//---------------------------------------------------------------------------------
//
//  Little Color Management System
//  Copyright (c) 1998-2020 Marti Maria Saguer
//
// 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.
//
//---------------------------------------------------------------------------------
//

#include "lcms2_internal.h"

//      inter PCS conversions XYZ <-> CIE L* a* b*
/*


       CIE 15:2004 CIELab is defined as:

       L* = 116*f(Y/Yn) - 16                     0 <= L* <= 100
       a* = 500*[f(X/Xn) - f(Y/Yn)]
       b* = 200*[f(Y/Yn) - f(Z/Zn)]

       and

              f(t) = t^(1/3)                     1 >= t >  (24/116)^3
                     (841/108)*t + (16/116)      0 <= t <= (24/116)^3


       Reverse transform is:

       X = Xn*[a* / 500 + (L* + 16) / 116] ^ 3   if (X/Xn) > (24/116)
         = Xn*(a* / 500 + L* / 116) / 7.787      if (X/Xn) <= (24/116)


       PCS in Lab2 is encoded as:

              8 bit Lab PCS:

                     L*      0..100 into a 0..ff byte.
                     a*      t + 128 range is -128.0  +127.0
                     b*

             16 bit Lab PCS:

                     L*     0..100  into a 0..ff00 word.
                     a*     t + 128  range is  -128.0  +127.9961
                     b*


Interchange Space   Component     Actual Range        Encoded Range
CIE XYZ             X             0 -> 1.99997        0x0000 -> 0xffff
CIE XYZ             Y             0 -> 1.99997        0x0000 -> 0xffff
CIE XYZ             Z             0 -> 1.99997        0x0000 -> 0xffff

Version 2,3
-----------

CIELAB (16 bit)     L*            0 -> 100.0          0x0000 -> 0xff00
CIELAB (16 bit)     a*            -128.0 -> +127.996  0x0000 -> 0x8000 -> 0xffff
CIELAB (16 bit)     b*            -128.0 -> +127.996  0x0000 -> 0x8000 -> 0xffff


Version 4
---------

CIELAB (16 bit)     L*            0 -> 100.0          0x0000 -> 0xffff
CIELAB (16 bit)     a*            -128.0 -> +127      0x0000 -> 0x8080 -> 0xffff
CIELAB (16 bit)     b*            -128.0 -> +127      0x0000 -> 0x8080 -> 0xffff

*/

// Conversions
void CMSEXPORT cmsXYZ2xyY(cmsCIExyY* Dest, const cmsCIEXYZ* Source)
{
    cmsFloat64Number ISum;

    ISum = 1./(Source -> X + Source -> Y + Source -> Z);

    Dest -> x = (Source -> X) * ISum;
    Dest -> y = (Source -> Y) * ISum;
    Dest -> Y = Source -> Y;
}

void CMSEXPORT cmsxyY2XYZ(cmsCIEXYZ* Dest, const cmsCIExyY* Source)
{
    Dest -> X = (Source -> x / Source -> y) * Source -> Y;
    Dest -> Y = Source -> Y;
    Dest -> Z = ((1 - Source -> x - Source -> y) / Source -> y) * Source -> Y;
}

/*
       The break point (24/116)^3 = (6/29)^3 is a very small amount of tristimulus 
       primary (0.008856).  Generally, this only happens for 
       nearly ideal blacks and for some orange / amber colors in transmission mode.  
       For example, the Z value of the orange turn indicator lamp lens on an 
       automobile will often be below this value.  But the Z does not 
       contribute to the perceived color directly.
*/

static
cmsFloat64Number f(cmsFloat64Number t)
{
    const cmsFloat64Number Limit = (24.0/116.0) * (24.0/116.0) * (24.0/116.0);

    if (t <= Limit)
        return (841.0/108.0) * t + (16.0/116.0);
    else
        return pow(t, 1.0/3.0);
}

static
cmsFloat64Number f_1(cmsFloat64Number t)
{
    const cmsFloat64Number Limit = (24.0/116.0);

    if (t <= Limit) {
        return (108.0/841.0) * (t - (16.0/116.0));
    }

    return t * t * t;
}


// Standard XYZ to Lab. it can handle negative XZY numbers in some cases
void CMSEXPORT cmsXYZ2Lab(const cmsCIEXYZ* WhitePoint, cmsCIELab* Lab, const cmsCIEXYZ* xyz)
{
    cmsFloat64Number fx, fy, fz;

    if (WhitePoint == NULL)
        WhitePoint = cmsD50_XYZ();

    fx = f(xyz->X / WhitePoint->X);
    fy = f(xyz->Y / WhitePoint->Y);
    fz = f(xyz->Z / WhitePoint->Z);

