forked from KolibriOS/kolibrios
511 lines
13 KiB
C
511 lines
13 KiB
C
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/*
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* Test 128-bit floating-point arithmetic on arm64:
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* build with two different compilers and compare the output.
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*
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* Copyright (c) 2015 Edmund Grimley Evans
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*
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* Copying and distribution of this file, with or without modification,
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* are permitted in any medium without royalty provided the copyright
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* notice and this notice are preserved. This file is offered as-is,
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* without any warranty.
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*/
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#include <stdint.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#define check(x) ((x) ? (void)0 : check_fail(#x, __FILE__, __LINE__))
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void check_fail(const char *assertion, const char *file, unsigned int line)
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{
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printf("%s:%d: Check (%s) failed.", file, line, assertion);
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exit(1);
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}
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typedef struct {
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unsigned long long x0, x1;
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} u128_t;
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float copy_fi(uint32_t x)
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{
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float f;
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memcpy(&f, &x, 4);
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return f;
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}
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double copy_di(uint64_t x)
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{
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double f;
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memcpy(&f, &x, 8);
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return f;
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}
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long double copy_ldi(u128_t x)
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{
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long double f;
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memcpy(&f, &x, 16);
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return f;
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}
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uint32_t copy_if(float f)
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{
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uint32_t x;
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memcpy(&x, &f, 4);
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return x;
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}
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uint64_t copy_id(double f)
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{
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uint64_t x;
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memcpy(&x, &f, 8);
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return x;
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}
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u128_t copy_ild(long double f)
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{
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u128_t x;
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memcpy(&x, &f, 16);
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return x;
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}
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long double make(int sgn, int exp, uint64_t high, uint64_t low)
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{
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u128_t x = { low,
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(0x0000ffffffffffff & high) |
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(0x7fff000000000000 & (uint64_t)exp << 48) |
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(0x8000000000000000 & (uint64_t)sgn << 63) };
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return copy_ldi(x);
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}
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void cmp(long double a, long double b)
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{
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u128_t ax = copy_ild(a);
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u128_t bx = copy_ild(b);
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int eq = (a == b);
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int ne = (a != b);
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int lt = (a < b);
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int le = (a <= b);
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int gt = (a > b);
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int ge = (a >= b);
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check(eq == 0 || eq == 1);
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check(lt == 0 || lt == 1);
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check(gt == 0 || gt == 1);
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check(ne == !eq && le == (lt | eq) && ge == (gt | eq));
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check(eq + lt + gt < 2);
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printf("cmp %016llx%016llx %016llx%016llx %d %d %d\n",
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ax.x1, ax.x0, bx.x1, bx.x0, lt, eq, gt);
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}
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void cmps(void)
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{
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int i, j;
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for (i = 0; i < 2; i++)
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for (j = 0; j < 2; j++)
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cmp(make(i, 0, 0, 0), make(j, 0, 0, 0));
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for (i = 0; i < 2; i++) {
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for (j = 0; j < 64; j++) {
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long double f1 = make(i, 32767, (uint64_t)1 << j, 0);
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long double f2 = make(i, 32767, 0, (uint64_t)1 << j);
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cmp(f1, 0);
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cmp(f2, 0);
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cmp(0, f1);
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cmp(0, f2);
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}
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}
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for (i = 0; i < 6; i++)
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for (j = 0; j < 6; j++)
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cmp(make(i & 1, i >> 1, 0, 0),
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make(j & 1, j >> 1, 0, 0));
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for (i = 0; i < 2; i++) {
