Windows下pip安装gmpy失败求助：编译错误及计算异常问题

1. gmpy安装失败报错 #

尝试在Windows下执行pip install gmpy时失败，报错信息如下：

PS C:\Users\ADMIN\Downloads> pip install gmpy
Collecting gmpy
  Using cached gmpy-1.17.zip (147 kB)
  Installing build dependencies ... done
  Getting requirements to build wheel ... done
  Preparing metadata (pyproject.toml) ... done
Building wheels for collected packages: gmpy
  Building wheel for gmpy (pyproject.toml) ... error 
  error: subprocess-exited-with-error

  × Building wheel for gmpy (pyproject.toml) did not run successfully.
  │ exit code: 1
  ╰─> [3 lines of output]
      gmpy.c
      src/gmpy.c(243): fatal error C1083: Cannot open include file: 'longintrepr.h': No such file or directory
      error: command 'C:\Program Files (x86)\Microsoft Visual Studio\2022\BuildTools\VC\Tools\MSVC\14.37.32822\bin\HostX86\x64\cl.exe' failed with exit code 2
      [end of output]

  note: This error originates from a subprocess, and is likely not a problem with pip.
  ERROR: Failed building wheel for gmpy
Failed to build gmpy
ERROR: Could not build wheels for gmpy, which is required to install pyproject.toml-based projects

2. gmpy2大数计算异常 #

pip install gmpy2可正常安装，但执行大数计算时出现异常：

N = 17740803753336460891508014077951088945415214329359164945595622460861617151883658129377771074141448545977293824812472806768754107334272113784618671425945265453677763300584120796664192793654787317526905676618168560287204392207536711238413377822113265783504873957094131330620182217422910507867161033695120195691266283498385072573721376398480018719760538723050237163598524153522595496137288270407836138586188296538117138982579560625325815068701431157466298638302885600982291990551448117534677697122276691651611734934147801954625280213769902451417946572231015611006746186167211313556716518863585799128114202130873384852581
e = 65537
ct = 7617664236008252568996899627946125782926068188323112773389474654757630578865481085502759186904920518615173703165984894164411436709177950136929724052191922739861682189280802963747906815275683543148623167088950096943169566195634558711652670745197446307315888349532981492405588457559228674864147994684328968321710022127803384848143475788457274558988285904875669797926919759123645348144531804252200718312650929926931919262408975771593313266992606751663814830129337536342634243623652919127335934704778878412649409415730419077839365246227059700689395639431013008985996793686430486195007712091309878718060405038405039494286
a = sqrt(N) +1 
b = (a*a) - N # 使用gmpy2时此处返回负数，无法计算p
#p = a - sqrt((b)) 
p = 133194608574583306560585537741344865434566457335756913474195376386565743253745136529892878182973405477415063521701522490974580141634005077732157132519942995782242635825758964371685299620951981666567270659322471350406909271667819474931143113141023059424058315681431599980321513448212682539665160717948701866681 
# 此结果为Ubuntu SageMath中使用gmpy得到的正确值

解决方案 #

针对gmpy安装失败 #

• 原因：gmpy是停止维护的旧版本，与Python 3.10+及Windows下的VS编译工具兼容性差，longintrepr.h头文件在新版Python中已被移除或路径变更。
• 解决方式：
  1. 优先使用gmpy2并修正计算逻辑（推荐）；
  2. 若必须使用gmpy，安装Python 3.9及以下版本，或寻找对应Python版本的预编译wheel包进行安装。

针对gmpy2计算异常 #

• 原因：gmpy2的sqrt()默认返回浮点数近似值，大数场景下精度丢失，导致a = sqrt(N)+1中的a可能小于真实的整数平方根加1，进而a*a < N，使得b为负数。
• 解决方式：使用gmpy2提供的isqrt()函数（精确整数平方根，返回不大于输入值的最大整数），修正代码如下：

import gmpy2

N = 17740803753336460891508014077951088945415214329359164945595622460861617151883658129377771074141448545977293824812472806768754107334272113784618671425945265453677763300584120796664192793654787317526905676618168560287204392207536711238413377822113265783504873957094131330620182217422910507867161033695120195691266283498385072573721376398480018719760538723050237163598524153522595496137288270407836138586188296538117138982579560625325815068701431157466298638302885600982291990551448117534677697122276691651611734934147801954625280213769902451417946572231015611006746186167211313556716518863585799128114202130873384852581
e = 65537
ct = 7617664236008252568996899627946125782926068188323112773389474654757630578865481085502759186904920518615173703165984894164411436709177950136929724052191922739861682189280802963747906815275683543148623167088950096943169566195634558711652670745197446307315888349532981492405588457559228674864147994684328968321710022127803384848143475788457274558988285904875669797926919759123645348144531804252200718312650929926931919262408975771593313266992606751663814830129337536342634243623652919127335934704778878412649409415730419077839365246227059700689395639431013008985996793686430486195007712091309878718060405038405039494286

# 用isqrt获取精确的整数平方根，再加1确保a大于sqrt(N)
a = gmpy2.isqrt(N) + 1
b = (a * a) - N
# 再次用isqrt计算b的整数平方根
p = a - gmpy2.isqrt(b)
print(p)

• 说明：gmpy2.isqrt()保证了计算的精确性，a会是大于sqrt(N)的最小整数，因此a*a必然大于N，b为正数，后续可正常计算得到正确的p值。

内容的提问来源于stack exchange，提问作者LilLee