    Lab->L = 116.0*fy - 16.0;
    Lab->a = 500.0*(fx - fy);
    Lab->b = 200.0*(fy - fz);
}


// Standard XYZ to Lab. It can return negative XYZ in some cases
void CMSEXPORT cmsLab2XYZ(const cmsCIEXYZ* WhitePoint, cmsCIEXYZ* xyz,  const cmsCIELab* Lab)
{
    cmsFloat64Number x, y, z;

    if (WhitePoint == NULL)
        WhitePoint = cmsD50_XYZ();

    y = (Lab-> L + 16.0) / 116.0;
    x = y + 0.002 * Lab -> a;
    z = y - 0.005 * Lab -> b;

    xyz -> X = f_1(x) * WhitePoint -> X;
    xyz -> Y = f_1(y) * WhitePoint -> Y;
    xyz -> Z = f_1(z) * WhitePoint -> Z;

}

static
cmsFloat64Number L2float2(cmsUInt16Number v)
{
    return (cmsFloat64Number) v / 652.800;
}

// the a/b part
static
cmsFloat64Number ab2float2(cmsUInt16Number v)
{
    return ((cmsFloat64Number) v / 256.0) - 128.0;
}

static
cmsUInt16Number L2Fix2(cmsFloat64Number L)
{
    return _cmsQuickSaturateWord(L *  652.8);
}

static
cmsUInt16Number ab2Fix2(cmsFloat64Number ab)
{
    return _cmsQuickSaturateWord((ab + 128.0) * 256.0);
}


static
cmsFloat64Number L2float4(cmsUInt16Number v)
{
    return (cmsFloat64Number) v / 655.35;
}

// the a/b part
static
cmsFloat64Number ab2float4(cmsUInt16Number v)
{
    return ((cmsFloat64Number) v / 257.0) - 128.0;
}


void CMSEXPORT cmsLabEncoded2FloatV2(cmsCIELab* Lab, const cmsUInt16Number wLab[3])
{
        Lab->L = L2float2(wLab[0]);
        Lab->a = ab2float2(wLab[1]);
        Lab->b = ab2float2(wLab[2]);
}


void CMSEXPORT cmsLabEncoded2Float(cmsCIELab* Lab, const cmsUInt16Number wLab[3])
{
        Lab->L = L2float4(wLab[0]);
        Lab->a = ab2float4(wLab[1]);
        Lab->b = ab2float4(wLab[2]);
}

static
cmsFloat64Number Clamp_L_doubleV2(cmsFloat64Number L)
{
    const cmsFloat64Number L_max = (cmsFloat64Number) (0xFFFF * 100.0) / 0xFF00;

    if (L < 0) L = 0;
    if (L > L_max) L = L_max;

    return L;
}


static
cmsFloat64Number Clamp_ab_doubleV2(cmsFloat64Number ab)
{
    if (ab < MIN_ENCODEABLE_ab2) ab = MIN_ENCODEABLE_ab2;
    if (ab > MAX_ENCODEABLE_ab2) ab = MAX_ENCODEABLE_ab2;

    return ab;
}

void CMSEXPORT cmsFloat2LabEncodedV2(cmsUInt16Number wLab[3], const cmsCIELab* fLab)
{
    cmsCIELab Lab;

