chu*_*ica 6 c floating-point infinity
在试验舍入模式时，FE_DOWNWARD( 和FE_TOWARDZERO) 显然无法形成预期的无穷大之和，而是DBL_MAX在添加DBL_MAX和 1 ULP时形成DBL_MAX。
以下是演示意外总和的测试代码。在不同的回合模式下，它会增加DBL_MAX接近 0.5 ULP 和 1.0 ULP 的值。FE_TONEAREST和中没有指出任何问题FE_UPWARD。
问题：
DBL_MAX问题之后的结果，所以也许我的数学库低于标准。请求就如何报告提供建议。编译器注释：
调用：Cygwin C 编译器
gcc -std=c11 -O0 -g3 -pedantic -Wall -Wextra -Wconversion -c -fmessage-length=0 -v -MMD -MP -MF"rand_i.d" -MT"rand_i .o" -o "rand_i.o" "../rand_i.c"
COLLECT_GCC=gcc
目标：x86_64-pc-cygwin
gcc 版本 11.3.0 (GCC)
GNU C11 (GCC) 版本 11.3.0 (x86_64-pc- cygwin）
由GNU C版本11.3.0、GMP版本6.2.1、MPFR版本4.1.0、MPC版本1.2.1、isl版本isl-0.25-GMP编译
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define STRINGIFY(x) #x
#define TOSTRING(x) STRINGIFY(x)
int main() {
const double max = DBL_MAX;
const double max_ulp = max - nextafter(max, 0);
int mode[] = {FE_DOWNWARD, FE_TONEAREST, FE_TOWARDZERO, FE_UPWARD};
const char *modes[] = {STRINGIFY(FE_DOWNWARD), STRINGIFY(FE_TONEAREST), //
STRINGIFY(FE_TOWARDZERO), STRINGIFY(FE_UPWARD)};
int n = sizeof mode / sizeof mode[0];
int p = (DBL_MANT_DIG + 2)/4;
int P = (LDBL_MANT_DIG + 2)/4;
printf("%s:%d\n", STRINGIFY(FLT_EVAL_METHOD), FLT_EVAL_METHOD);
printf("LDBL_MAX :%-24.*La %.*Lg\n", P, LDBL_MAX, LDBL_DECIMAL_DIG, LDBL_MAX);
printf("DBL_MAX :%-24.*a %.*g\n", p, max, DBL_DECIMAL_DIG, max);
printf("DBL_MAX_ULP:%-24.*a %.*g\n", p, max_ulp, DBL_DECIMAL_DIG, max_ulp);
printf("\n");
printf("mode: Addendum SUM (double) SUM (long double)\n");
for (int i = 0; i < n; i++) {
if (fesetround(mode[i])) {
perror("Invalid mode");
return -1;
}
double delta[] = {nextafter(max_ulp / 2, 0), max_ulp / 2, //
nextafter(max_ulp / 2, INFINITY), nextafter(max_ulp, 0), //
max_ulp, nextafter(max_ulp, INFINITY)};
const char *deltas[] = { "0.5 ulp-", "0.5 ulp", "0.5 ulp+", //
"ulp-", "ulp", "ulp+"};
int dn = sizeof delta / sizeof delta[0];
for (int d = 0; d < dn; d++) {
double sum = max + delta[d];
printf("mode:%-14s %-8s:%-24.*a sum:%-24.*a %-24.*La\n", //
modes[i], deltas[d], p, delta[d], p, sum, P, 0.0L + max + delta[d]);
}
puts("");
}
}
输出：注意 4条意外的行。
FLT_EVAL_METHOD:0
LDBL_MAX :0x1.fffffffffffffffep+16383 1.18973149535723176502e+4932
DBL_MAX :0x1.fffffffffffffp+1023 1.7976931348623157e+308
DBL_MAX_ULP:0x1.0000000000000p+971 1.9958403095347198e+292
mode: Addendum SUM (double) SUM (long double)
mode:FE_DOWNWARD 0.5 ulp-:0x1.fffffffffffffp+969 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffff7fep+1023
mode:FE_DOWNWARD 0.5 ulp :0x1.0000000000000p+970 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffff800p+1023
