third_party/skcms/skcms.c

/*
 * Copyright 2018 Google Inc.
 *
 * Use of this source code is governed by a BSD-style license that can be
 * found in the LICENSE file.
 */

#include "skcms.h"
#include "skcms_internal.h"
#include <assert.h>
#include <float.h>
#include <limits.h>
#include <stdlib.h>
#include <string.h>

static float minus_1_ulp(float x) {
    int32_t bits;
    memcpy(&bits, &x, sizeof(bits));
    bits = bits - 1;
    memcpy(&x, &bits, sizeof(bits));
    return x;
}

float skcms_eval_curve(const skcms_Curve* curve, float x) {
    if (curve->table_entries == 0) {
        return skcms_TransferFunction_eval(&curve->parametric, x);
    }

    float ix = fmaxf_(0, fminf_(x, 1)) * (curve->table_entries - 1);
    int   lo = (int)            ix,
          hi = (int)minus_1_ulp(ix + 1.0f);
    float t = ix - (float)lo;

    float l, h;
    if (curve->table_8) {
        l = curve->table_8[lo] * (1/255.0f);
        h = curve->table_8[hi] * (1/255.0f);
    } else {
        uint16_t be_l, be_h;
        memcpy(&be_l, curve->table_16 + 2*lo, 2);
        memcpy(&be_h, curve->table_16 + 2*hi, 2);
        uint16_t le_l = ((be_l << 8) | (be_l >> 8)) & 0xffff;
        uint16_t le_h = ((be_h << 8) | (be_h >> 8)) & 0xffff;
        l = le_l * (1/65535.0f);
        h = le_h * (1/65535.0f);
    }
    return l + (h-l)*t;
}

float skcms_MaxRoundtripError(const skcms_Curve* curve, const skcms_TransferFunction* inv_tf) {
    uint32_t N = curve->table_entries > 256 ? curve->table_entries : 256;
    const float dx = 1.0f / (N - 1);
    float err = 0;
    for (uint32_t i = 0; i < N; i++) {
        float x = i * dx,
              y = skcms_eval_curve(curve, x);
        err = fmaxf_(err, fabsf_(x - skcms_TransferFunction_eval(inv_tf, y)));
    }
    return err;
}

bool skcms_AreApproximateInverses(const skcms_Curve* curve, const skcms_TransferFunction* inv_tf) {
    return skcms_MaxRoundtripError(curve, inv_tf) < (1/512.0f);
}

// Additional ICC signature values that are only used internally
enum {
    // File signature
    skcms_Signature_acsp = 0x61637370,

    // Tag signatures
    skcms_Signature_rTRC = 0x72545243,
    skcms_Signature_gTRC = 0x67545243,
    skcms_Signature_bTRC = 0x62545243,
    skcms_Signature_kTRC = 0x6B545243,

    skcms_Signature_rXYZ = 0x7258595A,
    skcms_Signature_gXYZ = 0x6758595A,
    skcms_Signature_bXYZ = 0x6258595A,

    skcms_Signature_A2B0 = 0x41324230,
    skcms_Signature_A2B1 = 0x41324231,
    skcms_Signature_mAB  = 0x6D414220,

    skcms_Signature_CHAD = 0x63686164,

    // Type signatures
    skcms_Signature_curv = 0x63757276,
    skcms_Signature_mft1 = 0x6D667431,
    skcms_Signature_mft2 = 0x6D667432,
    skcms_Signature_para = 0x70617261,
    skcms_Signature_sf32 = 0x73663332,
    // XYZ is also a PCS signature, so it's defined in skcms.h
    // skcms_Signature_XYZ = 0x58595A20,
};

static uint16_t read_big_u16(const uint8_t* ptr) {
    uint16_t be;
    memcpy(&be, ptr, sizeof(be));
#if defined(_MSC_VER)
    return _byteswap_ushort(be);
#else
    return __builtin_bswap16(be);
#endif
}

static uint32_t read_big_u32(const uint8_t* ptr) {
    uint32_t be;
    memcpy(&be, ptr, sizeof(be));
#if defined(_MSC_VER)
    return _byteswap_ulong(be);
#else
    return __builtin_bswap32(be);
#endif
}

static int32_t read_big_i32(const uint8_t* ptr) {
    return (int32_t)read_big_u32(ptr);
}

static float read_big_fixed(const uint8_t* ptr) {
    return read_big_i32(ptr) * (1.0f / 65536.0f);
}

// Maps to an in-memory profile so that fields line up to the locations specified
// in ICC.1:2010, section 7.2
typedef struct {
    uint8_t size                [ 4];
    uint8_t cmm_type            [ 4];
    uint8_t version             [ 4];
    uint8_t profile_class       [ 4];
    uint8_t data_color_space    [ 4];
    uint8_t pcs                 [ 4];
    uint8_t creation_date_time  [12];
    uint8_t signature           [ 4];
    uint8_t platform            [ 4];
    uint8_t flags               [ 4];
    uint8_t device_manufacturer [ 4];
    uint8_t device_model        [ 4];
    uint8_t device_attributes   [ 8];
    uint8_t rendering_intent    [ 4];
    uint8_t illuminant_X        [ 4];
    uint8_t illuminant_Y        [ 4];
    uint8_t illuminant_Z        [ 4];
    uint8_t creator             [ 4];
    uint8_t profile_id          [16];
    uint8_t reserved            [28];
    uint8_t tag_count           [ 4]; // Technically not part of header, but required
} header_Layout;

typedef struct {
    uint8_t signature [4];
    uint8_t offset    [4];
    uint8_t size      [4];
} tag_Layout;

static const tag_Layout* get_tag_table(const skcms_ICCProfile* profile) {
    return (const tag_Layout*)(profile->buffer + SAFE_SIZEOF(header_Layout));
}

// s15Fixed16ArrayType is technically variable sized, holding N values. However, the only valid
// use of the type is for the CHAD tag that stores exactly nine values.
typedef struct {
    uint8_t type     [ 4];
    uint8_t reserved [ 4];
    uint8_t values   [36];
} sf32_Layout;

bool skcms_GetCHAD(const skcms_ICCProfile* profile, skcms_Matrix3x3* m) {
    skcms_ICCTag tag;
    if (!skcms_GetTagBySignature(profile, skcms_Signature_CHAD, &tag)) {
        return false;
    }

    if (tag.type != skcms_Signature_sf32 || tag.size < SAFE_SIZEOF(sf32_Layout)) {
        return false;
    }

    const sf32_Layout* sf32Tag = (const sf32_Layout*)tag.buf;
    const uint8_t* values = sf32Tag->values;
    for (int r = 0; r < 3; ++r)
    for (int c = 0; c < 3; ++c, values += 4) {
        m->vals[r][c] = read_big_fixed(values);
    }
    return true;
}

// XYZType is technically variable sized, holding N XYZ triples. However, the only valid uses of
// the type are for tags/data that store exactly one triple.
typedef struct {
    uint8_t type     [4];
    uint8_t reserved [4];
    uint8_t X        [4];
    uint8_t Y        [4];
    uint8_t Z        [4];
} XYZ_Layout;

static bool read_tag_xyz(const skcms_ICCTag* tag, float* x, float* y, float* z) {
    if (tag->type != skcms_Signature_XYZ || tag->size < SAFE_SIZEOF(XYZ_Layout)) {
        return false;
    }

    const XYZ_Layout* xyzTag = (const XYZ_Layout*)tag->buf;

    *x = read_big_fixed(xyzTag->X);
    *y = read_big_fixed(xyzTag->Y);
    *z = read_big_fixed(xyzTag->Z);
    return true;
}

static bool read_to_XYZD50(const skcms_ICCTag* rXYZ, const skcms_ICCTag* gXYZ,
                           const skcms_ICCTag* bXYZ, skcms_Matrix3x3* toXYZ) {
    return read_tag_xyz(rXYZ, &toXYZ->vals[0][0], &toXYZ->vals[1][0], &toXYZ->vals[2][0]) &&
           read_tag_xyz(gXYZ, &toXYZ->vals[0][1], &toXYZ->vals[1][1], &toXYZ->vals[2][1]) &&
           read_tag_xyz(bXYZ, &toXYZ->vals[0][2], &toXYZ->vals[1][2], &toXYZ->vals[2][2]);
}

typedef struct {
    uint8_t type          [4];
    uint8_t reserved_a    [4];
    uint8_t function_type [2];
    uint8_t reserved_b    [2];
    uint8_t parameters    [ ];  // 1, 3, 4, 5, or 7 s15.16 parameters, depending on function_type
} para_Layout;

static bool read_curve_para(const uint8_t* buf, uint32_t size,
                            skcms_Curve* curve, uint32_t* curve_size) {
    if (size < SAFE_SIZEOF(para_Layout)) {
        return false;
    }

    const para_Layout* paraTag = (const para_Layout*)buf;

    enum { kG = 0, kGAB = 1, kGABC = 2, kGABCD = 3, kGABCDEF = 4 };
    uint16_t function_type = read_big_u16(paraTag->function_type);
    if (function_type > kGABCDEF) {
        return false;
    }

    static const uint32_t curve_bytes[] = { 4, 12, 16, 20, 28 };
    if (size < SAFE_SIZEOF(para_Layout) + curve_bytes[function_type]) {
        return false;
    }

    if (curve_size) {
        *curve_size = SAFE_SIZEOF(para_Layout) + curve_bytes[function_type];
    }

    curve->table_entries = 0;
    curve->parametric.a  = 1.0f;
    curve->parametric.b  = 0.0f;
    curve->parametric.c  = 0.0f;
    curve->parametric.d  = 0.0f;
    curve->parametric.e  = 0.0f;
    curve->parametric.f  = 0.0f;
    curve->parametric.g  = read_big_fixed(paraTag->parameters);

    switch (function_type) {
        case kGAB:
            curve->parametric.a = read_big_fixed(paraTag->parameters + 4);
            curve->parametric.b = read_big_fixed(paraTag->parameters + 8);
            if (curve->parametric.a == 0) {
                return false;
            }
            curve->parametric.d = -curve->parametric.b / curve->parametric.a;
            break;
        case kGABC:
            curve->parametric.a = read_big_fixed(paraTag->parameters + 4);
            curve->parametric.b = read_big_fixed(paraTag->parameters + 8);
            curve->parametric.e = read_big_fixed(paraTag->parameters + 12);
            if (curve->parametric.a == 0) {
                return false;
            }
            curve->parametric.d = -curve->parametric.b / curve->parametric.a;
            curve->parametric.f = curve->parametric.e;
            break;
        case kGABCD:
            curve->parametric.a = read_big_fixed(paraTag->parameters + 4);
            curve->parametric.b = read_big_fixed(paraTag->parameters + 8);
            curve->parametric.c = read_big_fixed(paraTag->parameters + 12);
            curve->parametric.d = read_big_fixed(paraTag->parameters + 16);
            break;
        case kGABCDEF:
            curve->parametric.a = read_big_fixed(paraTag->parameters + 4);
            curve->parametric.b = read_big_fixed(paraTag->parameters + 8);
            curve->parametric.c = read_big_fixed(paraTag->parameters + 12);
            curve->parametric.d = read_big_fixed(paraTag->parameters + 16);
            curve->parametric.e = read_big_fixed(paraTag->parameters + 20);
            curve->parametric.f = read_big_fixed(paraTag->parameters + 24);
            break;
    }
    return skcms_TransferFunction_isValid(&curve->parametric);
}

typedef struct {
    uint8_t type          [4];
    uint8_t reserved      [4];
    uint8_t value_count   [4];
    uint8_t parameters    [ ];  // value_count parameters (8.8 if 1, uint16 (n*65535) if > 1)
} curv_Layout;

