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generate-ten-powers.scm
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generate-ten-powers.scm
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;; Copyright 2010 the V8 project authors. All rights reserved.
;; Redistribution and use in source and binary forms, with or without
;; modification, are permitted provided that the following conditions are
;; met:
;;
;; * Redistributions of source code must retain the above copyright
;; notice, this list of conditions and the following disclaimer.
;; * Redistributions in binary form must reproduce the above
;; copyright notice, this list of conditions and the following
;; disclaimer in the documentation and/or other materials provided
;; with the distribution.
;; * Neither the name of Google Inc. nor the names of its
;; contributors may be used to endorse or promote products derived
;; from this software without specific prior written permission.
;;
;; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
;; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
;; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
;; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
;; OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
;; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
;; LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
;; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
;; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
;; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
;; OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
;; This is a Scheme script for the Bigloo compiler. Bigloo must be compiled with
;; support for bignums. The compilation of the script can be done as follows:
;; bigloo -static-bigloo -o generate-ten-powers generate-ten-powers.scm
;;
;; Generate approximations of 10^k.
(module gen-ten-powers
(static (class Cached-Fast
v::bignum
e::bint
exact?::bool))
(main my-main))
;;----------------bignum shifts -----------------------------------------------
(define (bit-lshbx::bignum x::bignum by::bint)
(if (<fx by 0)
#z0
(*bx x (exptbx #z2 (fixnum->bignum by)))))
(define (bit-rshbx::bignum x::bignum by::bint)
(if (<fx by 0)
#z0
(/bx x (exptbx #z2 (fixnum->bignum by)))))
;;----------------the actual power generation -------------------------------
;; e should be an indication. it might be too small.
(define (round-n-cut n e nb-bits)
(define max-container (- (bit-lshbx #z1 nb-bits) 1))
(define (round n)
(case *round*
((down) n)
((up)
(+bx n
;; with the -1 it will only round up if the cut off part is
;; non-zero
(-bx (bit-lshbx #z1
(-fx (+fx e nb-bits) 1))
#z1)))
((round)
(+bx n
(bit-lshbx #z1
(-fx (+fx e nb-bits) 2))))))
(let* ((shift (-fx (+fx e nb-bits) 1))
(cut (bit-rshbx (round n) shift))
(exact? (=bx n (bit-lshbx cut shift))))
(if (<=bx cut max-container)
(values cut e exact?)
(round-n-cut n (+fx e 1) nb-bits))))
(define (rounded-/bx x y)
(case *round*
((down) (/bx x y))
((up) (+bx (/bx x y) #z1))
((round) (let ((tmp (/bx (*bx #z2 x) y)))
(if (zerobx? (remainderbx tmp #z2))
(/bx tmp #z2)
(+bx (/bx tmp #z2) #z1))))))
(define (generate-powers from to mantissa-size)
(let* ((nb-bits mantissa-size)
(offset (- from))
(nb-elements (+ (- from) to 1))
(vec (make-vector nb-elements))
(max-container (- (bit-lshbx #z1 nb-bits) 1)))
;; the negative ones. 10^-1, 10^-2, etc.
;; We already know, that we can't be exact, so exact? will always be #f.
;; Basically we will have a ten^i that we will *10 at each iteration. We
;; want to create the matissa of 1/ten^i. However the mantissa must be
;; normalized (start with a 1). -> we have to shift the number.
;; We shift by multiplying with two^e. -> We encode two^e*(1/ten^i) ==
;; two^e/ten^i.
(let loop ((i 1)
(ten^i #z10)
(two^e #z1)
(e 0))
(unless (< (- i) from)
(if (>bx (/bx (*bx #z2 two^e) ten^i) max-container)
;; another shift would make the number too big. We are
;; hence normalized now.
(begin
(vector-set! vec (-fx offset i)
(instantiate::Cached-Fast
(v (rounded-/bx two^e ten^i))
(e (negfx e))
(exact? #f)))
(loop (+fx i 1) (*bx ten^i #z10) two^e e))
(loop i ten^i (bit-lshbx two^e 1) (+fx e 1)))))
;; the positive ones 10^0, 10^1, etc.
;; start with 1.0. mantissa: 10...0 (1 followed by nb-bits-1 bits)
;; -> e = -(nb-bits-1)
;; exact? is true when the container can still hold the complete 10^i
(let loop ((i 0)
(n (bit-lshbx #z1 (-fx nb-bits 1)))
(e (-fx 1 nb-bits)))
(when (<= i to)
(receive (cut e exact?)
(round-n-cut n e nb-bits)
(vector-set! vec (+fx i offset)
(instantiate::Cached-Fast
(v cut)
(e e)
(exact? exact?)))
(loop (+fx i 1) (*bx n #z10) e))))
vec))
(define (print-c powers from to struct-type
cache-name max-distance-name offset-name macro64)
(define (display-power power k)
(with-access::Cached-Fast power (v e exact?)
