/* *  Test 128-bit floating-point arithmetic on arm64: *  build with two different compilers and compare the output. * *  Copyright (c) 2015 Edmund Grimley Evans * * Copying and distribution of this file, with or without modification, * are permitted in any medium without royalty provided the copyright * notice and this notice are preserved.  This file is offered as-is, * without any warranty. */ #include <stdint.h>#include <stdio.h>#include <stdlib.h>#include <string.h> #define check(x) ((x) ? (void)0 : check_fail(#x, __FILE__, __LINE__)) void check_fail(const char *assertion, const char *file, unsigned int line){    printf("%s:%d: Check (%s) failed.", file, line, assertion);    exit(1);} typedef struct {    unsigned long long x0, x1;} u128_t; float copy_fi(uint32_t x){    float f;    memcpy(&f, &x, 4);    return f;} double copy_di(uint64_t x){    double f;    memcpy(&f, &x, 8);    return f;} long double copy_ldi(u128_t x){    long double f;    memcpy(&f, &x, 16);    return f;} uint32_t copy_if(float f){    uint32_t x;    memcpy(&x, &f, 4);    return x;} uint64_t copy_id(double f){    uint64_t x;    memcpy(&x, &f, 8);    return x;} u128_t copy_ild(long double f){    u128_t x;    memcpy(&x, &f, 16);    return x;} long double make(int sgn, int exp, uint64_t high, uint64_t low){    u128_t x = { low,                 (0x0000ffffffffffff & high) |                 (0x7fff000000000000 & (uint64_t)exp << 48) |                 (0x8000000000000000 & (uint64_t)sgn << 63) };    return copy_ldi(x);} void cmp(long double a, long double b){    u128_t ax = copy_ild(a);    u128_t bx = copy_ild(b);    int eq = (a == b);    int ne = (a != b);    int lt = (a < b);    int le = (a <= b);    int gt = (a > b);    int ge = (a >= b);     check(eq == 0 || eq == 1);    check(lt == 0 || lt == 1);    check(gt == 0 || gt == 1);    check(ne == !eq && le == (lt | eq) && ge == (gt | eq));    check(eq + lt + gt < 2);     printf("cmp %016llx%016llx %016llx%016llx %d %d %d\n",           ax.x1, ax.x0, bx.x1, bx.x0, lt, eq, gt);} void cmps(void){    int i, j;     for (i = 0; i < 2; i++)        for (j = 0; j < 2; j++)            cmp(make(i, 0, 0, 0), make(j, 0, 0, 0));     for (i = 0; i < 2; i++) {        for (j = 0; j < 64; j++) {            long double f1 = make(i, 32767, (uint64_t)1 << j, 0);            long double f2 = make(i, 32767, 0, (uint64_t)1 << j);            cmp(f1, 0);            cmp(f2, 0);            cmp(0, f1);            cmp(0, f2);        }    }     for (i = 0; i < 6; i++)        for (j = 0; j < 6; j++)            cmp(make(i & 1, i >> 1, 0, 0),                make(j & 1, j >> 1, 0, 0));     for (i = 0; i < 2; i++) {        for (j = 0; j < 2; j++) {            int a, b;            for (a = 0; a < 2; a++) {                for (b = 0; b < 2; b++) {                    cmp(make(i, j, a, b), make(i, j, 0, 0));                    cmp(make(i, j, 0, 0), make(i, j, a, b));                }            }        }    }} void xop(const char *name, long double a, long double b, long double c){    u128_t ax = copy_ild(a);    u128_t bx = copy_ild(b);    u128_t cx = copy_ild(c);    printf("%s %016llx%016llx %016llx%016llx %016llx%016llx\n",           name, ax.x1, ax.x0, bx.x1, bx.x0, cx.x1, cx.x0);} void fadd(long double