static bool read_curve_curv(const uint8_t* buf, uint32_t size,
                            skcms_Curve* curve, uint32_t* curve_size) {
    if (size < SAFE_SIZEOF(curv_Layout)) {
        return false;
    }

    const curv_Layout* curvTag = (const curv_Layout*)buf;

    uint32_t value_count = read_big_u32(curvTag->value_count);
    if (size < SAFE_SIZEOF(curv_Layout) + value_count * SAFE_SIZEOF(uint16_t)) {
        return false;
    }

    if (curve_size) {
        *curve_size = SAFE_SIZEOF(curv_Layout) + value_count * SAFE_SIZEOF(uint16_t);
    }

    if (value_count < 2) {
        curve->table_entries = 0;
        curve->parametric.a  = 1.0f;
        curve->parametric.b  = 0.0f;
        curve->parametric.c  = 0.0f;
        curve->parametric.d  = 0.0f;
        curve->parametric.e  = 0.0f;
        curve->parametric.f  = 0.0f;
        if (value_count == 0) {
            // Empty tables are a shorthand for an identity curve
            curve->parametric.g = 1.0f;
        } else {
            // Single entry tables are a shorthand for simple gamma
            curve->parametric.g = read_big_u16(curvTag->parameters) * (1.0f / 256.0f);
        }
    } else {
        curve->table_8       = NULL;
        curve->table_16      = curvTag->parameters;
        curve->table_entries = value_count;
    }

    return true;
}

// Parses both curveType and parametricCurveType data. Ensures that at most 'size' bytes are read.
// If curve_size is not NULL, writes the number of bytes used by the curve in (*curve_size).
static bool read_curve(const uint8_t* buf, uint32_t size,
                       skcms_Curve* curve, uint32_t* curve_size) {
    if (!buf || size < 4 || !curve) {
        return false;
    }

    uint32_t type = read_big_u32(buf);
    if (type == skcms_Signature_para) {
        return read_curve_para(buf, size, curve, curve_size);
    } else if (type == skcms_Signature_curv) {
        return read_curve_curv(buf, size, curve, curve_size);
    }

    return false;
}

// mft1 and mft2 share a large chunk of data
typedef struct {
    uint8_t type                 [ 4];
    uint8_t reserved_a           [ 4];
    uint8_t input_channels       [ 1];
    uint8_t output_channels      [ 1];
    uint8_t grid_points          [ 1];
    uint8_t reserved_b           [ 1];
    uint8_t matrix               [36];
} mft_CommonLayout;

typedef struct {
    mft_CommonLayout common      [ 1];

    uint8_t tables               [  ];
} mft1_Layout;

typedef struct {
    mft_CommonLayout common      [ 1];

    uint8_t input_table_entries  [ 2];
    uint8_t output_table_entries [ 2];
    uint8_t tables               [  ];
} mft2_Layout;

static bool read_mft_common(const mft_CommonLayout* mftTag, skcms_A2B* a2b) {
    // MFT matrices are applied before the first set of curves, but must be identity unless the
    // input is PCSXYZ. We don't support PCSXYZ profiles, so we ignore this matrix. Note that the
    // matrix in skcms_A2B is applied later in the pipe, so supporting this would require another
    // field/flag.
    a2b->matrix_channels = 0;

    a2b->input_channels  = mftTag->input_channels[0];
    a2b->output_channels = mftTag->output_channels[0];

    // We require exactly three (ie XYZ/Lab/RGB) output channels
    if (a2b->output_channels != ARRAY_COUNT(a2b->output_curves)) {
        return false;
    }
    // We require at least one, and no more than four (ie CMYK) input channels
    if (a2b->input_channels < 1 || a2b->input_channels > ARRAY_COUNT(a2b->input_curves)) {
        return false;
    }

    for (uint32_t i = 0; i < a2b->input_channels; ++i) {
        a2b->grid_points[i] = mftTag->grid_points[0];
    }
    // The grid only makes sense with at least two points along each axis
    if (a2b->grid_points[0] < 2) {
        return false;
    }

    return true;
}

static bool init_a2b_tables(const uint8_t* table_base, uint64_t max_tables_len, uint32_t byte_width,
                            uint32_t input_table_entries, uint32_t output_table_entries,
                            skcms_A2B* a2b) {
    // byte_width is 1 or 2, [input|output]_table_entries are in [2, 4096], so no overflow
    uint32_t byte_len_per_input_table  = input_table_entries * byte_width;
    uint32_t byte_len_per_output_table = output_table_entries * byte_width;

    // [input|output]_channels are <= 4, so still no overflow
    uint32_t byte_len_all_input_tables  = a2b->input_channels * byte_len_per_input_table;
    uint32_t byte_len_all_output_tables = a2b->output_channels * byte_len_per_output_table;

    uint64_t grid_size = a2b->output_channels * byte_width;
    for (uint32_t axis = 0; axis < a2b->input_channels; ++axis) {
        grid_size *= a2b->grid_points[axis];
    }

    if (max_tables_len < byte_len_all_input_tables + grid_size + byte_len_all_output_tables) {
        return false;
    }

    for (uint32_t i = 0; i < a2b->input_channels; ++i) {
        a2b->input_curves[i].table_entries = input_table_entries;
        if (byte_width == 1) {
            a2b->input_curves[i].table_8  = table_base + i * byte_len_per_input_table;
            a2b->input_curves[i].table_16 = NULL;
        } else {
            a2b->input_curves[i].table_8  = NULL;
            a2b->input_curves[i].table_16 = table_base + i * byte_len_per_input_table;
        }
    }

    if (byte_width == 1) {
        a2b->grid_8  = table_base + byte_len_all_input_tables;
        a2b->grid_16 = NULL;
    } else {
        a2b->grid_8  = NULL;
        a2b->grid_16 = table_base + byte_len_all_input_tables;
    }

    const uint8_t* output_table_base = table_base + byte_len_all_input_tables + grid_size;
    for (uint32_t i = 0; i < a2b->output_channels; ++i) {
        a2b->output_curves[i].table_entries = output_table_entries;
        if (byte_width == 1) {
            a2b->output_curves[i].table_8  = output_table_base + i * byte_len_per_output_table;
            a2b->output_curves[i].table_16 = NULL;
        } else {
            a2b->output_curves[i].table_8  = NULL;
            a2b->output_curves[i].table_16 = output_table_base + i * byte_len_per_output_table;
        }
    }

    return true;
}

static bool read_tag_mft1(const skcms_ICCTag* tag, skcms_A2B* a2b) {
    if (tag->size < SAFE_SIZEOF(mft1_Layout)) {
        return false;
    }

    const mft1_Layout* mftTag = (const mft1_Layout*)tag->buf;
    if (!read_mft_common(mftTag->common, a2b)) {
        return false;
    }

    uint32_t input_table_entries  = 256;
    uint32_t output_table_entries = 256;

    return init_a2b_tables(mftTag->tables, tag->size - SAFE_SIZEOF(mft1_Layout), 1,
                           input_table_entries, output_table_entries, a2b);
}

static bool read_tag_mft2(const skcms_ICCTag* tag, skcms_A2B* a2b) {
    if (tag->size < SAFE_SIZEOF(mft2_Layout)) {
        return false;
    }

    const mft2_Layout* mftTag = (const mft2_Layout*)tag->buf;
    if (!read_mft_common(mftTag->common, a2b)) {
        return false;
    }

    uint32_t input_table_entries = read_big_u16(mftTag->input_table_entries);
    uint32_t output_table_entries = read_big_u16(mftTag->output_table_entries);

    // ICC spec mandates that 2 <= table_entries <= 4096
    if (input_table_entries < 2 || input_table_entries > 4096 ||
        output_table_entries < 2 || output_table_entries > 4096) {
        return false;
    }

    return init_a2b_tables(mftTag->tables, tag->size - SAFE_SIZEOF(mft2_Layout), 2,
                           input_table_entries, output_table_entries, a2b);
}

static bool read_curves(const uint8_t* buf, uint32_t size, uint32_t curve_offset,
                        uint32_t num_curves, skcms_Curve* curves) {
    for (uint32_t i = 0; i < num_curves; ++i) {
        if (curve_offset > size) {
            return false;
        }

        uint32_t curve_bytes;
        if (!read_curve(buf + curve_offset, size - curve_offset, &curves[i], &curve_bytes)) {
            return false;
        }

        if (curve_bytes > UINT32_MAX - 3) {
            return false;
        }
        curve_bytes = (curve_bytes + 3) & ~3U;

        uint64_t new_offset_64 = (uint64_t)curve_offset + curve_bytes;
        curve_offset = (uint32_t)new_offset_64;
        if (new_offset_64 != curve_offset) {
            return false;
        }
    }

    return true;
}

typedef struct {
    uint8_t type                 [ 4];
    uint8_t reserved_a           [ 4];
    uint8_t input_channels       [ 1];
    uint8_t output_channels      [ 1];
    uint8_t reserved_b           [ 2];
    uint8_t b_curve_offset       [ 4];
    uint8_t matrix_offset        [ 4];
    uint8_t m_curve_offset       [ 4];
    uint8_t clut_offset          [ 4];
    uint8_t a_curve_offset       [ 4];
} mAB_Layout;

typedef struct {
    uint8_t grid_points          [16];
    uint8_t grid_byte_width      [ 1];
    uint8_t reserved             [ 3];
    uint8_t data                 [  ];
} mABCLUT_Layout;

static bool read_tag_mab(const skcms_ICCTag* tag, skcms_A2B* a2b, bool pcs_is_xyz) {
    if (tag->size < SAFE_SIZEOF(mAB_Layout)) {
        return false;
    }

    const mAB_Layout* mABTag = (const mAB_Layout*)tag->buf;

    a2b->input_channels  = mABTag->input_channels[0];
    a2b->output_channels = mABTag->output_channels[0];

    // We require exactly three (ie XYZ/Lab/RGB) output channels
    if (a2b->output_channels != ARRAY_COUNT(a2b->output_curves)) {
        return false;
    }
    // We require no more than four (ie CMYK) input channels
    if (a2b->input_channels > ARRAY_COUNT(a2b->input_curves)) {
        return false;
    }

    uint32_t b_curve_offset = read_big_u32(mABTag->b_curve_offset);
    uint32_t matrix_offset  = read_big_u32(mABTag->matrix_offset);
    uint32_t m_curve_offset = read_big_u32(mABTag->m_curve_offset);
    uint32_t clut_offset    = read_big_u32(mABTag->clut_offset);
    uint32_t a_curve_offset = read_big_u32(mABTag->a_curve_offset);

    // "B" curves must be present
    if (0 == b_curve_offset) {
        return false;
    }

    if (!read_curves(tag->buf, tag->size, b_curve_offset, a2b->output_channels,
                     a2b->output_curves)) {
        return false;
    }

    // "M" curves and Matrix must be used together
    if (0 != m_curve_offset) {
        if (0 == matrix_offset) {
            return false;
        }
        a2b->matrix_channels = a2b->output_channels;
        if (!read_curves(tag->buf, tag->size, m_curve_offset, a2b->matrix_channels,
                         a2b->matrix_curves)) {
            return false;
        }