    Lab.L = Clamp_L_doubleV2(fLab ->L);
    Lab.a = Clamp_ab_doubleV2(fLab ->a);
    Lab.b = Clamp_ab_doubleV2(fLab ->b);

    wLab[0] = L2Fix2(Lab.L);
    wLab[1] = ab2Fix2(Lab.a);
    wLab[2] = ab2Fix2(Lab.b);
}


static
cmsFloat64Number Clamp_L_doubleV4(cmsFloat64Number L)
{
    if (L < 0) L = 0;
    if (L > 100.0) L = 100.0;

    return L;
}

static
cmsFloat64Number Clamp_ab_doubleV4(cmsFloat64Number ab)
{
    if (ab < MIN_ENCODEABLE_ab4) ab = MIN_ENCODEABLE_ab4;
    if (ab > MAX_ENCODEABLE_ab4) ab = MAX_ENCODEABLE_ab4;

    return ab;
}

static
cmsUInt16Number L2Fix4(cmsFloat64Number L)
{
    return _cmsQuickSaturateWord(L *  655.35);
}

static
cmsUInt16Number ab2Fix4(cmsFloat64Number ab)
{
    return _cmsQuickSaturateWord((ab + 128.0) * 257.0);
}

void CMSEXPORT cmsFloat2LabEncoded(cmsUInt16Number wLab[3], const cmsCIELab* fLab)
{
    cmsCIELab Lab;

    Lab.L = Clamp_L_doubleV4(fLab ->L);
    Lab.a = Clamp_ab_doubleV4(fLab ->a);
    Lab.b = Clamp_ab_doubleV4(fLab ->b);

    wLab[0] = L2Fix4(Lab.L);
    wLab[1] = ab2Fix4(Lab.a);
    wLab[2] = ab2Fix4(Lab.b);
}

// Auxiliary: convert to Radians
static
cmsFloat64Number RADIANS(cmsFloat64Number deg)
{
    return (deg * M_PI) / 180.;
}


// Auxiliary: atan2 but operating in degrees and returning 0 if a==b==0
static
cmsFloat64Number atan2deg(cmsFloat64Number a, cmsFloat64Number b)
{
   cmsFloat64Number h;

   if (a == 0 && b == 0)
            h   = 0;
    else
            h = atan2(a, b);

    h *= (180. / M_PI);

    while (h > 360.)
        h -= 360.;

    while ( h < 0)
        h += 360.;

    return h;
}


// Auxiliary: Square
static
cmsFloat64Number Sqr(cmsFloat64Number v)
{
    return v *  v;
}
// From cylindrical coordinates. No check is performed, then negative values are allowed
void CMSEXPORT cmsLab2LCh(cmsCIELCh* LCh, const cmsCIELab* Lab)
{
    LCh -> L = Lab -> L;
    LCh -> C = pow(Sqr(Lab ->a) + Sqr(Lab ->b), 0.5);
    LCh -> h = atan2deg(Lab ->b, Lab ->a);
}


// To cylindrical coordinates. No check is performed, then negative values are allowed
void CMSEXPORT cmsLCh2Lab(cmsCIELab* Lab, const cmsCIELCh* LCh)
{
    cmsFloat64Number h = (LCh -> h * M_PI) / 180.0;

    Lab -> L = LCh -> L;
    Lab -> a = LCh -> C * cos(h);
    Lab -> b = LCh -> C * sin(h);
}

// In XYZ All 3 components are encoded using 1.15 fixed point
static
cmsUInt16Number XYZ2Fix(cmsFloat64Number d)
{
    return _cmsQuickSaturateWord(d * 32768.0);
}

void CMSEXPORT cmsFloat2XYZEncoded(cmsUInt16Number XYZ[3], const cmsCIEXYZ* fXYZ)
{
    cmsCIEXYZ xyz;

    xyz.X = fXYZ -> X;
    xyz.Y = fXYZ -> Y;
    xyz.Z = fXYZ -> Z;

    // Clamp to encodeable values.
    if (xyz.Y <= 0) {

        xyz.X = 0;
        xyz.Y = 0;
        xyz.Z = 0;
    }

    if (xyz.X > MAX_ENCODEABLE_XYZ)
        xyz.X = MAX_ENCODEABLE_XYZ;

    if (xyz.X < 0)
        xyz.X = 0;

    if (xyz.Y > MAX_ENCODEABLE_XYZ)
        xyz.Y = MAX_ENCODEABLE_XYZ;

    if (xyz.Y < 0)
        xyz.Y = 0;

    if (xyz.Z > MAX_ENCODEABLE_XYZ)
        xyz.Z = MAX_ENCODEABLE_XYZ;

    if (xyz.Z < 0)
        xyz.Z = 0;


    XYZ[0] = XYZ2Fix(xyz.X);
    XYZ[1] = XYZ2Fix(xyz.Y);
    XYZ[2] = XYZ2Fix(xyz.Z);
}