a, long double b){    xop("add", a, b, a + b);} void fsub(long double a, long double b){    xop("sub", a, b, a - b);} void fmul(long double a, long double b){    xop("mul", a, b, a * b);} void fdiv(long double a, long double b){    xop("div", a, b, a / b);} void nanz(void){    // Check NaNs:    {        long double x[7];        int i, j, n = 0;        x[n++] = make(0, 32000, 0x95132b76effc, 0xd79035214b4f8d53);        x[n++] = make(1, 32001, 0xbe71d7a51587, 0x30601c6815d6c3ac);        x[n++] = make(0, 32767, 0, 1);        x[n++] = make(0, 32767, (uint64_t)1 << 46, 0);        x[n++] = make(1, 32767, (uint64_t)1 << 47, 0);        x[n++] = make(1, 32767, 0x7596c7099ad5, 0xe25fed2c58f73fc9);        x[n++] = make(0, 32767, 0x835d143360f9, 0x5e315efb35630666);        check(n == sizeof(x) / sizeof(*x));        for (i = 0; i < n; i++) {            for (j = 0; j < n; j++) {                fadd(x[i], x[j]);                fsub(x[i], x[j]);                fmul(x[i], x[j]);                fdiv(x[i], x[j]);            }        }    }     // Check infinities and zeroes:    {        long double x[6];        int i, j, n = 0;        x[n++] = make(1, 32000, 0x62acda85f700, 0x47b6c9f35edc4044);        x[n++] = make(0, 32001, 0x94b7abf55af7, 0x9f425fe354428e19);        x[n++] = make(0, 32767, 0, 0);        x[n++] = make(1, 32767, 0, 0);        x[n++] = make(0, 0, 0, 0);        x[n++] = make(1, 0, 0, 0);        check(n == sizeof(x) / sizeof(*x));        for (i = 0; i < n; i++) {            for (j = 0; j < n; j++) {                fadd(x[i], x[j]);                fsub(x[i], x[j]);                fmul(x[i], x[j]);                fdiv(x[i], x[j]);            }        }    }} void adds(void){    // Check shifting and add/sub:    {        int i;        for (i = -130; i <= 130; i++) {            int s1 = (uint32_t)i % 3 < 1;            int s2 = (uint32_t)i % 5 < 2;            fadd(make(s1, 16384    , 0x502c065e4f71a65d, 0xd2f9bdb031f4f031),                 make(s2, 16384 + i, 0xae267395a9bc1033, 0xb56b5800da1ba448));        }    }     // Check normalisation:    {        uint64_t a0 = 0xc6bab0a6afbef5ed;        uint64_t a1 = 0x4f84136c4a2e9b52;        int ee[] = { 0, 1, 10000 };        int e, i;        for (e = 0; e < sizeof(ee) / sizeof(*ee); e++) {            int exp = ee[e];            fsub(make(0, exp, a1, a0), make(0, 0, 0, 0));            for (i = 63; i >= 0; i--)                fsub(make(0, exp, a1 | (uint64_t)1 << i >> 1, a0),                     make(0, exp, a1 >> i << i, 0));            for (i = 63; i >=0; i--)                fsub(make(0, exp, a1, a0 | (uint64_t)1 << i >> 1),                     make(0, exp, a1, a0 >> i << i));        }    }     // Carry/overflow from rounding:    {        fadd(make(0, 114, -1, -1), make(0, 1, 0, 0));        fadd(make(0, 32766, -1, -1), make(0, 32653, 0, 0));        fsub(make(1, 32766, -1, -1), make(0, 32653, 0, 0));    }} void muls(void){    int i, j;     {        long double max = make(0, 32766, -1, -1);        long double min = make(0, 0, 0, 1);        fmul(max, max);        fmul(max, min);        fmul(min, min);    }     for (i = 117; i > 0; i--)        fmul(make(0, 16268, 0x643dcea76edc, 0xe0877a598403627a),             make(i & 1, i, 0, 0));     fmul(make(0, 16383, -1, -3), make(0, 16383, 0, 1));    // Round to next exponent:    fmul(make(0, 16383, -1, -2), make(0, 16383, 0, 1));    // Round from subnormal to normal:    fmul(make(0, 1, -1, -1), make(0, 16382, 0, 0));     for (i = 0; i < 2; i++)        for (j = 0; j < 112; j++)            fmul(make(0, 16383, (uint64_t)1 << i, 0),                 make(0, 16383,                      j < 64 ? 