--- /dev/null
+(in-package #:strictmath)
+; This file is taken from part of Evita Common Lisp.
+;
+; Copyright (C) 1996-2007 by Project Vogue.
+; Written by Yoshifumi "VOGUE" INOUE. (yosi@msn.com)
+;
+; Before that, it was based off of fdlibm
+;
+; See fdlibm (http://www.netlib.org/fdlibm/)
+; See http://sources.redhat.com/newlib/
+;
+; *
+; From fdlibm (http://www.netlib.org/fdlibm/)
+; See http://sources.redhat.com/newlib/
+;
+; /* @(#)e_rem_pio2.c 5.1 93/09/24 *
+; /*
+; * ====================================================
+; * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+; *
+; * Developed at SunPro, a Sun Microsystems, Inc. business.
+; * Permission to use, copy, modify, and distribute this
+; * software is freely granted, provided that this notice
+; * is preserved.
+; * ====================================================
+; *
+; *
+;
+; * __ieee754_rem_pio2(x,y)
+; *
+; * return the remainder of x rem pi/2 in y[0]+y[1]
+; * use __kernel_rem_pio2()
+; *
+
+;;; Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
+(defparameter +two-over-pi+
+ (make-array 66 :element-type '(unsigned-byte 32)
+ :initial-contents
+ #(#xA2F983 #x6E4E44 #x1529FC #x2757D1 #xF534DD #xC0DB62
+ #x95993C #x439041 #xFE5163 #xABDEBB #xC561B7 #x246E3A
+ #x424DD2 #xE00649 #x2EEA09 #xD1921C #xFE1DEB #x1CB129
+ #xA73EE8 #x8235F5 #x2EBB44 #x84E99C #x7026B4 #x5F7E41
+ #x3991D6 #x398353 #x39F49C #x845F8B #xBDF928 #x3B1FF8
+ #x97FFDE #x05980F #xEF2F11 #x8B5A0A #x6D1F6D #x367ECF
+ #x27CB09 #xB74F46 #x3F669E #x5FEA2D #x7527BA #xC7EBE5
+ #xF17B3D #x0739F7 #x8A5292 #xEA6BFB #x5FB11F #x8D5D08
+ #x560330 #x46FC7B #x6BABF0 #xCFBC20 #x9AF436 #x1DA9E3
+ #x91615E #xE61B08 #x659985 #x5F14A0 #x68408D #xFFD880
+ #x4D7327 #x310606 #x1556CA #x73A8C9 #x60E27B #xC08C6B)))
+
+(defparameter +npio2-hw+
+ (make-array 32 :element-type '(unsigned-byte 32)
+ :initial-contents
+ #(#x3FF921FB #x400921FB #x4012D97C #x401921FB #x401F6A7A #x4022D97C
+ #x4025FDBB #x402921FB #x402C463A #x402F6A7A #x4031475C #x4032D97C
+ #x40346B9C #x4035FDBB #x40378FDB #x403921FB #x403AB41B #x403C463A
+ #x403DD85A #x403F6A7A #x40407E4C #x4041475C #x4042106C #x4042D97C
+ #x4043A28C #x40446B9C #x404534AC #x4045FDBB #x4046C6CB #x40478FDB
+ #x404858EB #x404921FB)))
+
+;
+;
+; invpio2: 53 bits of 2/pi
+; pio2_1: first 33 bit of pi/2
+; pio2_1t: pi/2 - pio2_1
+; pio2_2: second 33 bit of pi/2
+; pio2_2t: pi/2 - (pio2_1+pio2_2)
+; pio2_3: third 33 bit of pi/2
+; pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
+;
+;
+
+(defun float64-rem-pio2-small (x ix hx)
+ (prog*
+ ((pio2_1 #+nil 1.57079632673412561417e+00 #.(encode-float64 #x3FF921FB #x54400000))
+ (pio2_1t #+nil 6.07710050650619224932e-11 #.(encode-float64 #x3DD0B461 #x1A626331))
+ (pio2_2 #+nil 6.07710050630396597660e-11 #.(encode-float64 #x3DD0B461 #x1A600000))
+ (pio2_2t #+nil 2.02226624879595063154e-21 #.(encode-float64 #x3BA3198A #x2E037073)))
+ (if (> hx 0)
+ (let ((z (- x pio2_1)))
+ (if (not (eql ix #x3ff921fb))
+ ;; 33+53 bit pi is good enough
+ (let*
+ ((y0 (- z pio2_1t))
+ (y1 (- (- z y0) pio2_1t)))
+ (return (values 1 y0 y1)))
+ ;; near pi/2, use 33+33+53 bit pi *
+ (let*
+ ((z (- z pio2_2))
+ (y0 (- z pio2_2t))
+ (y1 (- (- z y0) pio2_2t)))
+ (return (values 1 y0 y1)))))
+ ;; negative x
+ (let
+ ((z (+ x pio2_1)))
+ (if (not (eql ix #x3ff921fb))
+ ;; 33+53 bit pi is good enough
+ (let*
+ ((y0 (+ z pio2_1t))
+ (y1 (+ (- z y0) pio2_1t)))