//  To convert from Fixed 1.15 point to cmsFloat64Number
static
cmsFloat64Number XYZ2float(cmsUInt16Number v)
{
    cmsS15Fixed16Number fix32;

    // From 1.15 to 15.16
    fix32 = v << 1;

    // From fixed 15.16 to cmsFloat64Number
    return _cms15Fixed16toDouble(fix32);
}


void CMSEXPORT cmsXYZEncoded2Float(cmsCIEXYZ* fXYZ, const cmsUInt16Number XYZ[3])
{
    fXYZ -> X = XYZ2float(XYZ[0]);
    fXYZ -> Y = XYZ2float(XYZ[1]);
    fXYZ -> Z = XYZ2float(XYZ[2]);
}


// Returns dE on two Lab values
cmsFloat64Number CMSEXPORT cmsDeltaE(const cmsCIELab* Lab1, const cmsCIELab* Lab2)
{
    cmsFloat64Number dL, da, db;

    dL = fabs(Lab1 -> L - Lab2 -> L);
    da = fabs(Lab1 -> a - Lab2 -> a);
    db = fabs(Lab1 -> b - Lab2 -> b);

    return pow(Sqr(dL) + Sqr(da) + Sqr(db), 0.5);
}


// Return the CIE94 Delta E
cmsFloat64Number CMSEXPORT cmsCIE94DeltaE(const cmsCIELab* Lab1, const cmsCIELab* Lab2)
{
    cmsCIELCh LCh1, LCh2;
    cmsFloat64Number dE, dL, dC, dh, dhsq;
    cmsFloat64Number c12, sc, sh;

    dL = fabs(Lab1 ->L - Lab2 ->L);

    cmsLab2LCh(&LCh1, Lab1);
    cmsLab2LCh(&LCh2, Lab2);

    dC  = fabs(LCh1.C - LCh2.C);
    dE  = cmsDeltaE(Lab1, Lab2);

    dhsq = Sqr(dE) - Sqr(dL) - Sqr(dC);
    if (dhsq < 0)
        dh = 0;
    else
        dh = pow(dhsq, 0.5);

    c12 = sqrt(LCh1.C * LCh2.C);

    sc = 1.0 + (0.048 * c12);
    sh = 1.0 + (0.014 * c12);

    return sqrt(Sqr(dL)  + Sqr(dC) / Sqr(sc) + Sqr(dh) / Sqr(sh));
}


// Auxiliary
static
cmsFloat64Number ComputeLBFD(const cmsCIELab* Lab)
{
  cmsFloat64Number yt;

  if (Lab->L > 7.996969)
        yt = (Sqr((Lab->L+16)/116)*((Lab->L+16)/116))*100;
  else
        yt = 100 * (Lab->L / 903.3);

  return (54.6 * (M_LOG10E * (log(yt + 1.5))) - 9.6);
}


// bfd - gets BFD(1:1) difference between Lab1, Lab2
cmsFloat64Number CMSEXPORT cmsBFDdeltaE(const cmsCIELab* Lab1, const cmsCIELab* Lab2)
{
    cmsFloat64Number lbfd1,lbfd2,AveC,Aveh,dE,deltaL,
        deltaC,deltah,dc,t,g,dh,rh,rc,rt,bfd;
    cmsCIELCh LCh1, LCh2;


    lbfd1 = ComputeLBFD(Lab1);
    lbfd2 = ComputeLBFD(Lab2);
    deltaL = lbfd2 - lbfd1;

    cmsLab2LCh(&LCh1, Lab1);
    cmsLab2LCh(&LCh2, Lab2);

    deltaC = LCh2.C - LCh1.C;
    AveC = (LCh1.C+LCh2.C)/2;
    Aveh = (LCh1.h+LCh2.h)/2;

    dE = cmsDeltaE(Lab1, Lab2);

    if (Sqr(dE)>(Sqr(Lab2->L-Lab1->L)+Sqr(deltaC)))
        deltah = sqrt(Sqr(dE)-Sqr(Lab2->L-Lab1->L)-Sqr(deltaC));
    else
        deltah =0;


