ref: bfebb7aa5c152ac8be77db6a796b300af3817064
parent: 5f83cc98423474d0c7a26b0494e84168621467d0
author: Tor Andersson <tor.andersson@gmail.com>
date: Mon May 22 10:48:23 EDT 2017
Use grisu2 algorithm for locale independent dtoa. Use BSD strtod.
--- a/jsdtoa.c
+++ b/jsdtoa.c
@@ -1,155 +1,22 @@
-/* The authors of this software are Rob Pike and Ken Thompson.
- * Copyright (c) 2002 by Lucent Technologies.
- * Permission to use, copy, modify, and distribute this software for any
- * purpose without fee is hereby granted, provided that this entire notice
- * is included in all copies of any software which is or includes a copy
- * or modification of this software and in all copies of the supporting
- * documentation for such software.
- * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
- * WARRANTY. IN PARTICULAR, NEITHER THE AUTHORS NOR LUCENT TECHNOLOGIES MAKE ANY
- * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
- * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
- */
+/* Locale-independent implementations of string <-> double conversions. */
-#include <stdio.h>
-#include <math.h>
-#include <float.h>
-#include <string.h>
-#include <stdlib.h>
-#include <errno.h>
-
#include "jsi.h"
-typedef unsigned long ulong;
+#ifdef _MSC_VER
+typedef unsigned __int64 uint64_t;
+#else
+#include <stdint.h>
+#endif
-enum { NSIGNIF = 17 };+#include <errno.h>
+#include <assert.h>
-/*
- * first few powers of 10, enough for about 1/2 of the
- * total space for doubles.
- */
-static double pows10[] =
-{- 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
- 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
- 1e20, 1e21, 1e22, 1e23, 1e24, 1e25, 1e26, 1e27, 1e28, 1e29,
- 1e30, 1e31, 1e32, 1e33, 1e34, 1e35, 1e36, 1e37, 1e38, 1e39,
- 1e40, 1e41, 1e42, 1e43, 1e44, 1e45, 1e46, 1e47, 1e48, 1e49,
- 1e50, 1e51, 1e52, 1e53, 1e54, 1e55, 1e56, 1e57, 1e58, 1e59,
- 1e60, 1e61, 1e62, 1e63, 1e64, 1e65, 1e66, 1e67, 1e68, 1e69,
- 1e70, 1e71, 1e72, 1e73, 1e74, 1e75, 1e76, 1e77, 1e78, 1e79,
- 1e80, 1e81, 1e82, 1e83, 1e84, 1e85, 1e86, 1e87, 1e88, 1e89,
- 1e90, 1e91, 1e92, 1e93, 1e94, 1e95, 1e96, 1e97, 1e98, 1e99,
- 1e100, 1e101, 1e102, 1e103, 1e104, 1e105, 1e106, 1e107, 1e108, 1e109,
- 1e110, 1e111, 1e112, 1e113, 1e114, 1e115, 1e116, 1e117, 1e118, 1e119,
- 1e120, 1e121, 1e122, 1e123, 1e124, 1e125, 1e126, 1e127, 1e128, 1e129,
- 1e130, 1e131, 1e132, 1e133, 1e134, 1e135, 1e136, 1e137, 1e138, 1e139,
- 1e140, 1e141, 1e142, 1e143, 1e144, 1e145, 1e146, 1e147, 1e148, 1e149,
- 1e150, 1e151, 1e152, 1e153, 1e154, 1e155, 1e156, 1e157, 1e158, 1e159,
-};
-#define npows10 ((int)(sizeof(pows10)/sizeof(pows10[0])))
-#define pow10(x) fmtpow10(x)
+#ifndef TRUE
+#define TRUE 1
+#define FALSE 0
+#endif
-static double
-pow10(int n)
-{- double d;
- int neg;
-
- neg = 0;
- if(n < 0){- neg = 1;
- n = -n;
- }
-
- if(n < npows10)
- d = pows10[n];
- else{- d = pows10[npows10-1];
- for(;;){- n -= npows10 - 1;
- if(n < npows10){- d *= pows10[n];
- break;
- }
- d *= pows10[npows10 - 1];
- }
- }
- if(neg)
- return 1./d;
- return d;
-}
-
/*
- * add 1 to the decimal integer string a of length n.
