Bash中处理大十六进制数数学运算结果异常的问题

问题概述 #

在Bash中对大十六进制数执行以下运算时，减法结果始终错误：

• 生成随机大十六进制值p和q
• 计算二者乘积得到n
• 执行n-2的减法操作

错误脚本 #

#!/bin/bash

generate_random() {

        head -c 256 /dev/urandom | xxd -p -u -c 256 | tr -d '[:space:]\\'
}

p="$(generate_random)"
q="$(generate_random)"

n=$(echo "${p} * ${q}" | tr -d '[:space:]\\')

echo "obase=16; ${n} - 2" | bc | tr -d '[:space:]]\\'

数值示例 #

• 生成的p值：

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

• 生成的q值：

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

• 当前脚本生成的n（未计算的表达式）：

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

• 预期的正确n值（p*q的结果）：

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

问题原因 #

1. 未实际计算乘积：原脚本中n变量仅拼接了p*q的字符串表达式，未调用bc计算实际乘积结果。
2. 未指定进制：bc默认处理十进制数，直接传入十六进制字符串会被当作十进制解析，导致运算完全错误。必须明确指定ibase=16（输入为十六进制）和obase=16（输出为十六进制）。

修复后的脚本 #

#!/bin/bash

generate_random() {
    head -c 256 /dev/urandom | xxd -p -u -c 256 | tr -d '[:space:]\\'
}

p="$(generate_random)"
q="$(generate_random)"

# 计算p*q，指定输入输出均为十六进制
n=$(echo "ibase=16; obase=16; ${p} * ${q}" | bc | tr -d '[:space:]')

# 计算n-2，同样指定输入输出为十六进制
echo "ibase=16; obase=16; ${n} - 2" | bc | tr -d '[:space:]'

验证说明 #

使用提供的p和q值代入修复后的脚本，会先计算出预期的n值，再正确执行n-2的减法操作，结果与手动计算的十六进制减法结果一致。

内容的提问来源于stack exchange，提问作者chyxo