262 lines
10 KiB
ArmAsm
262 lines
10 KiB
ArmAsm
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; -*- Mode: Lisp -*- Filename: pmath.s
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; Last Revision: 12-Sep-85 1930ct
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;--------------------------------------------------------------------------;
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; ;
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; TI SCHEME -- PCS Compiler ;
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; Copyright 1985 (c) Texas Instruments ;
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; ;
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; Clyde R. Camp, David Bartley, ;
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; Mark Meyer, John Gateley ;
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; ;
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; Extended Arithmetic Routines ;
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; ;
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;--------------------------------------------------------------------------;
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(define exact? ; EXACT?
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(lambda (n)
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#!false))
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(define inexact? ; INEXACT?
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(lambda (n)
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#!true))
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(begin
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(define acos)
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(define asin)
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(define atan)
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(define cos)
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(define exp)
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(define expt)
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(define log)
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(define sin)
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(define sqrt)
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(define tan)
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(define pi)
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)
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(letrec
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(( *pi* 3.141592653589793) ; pi
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( *pi/2* (/ *pi* 2)) ; pi/2
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( *2pi* (+ *pi* *pi*)) ; 2pi
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( *e* 2.718281828459045) ; e
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(%bad-argument
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(lambda (name arg)
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(%error-invalid-operand name arg)))
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(signum
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(lambda (x)
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(cond ((negative? x) -1)
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((positive? x) 1)
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(else 0))))
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(power-loop
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(lambda (x n a) ; A is initially 1, N is non-negative
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(if (zero? n)
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a
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(power-loop (* x x)
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(quotient n 2)
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(if (odd? n) (* a x) a)))))
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(pcs-series
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(lambda (x y z)
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(if (null? y)
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z
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(pcs-series x (cdr y) (- 1.0 (* (/ x (car y)) z))))))
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(fact-series
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(lambda (x n result)
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(if (zero? n)
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result
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(fact-series x (- n 1) (+ 1 (* (/ x n) result))))))
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)
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(begin
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(set! sqrt
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(letrec ((loop (lambda (x gx)
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(let ((ngx (* 0.5 (+ gx (/ x gx)))))
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(if (>? (/ (abs (- ngx gx)) gx) 5e-15)
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(loop x ngx)
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ngx)))))
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(named-lambda (sqrt x)
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(if (or (not (number? x)) (negative? x))
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(%bad-argument 'SQRT x)
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(let ((x (float x)))
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(if (zero? x)
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x
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(cond ((>? x 1.0e10)(* 1.0e5 (sqrt (* x 1.0e-10))))
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((<? x 1.0e-10)(* 1.0e-5 (sqrt (* x 1.0e10))))
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(else (loop x 1.0)))))))))
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(set! sin
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(lambda (x)
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(if (not (number? x))
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(%bad-argument 'SIN x)
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(begin
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(set! x (/ x *2pi*))
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(set! x (* *2pi* (- x (truncate x))))
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(when (>? x *pi*)
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(set! x (- x *2pi*)))
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(if (>? x *pi/2*)
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(set! x (- *pi* x))
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(when (<? x (- *pi/2*))
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(set! x (- (+ *pi* x)))))
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; Now X lies in the interval [-pi/2, pi/2]
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(let ((term x)
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(x2 (* x x))
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(lim (ceiling (+ 12 (abs (* x 8))))))
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(let ((ssum (do ((sum x (+ sum term))
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(n 2 (+ n 2)))
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((>=? n lim) (+ sum term))
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(set! term (- (/ (* term x2)
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(* n (+ n 1)))))) ))
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; The following limits (sin x) to +/- 1
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; without it result can be 1.0 + 1e-18
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; which blows up ASIN
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(cond ((>? ssum 1.0) 1.0)
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((<? ssum -1.0) -1.0)
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(else ssum)) ) )))))
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(set! cos
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(lambda (x)
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(if (not (number? x))
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(%bad-argument 'COS x)
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(sin (+ x *pi/2*)))))
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(set! tan
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(lambda (x)
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(if (not (number? x))
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(%bad-argument 'TAN x)
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(let ((y (sin x))
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(z (cos x)))