- * if 99999 overflows into 10000, return 1 to tell caller
- * to move the virtual decimal point.
- */
-static int
-xadd1(char *a, int n)
-{- char *b;
- int c;
-
- if(n < 0 || n > NSIGNIF)
- return 0;
- for(b = a+n-1; b >= a; b--) {- c = *b + 1;
- if(c <= '9') {- *b = c;
- return 0;
- }
- *b = '0';
- }
- /*
- * need to overflow adding digit.
- * shift number down and insert 1 at beginning.
- * decimal is known to be 0s or we wouldn't
- * have gotten this far. (e.g., 99999+1 => 00000)
- */
- a[0] = '1';
- return 1;
-}
-
-/*
- * subtract 1 from the decimal integer string a.
- * if 10000 underflows into 09999, make it 99999
- * and return 1 to tell caller to move the virtual
- * decimal point. this way, xsub1 is inverse of xadd1.
- */
-static int
-xsub1(char *a, int n)
-{- char *b;
- int c;
-
- if(n < 0 || n > NSIGNIF)
- return 0;
- for(b = a+n-1; b >= a; b--) {- c = *b - 1;
- if(c >= '0') {- if(c == '0' && b == a) {- /*
- * just zeroed the top digit; shift everyone up.
- * decimal is known to be 9s or we wouldn't
- * have gotten this far. (e.g., 10000-1 => 09999)
- */
- *b = '9';
- return 1;
- }
- *b = c;
- return 0;
- }
- *b = '9';
- }
- /*
- * can't get here. the number a is always normalized
- * so that it has a nonzero first digit.
- */
- return 0;
-}
-
-/*
* format exponent like sprintf(p, "e%+d", e)
*/
void
@@ -177,674 +44,633 @@
}
/*
- * compute decimal integer m, exp such that:
- * f = m*10^exp
- * m is as short as possible with losing exactness
- * assumes special cases (NaN, +Inf, -Inf) have been handled.
+ * grisu2_59_56.c
+ *
+ * Grisu prints the optimal decimal representation of floating-point numbers.
+ *
+ * Copyright (c) 2009 Florian Loitsch
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to
+ * deal in the Software without restriction, including without limitation the
+ * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+ * sell copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+ * IN THE SOFTWARE.
*/
-void
-js_dtoa(double f, char *s, int *exp, int *neg, int *ns)
-{- int c, d, e2, e, ee, i, ndigit, oerrno;
- char tmp[NSIGNIF+10];
- double g;
- oerrno = errno; /* in case strtod smashes errno */
+typedef struct diy_fp_t {+ uint64_t f;
+ int e;
+} diy_fp_t;
- /*
- * make f non-negative.
- */
- *neg = 0;
- if(f < 0) {- f = -f;
- *neg = 1;
- }
+#define DIY_SIGNIFICAND_SIZE 64
+#define D_1_LOG2_10 0.30102999566398114 /* 1 / lg(10) */
- /*
- * must handle zero specially.