0 : (uint64_t)1 << (j - 64),                      j < 64 ? (uint64_t)1 << j : 0));} void divs(void){    int i;     {        long double max = make(0, 32766, -1, -1);        long double min = make(0, 0, 0, 1);        fdiv(max, max);        fdiv(max, min);        fdiv(min, max);        fdiv(min, min);    }     for (i = 0; i < 64; i++)        fdiv(make(0, 16383, -1, -1), make(0, 16383, -1, -(uint64_t)1 << i));    for (i = 0; i < 48; i++)        fdiv(make(0, 16383, -1, -1), make(0, 16383, -(uint64_t)1 << i, 0));} void cvtlsw(int32_t a){    long double f = a;    u128_t x = copy_ild(f);    printf("cvtlsw %08lx %016llx%016llx\n", (long)(uint32_t)a, x.x1, x.x0);} void cvtlsx(int64_t a){    long double f = a;    u128_t x = copy_ild(f);    printf("cvtlsx %016llx %016llx%016llx\n",           (long long)(uint64_t)a, x.x1, x.x0);} void cvtluw(uint32_t a){    long double f = a;    u128_t x = copy_ild(f);    printf("cvtluw %08lx %016llx%016llx\n", (long)a, x.x1, x.x0);} void cvtlux(uint64_t a){    long double f = a;    u128_t x = copy_ild(f);    printf("cvtlux %016llx %016llx%016llx\n", (long long)a, x.x1, x.x0);} void cvtil(long double a){    u128_t x = copy_ild(a);    int32_t b1 = a;    int64_t b2 = a;    uint32_t b3 = a;    uint64_t b4 = a;    printf("cvtswl %016llx%016llx %08lx\n",           x.x1, x.x0, (long)(uint32_t)b1);    printf("cvtsxl %016llx%016llx %016llx\n",           x.x1, x.x0, (long long)(uint64_t)b2);    printf("cvtuwl %016llx%016llx %08lx\n",           x.x1, x.x0, (long)b3);    printf("cvtuxl %016llx%016llx %016llx\n",           x.x1, x.x0, (long long)b4);} void cvtlf(float a){    uint32_t ax = copy_if(a);    long double b = a;    u128_t bx = copy_ild(b);    printf("cvtlf %08lx %016llx%016llx\n", (long)ax, bx.x1, bx.x0);} void cvtld(double a){    uint64_t ax = copy_id(a);    long double b = a;    u128_t bx = copy_ild(b);    printf("cvtld %016llx %016llx%016llx\n", (long long)ax, bx.x1, bx.x0);} void cvtfl(long double a){    u128_t ax = copy_ild(a);    float b = a;    uint32_t bx = copy_if(b);    printf("cvtfl %016llx%016llx %08lx\n", ax.x1, ax.x0, (long)bx);} void cvtdl(long double a){    u128_t ax = copy_ild(a);    double b = a;    uint64_t bx = copy_id(b);    printf("cvtdl %016llx%016llx %016llx\n", ax.x1, ax.x0, (long long)bx);} void cvts(void){    int i, j;     {        uint32_t x = 0xad040c5b;        cvtlsw(0);        for (i = 0; i < 31; i++)            cvtlsw(x >> (31 - i));        for (i = 0; i < 31; i++)            cvtlsw(-(x >> (31 - i)));        cvtlsw(0x80000000);    }    {        uint64_t x = 0xb630a248cad9afd2;        cvtlsx(0);        for (i = 0; i < 63; i++)            cvtlsx(x >> (63 - i));        for (i = 0; i < 63; i++)            cvtlsx(-(x >> (63 - i)));        cvtlsx(0x8000000000000000);    }    {        uint32_t x = 0xad040c5b;        cvtluw(0);        for (i = 0; i < 32; i++)            