mode:FE_DOWNWARD 0.5 ulp+:0x1.0000000000001p+970 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffff800p+1023
mode:FE_DOWNWARD ulp- :0x1.fffffffffffffp+970 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffffffep+1023
mode:FE_DOWNWARD ulp :0x1.0000000000000p+971 sum:0x1.fffffffffffffp+1023 0x1.0000000000000000p+1024
--> inf expected <--
mode:FE_DOWNWARD ulp+ :0x1.0000000000001p+971 sum:0x1.fffffffffffffp+1023 0x1.0000000000000000p+1024
--> inf expected <--
mode:FE_TONEAREST 0.5 ulp-:0x1.fffffffffffffp+969 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffff800p+1023
mode:FE_TONEAREST 0.5 ulp :0x1.0000000000000p+970 sum:inf 0x1.fffffffffffff800p+1023
mode:FE_TONEAREST 0.5 ulp+:0x1.0000000000001p+970 sum:inf 0x1.fffffffffffff800p+1023
mode:FE_TONEAREST ulp- :0x1.fffffffffffffp+970 sum:inf 0x1.0000000000000000p+1024
mode:FE_TONEAREST ulp :0x1.0000000000000p+971 sum:inf 0x1.0000000000000000p+1024
mode:FE_TONEAREST ulp+ :0x1.0000000000001p+971 sum:inf 0x1.0000000000000000p+1024
mode:FE_TOWARDZERO 0.5 ulp-:0x1.fffffffffffffp+969 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffff7fep+1023
mode:FE_TOWARDZERO 0.5 ulp :0x1.0000000000000p+970 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffff800p+1023
mode:FE_TOWARDZERO 0.5 ulp+:0x1.0000000000001p+970 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffff800p+1023
mode:FE_TOWARDZERO ulp- :0x1.fffffffffffffp+970 sum:0x1.fffffffffffffp+1023 0x1.fffffffffffffffep+1023
mode:FE_TOWARDZERO ulp :0x1.0000000000000p+971 sum:0x1.fffffffffffffp+1023 0x1.0000000000000000p+1024
--> inf expected <--
mode:FE_TOWARDZERO ulp+ :0x1.0000000000001p+971 sum:0x1.fffffffffffffp+1023 0x1.0000000000000000p+1024
--> inf expected <--
mode:FE_UPWARD 0.5 ulp-:0x1.fffffffffffffp+969 sum:inf 0x1.fffffffffffff800p+1023
mode:FE_UPWARD 0.5 ulp :0x1.0000000000000p+970 sum:inf 0x1.fffffffffffff800p+1023
mode:FE_UPWARD 0.5 ulp+:0x1.0000000000001p+970 sum:inf 0x1.fffffffffffff802p+1023
mode:FE_UPWARD ulp- :0x1.fffffffffffffp+970 sum:inf 0x1.0000000000000000p+1024
mode:FE_UPWARD ulp :0x1.0000000000000p+971 sum:inf 0x1.0000000000000000p+1024
mode:FE_UPWARD ulp+ :0x1.0000000000001p+971 sum:inf 0x1.0000000000000002p+1024
检查和处理溢出分两个阶段进行。请注意，实际的软件/电路可能使用不同的策略，但结果将就像这就是过程一样。
FE_NEAREST（“正常”模式），数字被修正为无穷大。FE_TOWARDZERO然而，对于，它被更正为+/-DBL_MAX。（对于其他舍入模式，它取决于符号：远离零舍入导致无穷大，向零舍入导致+/-DBL_MAX。）因此，给定模式的溢出规则让人想起该模式的舍入规则，但实际上并不相同。可以说FE_NEAREST这是一种奇怪的模式，因为在所有超出范围的情况下，它的行为就像（仅限 IEEE-754）远离零的舍入模式，而不是注意到无穷远比远得多DBL_MAX。但其他模式的基本行为是+/-DBL_MAX当其首选方向（给定符号）接近零时输出，当其首选方向远离零时输出无穷大。
另请注意，当阶段 1 的结果是可表示范围之外的值时，即使阶段 2 的结果是 ，仍然会发出溢出异常DBL_MAX。溢出并不表示“我做了无穷大”，而是“我必须做第二阶段”。