- */
- if(f == 0){- *exp = 0;
- s[0] = '0';
- s[1] = '\0';
- *ns = 1;
- return;
- }
+static const uint64_t powers_ten[] = {+ 0xbf29dcaba82fdeae, 0xeef453d6923bd65a, 0x9558b4661b6565f8, 0xbaaee17fa23ebf76,
+ 0xe95a99df8ace6f54, 0x91d8a02bb6c10594, 0xb64ec836a47146fa, 0xe3e27a444d8d98b8,
+ 0x8e6d8c6ab0787f73, 0xb208ef855c969f50, 0xde8b2b66b3bc4724, 0x8b16fb203055ac76,
+ 0xaddcb9e83c6b1794, 0xd953e8624b85dd79, 0x87d4713d6f33aa6c, 0xa9c98d8ccb009506,
+ 0xd43bf0effdc0ba48, 0x84a57695fe98746d, 0xa5ced43b7e3e9188, 0xcf42894a5dce35ea,
+ 0x818995ce7aa0e1b2, 0xa1ebfb4219491a1f, 0xca66fa129f9b60a7, 0xfd00b897478238d1,
+ 0x9e20735e8cb16382, 0xc5a890362fddbc63, 0xf712b443bbd52b7c, 0x9a6bb0aa55653b2d,
+ 0xc1069cd4eabe89f9, 0xf148440a256e2c77, 0x96cd2a865764dbca, 0xbc807527ed3e12bd,
+ 0xeba09271e88d976c, 0x93445b8731587ea3, 0xb8157268fdae9e4c, 0xe61acf033d1a45df,
+ 0x8fd0c16206306bac, 0xb3c4f1ba87bc8697, 0xe0b62e2929aba83c, 0x8c71dcd9ba0b4926,
+ 0xaf8e5410288e1b6f, 0xdb71e91432b1a24b, 0x892731ac9faf056f, 0xab70fe17c79ac6ca,
+ 0xd64d3d9db981787d, 0x85f0468293f0eb4e, 0xa76c582338ed2622, 0xd1476e2c07286faa,
+ 0x82cca4db847945ca, 0xa37fce126597973d, 0xcc5fc196fefd7d0c, 0xff77b1fcbebcdc4f,
+ 0x9faacf3df73609b1, 0xc795830d75038c1e, 0xf97ae3d0d2446f25, 0x9becce62836ac577,
+ 0xc2e801fb244576d5, 0xf3a20279ed56d48a, 0x9845418c345644d7, 0xbe5691ef416bd60c,
+ 0xedec366b11c6cb8f, 0x94b3a202eb1c3f39, 0xb9e08a83a5e34f08, 0xe858ad248f5c22ca,
+ 0x91376c36d99995be, 0xb58547448ffffb2e, 0xe2e69915b3fff9f9, 0x8dd01fad907ffc3c,
+ 0xb1442798f49ffb4b, 0xdd95317f31c7fa1d, 0x8a7d3eef7f1cfc52, 0xad1c8eab5ee43b67,
+ 0xd863b256369d4a41, 0x873e4f75e2224e68, 0xa90de3535aaae202, 0xd3515c2831559a83,
+ 0x8412d9991ed58092, 0xa5178fff668ae0b6, 0xce5d73ff402d98e4, 0x80fa687f881c7f8e,
+ 0xa139029f6a239f72, 0xc987434744ac874f, 0xfbe9141915d7a922, 0x9d71ac8fada6c9b5,
+ 0xc4ce17b399107c23, 0xf6019da07f549b2b, 0x99c102844f94e0fb, 0xc0314325637a193a,
+ 0xf03d93eebc589f88, 0x96267c7535b763b5, 0xbbb01b9283253ca3, 0xea9c227723ee8bcb,
+ 0x92a1958a7675175f, 0xb749faed14125d37, 0xe51c79a85916f485, 0x8f31cc0937ae58d3,
+ 0xb2fe3f0b8599ef08, 0xdfbdcece67006ac9, 0x8bd6a141006042be, 0xaecc49914078536d,
+ 0xda7f5bf590966849, 0x888f99797a5e012d, 0xaab37fd7d8f58179, 0xd5605fcdcf32e1d7,
+ 0x855c3be0a17fcd26, 0xa6b34ad8c9dfc070, 0xd0601d8efc57b08c, 0x823c12795db6ce57,
