真正的高精度科学计算器

郭先抢

50# 云梦 能上传部分源代码看看吗？ 我想看看源代码，并不是我想窃取你的劳动果实，而是我想学一学如何用visual basic 编程序

郭先抢

软件感觉不错，很想学一学你的程序！我是个vb菜鸟，只懂一点点，所以。。。

云梦

计算伽马函数的VB原代码示例： Function Gamma() Dim xm, MMU As Long Dim pRes As String Dim L0 As String Dim Gmz, srd As Single srd = DEG DEG = 1 fsgamma = "0" Gmz = 0 'x 是否为指定值标志 Zx = Ax If Ax.zs > -1 Then '判断 x 是否整数 Bx = Ax Bx.St = Left(Ax.St, Ax.zs + 1) Bx.zs = Len(Bx.St) - 1 hsfx = "-" Call Addition If Left(Ax.St, 1) = "0" Then '如果 x 是整数 xm = Val(Left(Zx.St, Zx.zs + 1)) '取整数部分进行判断 If Zx.bz = "" And (xm = 1 Or xm = 2) Then Gmz = 1 'x=1 x=2 时 If Zx.bz = "-" Or xm = 0 Then Gmz = 2 'x=0,-1,-2,-3.....时 End If End If Ax = Zx If Gmz = 0 Then If Ax.bz = "-" Then '负数的伽马 fsgamma = 1 Ax.bz = "" Bx.bz = "" Bx.St = "1" Bx.zs = 0 hsfx = "+" Call Addition Zx = Ax End If Px = Ax Wx = Ax Hg = Ax Select Case ychen Case Is = 64 MMU = 90 Case Is = 128 MMU = 130 Case Is = 256 MMU = 200 Case Is = 512 MMU = 540 Case Is = 1024 MMU = 8400 End Select If Zx.zs < 0 Then Ax = Px Wx = Px Bx.bz = "" Bx.St = "1" Bx.zs = 0 hsfx = "+" Call Addition Wx = Ax L0 = Mid(Ax.St, Ax.zs + 2) Cx = Hg Call mult_ Hg = Cx For xm = 2 To MMU 'Γ(10000+z) Ax.St = Trim(Str(xm)) Wx.zs = Len(Ax.St) - 1 Wx.St = Ax.St + L0 Ax = Wx Cx = Hg Call mult_ Hg = Cx Next xm Px = Wx Else L0 = Mid(Px.St, Px.zs + 2) If Val(Left(Zx.St, Zx.zs + 1)) < MMU Then For xm = 1 To MMU 'Γ(10000+z) Ax.St = Trim(Str(1 + Val(Left(Px.St, Px.zs + 1)))) Px.zs = Len(Ax.St) - 1 Px.St = Ax.St + L0 Ax = Px Cx = Hg Call mult_ Hg = Cx Next xm Else Hg = Zx Px = Zx End If End If Ux = Hg Ax = Px 'Px=1000+z Call Lnx 'lnz ix = Ax ' Ax = Px Bx.bz = "" Bx.St = "5" Bx.zs = -1 hsfx = "-" Call Addition 'z-1/2 Cx = Ax Ax = ix Call mult_ '(z-1/2)*lnz Bx = Px hsfx = "-" Call Addition '(z-1/2)Lnz-z Bx.bz = "" Bx.St = epx(15) 'ln(√2Pi) Bx.zs = -1 hsfx = "+" Call Addition 'Sx=(z-1/2)Lnz-z+ln(√2Pi) Sx = Ax ' Cx = Px '1000+z Ax = Cx Call mult_ 'z2 Tx = Ax 'Tx=z2 Lx = Px 'z Cx.bz = "" Cx.St = "12" Cx.zs = 1 Ax = Px Call mult_ 'z*12 Ax = Cx Cx.bz = "" Cx.St = "1" Cx.zs = 0 Call multx_ '1/(z*12) Ax.bz = "" Hg = Ax Hg.bz = "" '求和 ∑ For xm = 2 To 200 '(-1)[n-1]B2xm/(2xm(2xm-1)z[2xm-1]) Cx = Lx 'Lx=z(2xm-1) Ax = Tx 'Tx=z2 Call mult_ 'z3 Lx = Cx 'Lx=z3 Ax = Cx Cx.bz = "" Cx.St = CStr(2 * xm * (2 * xm - 1)) Cx.zs = Len(Cx.St) - 1 Call mult_ '2xm(2xm-1)z[2xm-1] Ax = Cx Cx = pm2(2 * xm) Call mult_ 'B2xm(分母)*2xm(2xm-1)z[2xm-1] Ax = Cx Cx = pz2(2 * xm) Call multx_ 'B2xm(分子)/{B2xm(分母)*2xm(2xm-1)z[2xm-1]} Wn = Cx Ax = Cx Bx = Hg hsfx = "+" Call Addition Hg = Ax If Wn.zs < -xChen Then Exit For Next xm Bx = Hg Ax = Sx hsfx = "+" Call Addition Sx = Ax 'Sum 求和结束 Ax = Ux Call Lnx Bx = Ax Ax = Sx hsfx = "-" Call Addition Sx = Ax Ax = Px Call Lnx Bx = Sx hsfx = "+" Call Addition If fsgamma = 1 Then Vx = Ax Ax.bz = "" Ax.St = Pi.Tag Ax.zs = 0 Cx = Zx Call mult_ Ax = Cx Call xSin Gammbz = Ax.bz Cx.bz = "" Cx.St = Pi.Tag Cx.zs = 0 Call multx_ Ax = Cx Call Lnx Bx = Vx hsfx = "-" Call Addition End If Else If Gmz = 1 Then 'x=1,2 时 Γ(x)=1 Ax.bz = "" Ax.St = "0" Ax.zs = "0" Else Text12.Text = "-→∞ (无穷大)" 'x=0,-1,-2,-3....时 Γ(x)=∞ End If End If DEG = srd '恢复三角函数制式(弧度,度,梯度)