    dc   = 0.035 * AveC / (1 + 0.00365 * AveC)+0.521;
    g    = sqrt(Sqr(Sqr(AveC))/(Sqr(Sqr(AveC))+14000));
    t    = 0.627+(0.055*cos((Aveh-254)/(180/M_PI))-
           0.040*cos((2*Aveh-136)/(180/M_PI))+
           0.070*cos((3*Aveh-31)/(180/M_PI))+
           0.049*cos((4*Aveh+114)/(180/M_PI))-
           0.015*cos((5*Aveh-103)/(180/M_PI)));

    dh    = dc*(g*t+1-g);
    rh    = -0.260*cos((Aveh-308)/(180/M_PI))-
           0.379*cos((2*Aveh-160)/(180/M_PI))-
           0.636*cos((3*Aveh+254)/(180/M_PI))+
           0.226*cos((4*Aveh+140)/(180/M_PI))-
           0.194*cos((5*Aveh+280)/(180/M_PI));

    rc = sqrt((AveC*AveC*AveC*AveC*AveC*AveC)/((AveC*AveC*AveC*AveC*AveC*AveC)+70000000));
    rt = rh*rc;

    bfd = sqrt(Sqr(deltaL)+Sqr(deltaC/dc)+Sqr(deltah/dh)+(rt*(deltaC/dc)*(deltah/dh)));

    return bfd;
}


//  cmc - CMC(l:c) difference between Lab1, Lab2
cmsFloat64Number CMSEXPORT cmsCMCdeltaE(const cmsCIELab* Lab1, const cmsCIELab* Lab2, cmsFloat64Number l, cmsFloat64Number c)
{
  cmsFloat64Number dE,dL,dC,dh,sl,sc,sh,t,f,cmc;
  cmsCIELCh LCh1, LCh2;

  if (Lab1 ->L == 0 && Lab2 ->L == 0) return 0;

  cmsLab2LCh(&LCh1, Lab1);
  cmsLab2LCh(&LCh2, Lab2);


  dL = Lab2->L-Lab1->L;
  dC = LCh2.C-LCh1.C;

  dE = cmsDeltaE(Lab1, Lab2);

  if (Sqr(dE)>(Sqr(dL)+Sqr(dC)))
            dh = sqrt(Sqr(dE)-Sqr(dL)-Sqr(dC));
  else
            dh =0;

  if ((LCh1.h > 164) && (LCh1.h < 345))
      t = 0.56 + fabs(0.2 * cos(((LCh1.h + 168)/(180/M_PI))));
  else
      t = 0.36 + fabs(0.4 * cos(((LCh1.h + 35 )/(180/M_PI))));

   sc  = 0.0638   * LCh1.C / (1 + 0.0131  * LCh1.C) + 0.638;
   sl  = 0.040975 * Lab1->L /(1 + 0.01765 * Lab1->L);

   if (Lab1->L<16)
         sl = 0.511;

   f   = sqrt((LCh1.C * LCh1.C * LCh1.C * LCh1.C)/((LCh1.C * LCh1.C * LCh1.C * LCh1.C)+1900));
   sh  = sc*(t*f+1-f);
   cmc = sqrt(Sqr(dL/(l*sl))+Sqr(dC/(c*sc))+Sqr(dh/sh));

   return cmc;
}

// dE2000 The weightings KL, KC and KH can be modified to reflect the relative
// importance of lightness, chroma and hue in different industrial applications
cmsFloat64Number CMSEXPORT cmsCIE2000DeltaE(const cmsCIELab* Lab1, const cmsCIELab* Lab2,
                                  cmsFloat64Number Kl, cmsFloat64Number Kc, cmsFloat64Number Kh)
{
    cmsFloat64Number L1  = Lab1->L;
    cmsFloat64Number a1  = Lab1->a;
    cmsFloat64Number b1  = Lab1->b;
    cmsFloat64Number C   = sqrt( Sqr(a1) + Sqr(b1) );

    cmsFloat64Number Ls = Lab2 ->L;
    cmsFloat64Number as = Lab2 ->a;
    cmsFloat64Number bs = Lab2 ->b;
    cmsFloat64Number Cs = sqrt( Sqr(as) + Sqr(bs) );

    cmsFloat64Number G = 0.5 * ( 1 - sqrt(pow((C + Cs) / 2 , 7.0) / (pow((C + Cs) / 2, 7.0) + pow(25.0, 7.0) ) ));

