1 ;; Copyright 2010 the V8 project authors. All rights reserved. 2 ;; Redistribution and use in source and binary forms, with or without 3 ;; modification, are permitted provided that the following conditions are 4 ;; met: 5 ;; 6 ;; * Redistributions of source code must retain the above copyright 7 ;; notice, this list of conditions and the following disclaimer. 8 ;; * Redistributions in binary form must reproduce the above 9 ;; copyright notice, this list of conditions and the following 10 ;; disclaimer in the documentation and/or other materials provided 11 ;; with the distribution. 12 ;; * Neither the name of Google Inc. nor the names of its 13 ;; contributors may be used to endorse or promote products derived 14 ;; from this software without specific prior written permission. 15 ;; 16 ;; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 17 ;; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 18 ;; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 19 ;; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 20 ;; OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 21 ;; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 22 ;; LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 23 ;; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 24 ;; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 25 ;; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 26 ;; OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 27 28 ;; This is a Scheme script for the Bigloo compiler. Bigloo must be compiled with 29 ;; support for bignums. The compilation of the script can be done as follows: 30 ;; bigloo -static-bigloo -o generate-ten-powers generate-ten-powers.scm 31 ;; 32 ;; Generate approximations of 10^k. 33 34 (module gen-ten-powers 35 (static (class Cached-Fast 36 v::bignum 37 e::bint 38 exact?::bool)) 39 (main my-main)) 40 41 42 ;;----------------bignum shifts ----------------------------------------------- 43 (define (bit-lshbx::bignum x::bignum by::bint) 44 (if (by 0) 45 #z0 46 (*bx x (exptbx #z2 (fixnum->bignum by))))) 47 48 (define (bit-rshbx::bignum x::bignum by::bint) 49 (if ( by 0) 50 #z0 51 (/bx x (exptbx #z2 (fixnum->bignum by))))) 52 53 ;;----------------the actual power generation ------------------------------- 54 55 ;; e should be an indication. it might be too small. 56 (define (round-n-cut n e nb-bits) 57 (define max-container (- (bit-lshbx #z1 nb-bits) 1)) 58 (define (round n) 59 (case *round* 60 ((down) n) 61 ((up) 62 (+bx n 63 ;; with the -1 it will only round up if the cut off part is 64 ;; non-zero 65 (-bx (bit-lshbx #z1 66 (-fx (+fx e nb-bits) 1)) 67 #z1))) 68 ((round) 69 (+bx n 70 (bit-lshbx #z1 71 (-fx (+fx e nb-bits) 2)))))) 72 (let* ((shift (-fx (+fx e nb-bits) 1)) 73 (cut (bit-rshbx (round n) shift)) 74 (exact? (=bx n (bit-lshbx cut shift)))) 75 (if (<=bx cut max-container) 76 (values cut e exact?) 77 (round-n-cut n (+fx e 1) nb-bits)))) 78 79 (define (rounded-/bx x y) 80 (case *round* 81 ((down) (/bx x y)) 82 ((up) (+bx (/bx x y) #z1)) 83 ((round) (let ((tmp (/bx (*bx #z2 x) y))) 84 (if (zerobx? (remainderbx tmp #z2)) 85 (/bx tmp #z2) 86 (+bx (/bx tmp #z2) #z1)))))) 87 88 (define (generate-powers from to mantissa-size) 89 (let* ((nb-bits mantissa-size) 90 (offset (- from)) 91 (nb-elements (+ (- from) to 1)) 92 (vec (make-vector nb-elements)) 93 (max-container (- (bit-lshbx #z1 nb-bits) 1))) 94 ;; the negative ones. 10^-1, 10^-2, etc. 95 ;; We already know, that we can't be exact, so exact? will always be #f. 96 ;; Basically we will have a ten^i that we will *10 at each iteration. We 97 ;; want to create the matissa of 1/ten^i. However the mantissa must be 98 ;; normalized (start with a 1). -> we have to shift the number. 