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for (j = 0; j < 2; j++) {
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int a, b;
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for (a = 0; a < 2; a++) {
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for (b = 0; b < 2; b++) {
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cmp(make(i, j, a, b), make(i, j, 0, 0));
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cmp(make(i, j, 0, 0), make(i, j, a, b));
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}
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}
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}
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}
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}
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void xop(const char *name, long double a, long double b, long double c)
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{
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u128_t ax = copy_ild(a);
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u128_t bx = copy_ild(b);
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u128_t cx = copy_ild(c);
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printf("%s %016llx%016llx %016llx%016llx %016llx%016llx\n",
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name, ax.x1, ax.x0, bx.x1, bx.x0, cx.x1, cx.x0);
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}
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void fadd(long double a, long double b)
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{
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xop("add", a, b, a + b);
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}
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void fsub(long double a, long double b)
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{
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xop("sub", a, b, a - b);
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}
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void fmul(long double a, long double b)
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{
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xop("mul", a, b, a * b);
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}
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void fdiv(long double a, long double b)
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{
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xop("div", a, b, a / b);
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}
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void nanz(void)
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{
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// Check NaNs:
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{
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long double x[7];
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int i, j, n = 0;
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x[n++] = make(0, 32000, 0x95132b76effc, 0xd79035214b4f8d53);
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x[n++] = make(1, 32001, 0xbe71d7a51587, 0x30601c6815d6c3ac);
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x[n++] = make(0, 32767, 0, 1);
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x[n++] = make(0, 32767, (uint64_t)1 << 46, 0);
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x[n++] = make(1, 32767, (uint64_t)1 << 47, 0);
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x[n++] = make(1, 32767, 0x7596c7099ad5, 0xe25fed2c58f73fc9);
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x[n++] = make(0, 32767, 0x835d143360f9, 0x5e315efb35630666);
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check(n == sizeof(x) / sizeof(*x));
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for (i = 0; i < n; i++) {
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for (j = 0; j < n; j++) {
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fadd(x[i], x[j]);
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fsub(x[i], x[j]);
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fmul(x[i], x[j]);
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fdiv(x[i], x[j]);
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}
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}
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}
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// Check infinities and zeroes:
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{
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long double x[6];
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int i, j, n = 0;
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x[n++] = make(1, 32000, 0x62acda85f700, 0x47b6c9f35edc4044);
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x[n++] = make(0, 32001, 0x94b7abf55af7, 0x9f425fe354428e19);
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x[n++] = make(0, 32767, 0, 0);
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x[n++] = make(1, 32767, 0, 0);
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x[n++] = make(0, 0, 0, 0);
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x[n++] = make(1, 0, 0, 0);
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check(n == sizeof(x) / sizeof(*x));
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for (i = 0; i < n; i++) {
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for (j = 0; j < n; j++) {
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fadd(x[i], x[j]);
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fsub(x[i], x[j]);
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fmul(x[i], x[j]);
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fdiv(x[i], x[j]);
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}
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}
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}
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}
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void adds(void)
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{
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// Check shifting and add/sub:
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{
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int i;
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for (i = -130; i <= 130; i++) {
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int s1 = (uint32_t)i % 3 < 1;
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int s2 = (uint32_t)i % 5 < 2;
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fadd(make(s1, 16384 , 0x502c065e4f71a65d, 0xd2f9bdb031f4f031),
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make(s2, 16384 + i, 0xae267395a9bc1033, 0xb56b5800da1ba448));
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}
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}
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// Check normalisation:
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{
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uint64_t a0 = 0xc6bab0a6afbef5ed;
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uint64_t a1 = 0x4f84136c4a2e9b52;
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int ee[] = { 0, 1, 10000 };
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int e, i;
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for (e = 0; e < sizeof(ee) / sizeof(*ee); e++) {
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int exp = ee[e];
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fsub(make(0, exp, a1, a0), make(0, 0, 0, 0));
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for (i = 63; i >= 0; i--)
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fsub(make(0, exp, a1 | (uint64_t)1 << i >> 1, a0),
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make(0, exp, a1 >> i << i, 0));