(let ((tmp-p (open-output-string)))
;; really hackish way of getting the digits
(display (format "~x" v) tmp-p)
(let ((str (close-output-port tmp-p)))
(printf " {~a(0x~a, ~a), ~a, ~a},\n"
macro64
(substring str 0 8)
(substring str 8 16)
e
k)))))
(define (print-powers-reduced n)
(print "static const " struct-type " " cache-name
"(" n ")"
"[] = {")
(let loop ((i 0)
(nb-elements 0)
(last-e 0)
(max-distance 0))
(cond
((>= i (vector-length powers))
(print " };")
(print "static const int " max-distance-name "(" n ") = "
max-distance ";")
(print "// nb elements (" n "): " nb-elements))
(else
(let* ((power (vector-ref powers i))
(e (Cached-Fast-e power)))
(display-power power (+ i from))
(loop (+ i n)
(+ nb-elements 1)
e
(cond
((=fx i 0) max-distance)
((> (- e last-e) max-distance) (- e last-e))
(else max-distance))))))))
(print "// Copyright 2010 the V8 project authors. All rights reserved.")
(print "// ------------ GENERATED FILE ----------------")
(print "// command used:")
(print "// "
(apply string-append (map (lambda (str)
(string-append " " str))
*main-args*))
" // NOLINT")
(print)
(print
"// This file is intended to be included inside another .h or .cc files\n"
"// with the following defines set:\n"
"// GRISU_CACHE_STRUCT: should expand to the name of a struct that will\n"
"// hold the cached powers of ten. Each entry will hold a 64-bit\n"
"// significand, a 16-bit signed binary exponent, and a 16-bit\n"
"// signed decimal exponent. Each entry will be constructed as follows:\n"
"// { significand, binary_exponent, decimal_exponent }.\n"
"// GRISU_CACHE_NAME(i): generates the name for the different caches.\n"
"// The parameter i will be a number in the range 1-20. A cache will\n"
"// hold every i'th element of a full cache. GRISU_CACHE_NAME(1) will\n"
"// thus hold all elements. The higher i the fewer elements it has.\n"
"// Ideally the user should only reference one cache and let the\n"
"// compiler remove the unused ones.\n"
"// GRISU_CACHE_MAX_DISTANCE(i): generates the name for the maximum\n"
"// binary exponent distance between all elements of a given cache.\n"
"// GRISU_CACHE_OFFSET: is used as variable name for the decimal\n"
"// exponent offset. It is equal to -cache[0].decimal_exponent.\n"
"// GRISU_UINT64_C: used to construct 64-bit values in a platform\n"
"// independent way. In order to encode 0x123456789ABCDEF0 the macro\n"
"// will be invoked as follows: GRISU_UINT64_C(0x12345678,9ABCDEF0).\n")
(print)
(print-powers-reduced 1)
(print-powers-reduced 2)
(print-powers-reduced 3)
(print-powers-reduced 4)
(print-powers-reduced 5)
(print-powers-reduced 6)
(print-powers-reduced 7)
(print-powers-reduced 8)
(print-powers-reduced 9)
(print-powers-reduced 10)
(print-powers-reduced 11)
(print-powers-reduced 12)
(print-powers-reduced 13)
(print-powers-reduced 14)
(print-powers-reduced 15)
(print-powers-reduced 16)
(print-powers-reduced 17)
(print-powers-reduced 18)
(print-powers-reduced 19)
(print-powers-reduced 20)
(print "static const int GRISU_CACHE_OFFSET = " (- from) ";"))
;;----------------main --------------------------------------------------------
(define *main-args* #f)
(define *mantissa-size* #f)
(define *dest* #f)
(define *round* #f)
(define *from* #f)
(define *to* #f)
(define (my-main args)
(set! *main-args* args)
(args-parse (cdr args)
(section "Help")
(("?") (args-parse-usage #f))
((("-h" "--help") (help "?, -h, --help" "This help message"))
(args-parse-usage #f))
(section "Misc")
(("-o" ?file (help "The output file"))
(set! *dest* file))
(("--mantissa-size" ?size (help "Container-size in bits"))
(set! *mantissa-size* (string->number size)))
(("--round" ?direction (help "Round bignums (down, round or up)"))
(set! *round* (string->symbol direction)))
(("--from" ?from (help "start at 10^from"))
(set! *from* (string->number from)))
(("--to" ?to (help "go up to 10^to"))
(set! *to* (string->number to)))
(else
(print "Illegal argument `" else "'. Usage:")
(args-parse-usage #f)))
(when (not *from*)
(error "generate-ten-powers"
"Missing from"
#f))
(when (not *to*)
(error "generate-ten-powers"
"Missing to"
#f))
(when (not *mantissa-size*)
(error "generate-ten-powers"
"Missing mantissa size"
#f))
(when (not (memv *round* '(up down round)))
(error "generate-ten-powers"
"Missing round-method"
*round*))
(let ((dividers (generate-powers *from* *to* *mantissa-size*))
(p (if (not *dest*)
(current-output-port)
(open-output-file *dest*))))
(unwind-protect
(with-output-to-port p
(lambda ()
(print-c dividers *from* *to*
"GRISU_CACHE_STRUCT" "GRISU_CACHE_NAME"
"GRISU_CACHE_MAX_DISTANCE" "GRISU_CACHE_OFFSET"
"GRISU_UINT64_C"
)))
(if *dest*
(close-output-port p)))))