云梦

计算实例： Gamma[Pi]=2.2880377953400324179595889090602339228896881533562224411993807454704710066085042825007253044679284747968492456163619736990086693068610684720719929526723030053489815429191959102611884193668794490992029541491572661438362658155059636402680610560412995023428572826183864816514132279851720320360861870024470511009961650028651601111561894239076005577921680490380611694414733267466945500752573250190012765539633365280130189120138691770838670048888356517427638773037998537252598048473914927354467723366483939306412743620 E0 Gamma[-0.9]=-1.0570564109631924262547207974739335769500642917875974825611111967149183759247578901707959771407163566441550287690113503822012272204536656437724552070348384652010074010435712807443049327495784005882882331444625260150178173814720139546897073184335868849137176626529366498372865716422604903386218900984502412837245905669753669097096301130708558392298748589544459136929945703037527541817131388712011444761809695207975411846305421133341651770623266953056232548078614752536919951874359416895723263937984783317257170929 E1

云梦

这款计算器不是提供给数学研究用的，它是工程计算人员的计算工具。适合、中、高、大学及非数学专业的学生、技术人员、工程师、数学爱好者等等。因此没有要求很高的计算精度，1024位已经足够了，一般常用64位和128位，这已经大大超出现有计算器的计算能力，且目前已经包含近200个常用函数、分布函数、积分函数、反函数、统计、解一元4次以下根、常用图形的面积和体积及众多的数学常数。 该计算器最大的特点是可以随时把自己常用和喜欢的函数、表达式纳入计算器，为特殊用途提供更多方便。

