ref: 2459e34d77e2e21ef829c0dfaafd99433899494f
dir: /appl/math/pi.b/
implement Pi;
include "sys.m";
sys: Sys;
include "draw.m";
include "math.m";
math: Math;
log: import math;
include "daytime.m";
daytime: Daytime;
LBASE: con 3; # 4
BASE: con 1000; # 10000
stderr: ref Sys->FD;
# spawn process for each series ?
Pi: module
{
init: fn(nil: ref Draw->Context, argv: list of string);
};
init(nil: ref Draw->Context, argv: list of string)
{
sys = load Sys Sys->PATH;
math = load Math Math->PATH;
daytime = load Daytime Daytime->PATH;
stderr = sys->fildes(2);
dp := 1000;
argv = tl argv;
if(argv != nil){
if(tl argv != nil){
picmp(hd argv, hd tl argv);
exit;
}
dp = int hd argv;
}
if(dp <= 0)
exit;
# t1 := daytime->now();
p2 := pi2(dp+1);
# t2 := daytime->now();
prpi(p2);
p1 := pi1(dp+1);
# t3 := daytime->now();
# sys->print("%d %d\n", t2-t1, t3-t2);
if(p1 == nil && p2 == nil)
fatal("too many dp: reduce dp or source base");
else if(p1 == nil)
p1 = p2;
else if(p2 == nil)
p2 = p1;
n1 := len p1;
n2 := len p2;
if(n1 != n2)
fatal(sys->sprint("lens differ %d %d", n1, n2));
f := array[10] of { * => 0 };
for(i := 0; i < n1; i++){
if(p1[i] != p2[i])
fatal(sys->sprint("arrays differ %d/%d: %d %d", i, n1, p1[i], p2[i]));
if(p1[i] < 0 || p1[i] >= BASE)
fatal(sys->sprint("bad array element %d: %d", i, p1[i]));
if(0){
p := p1[i];
for(j := 0; j < LBASE; j++){
f[p%10]++;
p /= 10;
}
}
}
# prpi(p1);
if(0){
t := 0;
for(i = 0; i < 10; i++){
sys->print("%d %d\n", i, f[i]);
t += f[i];
}
sys->print("T %d\n", t);
}
}
terms(dp: int, f: int, v: int): (int, int)
{
p := dp;
t := 0;
for(;;){
t = 2 + int ((real p*log(real 10)+log(real v))/log(real f));
if(!(t&1))
t++;
e := int (log(real (v*(t+1)/2))/log(real 10))+1;
if(dp <= p-e)
break;
p += e;
}
# sys->fprint(stderr, "dp=%d p=%d f=%d v=%d terms=%d\n", dp, p, f, v, t);
if(t < f*f)
k := f*f;
else
k = t;
m := BASE*k;
if(m < 0 || m < BASE || m < k || m/BASE != k || m/k != BASE)
return (-1, -1);
return (t, p);
}
prpi(p: array of int)
{
n := len p;
sys->print("π ≅ ");
m := BASE/10;
sys->print("%d.%.*d", p[0]/m, LBASE-1, p[0]%m);
for(i := 1; i < n; i++)
sys->print("%.*d", LBASE, p[i]);
sys->print("\n");
}
memcmp(b1: array of byte, b2: array of byte, n: int): (int, int, int)
{
for(i := 0; i < n; i++)
if(b1[i] != b2[i])
return (i, int b1[i], int b2[i]);
return (-1, 0, 0);
}
picmp(f1: string, f2: string)
{
fd1 := sys->open(f1, Sys->OREAD);
fd2 := sys->open(f2, Sys->OREAD);
if(fd1 == nil || fd2 == nil)
fatal(sys->sprint("cannot open %s or %s", f1, f2));
b1 := array[Sys->ATOMICIO] of byte;
b2 := array[Sys->ATOMICIO] of byte;
t := 0;
shouldexit := 0;
for(;;){
n1 := sys->read(fd1, b1, len b1);
n2 := sys->read(fd2, b2, len b2);
if(n1 <= 0 || n2 <= 0)
return;
if(shouldexit)
fatal("bad picmp");
if(n1 < n2)
(d, v1, v2) := memcmp(b1, b2, n1);
else
(d, v1, v2) = memcmp(b1, b2, n2);
if(d >= 0){
if(v1 == '\n' || v2 == '\n')
shouldexit = 1;
else
fatal(sys->sprint("%s %s differ at byte %d(%c %c)", f1, f2, t+d, v1, v2));
}
t += n1;
if(n1 != n2)
shouldexit = 1;
}
}
roundup(n: int, m: int): (int, int)
{
r := m*((n+m-1)/m);
return (r, r/m);
}
pi1(dp: int): array of int
{
fs := array[2] of { 5, 239 };
vs := array[2] of { 16, 4 };
ss := array[2] of { 1, -1 };