        // Read matrix, which is stored as a row-major 3x3, followed by the fourth column
        if (tag->size < matrix_offset + 12 * SAFE_SIZEOF(uint32_t)) {
            return false;
        }
        float encoding_factor = pcs_is_xyz ? 65535 / 32768.0f : 1.0f;
        const uint8_t* mtx_buf = tag->buf + matrix_offset;
        a2b->matrix.vals[0][0] = encoding_factor * read_big_fixed(mtx_buf + 0);
        a2b->matrix.vals[0][1] = encoding_factor * read_big_fixed(mtx_buf + 4);
        a2b->matrix.vals[0][2] = encoding_factor * read_big_fixed(mtx_buf + 8);
        a2b->matrix.vals[1][0] = encoding_factor * read_big_fixed(mtx_buf + 12);
        a2b->matrix.vals[1][1] = encoding_factor * read_big_fixed(mtx_buf + 16);
        a2b->matrix.vals[1][2] = encoding_factor * read_big_fixed(mtx_buf + 20);
        a2b->matrix.vals[2][0] = encoding_factor * read_big_fixed(mtx_buf + 24);
        a2b->matrix.vals[2][1] = encoding_factor * read_big_fixed(mtx_buf + 28);
        a2b->matrix.vals[2][2] = encoding_factor * read_big_fixed(mtx_buf + 32);
        a2b->matrix.vals[0][3] = encoding_factor * read_big_fixed(mtx_buf + 36);
        a2b->matrix.vals[1][3] = encoding_factor * read_big_fixed(mtx_buf + 40);
        a2b->matrix.vals[2][3] = encoding_factor * read_big_fixed(mtx_buf + 44);
    } else {
        if (0 != matrix_offset) {
            return false;
        }
        a2b->matrix_channels = 0;
    }

    // "A" curves and CLUT must be used together
    if (0 != a_curve_offset) {
        if (0 == clut_offset) {
            return false;
        }
        if (!read_curves(tag->buf, tag->size, a_curve_offset, a2b->input_channels,
                         a2b->input_curves)) {
            return false;
        }

        if (tag->size < clut_offset + SAFE_SIZEOF(mABCLUT_Layout)) {
            return false;
        }
        const mABCLUT_Layout* clut = (const mABCLUT_Layout*)(tag->buf + clut_offset);

        if (clut->grid_byte_width[0] == 1) {
            a2b->grid_8  = clut->data;
            a2b->grid_16 = NULL;
        } else if (clut->grid_byte_width[0] == 2) {
            a2b->grid_8  = NULL;
            a2b->grid_16 = clut->data;
        } else {
            return false;
        }

        uint64_t grid_size = a2b->output_channels * clut->grid_byte_width[0];
        for (uint32_t i = 0; i < a2b->input_channels; ++i) {
            a2b->grid_points[i] = clut->grid_points[i];
            // The grid only makes sense with at least two points along each axis
            if (a2b->grid_points[i] < 2) {
                return false;
            }
            grid_size *= a2b->grid_points[i];
        }
        if (tag->size < clut_offset + SAFE_SIZEOF(mABCLUT_Layout) + grid_size) {
            return false;
        }
    } else {
        if (0 != clut_offset) {
            return false;
        }

        // If there is no CLUT, the number of input and output channels must match
        if (a2b->input_channels != a2b->output_channels) {
            return false;
        }

        // Zero out the number of input channels to signal that we're skipping this stage
        a2b->input_channels = 0;
    }

    return true;
}

static bool read_a2b(const skcms_ICCTag* tag, skcms_A2B* a2b, bool pcs_is_xyz) {
    bool ok = false;
    if (tag->type == skcms_Signature_mft1) {
        ok = read_tag_mft1(tag, a2b);
    } else if (tag->type == skcms_Signature_mft2) {
        ok = read_tag_mft2(tag, a2b);
    } else if (tag->type == skcms_Signature_mAB) {
        ok = read_tag_mab(tag, a2b, pcs_is_xyz);
    }
    if (!ok) {
        return false;
    }

    // Detect and canonicalize identity tables.
    skcms_Curve* curves[] = {
        a2b->input_channels  > 0 ? a2b->input_curves  + 0 : NULL,
        a2b->input_channels  > 1 ? a2b->input_curves  + 1 : NULL,
        a2b->input_channels  > 2 ? a2b->input_curves  + 2 : NULL,
        a2b->input_channels  > 3 ? a2b->input_curves  + 3 : NULL,
        a2b->matrix_channels > 0 ? a2b->matrix_curves + 0 : NULL,
        a2b->matrix_channels > 1 ? a2b->matrix_curves + 1 : NULL,
        a2b->matrix_channels > 2 ? a2b->matrix_curves + 2 : NULL,
        a2b->output_channels > 0 ? a2b->output_curves + 0 : NULL,
        a2b->output_channels > 1 ? a2b->output_curves + 1 : NULL,
        a2b->output_channels > 2 ? a2b->output_curves + 2 : NULL,
    };

    for (int i = 0; i < ARRAY_COUNT(curves); i++) {
        skcms_Curve* curve = curves[i];

        if (curve && curve->table_entries && curve->table_entries <= (uint32_t)INT_MAX) {
            int N = (int)curve->table_entries;

            float c,d,f;
            if (N == skcms_fit_linear(curve, N, 1.0f/(2*N), &c,&d,&f)
                && c == 1.0f
                && f == 0.0f) {
                curve->table_entries = 0;
                curve->table_8       = NULL;
                curve->table_16      = NULL;
                curve->parametric    = (skcms_TransferFunction){1,1,0,0,0,0,0};
            }
        }
    }

    return true;
}

void skcms_GetTagByIndex(const skcms_ICCProfile* profile, uint32_t idx, skcms_ICCTag* tag) {
    if (!profile || !profile->buffer || !tag) { return; }
    if (idx > profile->tag_count) { return; }
    const tag_Layout* tags = get_tag_table(profile);
    tag->signature = read_big_u32(tags[idx].signature);
    tag->size      = read_big_u32(tags[idx].size);
    tag->buf       = read_big_u32(tags[idx].offset) + profile->buffer;
    tag->type      = read_big_u32(tag->buf);
}

bool skcms_GetTagBySignature(const skcms_ICCProfile* profile, uint32_t sig, skcms_ICCTag* tag) {
    if (!profile || !profile->buffer || !tag) { return false; }
    const tag_Layout* tags = get_tag_table(profile);
    for (uint32_t i = 0; i < profile->tag_count; ++i) {
        if (read_big_u32(tags[i].signature) == sig) {
            tag->signature = sig;
            tag->size      = read_big_u32(tags[i].size);
            tag->buf       = read_big_u32(tags[i].offset) + profile->buffer;
            tag->type      = read_big_u32(tag->buf);
            return true;
        }
    }
    return false;
}

static bool usable_as_src(const skcms_ICCProfile* profile) {
    return profile->has_A2B
       || (profile->has_trc && profile->has_toXYZD50);
}

bool skcms_Parse(const void* buf, size_t len, skcms_ICCProfile* profile) {
    assert(SAFE_SIZEOF(header_Layout) == 132);

    if (!profile) {
        return false;
    }
    memset(profile, 0, SAFE_SIZEOF(*profile));

    if (len < SAFE_SIZEOF(header_Layout)) {
        return false;
    }

    // Byte-swap all header fields
    const header_Layout* header = buf;
    profile->buffer              = buf;
    profile->size                = read_big_u32(header->size);
    uint32_t version             = read_big_u32(header->version);
    profile->data_color_space    = read_big_u32(header->data_color_space);
    profile->pcs                 = read_big_u32(header->pcs);
    uint32_t signature           = read_big_u32(header->signature);
    float illuminant_X           = read_big_fixed(header->illuminant_X);
    float illuminant_Y           = read_big_fixed(header->illuminant_Y);
    float illuminant_Z           = read_big_fixed(header->illuminant_Z);
    profile->tag_count           = read_big_u32(header->tag_count);

    // Validate signature, size (smaller than buffer, large enough to hold tag table),
    // and major version
    uint64_t tag_table_size = profile->tag_count * SAFE_SIZEOF(tag_Layout);
    if (signature != skcms_Signature_acsp ||
        profile->size > len ||
        profile->size < SAFE_SIZEOF(header_Layout) + tag_table_size ||
        (version >> 24) > 4) {
        return false;
    }

    // Validate that illuminant is D50 white
    if (fabsf_(illuminant_X - 0.9642f) > 0.0100f ||
        fabsf_(illuminant_Y - 1.0000f) > 0.0100f ||
        fabsf_(illuminant_Z - 0.8249f) > 0.0100f) {
        return false;
    }

    // Validate that all tag entries have sane offset + size
    const tag_Layout* tags = get_tag_table(profile);
    for (uint32_t i = 0; i < profile->tag_count; ++i) {
        uint32_t tag_offset = read_big_u32(tags[i].offset);
        uint32_t tag_size   = read_big_u32(tags[i].size);
        uint64_t tag_end    = (uint64_t)tag_offset + (uint64_t)tag_size;
        if (tag_size < 4 || tag_end > profile->size) {
            return false;
        }
    }

    if (profile->pcs != skcms_Signature_XYZ && profile->pcs != skcms_Signature_Lab) {
        return false;
    }

    bool pcs_is_xyz = profile->pcs == skcms_Signature_XYZ;

    // Pre-parse commonly used tags.
    skcms_ICCTag kTRC;
    if (profile->data_color_space == skcms_Signature_Gray &&
        skcms_GetTagBySignature(profile, skcms_Signature_kTRC, &kTRC)) {
        if (!read_curve(kTRC.buf, kTRC.size, &profile->trc[0], NULL)) {
            // Malformed tag
            return false;
        }
        profile->trc[1] = profile->trc[0];
        profile->trc[2] = profile->trc[0];
        profile->has_trc = true;

        if (pcs_is_xyz) {
            profile->toXYZD50.vals[0][0] = illuminant_X;
            profile->toXYZD50.vals[1][1] = illuminant_Y;
            profile->toXYZD50.vals[2][2] = illuminant_Z;
            profile->has_toXYZD50 = true;
        }
    } else {
        skcms_ICCTag rTRC, gTRC, bTRC;
        if (skcms_GetTagBySignature(profile, skcms_Signature_rTRC, &rTRC) &&
            skcms_GetTagBySignature(profile, skcms_Signature_gTRC, &gTRC) &&
            skcms_GetTagBySignature(profile, skcms_Signature_bTRC, &bTRC)) {
            if (!read_curve(rTRC.buf, rTRC.size, &profile->trc[0], NULL) ||
                !read_curve(gTRC.buf, gTRC.size, &profile->trc[1], NULL) ||
                !read_curve(bTRC.buf, bTRC.size, &profile->trc[2], NULL)) {
                // Malformed TRC tags
                return false;
            }
            profile->has_trc = true;
        }

        skcms_ICCTag rXYZ, gXYZ, bXYZ;
        if (skcms_GetTagBySignature(profile, skcms_Signature_rXYZ, &rXYZ) &&
            skcms_GetTagBySignature(profile, skcms_Signature_gXYZ, &gXYZ) &&
            skcms_GetTagBySignature(profile, skcms_Signature_bXYZ, &bXYZ)) {
            if (!read_to_XYZD50(&rXYZ, &gXYZ, &bXYZ, &profile->toXYZD50)) {
                // Malformed XYZ tags
                return false;
            }
            profile->has_toXYZD50 = true;
        }
    }

    skcms_ICCTag a2b_tag;

    // For now, we're preferring A2B0, like Skia does and the ICC spec tells us to.
    // TODO: prefer A2B1 (relative colormetric) over A2B0 (perceptual)?
    // This breaks with the ICC spec, but we think it's a good idea, given that TRC curves
    // and all our known users are thinking exclusively in terms of relative colormetric.
    const uint32_t sigs[] = { skcms_Signature_A2B0, skcms_Signature_A2B1 };
    for (int i = 0; i < ARRAY_COUNT(sigs); i++) {
        if (skcms_GetTagBySignature(profile, sigs[i], &a2b_tag)) {
            if (!read_a2b(&a2b_tag, &profile->A2B, pcs_is_xyz)) {
                // Malformed A2B tag
                return false;
            }
            profile->has_A2B = true;
            break;
        }
    }

    return usable_as_src(profile);
}


const skcms_ICCProfile* skcms_sRGB_profile() {
    static const skcms_ICCProfile sRGB_profile = {
        // These fields are moot when not a skcms_Parse()'d profile.
        .buffer    = NULL,
        .size      =    0,
        .tag_count =    0,