    cmsFloat64Number a_p = (1 + G ) * a1;
    cmsFloat64Number b_p = b1;
    cmsFloat64Number C_p = sqrt( Sqr(a_p) + Sqr(b_p));
    cmsFloat64Number h_p = atan2deg(b_p, a_p);


    cmsFloat64Number a_ps = (1 + G) * as;
    cmsFloat64Number b_ps = bs;
    cmsFloat64Number C_ps = sqrt(Sqr(a_ps) + Sqr(b_ps));
    cmsFloat64Number h_ps = atan2deg(b_ps, a_ps);

    cmsFloat64Number meanC_p =(C_p + C_ps) / 2;

    cmsFloat64Number hps_plus_hp  = h_ps + h_p;
    cmsFloat64Number hps_minus_hp = h_ps - h_p;

    cmsFloat64Number meanh_p = fabs(hps_minus_hp) <= 180.000001 ? (hps_plus_hp)/2 :
                            (hps_plus_hp) < 360 ? (hps_plus_hp + 360)/2 :
                                                 (hps_plus_hp - 360)/2;

    cmsFloat64Number delta_h = (hps_minus_hp) <= -180.000001 ?  (hps_minus_hp + 360) :
                            (hps_minus_hp) > 180 ? (hps_minus_hp - 360) :
                                                    (hps_minus_hp);
    cmsFloat64Number delta_L = (Ls - L1);
    cmsFloat64Number delta_C = (C_ps - C_p );


    cmsFloat64Number delta_H =2 * sqrt(C_ps*C_p) * sin(RADIANS(delta_h) / 2);

    cmsFloat64Number T = 1 - 0.17 * cos(RADIANS(meanh_p-30))
                 + 0.24 * cos(RADIANS(2*meanh_p))
                 + 0.32 * cos(RADIANS(3*meanh_p + 6))
                 - 0.2  * cos(RADIANS(4*meanh_p - 63));

    cmsFloat64Number Sl = 1 + (0.015 * Sqr((Ls + L1) /2- 50) )/ sqrt(20 + Sqr( (Ls+L1)/2 - 50) );

    cmsFloat64Number Sc = 1 + 0.045 * (C_p + C_ps)/2;
    cmsFloat64Number Sh = 1 + 0.015 * ((C_ps + C_p)/2) * T;

    cmsFloat64Number delta_ro = 30 * exp( -Sqr(((meanh_p - 275 ) / 25)));

    cmsFloat64Number Rc = 2 * sqrt(( pow(meanC_p, 7.0) )/( pow(meanC_p, 7.0) + pow(25.0, 7.0)));

    cmsFloat64Number Rt = -sin(2 * RADIANS(delta_ro)) * Rc;

    cmsFloat64Number deltaE00 = sqrt( Sqr(delta_L /(Sl * Kl)) +
                            Sqr(delta_C/(Sc * Kc))  +
                            Sqr(delta_H/(Sh * Kh))  +
                            Rt*(delta_C/(Sc * Kc)) * (delta_H / (Sh * Kh)));

    return deltaE00;
}

// This function returns a number of gridpoints to be used as LUT table. It assumes same number
// of gripdpoints in all dimensions. Flags may override the choice.
cmsUInt32Number CMSEXPORT _cmsReasonableGridpointsByColorspace(cmsColorSpaceSignature Colorspace, cmsUInt32Number dwFlags)
{
    cmsUInt32Number nChannels;

    // Already specified?
    if (dwFlags & 0x00FF0000) {
            // Yes, grab'em
            return (dwFlags >> 16) & 0xFF;
    }

    nChannels = cmsChannelsOf(Colorspace);