+ 0xa2cb1717b52481ed, 0xcb7ddcdda26da269, 0xfe5d54150b090b03, 0x9efa548d26e5a6e2,
+ 0xc6b8e9b0709f109a, 0xf867241c8cc6d4c1, 0x9b407691d7fc44f8, 0xc21094364dfb5637,
+ 0xf294b943e17a2bc4, 0x979cf3ca6cec5b5b, 0xbd8430bd08277231, 0xece53cec4a314ebe,
+ 0x940f4613ae5ed137, 0xb913179899f68584, 0xe757dd7ec07426e5, 0x9096ea6f3848984f,
+ 0xb4bca50b065abe63, 0xe1ebce4dc7f16dfc, 0x8d3360f09cf6e4bd, 0xb080392cc4349ded,
+ 0xdca04777f541c568, 0x89e42caaf9491b61, 0xac5d37d5b79b6239, 0xd77485cb25823ac7,
+ 0x86a8d39ef77164bd, 0xa8530886b54dbdec, 0xd267caa862a12d67, 0x8380dea93da4bc60,
+ 0xa46116538d0deb78, 0xcd795be870516656, 0x806bd9714632dff6, 0xa086cfcd97bf97f4,
+ 0xc8a883c0fdaf7df0, 0xfad2a4b13d1b5d6c, 0x9cc3a6eec6311a64, 0xc3f490aa77bd60fd,
+ 0xf4f1b4d515acb93c, 0x991711052d8bf3c5, 0xbf5cd54678eef0b7, 0xef340a98172aace5,
+ 0x9580869f0e7aac0f, 0xbae0a846d2195713, 0xe998d258869facd7, 0x91ff83775423cc06,
+ 0xb67f6455292cbf08, 0xe41f3d6a7377eeca, 0x8e938662882af53e, 0xb23867fb2a35b28e,
+ 0xdec681f9f4c31f31, 0x8b3c113c38f9f37f, 0xae0b158b4738705f, 0xd98ddaee19068c76,
+ 0x87f8a8d4cfa417ca, 0xa9f6d30a038d1dbc, 0xd47487cc8470652b, 0x84c8d4dfd2c63f3b,
+ 0xa5fb0a17c777cf0a, 0xcf79cc9db955c2cc, 0x81ac1fe293d599c0, 0xa21727db38cb0030,
+ 0xca9cf1d206fdc03c, 0xfd442e4688bd304b, 0x9e4a9cec15763e2f, 0xc5dd44271ad3cdba,
+ 0xf7549530e188c129, 0x9a94dd3e8cf578ba, 0xc13a148e3032d6e8, 0xf18899b1bc3f8ca2,
+ 0x96f5600f15a7b7e5, 0xbcb2b812db11a5de, 0xebdf661791d60f56, 0x936b9fcebb25c996,
+ 0xb84687c269ef3bfb, 0xe65829b3046b0afa, 0x8ff71a0fe2c2e6dc, 0xb3f4e093db73a093,
+ 0xe0f218b8d25088b8, 0x8c974f7383725573, 0xafbd2350644eead0, 0xdbac6c247d62a584,
+ 0x894bc396ce5da772, 0xab9eb47c81f5114f, 0xd686619ba27255a3, 0x8613fd0145877586,
+ 0xa798fc4196e952e7, 0xd17f3b51fca3a7a1, 0x82ef85133de648c5, 0xa3ab66580d5fdaf6,
+ 0xcc963fee10b7d1b3, 0xffbbcfe994e5c620, 0x9fd561f1fd0f9bd4, 0xc7caba6e7c5382c9,
+ 0xf9bd690a1b68637b, 0x9c1661a651213e2d, 0xc31bfa0fe5698db8, 0xf3e2f893dec3f126,
+ 0x986ddb5c6b3a76b8, 0xbe89523386091466, 0xee2ba6c0678b597f, 0x94db483840b717f0,
+ 0xba121a4650e4ddec, 0xe896a0d7e51e1566, 0x915e2486ef32cd60, 0xb5b5ada8aaff80b8,
+ 0xe3231912d5bf60e6, 0x8df5efabc5979c90, 0xb1736b96b6fd83b4, 0xddd0467c64bce4a1,
+ 0x8aa22c0dbef60ee4, 0xad4ab7112eb3929e, 0xd89d64d57a607745, 0x87625f056c7c4a8b,
+ 0xa93af6c6c79b5d2e, 0xd389b47879823479, 0x843610cb4bf160cc, 0xa54394fe1eedb8ff,