        // We choose to represent sRGB with its canonical transfer function,
        // and with its canonical XYZD50 gamut matrix.
        .data_color_space = skcms_Signature_RGB,
        .pcs              = skcms_Signature_XYZ,
        .has_trc      = true,
        .has_toXYZD50 = true,
        .has_A2B      = false,

        .trc = {
            {{0, {2.4f, (float)(1/1.055), (float)(0.055/1.055), (float)(1/12.92), 0.04045f, 0, 0 }}},
            {{0, {2.4f, (float)(1/1.055), (float)(0.055/1.055), (float)(1/12.92), 0.04045f, 0, 0 }}},
            {{0, {2.4f, (float)(1/1.055), (float)(0.055/1.055), (float)(1/12.92), 0.04045f, 0, 0 }}},
        },

        .toXYZD50 = {{
            { 0.436065674f, 0.385147095f, 0.143066406f },
            { 0.222488403f, 0.716873169f, 0.060607910f },
            { 0.013916016f, 0.097076416f, 0.714096069f },
        }},
    };
    return &sRGB_profile;
}

const skcms_ICCProfile* skcms_XYZD50_profile() {
    static const skcms_ICCProfile XYZD50_profile = {
        .buffer           = NULL,
        .size             = 0,
        .tag_count        = 0,

        .data_color_space = skcms_Signature_RGB,
        .pcs              = skcms_Signature_XYZ,
        .has_trc          = true,
        .has_toXYZD50     = true,
        .has_A2B          = false,

        .trc = {
            {{0, {1,1,0,0,0,0,0}}},
            {{0, {1,1,0,0,0,0,0}}},
            {{0, {1,1,0,0,0,0,0}}},
        },

        .toXYZD50 = {{
            {1,0,0},
            {0,1,0},
            {0,0,1},
        }},
    };

    return &XYZD50_profile;
}

const skcms_TransferFunction* skcms_sRGB_TransferFunction() {
    return &skcms_sRGB_profile()->trc[0].parametric;
}

const skcms_TransferFunction* skcms_sRGB_Inverse_TransferFunction() {
    static const skcms_TransferFunction sRGB_inv =
        { (float)(1/2.4), 1.137119f, 0, 12.92f, 0.0031308f, -0.055f, 0 };
    return &sRGB_inv;
}

const skcms_TransferFunction* skcms_Identity_TransferFunction() {
    static const skcms_TransferFunction identity = {1,1,0,0,0,0,0};
    return &identity;
}

const uint8_t skcms_252_random_bytes[] = {
    8, 179, 128, 204, 253, 38, 134, 184, 68, 102, 32, 138, 99, 39, 169, 215,
    119, 26, 3, 223, 95, 239, 52, 132, 114, 74, 81, 234, 97, 116, 244, 205, 30,
    154, 173, 12, 51, 159, 122, 153, 61, 226, 236, 178, 229, 55, 181, 220, 191,
    194, 160, 126, 168, 82, 131, 18, 180, 245, 163, 22, 246, 69, 235, 252, 57,
    108, 14, 6, 152, 240, 255, 171, 242, 20, 227, 177, 238, 96, 85, 16, 211,
    70, 200, 149, 155, 146, 127, 145, 100, 151, 109, 19, 165, 208, 195, 164,
    137, 254, 182, 248, 64, 201, 45, 209, 5, 147, 207, 210, 113, 162, 83, 225,
    9, 31, 15, 231, 115, 37, 58, 53, 24, 49, 197, 56, 120, 172, 48, 21, 214,
    129, 111, 11, 50, 187, 196, 34, 60, 103, 71, 144, 47, 203, 77, 80, 232,
    140, 222, 250, 206, 166, 247, 139, 249, 221, 72, 106, 27, 199, 117, 54,
    219, 135, 118, 40, 79, 41, 251, 46, 93, 212, 92, 233, 148, 28, 121, 63,
    123, 158, 105, 59, 29, 42, 143, 23, 0, 107, 176, 87, 104, 183, 156, 193,
    189, 90, 188, 65, 190, 17, 198, 7, 186, 161, 1, 124, 78, 125, 170, 133,
    174, 218, 67, 157, 75, 101, 89, 217, 62, 33, 141, 228, 25, 35, 91, 230, 4,
    2, 13, 73, 86, 167, 237, 84, 243, 44, 185, 66, 130, 110, 150, 142, 216, 88,
    112, 36, 224, 136, 202, 76, 94, 98, 175, 213
};

bool skcms_ApproximatelyEqualProfiles(const skcms_ICCProfile* A, const skcms_ICCProfile* B) {
    // For now this is the essentially the same strategy we use in test_only.c
    // for our skcms_Transform() smoke tests:
    //    1) transform A to XYZD50
    //    2) transform B to XYZD50
    //    3) return true if they're similar enough
    // Our current criterion in 3) is maximum 1 bit error per XYZD50 byte.

    // Here are 252 of a random shuffle of all possible bytes.
    // 252 is evenly divisible by 3 and 4.  Only 192, 10, 241, and 43 are missing.

    if (A->data_color_space != B->data_color_space) {
        return false;
    }

    // Interpret as RGB_888 if data color space is RGB or GRAY, RGBA_8888 if CMYK.
    skcms_PixelFormat fmt = skcms_PixelFormat_RGB_888;
    size_t npixels = 84;
    if (A->data_color_space == skcms_Signature_CMYK) {
        fmt = skcms_PixelFormat_RGBA_8888;
        npixels = 63;
    }

    uint8_t dstA[252],
            dstB[252];
    if (!skcms_Transform(
                skcms_252_random_bytes,     fmt, skcms_AlphaFormat_Unpremul, A,
                dstA, skcms_PixelFormat_RGB_888, skcms_AlphaFormat_Unpremul, skcms_XYZD50_profile(),
                npixels)) {
        return false;
    }
    if (!skcms_Transform(
                skcms_252_random_bytes,     fmt, skcms_AlphaFormat_Unpremul, B,
                dstB, skcms_PixelFormat_RGB_888, skcms_AlphaFormat_Unpremul, skcms_XYZD50_profile(),
                npixels)) {
        return false;
    }

    for (size_t i = 0; i < 252; i++) {
        if (abs((int)dstA[i] - (int)dstB[i]) > 1) {
            return false;
        }
    }
    return true;
}

bool skcms_TRCs_AreApproximateInverse(const skcms_ICCProfile* profile,
                                      const skcms_TransferFunction* inv_tf) {
    if (!profile || !profile->has_trc) {
        return false;
    }

    return skcms_AreApproximateInverses(&profile->trc[0], inv_tf) &&
           skcms_AreApproximateInverses(&profile->trc[1], inv_tf) &&
           skcms_AreApproximateInverses(&profile->trc[2], inv_tf);
}

static bool is_zero_to_one(float x) {
    return 0 <= x && x <= 1;
}

bool skcms_PrimariesToXYZD50(float rx, float ry,
                             float gx, float gy,
                             float bx, float by,
                             float wx, float wy,
                             skcms_Matrix3x3* toXYZD50) {
    if (!is_zero_to_one(rx) || !is_zero_to_one(ry) ||
        !is_zero_to_one(gx) || !is_zero_to_one(gy) ||
        !is_zero_to_one(bx) || !is_zero_to_one(by) ||
        !is_zero_to_one(wx) || !is_zero_to_one(wy) ||
        !toXYZD50) {
        return false;
    }

    // First, we need to convert xy values (primaries) to XYZ.
    skcms_Matrix3x3 primaries = {{
        { rx, gx, bx },
        { ry, gy, by },
        { 1 - rx - ry, 1 - gx - gy, 1 - bx - by },
    }};
    skcms_Matrix3x3 primaries_inv;
    if (!skcms_Matrix3x3_invert(&primaries, &primaries_inv)) {
        return false;
    }

    // Assumes that Y is 1.0f.
    skcms_Vector3 wXYZ = { { wx / wy, 1, (1 - wx - wy) / wy } };
    skcms_Vector3 XYZ = skcms_MV_mul(&primaries_inv, &wXYZ);

    skcms_Matrix3x3 toXYZ = {{
        { XYZ.vals[0],           0,           0 },
        {           0, XYZ.vals[1],           0 },
        {           0,           0, XYZ.vals[2] },
    }};
    toXYZ = skcms_Matrix3x3_concat(&primaries, &toXYZ);

    // Now convert toXYZ matrix to toXYZD50.
    skcms_Vector3 wXYZD50 = { { 0.96422f, 1.0f, 0.82521f } };

    // Calculate the chromatic adaptation matrix.  We will use the Bradford method, thus
    // the matrices below.  The Bradford method is used by Adobe and is widely considered
    // to be the best.
    skcms_Matrix3x3 xyz_to_lms = {{
        {  0.8951f,  0.2664f, -0.1614f },
        { -0.7502f,  1.7135f,  0.0367f },
        {  0.0389f, -0.0685f,  1.0296f },
    }};
    skcms_Matrix3x3 lms_to_xyz = {{
        {  0.9869929f, -0.1470543f, 0.1599627f },
        {  0.4323053f,  0.5183603f, 0.0492912f },
        { -0.0085287f,  0.0400428f, 0.9684867f },
    }};

    skcms_Vector3 srcCone = skcms_MV_mul(&xyz_to_lms, &wXYZ);
    skcms_Vector3 dstCone = skcms_MV_mul(&xyz_to_lms, &wXYZD50);

    skcms_Matrix3x3 DXtoD50 = {{
        { dstCone.vals[0] / srcCone.vals[0], 0, 0 },
        { 0, dstCone.vals[1] / srcCone.vals[1], 0 },
        { 0, 0, dstCone.vals[2] / srcCone.vals[2] },
    }};
    DXtoD50 = skcms_Matrix3x3_concat(&DXtoD50, &xyz_to_lms);
    DXtoD50 = skcms_Matrix3x3_concat(&lms_to_xyz, &DXtoD50);

    *toXYZD50 = skcms_Matrix3x3_concat(&DXtoD50, &toXYZ);
    return true;
}


bool skcms_Matrix3x3_invert(const skcms_Matrix3x3* src, skcms_Matrix3x3* dst) {
    double a00 = src->vals[0][0],
           a01 = src->vals[1][0],
           a02 = src->vals[2][0],
           a10 = src->vals[0][1],
           a11 = src->vals[1][1],
           a12 = src->vals[2][1],
           a20 = src->vals[0][2],
           a21 = src->vals[1][2],
           a22 = src->vals[2][2];

    double b0 = a00*a11 - a01*a10,
           b1 = a00*a12 - a02*a10,
           b2 = a01*a12 - a02*a11,
           b3 = a20,
           b4 = a21,
           b5 = a22;

    double determinant = b0*b5
                       - b1*b4
                       + b2*b3;

    if (determinant == 0) {
        return false;
    }

    double invdet = 1.0 / determinant;
    if (invdet > +FLT_MAX || invdet < -FLT_MAX || !isfinitef_((float)invdet)) {
        return false;
    }

    b0 *= invdet;
    b1 *= invdet;
    b2 *= invdet;
    b3 *= invdet;
    b4 *= invdet;
    b5 *= invdet;

    dst->vals[0][0] = (float)( a11*b5 - a12*b4 );
    dst->vals[1][0] = (float)( a02*b4 - a01*b5 );
    dst->vals[2][0] = (float)(        +     b2 );
    dst->vals[0][1] = (float)( a12*b3 - a10*b5 );
    dst->vals[1][1] = (float)( a00*b5 - a02*b3 );
    dst->vals[2][1] = (float)(        -     b1 );
    dst->vals[0][2] = (float)( a10*b4 - a11*b3 );
    dst->vals[1][2] = (float)( a01*b3 - a00*b4 );
    dst->vals[2][2] = (float)(        +     b0 );

    for (int r = 0; r < 3; ++r)
    for (int c = 0; c < 3; ++c) {
        if (!isfinitef_(dst->vals[r][c])) {
            return false;
        }
    }
    return true;
}

skcms_Matrix3x3 skcms_Matrix3x3_concat(const skcms_Matrix3x3* A, const skcms_Matrix3x3* B) {
    skcms_Matrix3x3 m = { { { 0,0,0 },{ 0,0,0 },{ 0,0,0 } } };
    for (int r = 0; r < 3; r++)
        for (int c = 0; c < 3; c++) {
            m.vals[r][c] = A->vals[r][0] * B->vals[0][c]
                         + A->vals[r][1] * B->vals[1][c]
                         + A->vals[r][2] * B->vals[2][c];
        }
    return m;
}

skcms_Vector3 skcms_MV_mul(const skcms_Matrix3x3* m, const skcms_Vector3* v) {
    skcms_Vector3 dst = {{0,0,0}};
    for (int row = 0; row < 3; ++row) {
        dst.vals[row] = m->vals[row][0] * v->vals[0]
                      + m->vals[row][1] * v->vals[1]
                      + m->vals[row][2] * v->vals[2];
    }
    return dst;
}

