 0x7ff00000 {

        /* erfc(nan)=nan, erfc(+-inf)=0,2 */

        return 2.0 * (sign as f64) + 1.0 / x;

    }

    if ix < 0x3feb0000 {

        /* |x| < 0.84375 */

        if ix < 0x3c700000 {

            /* |x| < 2**-56 */

            return 1.0 - x;

        }

        z = x * x;

        r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4)));

        s = 1.0 + z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5))));

        y = r / s;

        if sign != 0 || ix < 0x3fd00000 {

            /* x < 1/4 */

            return 1.0 - (x + x * y);

        }

        return 0.5 - (x - 0.5 + x * y);

    }

    if ix < 0x403c0000 {

        /* 0.84375 <= |x| < 28 */

        if sign != 0 {

            return 2.0 - erfc2(ix, x);

        } else {

            return erfc2(ix, x);

        }

    }

    let x1p_1022 = f64::from_bits(0x0010000000000000);

    if sign != 0 { 2.0 - x1p_1022 } else { x1p_1022 * x1p_1022 }

}