+ 0xce947a3da6a9273e, 0x811ccc668829b887, 0xa163ff802a3426a9, 0xc9bcff6034c13053,
+ 0xfc2c3f3841f17c68, 0x9d9ba7832936edc1, 0xc5029163f384a931, 0xf64335bcf065d37d,
+ 0x99ea0196163fa42e, 0xc06481fb9bcf8d3a, 0xf07da27a82c37088, 0x964e858c91ba2655,
+ 0xbbe226efb628afeb, 0xeadab0aba3b2dbe5, 0x92c8ae6b464fc96f, 0xb77ada0617e3bbcb,
+ 0xe55990879ddcaabe, 0x8f57fa54c2a9eab7, 0xb32df8e9f3546564, 0xdff9772470297ebd,
+ 0x8bfbea76c619ef36, 0xaefae51477a06b04, 0xdab99e59958885c5, 0x88b402f7fd75539b,
+ 0xaae103b5fcd2a882, 0xd59944a37c0752a2, 0x857fcae62d8493a5, 0xa6dfbd9fb8e5b88f,
+ 0xd097ad07a71f26b2, 0x825ecc24c8737830, 0xa2f67f2dfa90563b, 0xcbb41ef979346bca,
+ 0xfea126b7d78186bd, 0x9f24b832e6b0f436, 0xc6ede63fa05d3144, 0xf8a95fcf88747d94,
+ 0x9b69dbe1b548ce7d, 0xc24452da229b021c, 0xf2d56790ab41c2a3, 0x97c560ba6b0919a6,
+ 0xbdb6b8e905cb600f, 0xed246723473e3813, 0x9436c0760c86e30c, 0xb94470938fa89bcf,
+ 0xe7958cb87392c2c3, 0x90bd77f3483bb9ba, 0xb4ecd5f01a4aa828, 0xe2280b6c20dd5232,
+ 0x8d590723948a535f, 0xb0af48ec79ace837, 0xdcdb1b2798182245, 0x8a08f0f8bf0f156b,
+ 0xac8b2d36eed2dac6, 0xd7adf884aa879177, 0x86ccbb52ea94baeb, 0xa87fea27a539e9a5,
+ 0xd29fe4b18e88640f, 0x83a3eeeef9153e89, 0xa48ceaaab75a8e2b, 0xcdb02555653131b6,
+ 0x808e17555f3ebf12, 0xa0b19d2ab70e6ed6, 0xc8de047564d20a8c, 0xfb158592be068d2f,
+ 0x9ced737bb6c4183d, 0xc428d05aa4751e4d, 0xf53304714d9265e0, 0x993fe2c6d07b7fac,
+ 0xbf8fdb78849a5f97, 0xef73d256a5c0f77d, 0x95a8637627989aae, 0xbb127c53b17ec159,
+ 0xe9d71b689dde71b0, 0x9226712162ab070e, 0xb6b00d69bb55c8d1, 0xe45c10c42a2b3b06,
+ 0x8eb98a7a9a5b04e3, 0xb267ed1940f1c61c, 0xdf01e85f912e37a3, 0x8b61313bbabce2c6,
+ 0xae397d8aa96c1b78, 0xd9c7dced53c72256, 0x881cea14545c7575, 0xaa242499697392d3,
+ 0xd4ad2dbfc3d07788, 0x84ec3c97da624ab5, 0xa6274bbdd0fadd62, 0xcfb11ead453994ba,
+ 0x81ceb32c4b43fcf5, 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3e, 0xfd87b5f28300ca0e,
+ 0x9e74d1b791e07e48, 0xc612062576589ddb, 0xf79687aed3eec551, 0x9abe14cd44753b53,
+ 0xc16d9a0095928a27, 0xf1c90080baf72cb1, 0x971da05074da7bef, 0xbce5086492111aeb,
+ 0xec1e4a7db69561a5, 0x9392ee8e921d5d07, 0xb877aa3236a4b449, 0xe69594bec44de15b,
+ 0x901d7cf73ab0acd9, 0xb424dc35095cd80f, 0xe12e13424bb40e13, 0x8cbccc096f5088cc,
+ 0xafebff0bcb24aaff, 0xdbe6fecebdedd5bf, 0x89705f4136b4a597, 0xabcc77118461cefd,
+ 0xd6bf94d5e57a42bc, 0x8637bd05af6c69b6, 0xa7c5ac471b478423, 0xd1b71758e219652c,