#if defined(__clang__) || defined(__GNUC__)
    #define small_memcpy __builtin_memcpy
#else
    #define small_memcpy memcpy
#endif

float log2f_(float x) {
    // The first approximation of log2(x) is its exponent 'e', minus 127.
    int32_t bits;
    small_memcpy(&bits, &x, sizeof(bits));

    float e = (float)bits * (1.0f / (1<<23));

    // If we use the mantissa too we can refine the error signficantly.
    int32_t m_bits = (bits & 0x007fffff) | 0x3f000000;
    float m;
    small_memcpy(&m, &m_bits, sizeof(m));

    return (e - 124.225514990f
              -   1.498030302f*m
              -   1.725879990f/(0.3520887068f + m));
}

float exp2f_(float x) {
    float fract = x - floorf_(x);

    float fbits = (1.0f * (1<<23)) * (x + 121.274057500f
                                        -   1.490129070f*fract
                                        +  27.728023300f/(4.84252568f - fract));
    if (fbits > INT_MAX) {
        return INFINITY_;
    } else if (fbits < INT_MIN) {
        return -INFINITY_;
    }
    int32_t bits = (int32_t)fbits;
    small_memcpy(&x, &bits, sizeof(x));
    return x;
}

float powf_(float x, float y) {
    return (x == 0) || (x == 1) ? x
                                : exp2f_(log2f_(x) * y);
}

float skcms_TransferFunction_eval(const skcms_TransferFunction* tf, float x) {
    float sign = x < 0 ? -1.0f : 1.0f;
    x *= sign;

    return sign * (x < tf->d ? tf->c * x + tf->f
                             : powf_(tf->a * x + tf->b, tf->g) + tf->e);
}

bool skcms_TransferFunction_isValid(const skcms_TransferFunction* tf) {
    // Reject obviously malformed inputs
    if (!isfinitef_(tf->a + tf->b + tf->c + tf->d + tf->e + tf->f + tf->g)) {
        return false;
    }

    // All of these parameters should be non-negative
    if (tf->a < 0 || tf->c < 0 || tf->d < 0 || tf->g < 0) {
        return false;
    }

    return true;
}

// TODO: Adjust logic here? This still assumes that purely linear inputs will have D > 1, which
// we never generate. It also emits inverted linear using the same formulation. Standardize on
// G == 1 here, too?
bool skcms_TransferFunction_invert(const skcms_TransferFunction* src, skcms_TransferFunction* dst) {
    // Original equation is:       y = (ax + b)^g + e   for x >= d
    //                             y = cx + f           otherwise
    //
    // so 1st inverse is:          (y - e)^(1/g) = ax + b
    //                             x = ((y - e)^(1/g) - b) / a
    //
    // which can be re-written as: x = (1/a)(y - e)^(1/g) - b/a
    //                             x = ((1/a)^g)^(1/g) * (y - e)^(1/g) - b/a
    //                             x = ([(1/a)^g]y + [-((1/a)^g)e]) ^ [1/g] + [-b/a]
    //
    // and 2nd inverse is:         x = (y - f) / c
    // which can be re-written as: x = [1/c]y + [-f/c]
    //
    // and now both can be expressed in terms of the same parametric form as the
    // original - parameters are enclosed in square brackets.
    skcms_TransferFunction tf_inv = { 0, 0, 0, 0, 0, 0, 0 };

    // This rejects obviously malformed inputs, as well as decreasing functions
    if (!skcms_TransferFunction_isValid(src)) {
        return false;
    }

    // There are additional constraints to be invertible
    bool has_nonlinear = (src->d <= 1);
    bool has_linear = (src->d > 0);

    // Is the linear section not invertible?
    if (has_linear && src->c == 0) {
        return false;
    }

    // Is the nonlinear section not invertible?
    if (has_nonlinear && (src->a == 0 || src->g == 0)) {
        return false;
    }

    // If both segments are present, they need to line up
    if (has_linear && has_nonlinear) {
        float l_at_d = src->c * src->d + src->f;
        float n_at_d = powf_(src->a * src->d + src->b, src->g) + src->e;
        if (fabsf_(l_at_d - n_at_d) > (1 / 512.0f)) {
            return false;
        }
    }

    // Invert linear segment
    if (has_linear) {
        tf_inv.c = 1.0f / src->c;
        tf_inv.f = -src->f / src->c;
    }

    // Invert nonlinear segment
    if (has_nonlinear) {
        tf_inv.g = 1.0f / src->g;
        tf_inv.a = powf_(1.0f / src->a, src->g);
        tf_inv.b = -tf_inv.a * src->e;
        tf_inv.e = -src->b / src->a;
    }

    if (!has_linear) {
        tf_inv.d = 0;
    } else if (!has_nonlinear) {
        // Any value larger than 1 works
        tf_inv.d = 2.0f;
    } else {
        tf_inv.d = src->c * src->d + src->f;
    }

    *dst = tf_inv;
    return true;
}

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ //

// From here below we're approximating an skcms_Curve with an skcms_TransferFunction{g,a,b,c,d,e,f}:
//
//   tf(x) =  cx + f          x < d
//   tf(x) = (ax + b)^g + e   x ≥ d
//
// When fitting, we add the additional constraint that both pieces meet at d:
//
//   cd + f = (ad + b)^g + e
//
// Solving for e and folding it through gives an alternate formulation of the non-linear piece:
//
//   tf(x) =                           cx + f   x < d
//   tf(x) = (ax + b)^g - (ad + b)^g + cd + f   x ≥ d
//
// Our overall strategy is then:
//    For a couple tolerances,
//       - skcms_fit_linear(): fit c,d,f iteratively to as many points as our tolerance allows
//       - invert c,d,f
//       - fit_nonlinear():    fit g,a,b using Gauss-Newton given those inverted c,d,f
//                             (and by constraint, inverted e) to the inverse of the table.
//    Return the parameters with least maximum error.
//
// To run Gauss-Newton to find g,a,b, we'll also need the gradient of the residuals
// of round-trip f_inv(x), the inverse of the non-linear piece of f(x).
//
//    let y = Table(x)
//    r(x) = x - f_inv(y)
//
//    ∂r/∂g = ln(ay + b)*(ay + b)^g
//          - ln(ad + b)*(ad + b)^g
//    ∂r/∂a = yg(ay + b)^(g-1)
//          - dg(ad + b)^(g-1)
//    ∂r/∂b =  g(ay + b)^(g-1)
//          -  g(ad + b)^(g-1)

// Return the residual of roundtripping skcms_Curve(x) through f_inv(y) with parameters P,
// and fill out the gradient of the residual into dfdP.
static float rg_nonlinear(float x,
                          const skcms_Curve* curve,
                          const skcms_TransferFunction* tf,
                          const float P[3],
                          float dfdP[3]) {
    const float y = skcms_eval_curve(curve, x);

    const float g = P[0],  a = P[1],  b = P[2],
                c = tf->c, d = tf->d, f = tf->f;

    const float Y = fmaxf_(a*y + b, 0.0f),
                D =        a*d + b;
    assert (D >= 0);

    // The gradient.
    dfdP[0] = 0.69314718f*log2f_(Y)*powf_(Y, g)
            - 0.69314718f*log2f_(D)*powf_(D, g);
    dfdP[1] = y*g*powf_(Y, g-1)
            - d*g*powf_(D, g-1);
    dfdP[2] =   g*powf_(Y, g-1)
            -   g*powf_(D, g-1);

    // The residual.
    const float f_inv = powf_(Y, g)
                      - powf_(D, g)
                      + c*d + f;
    return x - f_inv;
}

int skcms_fit_linear(const skcms_Curve* curve, int N, float tol, float* c, float* d, float* f) {
    assert(N > 1);
    // We iteratively fit the first points to the TF's linear piece.
    // We want the cx + f line to pass through the first and last points we fit exactly.
    //
    // As we walk along the points we find the minimum and maximum slope of the line before the
    // error would exceed our tolerance.  We stop when the range [slope_min, slope_max] becomes
    // emtpy, when we definitely can't add any more points.
    //
    // Some points' error intervals may intersect the running interval but not lie fully
    // within it.  So we keep track of the last point we saw that is a valid end point candidate,
    // and once the search is done, back up to build the line through *that* point.
    const float dx = 1.0f / (N - 1);

    int lin_points = 1;
    *f = skcms_eval_curve(curve, 0);

    float slope_min = -INFINITY_;
    float slope_max = +INFINITY_;
    for (int i = 1; i < N; ++i) {
        float x = i * dx;
        float y = skcms_eval_curve(curve, x);

        float slope_max_i = (y + tol - *f) / x,
              slope_min_i = (y - tol - *f) / x;
        if (slope_max_i < slope_min || slope_max < slope_min_i) {
            // Slope intervals would no longer overlap.
            break;
        }
        slope_max = fminf_(slope_max, slope_max_i);
        slope_min = fmaxf_(slope_min, slope_min_i);

        float cur_slope = (y - *f) / x;
        if (slope_min <= cur_slope && cur_slope <= slope_max) {
            lin_points = i + 1;
            *c = cur_slope;
        }
    }

    // Set D to the last point that met our tolerance.
    *d = (lin_points - 1) * dx;
    return lin_points;
}

static bool gauss_newton_step(const skcms_Curve* curve,
                              const skcms_TransferFunction* tf,
                              float P[3],
                              float x0, float dx, int N) {
    // We'll sample x from the range [x0,x1] (both inclusive) N times with even spacing.
    //
    // We want to do P' = P + (Jf^T Jf)^-1 Jf^T r(P),
    //   where r(P) is the residual vector
    //   and Jf is the Jacobian matrix of f(), ∂r/∂P.
    //
    // Let's review the shape of each of these expressions:
    //   r(P)   is [N x 1], a column vector with one entry per value of x tested
    //   Jf     is [N x 3], a matrix with an entry for each (x,P) pair
    //   Jf^T   is [3 x N], the transpose of Jf
    //
    //   Jf^T Jf   is [3 x N] * [N x 3] == [3 x 3], a 3x3 matrix,
    //                                              and so is its inverse (Jf^T Jf)^-1
    //   Jf^T r(P) is [3 x N] * [N x 1] == [3 x 1], a column vector with the same shape as P
    //
    // Our implementation strategy to get to the final ∆P is
    //   1) evaluate Jf^T Jf,   call that lhs
    //   2) evaluate Jf^T r(P), call that rhs
    //   3) invert lhs
    //   4) multiply inverse lhs by rhs
    //
    // This is a friendly implementation strategy because we don't have to have any
    // buffers that scale with N, and equally nice don't have to perform any matrix
    // operations that are variable size.
    //
    // Other implementation strategies could trade this off, e.g. evaluating the
    // pseudoinverse of Jf ( (Jf^T Jf)^-1 Jf^T ) directly, then multiplying that by
    // the residuals.  That would probably require implementing singular value
    // decomposition, and would create a [3 x N] matrix to be multiplied by the
    // [N x 1] residual vector, but on the upside I think that'd eliminate the
    // possibility of this gauss_newton_step() function ever failing.