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for (i = 63; i >=0; i--)
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fsub(make(0, exp, a1, a0 | (uint64_t)1 << i >> 1),
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make(0, exp, a1, a0 >> i << i));
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}
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}
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// Carry/overflow from rounding:
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{
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fadd(make(0, 114, -1, -1), make(0, 1, 0, 0));
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fadd(make(0, 32766, -1, -1), make(0, 32653, 0, 0));
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fsub(make(1, 32766, -1, -1), make(0, 32653, 0, 0));
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}
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}
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void muls(void)
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{
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int i, j;
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{
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long double max = make(0, 32766, -1, -1);
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long double min = make(0, 0, 0, 1);
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fmul(max, max);
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fmul(max, min);
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fmul(min, min);
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}
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for (i = 117; i > 0; i--)
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fmul(make(0, 16268, 0x643dcea76edc, 0xe0877a598403627a),
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make(i & 1, i, 0, 0));
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fmul(make(0, 16383, -1, -3), make(0, 16383, 0, 1));
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// Round to next exponent:
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fmul(make(0, 16383, -1, -2), make(0, 16383, 0, 1));
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// Round from subnormal to normal:
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fmul(make(0, 1, -1, -1), make(0, 16382, 0, 0));
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for (i = 0; i < 2; i++)
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for (j = 0; j < 112; j++)
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fmul(make(0, 16383, (uint64_t)1 << i, 0),
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make(0, 16383,
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j < 64 ? 0 : (uint64_t)1 << (j - 64),
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j < 64 ? (uint64_t)1 << j : 0));
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}
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void divs(void)
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{
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int i;
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{
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long double max = make(0, 32766, -1, -1);
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long double min = make(0, 0, 0, 1);
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fdiv(max, max);
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fdiv(max, min);
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fdiv(min, max);
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fdiv(min, min);
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}
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for (i = 0; i < 64; i++)
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fdiv(make(0, 16383, -1, -1), make(0, 16383, -1, -(uint64_t)1 << i));
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for (i = 0; i < 48; i++)
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fdiv(make(0, 16383, -1, -1), make(0, 16383, -(uint64_t)1 << i, 0));
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}
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void cvtlsw(int32_t a)
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{
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long double f = a;
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u128_t x = copy_ild(f);
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printf("cvtlsw %08lx %016llx%016llx\n", (long)(uint32_t)a, x.x1, x.x0);
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}
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void cvtlsx(int64_t a)
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{
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long double f = a;
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u128_t x = copy_ild(f);
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printf("cvtlsx %016llx %016llx%016llx\n",
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(long long)(uint64_t)a, x.x1, x.x0);
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}
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void cvtluw(uint32_t a)
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{
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long double f = a;
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u128_t x = copy_ild(f);
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printf("cvtluw %08lx %016llx%016llx\n", (long)a, x.x1, x.x0);
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}
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void cvtlux(uint64_t a)
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{
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long double f = a;
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u128_t x = copy_ild(f);
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printf("cvtlux %016llx %016llx%016llx\n", (long long)a, x.x1, x.x0);
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}
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void cvtil(long double a)
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{
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u128_t x = copy_ild(a);
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int32_t b1 = a;
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int64_t b2 = a;
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uint32_t b3 = a;
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uint64_t b4 = a;
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printf("cvtswl %016llx%016llx %08lx\n",
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x.x1, x.x0, (long)(uint32_t)b1);
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printf("cvtsxl %016llx%016llx %016llx\n",
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x.x1, x.x0, (long long)(uint64_t)b2);
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printf("cvtuwl %016llx%016llx %08lx\n",
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x.x1, x.x0, (long)b3);
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printf("cvtuxl %016llx%016llx %016llx\n",
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x.x1, x.x0, (long long)b4);
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}
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void cvtlf(float a)
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{
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uint32_t ax = copy_if(a);
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long double b = a;
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u128_t bx = copy_ild(b);
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printf("cvtlf %08lx %016llx%016llx\n", (long)ax, bx.x1, bx.x0);
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}
|
||
|
|
|
||
|
|
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;
|
||
|
|
}
|