前陣子 Adobe 和 Google 聯手各自用不同的名字釋出了一款新的中文黑體字形，Source Han Sans 思源黑體，也叫做 Noto Sans (反腐字？)。開心試用之後，把系統字形都換過來，也開始想要怎麼樣才可以達到最佳的顯示效果，尤其是 Adobe 和 Google 曾經給 FreeType 貢獻了 CFF 字形引擎的改進，思源黑體也是以 CFF 技術設計，終於可以試試看中文的效果怎麼樣了啊！
PUSHB[000] # Push one byte onto the stack.
3 # Value for loop variable.
SLOOP[] # Set the loop count to 3.
PUSHB[002] # Push three bytes onto the stack.
5 # Point number.
46 # Point number.
43 # Point number.
ALIGNRP[] # Align the points 5, 46 and 43 with rp0 (point 8). This will
# align the height of the two lower serifs.
有人問說：那為什麼不乾脆隨時打開 Hinting 就好？據我所知目前的自由 PDF Viewer 都是預設關閉 Hinting 的，除了上述的理由外，我猜大概是因為 Hinting 有可能大幅度的改變一個字符的寬度，如下圖：
可以發現三種顯示方式的寬度都不一樣，而 PDF 是一種接近印刷品質的檔案格 式，有可能在輸出 PDF 的時候已經丟失動態改變寬度的能力，kern 的修正也已 經沒辦法修改，這時候如過還讓 Hinting 去改變字符的寬度的話，很有可能得到 不理想的結果。不過以上只是我的猜想，還沒有找各 PDF Viewer 的作者證實。 至於封閉的商業 PDF Viewer 又是怎麼做的就更不得而知了。
結論：快升級到最新的 FreeType 吧！如果還有遇到顯示錯誤的 PDF 可以寄給 我，如果以上筆記有疏漏錯誤的地方歡迎指正 ?
#include <stdio.h>
#include <math.h>
int factorCount (long n)
{
double square = sqrt (n);
int isquare = (int) square;
int count = isquare == square ? -1 : 0;
long candidate;
for (candidate = 1; candidate <= isquare; candidate ++)
if (0 == n % candidate) count += 2;
return count;
}
int main ()
{
long triangle = 1;
int index = 1;
while (factorCount (triangle) < 1001)
{
index ++;
triangle += index;
}
printf ("%ld\n", triangle);
}
我的執行時間約為 5.48s
% gcc -lm -o euler12.bin euler12.c
% time ./euler12.bin
842161320
./euler12.bin 5.48s user 0.00s system 99% cpu 5.484 total
手癢想看看據說可以編譯出不錯的機器碼的 Common Lisp 速度怎麼樣，於是第 一個版本如下 (用 sbcl 執行)：
(defun factor-count (n)
(let* ((square (sqrt n))
(squaref (floor square))
(count (if (eql squaref square) -1 0)))
(loop
for cand from 1 to squaref
count (eql 0 (rem n cand)) into c
finally (return (+ count c c)))))
(defun first-triangle-over (n)
(loop
for idx from 1
sum idx into triangle
until (>= (factor-count triangle) n)
finally (return triangle)))
;; (time (first-triangle-over 1000))
;; Evaluation took:
;; 11.192 seconds of real time
;; 11.184699 seconds of total run time (11.184699 user, 0.000000 system)
;; 99.94% CPU
;; 30,135,882,489 processor cycles
;; 32,912 bytes consed
;;
;; 842161320
還不錯，11.192s，這個版本採用原文中給 haskell 的建議，使用 rem 而不是 mod，可以 加快一點速度。再給一點關於型別的提示，然後把第一個 function inline，第 二版可以跑出和 C 版本差不多的成績 5.563s 🙂
(declaim (inline factor-count)) ;; <----
(defun factor-count (n)
(let* ((square (sqrt n))
(squaref (floor square))
(count (if (eql squaref square) -1 0)))
(loop
for cand from 1 to squaref
count (eql 0 (rem n cand)) into c
finally (return (+ count c c)))))
(defun first-triangle-over (n)
(loop
for idx of-type fixnum from 1 ;; <----
sum idx into triangle of-type fixnum ;; <----
until (>= (factor-count triangle) n)
finally (return triangle)))
;; (time (first-triangle-over 1000))
;; Evaluation took:
;; 5.563 seconds of real time
;; 5.556347 seconds of total run time (5.556347 user, 0.000000 system)
;; 99.87% CPU
;; 14,970,270,903 processor cycles
;; 32,768 bytes consed
;;
;; 842161320
Let us change our traditional attitude to the construction of programs: Instead of imagining that our main task is to instruct a computer what to do, let us concentrate rather on explaining to human beings what we want a computer to do.
<<分割欄位>>=
txt_field_lines = [line.split() for line in lines]
@
這篇 blog 經過 notangle 的處理，會變成以下的 python 程式：
# notangle -R'接受字串的 function' literate-programming.mdwn
def mul_n_sum(data):
lines = data.strip().split('\n')
txt_field_lines = [line.split() for line in lines]
field_lines = [[int(field1), int(field2)] for field1, field2 in txt_field_lines]
return sum([field1 * field2 for field1, field2 in field_lines])