    // HighResPrecalc is maximum resolution
    if (dwFlags & cmsFLAGS_HIGHRESPRECALC) {

        if (nChannels > 4)
                return 7;       // 7 for Hifi

        if (nChannels == 4)     // 23 for CMYK
                return 23;

        return 49;      // 49 for RGB and others
    }


    // LowResPrecal is lower resolution
    if (dwFlags & cmsFLAGS_LOWRESPRECALC) {

        if (nChannels > 4)
                return 6;       // 6 for more than 4 channels

        if (nChannels == 1)
                return 33;      // For monochrome

        return 17;              // 17 for remaining
    }

    // Default values
    if (nChannels > 4)
                return 7;       // 7 for Hifi

    if (nChannels == 4)
                return 17;      // 17 for CMYK

    return 33;                  // 33 for RGB
}


cmsBool  _cmsEndPointsBySpace(cmsColorSpaceSignature Space,
                             cmsUInt16Number **White,
                             cmsUInt16Number **Black,
                             cmsUInt32Number *nOutputs)
{
       // Only most common spaces

       static cmsUInt16Number RGBblack[4]  = { 0, 0, 0 };
       static cmsUInt16Number RGBwhite[4]  = { 0xffff, 0xffff, 0xffff };
       static cmsUInt16Number CMYKblack[4] = { 0xffff, 0xffff, 0xffff, 0xffff };   // 400% of ink
       static cmsUInt16Number CMYKwhite[4] = { 0, 0, 0, 0 };
       static cmsUInt16Number LABblack[4]  = { 0, 0x8080, 0x8080 };               // V4 Lab encoding
       static cmsUInt16Number LABwhite[4]  = { 0xFFFF, 0x8080, 0x8080 };
       static cmsUInt16Number CMYblack[4]  = { 0xffff, 0xffff, 0xffff };
       static cmsUInt16Number CMYwhite[4]  = { 0, 0, 0 };
       static cmsUInt16Number Grayblack[4] = { 0 };
       static cmsUInt16Number GrayWhite[4] = { 0xffff };

       switch (Space) {

       case cmsSigGrayData: if (White)    *White = GrayWhite;
                           if (Black)    *Black = Grayblack;
                           if (nOutputs) *nOutputs = 1;
                           return TRUE;

       case cmsSigRgbData:  if (White)    *White = RGBwhite;
                           if (Black)    *Black = RGBblack;
                           if (nOutputs) *nOutputs = 3;
                           return TRUE;

       case cmsSigLabData:  if (White)    *White = LABwhite;
                           if (Black)    *Black = LABblack;
                           if (nOutputs) *nOutputs = 3;
                           return TRUE;

       case cmsSigCmykData: if (White)    *White = CMYKwhite;
                           if (Black)    *Black = CMYKblack;
                           if (nOutputs) *nOutputs = 4;
                           return TRUE;

       case cmsSigCmyData:  if (White)    *White = CMYwhite;
                           if (Black)    *Black = CMYblack;
                           if (nOutputs) *nOutputs = 3;
                           return TRUE;

       default:;
       }

  return FALSE;
}


// Several utilities -------------------------------------------------------

// Translate from our colorspace to ICC representation

cmsColorSpaceSignature CMSEXPORT _cmsICCcolorSpace(int OurNotation)
{
       switch (OurNotation) {

       case 1:
       case PT_GRAY: return cmsSigGrayData;

       case 2:
       case PT_RGB:  return cmsSigRgbData;

       case PT_CMY:  return cmsSigCmyData;
       case PT_CMYK: return cmsSigCmykData;
       case PT_YCbCr:return cmsSigYCbCrData;
       case PT_YUV:  return cmsSigLuvData;
       case PT_XYZ:  return cmsSigXYZData;

       case PT_LabV2:
       case PT_Lab:  return cmsSigLabData;

       case PT_YUVK: return cmsSigLuvKData;
       case PT_HSV:  return cmsSigHsvData;
       case PT_HLS:  return cmsSigHlsData;
       case PT_Yxy:  return cmsSigYxyData;

       case PT_MCH1: return cmsSigMCH1Data;
       case PT_MCH2: return cmsSigMCH2Data;
       case PT_MCH3: return cmsSigMCH3Data;
       case PT_MCH4: return cmsSigMCH4Data;
       case PT_MCH5: return cmsSigMCH5Data;
       case PT_MCH6: return cmsSigMCH6Data;
       case PT_MCH7: return cmsSigMCH7Data;
       case PT_MCH8: return cmsSigMCH8Data;

       case PT_MCH9:  return cmsSigMCH9Data;
       case PT_MCH10: return cmsSigMCHAData;
       case PT_MCH11: return cmsSigMCHBData;
       case PT_MCH12: return cmsSigMCHCData;
       case PT_MCH13: return cmsSigMCHDData;
       case PT_MCH14: return cmsSigMCHEData;
       case PT_MCH15: return cmsSigMCHFData;