    // 0) start off with lhs and rhs safely zeroed.
    skcms_Matrix3x3 lhs = {{ {0,0,0}, {0,0,0}, {0,0,0} }};
    skcms_Vector3   rhs = {  {0,0,0} };

    // 1,2) evaluate lhs and evaluate rhs
    //   We want to evaluate Jf only once, but both lhs and rhs involve Jf^T,
    //   so we'll have to update lhs and rhs at the same time.
    for (int i = 0; i < N; i++) {
        float x = x0 + i*dx;

        float dfdP[3] = {0,0,0};
        float resid = rg_nonlinear(x,curve,tf,P, dfdP);

        for (int r = 0; r < 3; r++) {
            for (int c = 0; c < 3; c++) {
                lhs.vals[r][c] += dfdP[r] * dfdP[c];
            }
            rhs.vals[r] += dfdP[r] * resid;
        }
    }

    // If any of the 3 P parameters are unused, this matrix will be singular.
    // Detect those cases and fix them up to indentity instead, so we can invert.
    for (int k = 0; k < 3; k++) {
        if (lhs.vals[0][k]==0 && lhs.vals[1][k]==0 && lhs.vals[2][k]==0 &&
            lhs.vals[k][0]==0 && lhs.vals[k][1]==0 && lhs.vals[k][2]==0) {
            lhs.vals[k][k] = 1;
        }
    }

    // 3) invert lhs
    skcms_Matrix3x3 lhs_inv;
    if (!skcms_Matrix3x3_invert(&lhs, &lhs_inv)) {
        return false;
    }

    // 4) multiply inverse lhs by rhs
    skcms_Vector3 dP = skcms_MV_mul(&lhs_inv, &rhs);
    P[0] += dP.vals[0];
    P[1] += dP.vals[1];
    P[2] += dP.vals[2];
    return isfinitef_(P[0]) && isfinitef_(P[1]) && isfinitef_(P[2]);
}


// Fit the points in [L,N) to the non-linear piece of tf, or return false if we can't.
static bool fit_nonlinear(const skcms_Curve* curve, int L, int N, skcms_TransferFunction* tf) {
    float P[3] = { tf->g, tf->a, tf->b };

    // No matter where we start, dx should always represent N even steps from 0 to 1.
    const float dx = 1.0f / (N-1);

    for (int j = 0; j < 3/*TODO: tune*/; j++) {
        // These extra constraints a >= 0 and ad+b >= 0 are not modeled in the optimization.
        // We don't really know how to fix up a if it goes negative.
        if (P[1] < 0) {
            return false;
        }
        // If ad+b goes negative, we feel just barely not uneasy enough to tweak b so ad+b is zero.
        if (P[1] * tf->d + P[2] < 0) {
            P[2] = -P[1] * tf->d;
        }
        assert (P[1] >= 0 &&
                P[1] * tf->d + P[2] >= 0);

        if (!gauss_newton_step(curve, tf,
                               P,
                               L*dx, dx, N-L)) {
            return false;
        }
    }

    // We need to apply our fixups one last time
    if (P[1] < 0) {
        return false;
    }
    if (P[1] * tf->d + P[2] < 0) {
        P[2] = -P[1] * tf->d;
    }

    tf->g = P[0];
    tf->a = P[1];
    tf->b = P[2];
    tf->e =   tf->c*tf->d + tf->f
      - powf_(tf->a*tf->d + tf->b, tf->g);
    return true;
}

bool skcms_ApproximateCurve(const skcms_Curve* curve,
                            skcms_TransferFunction* approx,
                            float* max_error) {
    if (!curve || !approx || !max_error) {
        return false;
    }

    if (curve->table_entries == 0) {
        // No point approximating an skcms_TransferFunction with an skcms_TransferFunction!
        return false;
    }

    if (curve->table_entries == 1 || curve->table_entries > (uint32_t)INT_MAX) {
        // We need at least two points, and must put some reasonable cap on the maximum number.
        return false;
    }

    int N = (int)curve->table_entries;
    const float dx = 1.0f / (N - 1);

    *max_error = INFINITY_;
    const float kTolerances[] = { 1.5f / 65535.0f, 1.0f / 512.0f };
    for (int t = 0; t < ARRAY_COUNT(kTolerances); t++) {
        skcms_TransferFunction tf,
                               tf_inv;
        int L = skcms_fit_linear(curve, N, kTolerances[t], &tf.c, &tf.d, &tf.f);

        if (L == N) {
            // If the entire data set was linear, move the coefficients to the nonlinear portion
            // with G == 1.  This lets use a canonical representation with d == 0.
            tf.g = 1;
            tf.a = tf.c;
            tf.b = tf.f;
            tf.c = tf.d = tf.e = tf.f = 0;
        } else if (L == N - 1) {
            // Degenerate case with only two points in the nonlinear segment. Solve directly.
            tf.g = 1;
            tf.a = (skcms_eval_curve(curve, (N-1)*dx) -
                    skcms_eval_curve(curve, (N-2)*dx))
                 / dx;
            tf.b = skcms_eval_curve(curve, (N-2)*dx)
                 - tf.a * (N-2)*dx;
            tf.e = 0;
        } else {
            // Start by guessing a gamma-only curve through the midpoint.
            int mid = (L + N) / 2;
            float mid_x = mid / (N - 1.0f);
            float mid_y = skcms_eval_curve(curve, mid_x);
            tf.g = log2f_(mid_y) / log2f_(mid_x);;
            tf.a = 1;
            tf.b = 0;
            tf.e =    tf.c*tf.d + tf.f
              - powf_(tf.a*tf.d + tf.b, tf.g);


            if (!skcms_TransferFunction_invert(&tf, &tf_inv) ||
                !fit_nonlinear(curve, L,N, &tf_inv)) {
                continue;
            }

            // We fit tf_inv, so calculate tf to keep in sync.
            if (!skcms_TransferFunction_invert(&tf_inv, &tf)) {
                continue;
            }
        }

        // We find our error by roundtripping the table through tf_inv.
        //
        // (The most likely use case for this approximation is to be inverted and
        // used as the transfer function for a destination color space.)
        //
        // We've kept tf and tf_inv in sync above, but we can't guarantee that tf is
        // invertible, so re-verify that here (and use the new inverse for testing).
        if (!skcms_TransferFunction_invert(&tf, &tf_inv)) {
            continue;
        }

        float err = skcms_MaxRoundtripError(curve, &tf_inv);
        if (*max_error > err) {
            *max_error = err;
            *approx    = tf;
        }
    }
    return isfinitef_(*max_error);
}

// Without this wasm would try to use the N=4 128-bit vector code path,
// which while ideal, causes tons of compiler problems.  This would be
// a good thing to revisit as emcc matures (currently 1.38.5).
#if 1 && defined(__EMSCRIPTEN_major__)
    #if !defined(SKCMS_PORTABLE)
        #define  SKCMS_PORTABLE
    #endif
#endif

extern bool g_skcms_dump_profile;
bool g_skcms_dump_profile = false;

#if !defined(NDEBUG) && defined(__clang__)
    // Basic profiling tools to time each Op.  Not at all thread safe.

    #include <stdio.h>
    #include <stdlib.h>

    #if defined(__arm__) || defined(__aarch64__)
        #include <time.h>
        static const char* now_units = "ticks";
        static uint64_t now() { return (uint64_t)clock(); }
    #else
        static const char* now_units = "cycles";
        static uint64_t now() { return __builtin_readcyclecounter(); }
    #endif

    #define M(op) +1
    static uint64_t counts[FOREACH_Op(M)];
    #undef M

    static void profile_dump_stats() {
    #define M(op) #op,
        static const char* names[] = { FOREACH_Op(M) };
    #undef M
        for (int i = 0; i < ARRAY_COUNT(counts); i++) {
            if (counts[i]) {
                fprintf(stderr, "%16s: %12llu %s\n",
                        names[i], (unsigned long long)counts[i], now_units);
            }
        }
    }

    static inline Op profile_next_op(Op op) {
        if (__builtin_expect(g_skcms_dump_profile, false)) {
            static uint64_t start    = 0;
            static uint64_t* current = NULL;

            if (!current) {
                atexit(profile_dump_stats);
            } else {
                *current += now() - start;
            }

            current = &counts[op];
            start   = now();
        }
        return op;
    }
#else
    static inline Op profile_next_op(Op op) {
        (void)g_skcms_dump_profile;
        return op;
    }
#endif

#if defined(__clang__)
    typedef float    __attribute__((ext_vector_type(4)))   Fx4;
    typedef int32_t  __attribute__((ext_vector_type(4))) I32x4;
    typedef uint64_t __attribute__((ext_vector_type(4))) U64x4;
    typedef uint32_t __attribute__((ext_vector_type(4))) U32x4;
    typedef uint16_t __attribute__((ext_vector_type(4))) U16x4;
    typedef uint8_t  __attribute__((ext_vector_type(4)))  U8x4;

    typedef float    __attribute__((ext_vector_type(8)))   Fx8;
    typedef int32_t  __attribute__((ext_vector_type(8))) I32x8;
    typedef uint64_t __attribute__((ext_vector_type(8))) U64x8;
    typedef uint32_t __attribute__((ext_vector_type(8))) U32x8;
    typedef uint16_t __attribute__((ext_vector_type(8))) U16x8;
    typedef uint8_t  __attribute__((ext_vector_type(8)))  U8x8;

    typedef float    __attribute__((ext_vector_type(16)))   Fx16;
    typedef int32_t  __attribute__((ext_vector_type(16))) I32x16;
    typedef uint64_t __attribute__((ext_vector_type(16))) U64x16;
    typedef uint32_t __attribute__((ext_vector_type(16))) U32x16;
    typedef uint16_t __attribute__((ext_vector_type(16))) U16x16;
    typedef uint8_t  __attribute__((ext_vector_type(16)))  U8x16;
#elif defined(__GNUC__)
    typedef float    __attribute__((vector_size(16)))   Fx4;
    typedef int32_t  __attribute__((vector_size(16))) I32x4;
    typedef uint64_t __attribute__((vector_size(32))) U64x4;
    typedef uint32_t __attribute__((vector_size(16))) U32x4;
    typedef uint16_t __attribute__((vector_size( 8))) U16x4;
    typedef uint8_t  __attribute__((vector_size( 4)))  U8x4;

    typedef float    __attribute__((vector_size(32)))   Fx8;
    typedef int32_t  __attribute__((vector_size(32))) I32x8;
    typedef uint64_t __attribute__((vector_size(64))) U64x8;
    typedef uint32_t __attribute__((vector_size(32))) U32x8;
    typedef uint16_t __attribute__((vector_size(16))) U16x8;
    typedef uint8_t  __attribute__((vector_size( 8)))  U8x8;

    typedef float    __attribute__((vector_size( 64)))   Fx16;
    typedef int32_t  __attribute__((vector_size( 64))) I32x16;
    typedef uint64_t __attribute__((vector_size(128))) U64x16;
    typedef uint32_t __attribute__((vector_size( 64))) U32x16;
    typedef uint16_t __attribute__((vector_size( 32))) U16x16;
    typedef uint8_t  __attribute__((vector_size( 16)))  U8x16;
#endif

// First, instantiate our default exec_ops() implementation using the default compiliation target.