+ (return (values -1 y0 y1)))
+ ;; near pi/2, use 33+33+53 bit pi
+ (let*
+ ((z (+ z pio2_2))
+ (y0 (+ z pio2_2t))
+ (y1 (+ (- z y0) pio2_2t)))
+ (return (values -1 y0 y1))))))))
+
+(defun float64-rem-pio2-medium (x ix hx)
+ (prog*
+ ((half #+nil 5.00000000000000000000e-01 #.(encode-float64 #x3FE00000 #x00000000))
+ (invpio2 #+nil 6.36619772367581382433e-01 #.(encode-float64 #x3FE45F30 #x6DC9C883))
+ (pio2_1 #+nil 1.57079632673412561417e+00 #.(encode-float64 #x3FF921FB #x54400000))
+ (pio2_1t #+nil 6.07710050650619224932e-11 #.(encode-float64 #x3DD0B461 #x1A626331))
+ (pio2_2 #+nil 6.07710050630396597660e-11 #.(encode-float64 #x3DD0B461 #x1A600000))
+ (pio2_2t #+nil 2.02226624879595063154e-21 #.(encode-float64 #x3BA3198A #x2E037073))
+ (pio2_3 #+nil 2.02226624871116645580e-21 #.(encode-float64 #x3BA3198A #x2E000000))
+ (pio2_3t #+nil 8.47842766036889956997e-32 #.(encode-float64 #x397B839A #x252049C1)))
+ (let*
+ ((tt (float64-abs x))
+ (n (truncate (+ (* tt invpio2) half)))
+ (fn (float n 0d0))
+ (r (- tt (* fn pio2_1)))
+ (w (* fn pio2_1t)) ; 1st round good to 85 bit *
+ (y0 (- r w)))
+ ;; quick check no cancellation
+ (unless (and (< n 32) (not (eql ix (elt +npio2-hw+ (- n 1)))))
+ (let*
+ ((j (ash ix -20))
+ (high (decode-float64 y0))
+ (i (- j (logand (ash high -20) #x7ff))))
+ ;; 2nd iteration needed, good to 118 *
+ (when (> i 16)
+ (setq tt r)
+ (setq w (* fn pio2_2))
+ (setq r (- tt w))
+ (setq w (- (* fn pio2_2t) (- (- tt r) w)))
+ (setq y0 (- r w))
+ (setq high (decode-float64 y0))
+ (setq i (- j (logand (ash high -20) #x7ff)))
+
+ ;; 3rd iteration need, 151 bits acc *
+ (when (> i 49)
+ (setq tt r) ; will cover all possible cases *
+ (setq w (* fn pio2_3))
+ (setq r (- tt w))
+ (setq w (- (* fn pio2_3t) (- (- tt r) w)))
+ (setq y0 (- r w))))))
+ (let ((y1 (- (- r y0) w)))
+ (if (< hx 0)
+ (return (values (- n) (- y0) (- y1)))
+ (return (values n y0 y1)))))))
+
+(defun float64-rem-pio2 (x)
+ (declare (values fixnum double-float double-float))
+ (declare (type double-float x))
+ (prog
+ ((two24 #+nil 1.67772160000000000000e+07 #.(encode-float64 #x41700000 #x00000000)))
+ (multiple-value-bind (hx lx) (decode-float64 x)
+ (let
+ ((ix (logand hx #x7fffffff)))
+
+ (when (<= ix #x3fe921fb) (return (values 0 x 0d0))) ;; |x| ~<= pi/4 , no need for reduction
+ (when (< ix #x4002d97c) (return (float64-rem-pio2-small x ix hx))) ;; |x| < 3pi/4, special case with n=+-1
+ (when (<= ix #x413921fb) (return (float64-rem-pio2-medium x ix hx))) ;; |x| ~<= 2^19*(pi/2), medium size
+
+ ;; all other (large) arguments
+ (when (>= ix #x7ff00000) ; x is inf or NaN *
+ (let ((nan (- x x))) (return (values 0 nan nan))))
+
+ ;; set z = scalbn(|x|,ilogb(x)-23)
+ (let*
+ ((e0 (- (ash ix -20) 1046)) ;; e0 = ilogb(z)-23
+ (z0 (encode-float64 (- ix (ash e0 20)) lx))
+ (tx0 (float (truncate z0) 0d0))
+ (z1 (* (- z0 tx0) two24))
+ (tx1 (float (truncate z1) 0d0))
+ (z2 (* (- z1 tx1) two24))
+ (tx2 z2))
+ (multiple-value-bind (n y0 y1)
+ (let
+ ((nx
+ (cond ;; skip zero term
+ ((not (zerop tx2)) 3)
+ ((not (zerop tx1)) 2)
+ ((not (zerop tx0)) 1)
+ (t 0))))
+ (let
+ ((tx (make-array 3 :element-type 'double-float)))
+ (setf (elt tx 0) tx0)
+ (setf (elt tx 1) tx1)
+ (setf (elt tx 2) tx2)
+ (float64-kernel-rem-pio2 tx e0 nx 2 +two-over-pi+)))
+ (if (< hx 0)
+ (return (values (- n) (- y0) (- y1)))
+ (return (values n y0 y1)))))))))
projects / clnl / blobdiff