+ 0x83126e978d4fdf3b, 0xa3d70a3d70a3d70a, 0xcccccccccccccccd, 0x8000000000000000,
+ 0xa000000000000000, 0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000,
+ 0xc350000000000000, 0xf424000000000000, 0x9896800000000000, 0xbebc200000000000,
+ 0xee6b280000000000, 0x9502f90000000000, 0xba43b74000000000, 0xe8d4a51000000000,
+ 0x9184e72a00000000, 0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000,
+ 0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000, 0xad78ebc5ac620000,
+ 0xd8d726b7177a8000, 0x878678326eac9000, 0xa968163f0a57b400, 0xd3c21bcecceda100,
+ 0x84595161401484a0, 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940984,
+ 0xa18f07d736b90be5, 0xc9f2c9cd04674edf, 0xfc6f7c4045812296, 0x9dc5ada82b70b59e,
+ 0xc5371912364ce305, 0xf684df56c3e01bc7, 0x9a130b963a6c115c, 0xc097ce7bc90715b3,
+ 0xf0bdc21abb48db20, 0x96769950b50d88f4, 0xbc143fa4e250eb31, 0xeb194f8e1ae525fd,
+ 0x92efd1b8d0cf37be, 0xb7abc627050305ae, 0xe596b7b0c643c719, 0x8f7e32ce7bea5c70,
+ 0xb35dbf821ae4f38c, 0xe0352f62a19e306f, 0x8c213d9da502de45, 0xaf298d050e4395d7,
+ 0xdaf3f04651d47b4c, 0x88d8762bf324cd10, 0xab0e93b6efee0054, 0xd5d238a4abe98068,
+ 0x85a36366eb71f041, 0xa70c3c40a64e6c52, 0xd0cf4b50cfe20766, 0x82818f1281ed44a0,
+ 0xa321f2d7226895c8, 0xcbea6f8ceb02bb3a, 0xfee50b7025c36a08, 0x9f4f2726179a2245,
+ 0xc722f0ef9d80aad6, 0xf8ebad2b84e0d58c, 0x9b934c3b330c8577, 0xc2781f49ffcfa6d5,
+ 0xf316271c7fc3908b, 0x97edd871cfda3a57, 0xbde94e8e43d0c8ec, 0xed63a231d4c4fb27,
+ 0x945e455f24fb1cf9, 0xb975d6b6ee39e437, 0xe7d34c64a9c85d44, 0x90e40fbeea1d3a4b,
+ 0xb51d13aea4a488dd, 0xe264589a4dcdab15, 0x8d7eb76070a08aed, 0xb0de65388cc8ada8,
+ 0xdd15fe86affad912, 0x8a2dbf142dfcc7ab, 0xacb92ed9397bf996, 0xd7e77a8f87daf7fc,
+ 0x86f0ac99b4e8dafd, 0xa8acd7c0222311bd, 0xd2d80db02aabd62c, 0x83c7088e1aab65db,
+ 0xa4b8cab1a1563f52, 0xcde6fd5e09abcf27, 0x80b05e5ac60b6178, 0xa0dc75f1778e39d6,
+ 0xc913936dd571c84c, 0xfb5878494ace3a5f, 0x9d174b2dcec0e47b, 0xc45d1df942711d9a,
+ 0xf5746577930d6501, 0x9968bf6abbe85f20, 0xbfc2ef456ae276e9, 0xefb3ab16c59b14a3,
+ 0x95d04aee3b80ece6, 0xbb445da9ca61281f, 0xea1575143cf97227, 0x924d692ca61be758,
+ 0xb6e0c377cfa2e12e, 0xe498f455c38b997a, 0x8edf98b59a373fec, 0xb2977ee300c50fe7,
+ 0xdf3d5e9bc0f653e1, 0x8b865b215899f46d, 0xae67f1e9aec07188, 0xda01ee641a708dea,