#if defined(SKCMS_PORTABLE) || !(defined(__clang__) || defined(__GNUC__))
    #define N 1

    #define F   float
    #define U64 uint64_t
    #define U32 uint32_t
    #define I32 int32_t
    #define U16 uint16_t
    #define U8  uint8_t

    #define F0 0.0f
    #define F1 1.0f

#elif defined(__AVX512F__)
    #define N 16

    #define F     Fx16
    #define U64 U64x16
    #define U32 U32x16
    #define I32 I32x16
    #define U16 U16x16
    #define U8   U8x16

    #define F0 (F){0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0}
    #define F1 (F){1,1,1,1, 1,1,1,1, 1,1,1,1, 1,1,1,1}
#elif defined(__AVX__)
    #define N 8

    #define F     Fx8
    #define U64 U64x8
    #define U32 U32x8
    #define I32 I32x8
    #define U16 U16x8
    #define U8   U8x8

    #define F0 (F){0,0,0,0, 0,0,0,0}
    #define F1 (F){1,1,1,1, 1,1,1,1}
#else
    #define N 4

    #define F     Fx4
    #define U64 U64x4
    #define U32 U32x4
    #define I32 I32x4
    #define U16 U16x4
    #define U8   U8x4

    #define F0 (F){0,0,0,0}
    #define F1 (F){1,1,1,1}
#endif

#define NS(id) id
#define ATTR
    #include "src/Transform_inl.h"
#undef N
#undef F
#undef U64
#undef U32
#undef I32
#undef U16
#undef U8
#undef F0
#undef F1
#undef NS
#undef ATTR

// Now, instantiate any other versions of run_program() we may want for runtime detection.
#if !defined(SKCMS_PORTABLE) && (defined(__clang__) || defined(__GNUC__)) \
        && defined(__x86_64__) && !defined(__AVX2__)
    #define N 8
    #define F     Fx8
    #define U64 U64x8
    #define U32 U32x8
    #define I32 I32x8
    #define U16 U16x8
    #define U8   U8x8
    #define F0 (F){0,0,0,0, 0,0,0,0}
    #define F1 (F){1,1,1,1, 1,1,1,1}

    #define NS(id) id ## _hsw
    #define ATTR __attribute__((target("avx2,f16c")))

    // We check these guards to see if we have support for these features.
    // They're likely _not_ defined here in our baseline build config.
    #ifndef __AVX__
        #define __AVX__ 1
        #define UNDEF_AVX
    #endif
    #ifndef __F16C__
        #define __F16C__ 1
        #define UNDEF_F16C
    #endif
    #ifndef __AVX2__
        #define __AVX2__ 1
        #define UNDEF_AVX2
    #endif

    #include "src/Transform_inl.h"

    #undef N
    #undef F
    #undef U64
    #undef U32
    #undef I32
    #undef U16
    #undef U8
    #undef F0
    #undef F1
    #undef NS
    #undef ATTR

    #ifdef UNDEF_AVX
        #undef __AVX__
        #undef UNDEF_AVX
    #endif
    #ifdef UNDEF_F16C
        #undef __F16C__
        #undef UNDEF_F16C
    #endif
    #ifdef UNDEF_AVX2
        #undef __AVX2__
        #undef UNDEF_AVX2
    #endif

    #define TEST_FOR_HSW

    static bool hsw_ok_ = false;
    static void check_hsw_ok() {
        // See http://www.sandpile.org/x86/cpuid.htm

        // First, a basic cpuid(1).
        uint32_t eax, ebx, ecx, edx;
        __asm__ __volatile__("cpuid" : "=a"(eax), "=b"(ebx), "=c"(ecx), "=d"(edx)
                                     : "0"(1), "2"(0));

        // Sanity check for prerequisites.
        if ((edx & (1<<25)) != (1<<25)) { return; }   // SSE
        if ((edx & (1<<26)) != (1<<26)) { return; }   // SSE2
        if ((ecx & (1<< 0)) != (1<< 0)) { return; }   // SSE3
        if ((ecx & (1<< 9)) != (1<< 9)) { return; }   // SSSE3
        if ((ecx & (1<<19)) != (1<<19)) { return; }   // SSE4.1
        if ((ecx & (1<<20)) != (1<<20)) { return; }   // SSE4.2

        if ((ecx & (3<<26)) != (3<<26)) { return; }   // XSAVE + OSXSAVE

        {
            uint32_t eax_xgetbv, edx_xgetbv;
            __asm__ __volatile__("xgetbv" : "=a"(eax_xgetbv), "=d"(edx_xgetbv) : "c"(0));
            if ((eax_xgetbv & (3<<1)) != (3<<1)) { return; }  // XMM+YMM state saved?
        }

        if ((ecx & (1<<28)) != (1<<28)) { return; }   // AVX
        if ((ecx & (1<<29)) != (1<<29)) { return; }   // F16C
        if ((ecx & (1<<12)) != (1<<12)) { return; }   // FMA  (TODO: not currently used)

        // Call cpuid(7) to check for our final AVX2 feature bit!
        __asm__ __volatile__("cpuid" : "=a"(eax), "=b"(ebx), "=c"(ecx), "=d"(edx)
                                     : "0"(7), "2"(0));
        if ((ebx & (1<< 5)) != (1<< 5)) { return; }   // AVX2

        hsw_ok_ = true;
    }

    #if defined(_MSC_VER)
        #include <Windows.h>
        INIT_ONCE check_hsw_ok_once = INIT_ONCE_STATIC_INIT;

        static BOOL check_hsw_ok_InitOnce_wrapper(INIT_ONCE* once, void* param, void** ctx) {
            (void)once;
            (void)param;
            (void)ctx;
            check_hsw_ok();
            return TRUE;
        }

        static bool hsw_ok() {
            InitOnceExecuteOnce(&check_hsw_ok_once, check_hsw_ok_InitOnce_wrapper, NULL, NULL);
            return hsw_ok_;
        }
    #else
        #include <pthread.h>
        static pthread_once_t check_hsw_ok_once = PTHREAD_ONCE_INIT;

        static bool hsw_ok() {
            pthread_once(&check_hsw_ok_once, check_hsw_ok);
            return hsw_ok_;
        }
    #endif

#endif

static bool is_identity_tf(const skcms_TransferFunction* tf) {
    return tf->g == 1 && tf->a == 1
        && tf->b == 0 && tf->c == 0 && tf->d == 0 && tf->e == 0 && tf->f == 0;
}

typedef struct {
    Op          op;
    const void* arg;
} OpAndArg;

static OpAndArg select_curve_op(const skcms_Curve* curve, int channel) {
    static const struct { Op parametric, table_8, table_16; } ops[] = {
        { Op_tf_r, Op_table_8_r, Op_table_16_r },
        { Op_tf_g, Op_table_8_g, Op_table_16_g },
        { Op_tf_b, Op_table_8_b, Op_table_16_b },
        { Op_tf_a, Op_table_8_a, Op_table_16_a },
    };

    if (curve->table_entries == 0) {
        return is_identity_tf(&curve->parametric)
            ? (OpAndArg){ Op_noop, NULL }
            : (OpAndArg){ ops[channel].parametric, &curve->parametric };
    } else if (curve->table_8) {
        return (OpAndArg){ ops[channel].table_8,  curve };
    } else if (curve->table_16) {
        return (OpAndArg){ ops[channel].table_16, curve };
    }

    assert(false);
    return (OpAndArg){Op_noop,NULL};
}

static size_t bytes_per_pixel(skcms_PixelFormat fmt) {
    switch (fmt >> 1) {   // ignore rgb/bgr
        case skcms_PixelFormat_A_8           >> 1: return  1;
        case skcms_PixelFormat_G_8           >> 1: return  1;
        case skcms_PixelFormat_ABGR_4444     >> 1: return  2;
        case skcms_PixelFormat_RGB_565       >> 1: return  2;
        case skcms_PixelFormat_RGB_888       >> 1: return  3;
        case skcms_PixelFormat_RGBA_8888     >> 1: return  4;
        case skcms_PixelFormat_RGBA_1010102  >> 1: return  4;
        case skcms_PixelFormat_RGB_161616    >> 1: return  6;
        case skcms_PixelFormat_RGBA_16161616 >> 1: return  8;
        case skcms_PixelFormat_RGB_hhh       >> 1: return  6;
        case skcms_PixelFormat_RGBA_hhhh     >> 1: return  8;
        case skcms_PixelFormat_RGB_fff       >> 1: return 12;
        case skcms_PixelFormat_RGBA_ffff     >> 1: return 16;
    }
    assert(false);
    return 0;
}

static bool prep_for_destination(const skcms_ICCProfile* profile,
                                 skcms_Matrix3x3* fromXYZD50,
                                 skcms_TransferFunction* invR,
                                 skcms_TransferFunction* invG,
                                 skcms_TransferFunction* invB) {
    // We only support destinations with parametric transfer functions
    // and with gamuts that can be transformed from XYZD50.
    return profile->has_trc
        && profile->has_toXYZD50
        && profile->trc[0].table_entries == 0
        && profile->trc[1].table_entries == 0
        && profile->trc[2].table_entries == 0
        && skcms_TransferFunction_invert(&profile->trc[0].parametric, invR)
        && skcms_TransferFunction_invert(&profile->trc[1].parametric, invG)
        && skcms_TransferFunction_invert(&profile->trc[2].parametric, invB)
        && skcms_Matrix3x3_invert(&profile->toXYZD50, fromXYZD50);
}

bool skcms_Transform(const void*             src,
                     skcms_PixelFormat       srcFmt,
                     skcms_AlphaFormat       srcAlpha,
                     const skcms_ICCProfile* srcProfile,
                     void*                   dst,
                     skcms_PixelFormat       dstFmt,
                     skcms_AlphaFormat       dstAlpha,
                     const skcms_ICCProfile* dstProfile,
                     size_t                  nz) {
    const size_t dst_bpp = bytes_per_pixel(dstFmt),
                 src_bpp = bytes_per_pixel(srcFmt);
    // Let's just refuse if the request is absurdly big.
    if (nz * dst_bpp > INT_MAX || nz * src_bpp > INT_MAX) {
        return false;
    }
    int n = (int)nz;

    // Null profiles default to sRGB. Passing null for both is handy when doing format conversion.
    if (!srcProfile) {
        srcProfile = skcms_sRGB_profile();
    }
    if (!dstProfile) {
        dstProfile = skcms_sRGB_profile();
    }

    // We can't transform in place unless the PixelFormats are the same size.
    if (dst == src && (dstFmt >> 1) != (srcFmt >> 1)) {
        return false;
    }
    // TODO: this check lazilly disallows U16 <-> F16, but that would actually be fine.
    // TODO: more careful alias rejection (like, dst == src + 1)?