云梦

百度里可以找到该计算器前期vb源码，只包括常用函数。

云梦

上面的是伽马的内部调用函数，下面才是主函数。 Private Sub Command39_Click() '2012-08.09 Call StoF Dim pRes As String Select Case Text8.Text Case Is = "" 'Gamma函数 NameF.Text = "Γ(x) =" Call SJbz Call Gamma If Ax.zs > 15 Then Cx = Ax Ax.St = epx(11) Ax.bz = "" Ax.zs = -1 Call mult_ Ax = Cx Ax.St = Mid(Cx.St, Cx.zs + 2) For i = 1 To xChen If Mid(Ax.St, i, 1) <> "0" Then Ax.St = Mid(Ax.St, i): Exit For Next i Ax.zs = -i Sx.St = Left(Cx.St, Cx.zs + 1) Cx.St = epx(10) Cx.bz = "" Cx.zs = 0 Call mult_ Call Exp 'Ln(gamma) If Val(Sx.St) < 10 ^ 16 Then Ax.zs = Val(Sx.St) Call sc(Ax.bz, Ax.St, Ax.zs) Else If Val(Sx.St) < 32 Then pRes = Left(Ax.St, 1) + "." + Mid(Ax.St, 2, 10) + " E" + Sx.St Else pRes = Left(Ax.St, 1) + "." + Mid(Ax.St, 2, 10) + " E" + Str(Val(Sx.St)) End If Prints.Text = pRes pRes = Left(Ax.St, 1) + "." + Mid(Ax.St, 2, ychen - 1) + " E" + Sx.St Text11.Text = pRes End If Else Call Exp Ax.bz = IIf(fsgamma = 1, Gammbz, Ax.bz) Call sc(Ax.bz, Ax.St, Ax.zs) End If 可以计算到9x10^11次方的伽马。

liangbch

1. 作为一个同样致力于数学函数的高精度计算的工作者，首先，我对楼主的产品表示肯定和鼓励。 2。这类软件，往大了说，叫做计算机代数系统(Computer algebra system), 大块头的商业软件Maple，Mathcad，Mathematica就属于此类。轻量级的OPen Source的PARI/GP也属于此类。见http://en.wikipedia.org/wiki/Computer_algebra_system。 往小了说，叫做任意精度计算(Arbitrary-precision arithmetic),见http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic。 以库形式发布的有GMP，CLN，MPFR，MIRACL，NTL。提供库和一体化程序的bc,PARI/GP,Maple，Maxima，Mathematica，sage等。 3. 关于界面问题。对于计算器这种软件来说。命令行/脚本形式的接口是最好的。他可以完成批量计算，可以解决复杂的问题。但对于初学者，命令行语法不变记忆，较难学习，所以GUI形式的接口可能是最简单的。 4. 我推荐PARI/GP 和bc(Linux下的命令行计算器),这两个软件都是free的，而且是轻量级的，易于学习，功能也够用。昨天晚上，我还给我儿子讲了45分钟的课，关于PARI用法的。 顺便说一下，我自己也致力于这类软件的开发，23年前，我就用只有8位10数精度的计算器，用了一个寒假的时间，算出精度达26位数字的对数表，那时我没有见过电脑。考大学时，报考的是计算机专业，这完全是从我的兴趣出发，那时我以为计算机可以直接计算几百位10进制数，上了大学，就有了电脑，就可以将初等函数算到更高的精度了。我从未放弃此类研究。我的一个重要的理想就是开发出比GMP更快的大数运算库。

郭先抢

1. 作为一个同样致力于数学函数的高精度计算的工作者，首先，我对楼主的产品表示肯定和鼓励。 2。这类软件，往大了说，叫做计算机代数系统(Computer algebra system), 大块头的商业软件Maple，Mathcad，Mathe ... liangbch 发表于 2013-1-14 12:01

你把mathematica软件破解了，你就能超过GMP了

郭先抢

我也想搞一个类似的计算器，只不过是用来求解专业的问题，最近在看vb的书籍，学习是很重要的， 但是我却是一个菜鸟，对很多东西都不懂！