+ 0x884134fe908658b2, 0xaa51823e34a7eedf, 0xd4e5e2cdc1d1ea96, 0x850fadc09923329e,
+ 0xa6539930bf6bff46, 0xcfe87f7cef46ff17, 0x81f14fae158c5f6e, 0xa26da3999aef774a,
+ 0xcb090c8001ab551c, 0xfdcb4fa002162a63, 0x9e9f11c4014dda7e, 0xc646d63501a1511e,
+ 0xf7d88bc24209a565, 0x9ae757596946075f, 0xc1a12d2fc3978937, 0xf209787bb47d6b85,
+ 0x9745eb4d50ce6333, 0xbd176620a501fc00, 0xec5d3fa8ce427b00, 0x93ba47c980e98ce0,
+ 0xb8a8d9bbe123f018, 0xe6d3102ad96cec1e, 0x9043ea1ac7e41393, 0xb454e4a179dd1877,
+ 0xe16a1dc9d8545e95, 0x8ce2529e2734bb1d, 0xb01ae745b101e9e4, 0xdc21a1171d42645d,
+ 0x899504ae72497eba, 0xabfa45da0edbde69, 0xd6f8d7509292d603, 0x865b86925b9bc5c2,
+ 0xa7f26836f282b733, 0xd1ef0244af2364ff, 0x8335616aed761f1f, 0xa402b9c5a8d3a6e7,
+ 0xcd036837130890a1, 0x802221226be55a65, 0xa02aa96b06deb0fe, 0xc83553c5c8965d3d,
+ 0xfa42a8b73abbf48d, 0x9c69a97284b578d8, 0xc38413cf25e2d70e, 0xf46518c2ef5b8cd1,
+ 0x98bf2f79d5993803, 0xbeeefb584aff8604, 0xeeaaba2e5dbf6785, 0x952ab45cfa97a0b3,
+ 0xba756174393d88e0, 0xe912b9d1478ceb17, 0x91abb422ccb812ef, 0xb616a12b7fe617aa,
+ 0xe39c49765fdf9d95, 0x8e41ade9fbebc27d, 0xb1d219647ae6b31c, 0xde469fbd99a05fe3,
+ 0x8aec23d680043bee, 0xada72ccc20054aea, 0xd910f7ff28069da4, 0x87aa9aff79042287,
+ 0xa99541bf57452b28, 0xd3fa922f2d1675f2, 0x847c9b5d7c2e09b7, 0xa59bc234db398c25,
+ 0xcf02b2c21207ef2f, 0x8161afb94b44f57d, 0xa1ba1ba79e1632dc, 0xca28a291859bbf93,
+ 0xfcb2cb35e702af78, 0x9defbf01b061adab, 0xc56baec21c7a1916, 0xf6c69a72a3989f5c,
+ 0x9a3c2087a63f6399, 0xc0cb28a98fcf3c80, 0xf0fdf2d3f3c30b9f, 0x969eb7c47859e744,
+ 0xbc4665b596706115, 0xeb57ff22fc0c795a, 0x9316ff75dd87cbd8, 0xb7dcbf5354e9bece,
+ 0xe5d3ef282a242e82, 0x8fa475791a569d11, 0xb38d92d760ec4455, 0xe070f78d3927556b,
+ 0x8c469ab843b89563, 0xaf58416654a6babb, 0xdb2e51bfe9d0696a, 0x88fcf317f22241e2,
+ 0xab3c2fddeeaad25b, 0xd60b3bd56a5586f2, 0x85c7056562757457, 0xa738c6bebb12d16d,
+ 0xd106f86e69d785c8, 0x82a45b450226b39d, 0xa34d721642b06084, 0xcc20ce9bd35c78a5,
+ 0xff290242c83396ce, 0x9f79a169bd203e41, 0xc75809c42c684dd1, 0xf92e0c3537826146,
+ 0x9bbcc7a142b17ccc, 0xc2abf989935ddbfe, 0xf356f7ebf83552fe, 0x98165af37b2153df,
+ 0xbe1bf1b059e9a8d6, 0xeda2ee1c7064130c, 0x9485d4d1c63e8be8, 0xb9a74a0637ce2ee1,
+ 0xe8111c87c5c1ba9a, 0x910ab1d4db9914a0, 0xb54d5e4a127f59c8, 0xe2a0b5dc971f303a,
+ 0x8da471a9de737e24, 0xb10d8e1456105dad, 0xdd50f1996b947519, 0x8a5296ffe33cc930,