99 ;; We shift by multiplying with two^e. -> We encode two^e*(1/ten^i) == 100 ;; two^e/ten^i. 101 (let loop ((i 1) 102 (ten^i #z10) 103 (two^e #z1) 104 (e 0)) 105 (unless (< (- i) from) 106 (if (>bx (/bx (*bx #z2 two^e) ten^i) max-container) 107 ;; another shift would make the number too big. We are 108 ;; hence normalized now. 109 (begin 110 (vector-set! vec (-fx offset i) 111 (instantiate::Cached-Fast 112 (v (rounded-/bx two^e ten^i)) 113 (e (negfx e)) 114 (exact? #f))) 115 (loop (+fx i 1) (*bx ten^i #z10) two^e e)) 116 (loop i ten^i (bit-lshbx two^e 1) (+fx e 1))))) 117 ;; the positive ones 10^0, 10^1, etc. 118 ;; start with 1.0. mantissa: 10...0 (1 followed by nb-bits-1 bits) 119 ;; -> e = -(nb-bits-1) 120 ;; exact? is true when the container can still hold the complete 10^i 121 (let loop ((i 0) 122 (n (bit-lshbx #z1 (-fx nb-bits 1))) 123 (e (-fx 1 nb-bits))) 124 (when (<= i to) 125 (receive (cut e exact?) 126 (round-n-cut n e nb-bits) 127 (vector-set! vec (+fx i offset) 128 (instantiate::Cached-Fast 129 (v cut) 130 (e e) 131 (exact? exact?))) 132 (loop (+fx i 1) (*bx n #z10) e)))) 133 vec)) 134 135 (define (print-c powers from to struct-type 136 cache-name max-distance-name offset-name macro64) 137 (define (display-power power k) 138 (with-access::Cached-Fast power (v e exact?) 139 (let ((tmp-p (open-output-string))) 140 ;; really hackish way of getting the digits 141 (display (format "~x" v) tmp-p) 142 (let ((str (close-output-port tmp-p))) 143 (printf " {~a(0x~a, ~a), ~a, ~a},\n" 144 macro64 145 (substring str 0 8) 146 (substring str 8 16) 147 e 148 k))))) 149 (define (print-powers-reduced n) 150 (print "static const " struct-type " " cache-name 151 "(" n ")" 152 "[] = {") 153 (let loop ((i 0) 154 (nb-elements 0) 155 (last-e 0) 156 (max-distance 0)) 157 (cond 158 ((>= i (vector-length powers)) 159 (print " };") 160 (print "static const int " max-distance-name "(" n ") = " 161 max-distance ";") 162 (print "// nb elements (" n "): " nb-elements)) 163 (else 164 (let* ((power (vector-ref powers i)) 165 (e (Cached-Fast-e power))) 166 (display-power power (+ i from)) 167 (loop (+ i n) 168 (+ nb-elements 1) 169 e 170 (cond 171 ((=fx i 0) max-distance) 172 ((> (- e last-e) max-distance) (- e last-e)) 173 (else max-distance)))))))) 174 (print "// Copyright 2010 the V8 project authors. All rights reserved.") 175 (print "// ------------ GENERATED FILE ----------------") 176 (print "// command used:") 177 (print "// " 178 (apply string-append (map (lambda (str) 179 (string-append " " str)) 180 *main-args*)) 181 " // NOLINT") 182 (print) 183 (print 184 "// This file is intended to be included inside another .h or .cc files\n" 185 "// with the following defines set:\n" 186 "// GRISU_CACHE_STRUCT: should expand to the name of a struct that will\n" 187 "// hold the cached powers of ten. Each entry will hold a 64-bit\n" 188 "// significand, a 16-bit signed binary exponent, and a 16-bit\n" 189 "// signed decimal exponent. Each entry will be constructed as follows:\n" 190 "// { significand, binary_exponent, decimal_exponent }.\n" 191 "// GRISU_CACHE_NAME(i): generates the name for the different caches.