# sys->fprint(stderr, "π1\n");
return pi(dp, fs, vs, ss);
}
pi2(dp: int): array of int
{
fs := array[3] of { 18, 57, 239 };
vs := array[3] of { 48, 32, 20 };
ss := array[3] of { 1, 1, -1 };
# sys->fprint(stderr, "π2\n");
return pi(dp, fs, vs, ss);
}
pi3(dp: int): array of int
{
fs := array[4] of { 57, 239, 682, 12943 };
vs := array[4] of { 176, 28, 48, 96 };
ss := array[4] of { 1, 1, -1, 1 };
# sys->fprint(stderr, "π3\n");
return pi(dp, fs, vs, ss);
}
pi(dp: int, fs: array of int, vs: array of int, ss: array of int): array of int
{
k := len fs;
n := cn := adp := 0;
(dp, n) = roundup(dp, LBASE);
cdp := dp;
m := array[k] of int;
for(i := 0; i < k; i++){
(m[i], adp) = terms(dp+1, fs[i], vs[i]);
if(m[i] < 0)
return nil;
if(adp > cdp)
cdp = adp;
}
(cdp, cn) = roundup(cdp, LBASE);
a := array[cn] of int;
p := array[cn] of int;
for(i = 0; i < cn; i++)
p[i] = 0;
for(i = 0; i < k; i++){
series(m[i], cn, fs[i], (vs[i]*BASE)/10, ss[i], a, p);
# sys->fprint(stderr, "term %d done\n", i+1);
}
return p[0: n];
}
series(m: int, n: int, f: int, v: int, s: int, a: array of int, p: array of int)
{
i, j, k, q, r, r1, r2, n0: int;
v *= f;
f *= f;
for(j = 0; j < n; j++)
a[j] = 0;
a[0] = v;
if(s == 1)
series1(m, n, f, v, a, p);
else
series2(m, n, f, v, a, p);
return;
# following code now split
n0 = 0; # reaches n when very close to m so no check needed
for(i = 1; i <= m; i += 2){
r1 = r2 = 0;
for(j = n0; j < n; j++){
v = a[j]+r1;
q = v/f;
r1 = (v-q*f)*BASE;
a[j] = q;
v = q+r2;
q = v/i;
r2 = (v-q*i)*BASE;
for(k = j; q > 0; k--){
r = p[k]+s*q;
if(r >= BASE){
p[k] = r-BASE;
q = 1;
}
else if(r < 0){
p[k] = r+BASE;
q = 1;
}
else{
p[k] = r;
q = 0;
}
}
}
for(j = n0; j < n; j++){
if(a[j] == 0)
n0++;
else
break;
}
s = -s;
}
}
series1(m: int, n: int, f: int, v: int, a: array of int, p: array of int)
{
i, j, k, q, r, r1, r2, n0: int;
n0 = 0;
for(i = 1; i <= m; i += 2){
r1 = r2 = 0;
for(j = n0; j < n; j++){
v = a[j]+r1;
q = v/f;
r1 = (v-q*f)*BASE;
a[j] = q;
v = q+r2;
q = v/i;
r2 = (v-q*i)*BASE;
for(k = j; q > 0; k--){
r = p[k]+q;
if(r >= BASE){
p[k] = r-BASE;
q = 1;
}
else{
p[k] = r;
q = 0;
}
}
}
for(j = n0; j < n; j++){
if(a[j] == 0)
n0++;
else
break;
}
i += 2;
r1 = r2 = 0;
for(j = n0; j < n; j++){
v = a[j]+r1;
q = v/f;
r1 = (v-q*f)*BASE;
a[j] = q;
v = q+r2;
q = v/i;
r2 = (v-q*i)*BASE;
for(k = j; q > 0; k--){
r = p[k]-q;
if(r < 0){
p[k] = r+BASE;
q = 1;
}
else{
p[k] = r;
q = 0;
}
}
}
for(j = n0; j < n; j++){
if(a[j] == 0)
n0++;
else
break;
}
}
}
series2(m: int, n: int, f: int, v: int, a: array of int, p: array of int)
{
i, j, k, q, r, r1, r2, n0: int;
n0 = 0;
for(i = 1; i <= m; i += 2){
r1 = r2 = 0;
for(j = n0; j < n; j++){
v = a[j]+r1;
q = v/f;
r1 = (v-q*f)*BASE;
a[j] = q;
v = q+r2;
q = v/i;
r2 = (v-q*i)*BASE;
for(k = j; q > 0; k--){
r = p[k]-q;
if(r < 0){
p[k] = r+BASE;
q = 1;
}
else{
p[k] = r;
q = 0;
}
}
}
for(j = n0; j < n; j++){
if(a[j] == 0)
n0++;
else
break;
}
i += 2;
r1 = r2 = 0;
for(j = n0; j < n; j++){
v = a[j]+r1;
q = v/f;
r1 = (v-q*f)*BASE;
a[j] = q;
v = q+r2;
q = v/i;
r2 = (v-q*i)*BASE;
for(k = j; q > 0; k--){
r = p[k]+q;
if(r >= BASE){
p[k] = r-BASE;
q = 1;
}
else{
p[k] = r;
q = 0;
}
}
}
for(j = n0; j < n; j++){
if(a[j] == 0)
n0++;
else
break;
}
}
}
fatal(e: string)
{
sys->print("%s\n", e);
exit;
}