       default:  return (cmsColorSpaceSignature) 0;
       }
}


int CMSEXPORT _cmsLCMScolorSpace(cmsColorSpaceSignature ProfileSpace)
{
    switch (ProfileSpace) {

    case cmsSigGrayData: return  PT_GRAY;
    case cmsSigRgbData:  return  PT_RGB;
    case cmsSigCmyData:  return  PT_CMY;
    case cmsSigCmykData: return  PT_CMYK;
    case cmsSigYCbCrData:return  PT_YCbCr;
    case cmsSigLuvData:  return  PT_YUV;
    case cmsSigXYZData:  return  PT_XYZ;
    case cmsSigLabData:  return  PT_Lab;
    case cmsSigLuvKData: return  PT_YUVK;
    case cmsSigHsvData:  return  PT_HSV;
    case cmsSigHlsData:  return  PT_HLS;
    case cmsSigYxyData:  return  PT_Yxy;

    case cmsSig1colorData:
    case cmsSigMCH1Data: return PT_MCH1;

    case cmsSig2colorData:
    case cmsSigMCH2Data: return PT_MCH2;

    case cmsSig3colorData:
    case cmsSigMCH3Data: return PT_MCH3;

    case cmsSig4colorData:
    case cmsSigMCH4Data: return PT_MCH4;

    case cmsSig5colorData:
    case cmsSigMCH5Data: return PT_MCH5;

    case cmsSig6colorData:
    case cmsSigMCH6Data: return PT_MCH6;

    case cmsSigMCH7Data:
    case cmsSig7colorData:return PT_MCH7;

    case cmsSigMCH8Data:
    case cmsSig8colorData:return PT_MCH8;

    case cmsSigMCH9Data:
    case cmsSig9colorData:return PT_MCH9;

    case cmsSigMCHAData:
    case cmsSig10colorData:return PT_MCH10;

    case cmsSigMCHBData:
    case cmsSig11colorData:return PT_MCH11;

    case cmsSigMCHCData:
    case cmsSig12colorData:return PT_MCH12;

    case cmsSigMCHDData:
    case cmsSig13colorData:return PT_MCH13;

    case cmsSigMCHEData:
    case cmsSig14colorData:return PT_MCH14;

    case cmsSigMCHFData:
    case cmsSig15colorData:return PT_MCH15;

    default:  return (cmsColorSpaceSignature) 0;
    }
}


cmsUInt32Number CMSEXPORT cmsChannelsOf(cmsColorSpaceSignature ColorSpace)
{
    switch (ColorSpace) {

    case cmsSigMCH1Data:
    case cmsSig1colorData:
    case cmsSigGrayData: return 1;

    case cmsSigMCH2Data:
    case cmsSig2colorData:  return 2;

    case cmsSigXYZData:
    case cmsSigLabData:
    case cmsSigLuvData:
    case cmsSigYCbCrData:
    case cmsSigYxyData:
    case cmsSigRgbData:
    case cmsSigHsvData:
    case cmsSigHlsData:
    case cmsSigCmyData:
    case cmsSigMCH3Data:
    case cmsSig3colorData:  return 3;

    case cmsSigLuvKData:
    case cmsSigCmykData:
    case cmsSigMCH4Data:
    case cmsSig4colorData:  return 4;

    case cmsSigMCH5Data:
    case cmsSig5colorData:  return 5;

    case cmsSigMCH6Data:
    case cmsSig6colorData:  return 6;

    case cmsSigMCH7Data:
    case cmsSig7colorData:  return  7;

    case cmsSigMCH8Data:
    case cmsSig8colorData:  return  8;

    case cmsSigMCH9Data:
    case cmsSig9colorData:  return  9;

    case cmsSigMCHAData:
    case cmsSig10colorData: return 10;

    case cmsSigMCHBData:
    case cmsSig11colorData: return 11;

    case cmsSigMCHCData:
    case cmsSig12colorData: return 12;

    case cmsSigMCHDData:
    case cmsSig13colorData: return 13;

    case cmsSigMCHEData:
    case cmsSig14colorData: return 14;

    case cmsSigMCHFData:
    case cmsSig15colorData: return 15;

    default: return 3;
    }
}