    Op          program  [32];
    const void* arguments[32];

    Op*          ops  = program;
    const void** args = arguments;

    skcms_TransferFunction inv_dst_tf_r, inv_dst_tf_g, inv_dst_tf_b;
    skcms_Matrix3x3        from_xyz;

    switch (srcFmt >> 1) {
        default: return false;
        case skcms_PixelFormat_A_8           >> 1: *ops++ = Op_load_a8;       break;
        case skcms_PixelFormat_G_8           >> 1: *ops++ = Op_load_g8;       break;
        case skcms_PixelFormat_ABGR_4444     >> 1: *ops++ = Op_load_4444;     break;
        case skcms_PixelFormat_RGB_565       >> 1: *ops++ = Op_load_565;      break;
        case skcms_PixelFormat_RGB_888       >> 1: *ops++ = Op_load_888;      break;
        case skcms_PixelFormat_RGBA_8888     >> 1: *ops++ = Op_load_8888;     break;
        case skcms_PixelFormat_RGBA_1010102  >> 1: *ops++ = Op_load_1010102;  break;
        case skcms_PixelFormat_RGB_161616    >> 1: *ops++ = Op_load_161616;   break;
        case skcms_PixelFormat_RGBA_16161616 >> 1: *ops++ = Op_load_16161616; break;
        case skcms_PixelFormat_RGB_hhh       >> 1: *ops++ = Op_load_hhh;      break;
        case skcms_PixelFormat_RGBA_hhhh     >> 1: *ops++ = Op_load_hhhh;     break;
        case skcms_PixelFormat_RGB_fff       >> 1: *ops++ = Op_load_fff;      break;
        case skcms_PixelFormat_RGBA_ffff     >> 1: *ops++ = Op_load_ffff;     break;
    }
    if (srcFmt & 1) {
        *ops++ = Op_swap_rb;
    }
    skcms_ICCProfile gray_dst_profile;
    if ((dstFmt >> 1) == (skcms_PixelFormat_G_8 >> 1)) {
        // When transforming to gray, stop at XYZ (by setting toXYZ to identity), then transform
        // luminance (Y) by the destination transfer function.
        gray_dst_profile = *dstProfile;
        skcms_SetXYZD50(&gray_dst_profile, &skcms_XYZD50_profile()->toXYZD50);
        dstProfile = &gray_dst_profile;
    }

    if (srcProfile->data_color_space == skcms_Signature_CMYK) {
        // Photoshop creates CMYK images as inverse CMYK.
        // These happen to be the only ones we've _ever_ seen.
        *ops++ = Op_invert;
        // With CMYK, ignore the alpha type, to avoid changing K or conflating CMY with K.
        srcAlpha = skcms_AlphaFormat_Unpremul;
    }

    if (srcAlpha == skcms_AlphaFormat_Opaque) {
        *ops++ = Op_force_opaque;
    } else if (srcAlpha == skcms_AlphaFormat_PremulAsEncoded) {
        *ops++ = Op_unpremul;
    }

    // TODO: We can skip this work if both srcAlpha and dstAlpha are PremulLinear, and the profiles
    // are the same. Also, if dstAlpha is PremulLinear, and SrcAlpha is Opaque.
    if (dstProfile != srcProfile ||
        srcAlpha == skcms_AlphaFormat_PremulLinear ||
        dstAlpha == skcms_AlphaFormat_PremulLinear) {

        if (!prep_for_destination(dstProfile,
                                  &from_xyz, &inv_dst_tf_r, &inv_dst_tf_b, &inv_dst_tf_g)) {
            return false;
        }

        if (srcProfile->has_A2B) {
            if (srcProfile->A2B.input_channels) {
                for (int i = 0; i < (int)srcProfile->A2B.input_channels; i++) {
                    OpAndArg oa = select_curve_op(&srcProfile->A2B.input_curves[i], i);
                    if (oa.op != Op_noop) {
                        *ops++  = oa.op;
                        *args++ = oa.arg;
                    }
                }
                switch (srcProfile->A2B.input_channels) {
                    case 3: *ops++ = srcProfile->A2B.grid_8 ? Op_clut_3D_8 : Op_clut_3D_16; break;
                    case 4: *ops++ = srcProfile->A2B.grid_8 ? Op_clut_4D_8 : Op_clut_4D_16; break;
                    default: return false;
                }
                *args++ = &srcProfile->A2B;
            }

            if (srcProfile->A2B.matrix_channels == 3) {
                for (int i = 0; i < 3; i++) {
                    OpAndArg oa = select_curve_op(&srcProfile->A2B.matrix_curves[i], i);
                    if (oa.op != Op_noop) {
                        *ops++  = oa.op;
                        *args++ = oa.arg;
                    }
                }

                static const skcms_Matrix3x4 I = {{
                    {1,0,0,0},
                    {0,1,0,0},
                    {0,0,1,0},
                }};
                if (0 != memcmp(&I, &srcProfile->A2B.matrix, sizeof(I))) {
                    *ops++  = Op_matrix_3x4;
                    *args++ = &srcProfile->A2B.matrix;
                }
            }

            if (srcProfile->A2B.output_channels == 3) {
                for (int i = 0; i < 3; i++) {
                    OpAndArg oa = select_curve_op(&srcProfile->A2B.output_curves[i], i);
                    if (oa.op != Op_noop) {
                        *ops++  = oa.op;
                        *args++ = oa.arg;
                    }
                }
            }

            if (srcProfile->pcs == skcms_Signature_Lab) {
                *ops++ = Op_lab_to_xyz;
            }

        } else if (srcProfile->has_trc && srcProfile->has_toXYZD50) {
            for (int i = 0; i < 3; i++) {
                OpAndArg oa = select_curve_op(&srcProfile->trc[i], i);
                if (oa.op != Op_noop) {
                    *ops++  = oa.op;
                    *args++ = oa.arg;
                }
            }
        } else {
            return false;
        }

        // At this point our source colors are linear, either RGB (XYZ-type profiles)
        // or XYZ (A2B-type profiles). Unpremul is a linear operation (multiply by a
        // constant 1/a), so either way we can do it now if needed.
        if (srcAlpha == skcms_AlphaFormat_PremulLinear) {
            *ops++ = Op_unpremul;
        }

        // A2B sources should already be in XYZD50 at this point.
        // Others still need to be transformed using their toXYZD50 matrix.
        // N.B. There are profiles that contain both A2B tags and toXYZD50 matrices.
        // If we use the A2B tags, we need to ignore the XYZD50 matrix entirely.
        assert (srcProfile->has_A2B || srcProfile->has_toXYZD50);
        static const skcms_Matrix3x3 I = {{
            { 1.0f, 0.0f, 0.0f },
            { 0.0f, 1.0f, 0.0f },
            { 0.0f, 0.0f, 1.0f },
        }};
        const skcms_Matrix3x3* to_xyz = srcProfile->has_A2B ? &I : &srcProfile->toXYZD50;

        // There's a chance the source and destination gamuts are identical,
        // in which case we can skip the gamut transform.
        if (0 != memcmp(&dstProfile->toXYZD50, to_xyz, sizeof(skcms_Matrix3x3))) {
            // Concat the entire gamut transform into from_xyz,
            // now slightly misnamed but it's a handy spot to stash the result.
            from_xyz = skcms_Matrix3x3_concat(&from_xyz, to_xyz);
            *ops++  = Op_matrix_3x3;
            *args++ = &from_xyz;
        }

        if (dstAlpha == skcms_AlphaFormat_PremulLinear) {
            *ops++ = Op_premul;
        }

        // Encode back to dst RGB using its parametric transfer functions.
        if (!is_identity_tf(&inv_dst_tf_r)) { *ops++ = Op_tf_r; *args++ = &inv_dst_tf_r; }
        if (!is_identity_tf(&inv_dst_tf_g)) { *ops++ = Op_tf_g; *args++ = &inv_dst_tf_g; }
        if (!is_identity_tf(&inv_dst_tf_b)) { *ops++ = Op_tf_b; *args++ = &inv_dst_tf_b; }
    }

    if (dstAlpha == skcms_AlphaFormat_Opaque) {
        *ops++ = Op_force_opaque;
    } else if (dstAlpha == skcms_AlphaFormat_PremulAsEncoded) {
        *ops++ = Op_premul;
    }
    if (dstFmt & 1) {
        *ops++ = Op_swap_rb;
    }
    if (dstFmt < skcms_PixelFormat_RGB_hhh) {
        *ops++ = Op_clamp;
    }
    switch (dstFmt >> 1) {
        default: return false;
        case skcms_PixelFormat_A_8           >> 1: *ops++ = Op_store_a8;       break;
        case skcms_PixelFormat_G_8           >> 1: *ops++ = Op_store_g8;       break;
        case skcms_PixelFormat_ABGR_4444     >> 1: *ops++ = Op_store_4444;     break;
        case skcms_PixelFormat_RGB_565       >> 1: *ops++ = Op_store_565;      break;
        case skcms_PixelFormat_RGB_888       >> 1: *ops++ = Op_store_888;      break;
        case skcms_PixelFormat_RGBA_8888     >> 1: *ops++ = Op_store_8888;     break;
        case skcms_PixelFormat_RGBA_1010102  >> 1: *ops++ = Op_store_1010102;  break;
        case skcms_PixelFormat_RGB_161616    >> 1: *ops++ = Op_store_161616;   break;
        case skcms_PixelFormat_RGBA_16161616 >> 1: *ops++ = Op_store_16161616; break;
        case skcms_PixelFormat_RGB_hhh       >> 1: *ops++ = Op_store_hhh;      break;
        case skcms_PixelFormat_RGBA_hhhh     >> 1: *ops++ = Op_store_hhhh;     break;
        case skcms_PixelFormat_RGB_fff       >> 1: *ops++ = Op_store_fff;      break;
        case skcms_PixelFormat_RGBA_ffff     >> 1: *ops++ = Op_store_ffff;     break;
    }

    void (*run)(const Op*, const void**, const char*, char*, int, size_t,size_t) = run_program;
#if defined(TEST_FOR_HSW)
    if (hsw_ok()) {
        run = run_program_hsw;
    }
#endif
    run(program, arguments, src, dst, n, src_bpp,dst_bpp);
    return true;
}

static void assert_usable_as_destination(const skcms_ICCProfile* profile) {
#if defined(NDEBUG)
    (void)profile;
#else
    skcms_Matrix3x3 fromXYZD50;
    skcms_TransferFunction invR, invG, invB;
    assert(prep_for_destination(profile, &fromXYZD50, &invR, &invG, &invB));
#endif
}

bool skcms_MakeUsableAsDestination(skcms_ICCProfile* profile) {
    skcms_Matrix3x3 fromXYZD50;
    if (!profile->has_trc || !profile->has_toXYZD50
        || !skcms_Matrix3x3_invert(&profile->toXYZD50, &fromXYZD50)) {
        return false;
    }

    skcms_TransferFunction tf[3];
    for (int i = 0; i < 3; i++) {
        skcms_TransferFunction inv;
        if (profile->trc[i].table_entries == 0
            && skcms_TransferFunction_invert(&profile->trc[i].parametric, &inv)) {
            tf[i] = profile->trc[i].parametric;
            continue;
        }

        float max_error;
        // Parametric curves from skcms_ApproximateCurve() are guaranteed to be invertible.
        if (!skcms_ApproximateCurve(&profile->trc[i], &tf[i], &max_error)) {
            return false;
        }
    }

    for (int i = 0; i < 3; ++i) {
        profile->trc[i].table_entries = 0;
        profile->trc[i].parametric = tf[i];
    }

    assert_usable_as_destination(profile);
    return true;
}

bool skcms_MakeUsableAsDestinationWithSingleCurve(skcms_ICCProfile* profile) {
    // Operate on a copy of profile, so we can choose the best TF for the original curves
    skcms_ICCProfile result = *profile;
    if (!skcms_MakeUsableAsDestination(&result)) {
        return false;
    }

    int best_tf = 0;
    float min_max_error = INFINITY_;
    for (int i = 0; i < 3; i++) {
        skcms_TransferFunction inv;
        skcms_TransferFunction_invert(&result.trc[i].parametric, &inv);

        float err = 0;
        for (int j = 0; j < 3; ++j) {
            err = fmaxf_(err, skcms_MaxRoundtripError(&profile->trc[j], &inv));
        }
        if (min_max_error > err) {
            min_max_error = err;
            best_tf = i;
        }
    }

    for (int i = 0; i < 3; i++) {
        result.trc[i].parametric = result.trc[best_tf].parametric;
    }

    *profile = result;
    assert_usable_as_destination(profile);
    return true;
}