tinycc/tests/testfp.c

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/*
* 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();
}
int main()
{
#ifdef __aarch64__
tests();
#else
printf("This test program is intended for a little-endian architecture\n"
"with an IEEE-standard 128-bit long double.\n");
#endif
return 0;
}