qt5base-lts/util/qfloat16-tables/gen_qfloat16_tables.cpp

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#include <stdint.h>
#include <stdio.h>

/*
 * This tool generates the tables used by qfloat16 to implement a
 * software-emulated version of IEEE 754 binary16. qfloat16 automatically uses
 * CPU instructions to convert to and from float (IEEE 754 binary32), but if
 * the CPU is not guaranteed to have those instructions available at compile
 * time, then qfloat16 needs the tables to perform the conversion with
 * reasonable performance.
 *
 * Because Qt requires float to be IEEE 754 binary32, these tables are
 * platform-independent and will never change.
 */

uint32_t convertmantissa(int32_t i)
{
    uint32_t m = i << 13; // Zero pad mantissa bits
    uint32_t e = 0; // Zero exponent

    while (!(m & 0x00800000)) {   // While not normalized
        e -= 0x00800000;     // Decrement exponent (1<<23)
        m <<= 1;             // Shift mantissa
    }
    m &= ~0x00800000;          // Clear leading 1 bit
    e += 0x38800000;           // Adjust bias ((127-14)<<23)
    return m | e;            // Return combined number
}

// we first build these tables up and then print them out as a separate step in order
// to more closely map the implementation given in the paper.
uint32_t basetable[512];
uint32_t shifttable[512];
uint32_t roundtable[512];

int main()
{
    uint32_t i;

    printf("/* This file was generated by util/qfloat16-tables/gen_qfloat16_tables.cpp */\n\n");
    printf("#include <QtCore/qfloat16.h>\n\n");

    printf("QT_BEGIN_NAMESPACE\n\n");
    printf("#if !defined(__ARM_FP16_FORMAT_IEEE)\n\n");

    printf("const quint32 qfloat16::mantissatable[2048] = {\n");
    printf("0,\n");
    for (i = 1; i < 1024; i++)
        printf("0x%XU,\n", convertmantissa(i));
    for (i = 1024; i < 2048; i++)
        printf("0x%XU,\n", 0x38000000U + ((i - 1024) << 13));
    printf("};\n\n");

    printf("const quint32 qfloat16::exponenttable[64] = {\n");
    printf("0,\n");
    for (i = 1; i < 31; i++)
        printf("0x%XU,\n", i << 23);
    printf("0x47800000U,\n");  // 31
    printf("0x80000000U,\n");  // 32
    for (i = 33; i < 63; i++)
        printf("0x%XU,\n", 0x80000000U + ((i - 32) << 23));
    printf("0xC7800000U,\n");  // 63
    printf("};\n\n");

    printf("const quint32 qfloat16::offsettable[64] = {\n");
    printf("0,\n");
    for (i = 1; i < 32; i++)
        printf("1024U,\n");
    printf("0,\n");
    for (i = 33; i < 64; i++)
        printf("1024U,\n");
    printf("};\n\n");

    int32_t e;
    for (i = 0; i < 256; ++i) {
        e = i - 127;
        if (e < -25) {   // Very small numbers map to zero
            basetable[i | 0x000] = 0x0000;
            basetable[i | 0x100] = 0x8000;
            shifttable[i | 0x000] = 24;
            shifttable[i | 0x100] = 24;
            roundtable[i | 0x000] = 0;
            roundtable[i | 0x100] = 0;

        } else if (e < -14) {             // Small numbers map to denorms
            basetable[i | 0x000] = (0x0400 >> (-e - 14));
            basetable[i | 0x100] = (0x0400 >> (-e - 14)) | 0x8000;
            shifttable[i | 0x000] = -e - 1;
            shifttable[i | 0x100] = -e - 1;
            if (e == -25) {
                // rounds up
                roundtable[i | 0x000] = (1 << 24);
                roundtable[i | 0x100] = (1 << 24);
            } else if (e == -24) {
                // rounds half up
                roundtable[i | 0x000] = (1 << 22) + 1;
                roundtable[i | 0x100] = (1 << 22) + 1;
            } else {
                roundtable[i | 0x000] = (1 << (-e - 2));
                roundtable[i | 0x100] = (1 << (-e - 2));
            }

        } else if (e <= 15) {            // Normal numbers just lose precision
            basetable[i | 0x000] = ((e + 15) << 10);
            basetable[i | 0x100] = ((e + 15) << 10) | 0x8000;
            shifttable[i | 0x000] = 13;
            shifttable[i | 0x100] = 13;
            roundtable[i | 0x000] = (1 << 12);
            roundtable[i | 0x100] = (1 << 12);

        } else if (e < 128) {            // Large numbers map to Infinity
            basetable[i | 0x000] = 0x7C00;
            basetable[i | 0x100] = 0xFC00;
            shifttable[i | 0x000] = 24;
            shifttable[i | 0x100] = 24;
            roundtable[i | 0x000] = 0;
            roundtable[i | 0x100] = 0;

        } else {                     // Infinity and NaN's stay Infinity and NaN's
            basetable[i | 0x000] = 0x7C00;
            basetable[i | 0x100] = 0xFC00;
            shifttable[i | 0x000] = 13;
            shifttable[i | 0x100] = 13;
            roundtable[i | 0x000] = 0;
            roundtable[i | 0x100] = 0;
        }
    }

    printf("const quint16 qfloat16::basetable[512] = {\n");
    for (i = 0; i < 512; i++)
        printf("0x%XU,\n", basetable[i]);

    printf("};\n\n");

    printf("const quint16 qfloat16::shifttable[512] = {\n");
    for (i = 0; i < 512; i++)
        printf("0x%XU,\n", shifttable[i]);

    printf("};\n\n");

    printf("const quint32 qfloat16::roundtable[512] = {\n");
    for (i = 0; i < 512; i++)
        printf("0x%XU,\n", roundtable[i]);

    printf("};\n\n");

    printf("#endif // !__ARM_FP16_FORMAT_IEEE\n\n");
    printf("QT_END_NAMESPACE\n");
    return 0;
}