\n" 192 "// The parameter i will be a number in the range 1-20. A cache will\n" 193 "// hold every i'th element of a full cache. GRISU_CACHE_NAME(1) will\n" 194 "// thus hold all elements. The higher i the fewer elements it has.\n" 195 "// Ideally the user should only reference one cache and let the\n" 196 "// compiler remove the unused ones.\n" 197 "// GRISU_CACHE_MAX_DISTANCE(i): generates the name for the maximum\n" 198 "// binary exponent distance between all elements of a given cache.\n" 199 "// GRISU_CACHE_OFFSET: is used as variable name for the decimal\n" 200 "// exponent offset. It is equal to -cache[0].decimal_exponent.\n" 201 "// GRISU_UINT64_C: used to construct 64-bit values in a platform\n" 202 "// independent way. In order to encode 0x123456789ABCDEF0 the macro\n" 203 "// will be invoked as follows: GRISU_UINT64_C(0x12345678,9ABCDEF0).\n") 204 (print) 205 (print-powers-reduced 1) 206 (print-powers-reduced 2) 207 (print-powers-reduced 3) 208 (print-powers-reduced 4) 209 (print-powers-reduced 5) 210 (print-powers-reduced 6) 211 (print-powers-reduced 7) 212 (print-powers-reduced 8) 213 (print-powers-reduced 9) 214 (print-powers-reduced 10) 215 (print-powers-reduced 11) 216 (print-powers-reduced 12) 217 (print-powers-reduced 13) 218 (print-powers-reduced 14) 219 (print-powers-reduced 15) 220 (print-powers-reduced 16) 221 (print-powers-reduced 17) 222 (print-powers-reduced 18) 223 (print-powers-reduced 19) 224 (print-powers-reduced 20) 225 (print "static const int GRISU_CACHE_OFFSET = " (- from) ";")) 226 227 ;;----------------main -------------------------------------------------------- 228 (define *main-args* #f) 229 (define *mantissa-size* #f) 230 (define *dest* #f) 231 (define *round* #f) 232 (define *from* #f) 233 (define *to* #f) 234 235 (define (my-main args) 236 (set! *main-args* args) 237 (args-parse (cdr args) 238 (section "Help") 239 (("?") (args-parse-usage #f)) 240 ((("-h" "--help") (help "?, -h, --help" "This help message")) 241 (args-parse-usage #f)) 242 (section "Misc") 243 (("-o" ?file (help "The output file")) 244 (set! *dest* file)) 245 (("--mantissa-size" ?size (help "Container-size in bits")) 246 (set! *mantissa-size* (string->number size))) 247 (("--round" ?direction (help "Round bignums (down, round or up)")) 248 (set! *round* (string->symbol direction))) 249 (("--from" ?from (help "start at 10^from")) 250 (set! *from* (string->number from))) 251 (("--to" ?to (help "go up to 10^to")) 252 (set! *to* (string->number to))) 253 (else 254 (print "Illegal argument `" else "'. Usage:") 255 (args-parse-usage #f))) 256 (when (not *from*) 257 (error "generate-ten-powers" 258 "Missing from" 259 #f)) 260 (when (not *to*) 261 (error "generate-ten-powers" 262 "Missing to" 263 #f)) 264 (when (not *mantissa-size*) 265 (error "generate-ten-powers" 266 "Missing mantissa size" 267 #f)) 268 (when (not (memv *round* '(up down round))) 269 (error "generate-ten-powers" 270 "Missing round-method" 271 *round*)) 272 273 (let ((dividers (generate-powers *from* *to* *mantissa-size*)) 274 (p (if (not *dest*) 275 (current-output-port) 276 (open-output-file *dest*)))) 277 (unwind-protect 278 (with-output-to-port p 279 (lambda () 280 (print-c dividers *from* *to* 281 "GRISU_CACHE_STRUCT" "GRISU_CACHE_NAME" 282 "GRISU_CACHE_MAX_DISTANCE" "GRISU_CACHE_OFFSET" 283 "GRISU_UINT64_C" 284 ))) 285 (if *dest* 286 (close-output-port p))))) 287