cvtluw(x >> (31 - i));    }    {        uint64_t x = 0xb630a248cad9afd2;        cvtlux(0);        for (i = 0; i < 64; i++)            cvtlux(x >> (63 - i));    }     for (i = 0; i < 2; i++) {        cvtil(make(i, 32767, 0, 1));        cvtil(make(i, 32767, (uint64_t)1 << 47, 0));        cvtil(make(i, 32767, 123, 456));        cvtil(make(i, 32767, 0, 0));        cvtil(make(i, 16382, -1, -1));        cvtil(make(i, 16383, -1, -1));        cvtil(make(i, 16384, 0x7fffffffffff, -1));        cvtil(make(i, 16384, 0x800000000000, 0));        for (j = 0; j < 68; j++)            cvtil(make(i, 16381 + j, 0xd4822c0a10ec, 0x1fe2f8b2669f5c9d));    }     cvtlf(copy_fi(0x00000000));    cvtlf(copy_fi(0x456789ab));    cvtlf(copy_fi(0x7f800000));    cvtlf(copy_fi(0x7f923456));    cvtlf(copy_fi(0x7fdbcdef));    cvtlf(copy_fi(0x80000000));    cvtlf(copy_fi(0xabcdef12));    cvtlf(copy_fi(0xff800000));    cvtlf(copy_fi(0xff923456));    cvtlf(copy_fi(0xffdbcdef));     cvtld(copy_di(0x0000000000000000));    cvtld(copy_di(0x456789abcdef0123));    cvtld(copy_di(0x7ff0000000000000));    cvtld(copy_di(0x7ff123456789abcd));    cvtld(copy_di(0x7ffabcdef1234567));    cvtld(copy_di(0x8000000000000000));    cvtld(copy_di(0xcdef123456789abc));    cvtld(copy_di(0xfff0000000000000));    cvtld(copy_di(0xfff123456789abcd));    cvtld(copy_di(0xfffabcdef1234567));     for (i = 0; i < 2; i++) {                   \        cvtfl(make(i, 0, 0, 0));        cvtfl(make(i, 16232, -1, -1));        cvtfl(make(i, 16233, 0, 0));        cvtfl(make(i, 16233, 0, 1));        cvtfl(make(i, 16383, 0xab0ffd000000, 0));        cvtfl(make(i, 16383, 0xab0ffd000001, 0));        cvtfl(make(i, 16383, 0xab0ffeffffff, 0));        cvtfl(make(i, 16383, 0xab0fff000000, 0));        cvtfl(make(i, 16383, 0xab0fff000001, 0));        cvtfl(make(i, 16510, 0xfffffeffffff, -1));        cvtfl(make(i, 16510, 0xffffff000000, 0));        cvtfl(make(i, 16511, 0, 0));        cvtfl(make(i, 32767, 0, 0));        cvtfl(make(i, 32767, 0, 1));        cvtfl(make(i, 32767, 0x4cbe01ac5f40, 0x75cee3c6afbb00b5));        cvtfl(make(i, 32767, 0x800000000000, 1));        cvtfl(make(i, 32767, 0xa11caaaf6a52, 0x696033e871eab099));    }     for (i = 0; i < 2; i++) {        cvtdl(make(i, 0, 0, 0));        cvtdl(make(i, 15307, -1, -1));        cvtdl(make(i, 15308, 0, 0));        cvtdl(make(i, 15308, 0, 1));        cvtdl(make(i, 16383, 0xabc123abc0ff, 0xe800000000000000));        cvtdl(make(i, 16383, 0xabc123abc0ff, 0xe800000000000001));        cvtdl(make(i, 16383, 0xabc123abc0ff, 0xf7ffffffffffffff));        cvtdl(make(i, 16383, 0xabc123abc0ff, 0xf800000000000000));        cvtdl(make(i, 16383, 0xabc123abc0ff, 0xf800000000000001));        cvtdl(make(i, 17406, 0xffffffffffff, 0xf7ffffffffffffff));        cvtdl(make(i, 17406, 0xffffffffffff, 0xf800000000000000));        cvtdl(make(i, 17407, 0, 0));        cvtdl(make(i, 32767, 0, 0));        cvtdl(make(i, 32767, 0, 1));        cvtdl(make(i, 32767, 0x4cbe01ac5f40, 0x75cee3c6afbb00b5));        cvtdl(make(i, 32767, 0x800000000000, 1));        cvtdl(make(i, 32767, 0xa11caaaf6a52, 0x696033e871eab099));    }} void tests(void){    cmps();    nanz();    adds();    muls();    divs();    cvts();} 

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