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(if (zero? z)
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(%bad-argument 'TAN x)
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(/ y z))))))
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(set! atan
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(named-lambda (atan y . z)
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(if (not (number? y))
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(%bad-argument 'ATAN y)
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(letrec ((loop (lambda (y k)
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(if (=? k 10)
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0.0
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(/ (* y k k)
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(+ 1 k k (loop y (+ k 1)) ))))) )
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(if (null? z)
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(cond ((negative? y)
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(minus (atan (minus y))))
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((>? y 1.0)
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(- *pi/2* (atan (/ 1.0 y))))
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(else
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(/ y (+ 1 (loop (* y y) 1)))))
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(let ((x (car z)))
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(cond ((not (number? x))
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(%bad-argument 'ATAN x))
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((zero? x)
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(cond ((zero? y)
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(%bad-argument 'ATAN
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x))
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((negative? y)
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(minus *pi/2*))
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(else *pi/2*)))
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((zero? y)
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(if (positive? x) 0.0 *pi*))
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((positive? y)
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(if (>? x 0)
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(atan (/ y x))
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(- *pi/2* (atan (/ x y)))))
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((and (<? x 0)
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(<? y 0))
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(minus (- *pi* (atan (/ y x)))))
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(else
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(minus (+ *pi/2* (atan (/ x y)))))) )
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)))))
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(set! acos
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(lambda (x)
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(if (or (not (number? x))
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(>? (abs x) 1.0))
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(%bad-argument 'ACOS x)
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(atan (sqrt (- 1.0 (* x x))) x))))
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(set! pi *pi*)
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(set! asin
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(lambda (x)
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(if (or (not (number? x))
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(>? (abs x) 1.0))
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(%bad-argument 'ASIN x)
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(atan x (sqrt (- 1.0 (* x x)))))))
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(set! log
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(named-lambda (log x . base)
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(letrec
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((ln (lambda (x)
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(cond ((=? x 1) 0)
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((<? x 1.0) (minus (ln (/ x))))
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((>? x *e*) (1+ (ln (/ x *e*))))
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(else (let ((y (/ (-1+ x) (1+ x))))
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(* (pcs-series (* y y)
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'(-1.0952380952381
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-1.10526315789474
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-1.11764705882353
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-1.33333333333333
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-1.15384615384615
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-1.18181818181818
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-1.22222222222222
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-1.28571428571429
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-1.4
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-1.66666666666667
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-3.0)
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1.0)
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(+ y y)))) ))))
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(if (or (not (number? x)) (<=? x 0))
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(%bad-argument 'LOG x)
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(let ((lnx (ln x)))
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(if (null? base)
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lnx
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(let ((non-e-base (car base)))
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(if (or (not (number? non-e-base))
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(not (positive? non-e-base)))
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(%bad-argument 'LOG non-e-base)
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(/ lnx (log non-e-base))))))))))
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(set! exp
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(named-lambda (exp x)
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(cond ((not (number? x))
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(%bad-argument 'EXP x))
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((zero? x) 1.0)
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((negative? x) (/ (exp (- x))))
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((integer? x) (power-loop *e* x 1))
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(else
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(let* ((q (truncate x))
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(p (- x q)))
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(* (power-loop *e* q 1)
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(fact-series p 12 1)))))))
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(set! expt
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(named-lambda (expt a x)
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(cond ((not (number? a))
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(%bad-argument 'EXPT a))
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((not (number? x))
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(%bad-argument 'EXPT x))
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((and (zero? a) (zero? x) (not (integer? x)))
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(%bad-argument 'EXPT x))
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((zero? x) (if (integer? a) 1 1.0))
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((negative? x) (/ (expt a (minus x))))
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((integer? x) (power-loop a x 1))
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(else
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(let* ((z (* x (log (abs a))))
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(q (truncate z))
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(p (- z q)))
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(* (if (negative? q)
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(/ (power-loop *e* (minus q) 1))
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(power-loop *e* q 1))
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(signum a)
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(fact-series p 12 1))))) ))
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))
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