+ 0xace73cbfdc0bfb7b, 0xd8210befd30efa5a, 0x8714a775e3e95c78, 0xa8d9d1535ce3b396,
+ 0xd31045a8341ca07c, 0x83ea2b892091e44e, 0xa4e4b66b68b65d61, 0xce1de40642e3f4b9,
+ 0x80d2ae83e9ce78f4, 0xa1075a24e4421731, 0xc94930ae1d529cfd, 0xfb9b7cd9a4a7443c,
+ 0x9d412e0806e88aa6, 0xc491798a08a2ad4f, 0xf5b5d7ec8acb58a3, 0x9991a6f3d6bf1766,
+ 0xbff610b0cc6edd3f, 0xeff394dcff8a948f, 0x95f83d0a1fb69cd9, 0xbb764c4ca7a44410,
+ 0xea53df5fd18d5514, 0x92746b9be2f8552c, 0xb7118682dbb66a77, 0xe4d5e82392a40515,
+ 0x8f05b1163ba6832d, 0xb2c71d5bca9023f8, 0xdf78e4b2bd342cf7, 0x8bab8eefb6409c1a,
+ 0xae9672aba3d0c321, 0xda3c0f568cc4f3e9, 0x8865899617fb1871, 0xaa7eebfb9df9de8e,
+ 0xd51ea6fa85785631, 0x8533285c936b35df, 0xa67ff273b8460357, 0xd01fef10a657842c,
+ 0x8213f56a67f6b29c, 0xa298f2c501f45f43, 0xcb3f2f7642717713, 0xfe0efb53d30dd4d8,
+ 0x9ec95d1463e8a507, 0xc67bb4597ce2ce49, 0xf81aa16fdc1b81db, 0x9b10a4e5e9913129,
+ 0xc1d4ce1f63f57d73, 0xf24a01a73cf2dcd0, 0x976e41088617ca02, 0xbd49d14aa79dbc82,
+ 0xec9c459d51852ba3, 0x93e1ab8252f33b46, 0xb8da1662e7b00a17, 0xe7109bfba19c0c9d,
+ 0x906a617d450187e2, 0xb484f9dc9641e9db, 0xe1a63853bbd26451, 0x8d07e33455637eb3,
+ 0xb049dc016abc5e60, 0xdc5c5301c56b75f7, 0x89b9b3e11b6329bb, 0xac2820d9623bf429,
+ 0xd732290fbacaf134, 0x867f59a9d4bed6c0, 0xa81f301449ee8c70, 0xd226fc195c6a2f8c,
+ 0x83585d8fd9c25db8, 0xa42e74f3d032f526, 0xcd3a1230c43fb26f, 0x80444b5e7aa7cf85,
+ 0xa0555e361951c367, 0xc86ab5c39fa63441, 0xfa856334878fc151, 0x9c935e00d4b9d8d2,
+ 0xc3b8358109e84f07, 0xf4a642e14c6262c9, 0x98e7e9cccfbd7dbe, 0xbf21e44003acdd2d,
+ 0xeeea5d5004981478, 0x95527a5202df0ccb, 0xbaa718e68396cffe, 0xe950df20247c83fd,
+ 0x91d28b7416cdd27e, 0xb6472e511c81471e, 0xe3d8f9e563a198e5, 0x8e679c2f5e44ff8f,
+ 0xb201833b35d63f73, 0xde81e40a034bcf50, 0x8b112e86420f6192, 0xadd57a27d29339f6,
+ 0xd94ad8b1c7380874, 0x87cec76f1c830549, 0xa9c2794ae3a3c69b, 0xd433179d9c8cb841,
+ 0x849feec281d7f329, 0xa5c7ea73224deff3, 0xcf39e50feae16bf0, 0x81842f29f2cce376,
+ 0xa1e53af46f801c53, 0xca5e89b18b602368, 0xfcf62c1dee382c42, 0x9e19db92b4e31ba9,
+ 0xc5a05277621be294, 0xf70867153aa2db39, 0x9a65406d44a5c903, 0xc0fe908895cf3b44,
+ 0xf13e34aabb430a15, 0x96c6e0eab509e64d, 0xbc789925624c5fe1, 0xeb96bf6ebadf77d9,
+ 0x933e37a534cbaae8, 0xb80dc58e81fe95a1, 0xe61136f2227e3b0a, 0x8fcac257558ee4e6,
+ 0xb3bd72ed2af29e20, 0xe0accfa875af45a8, 0x8c6c01c9498d8b89, 0xaf87023b9bf0ee6b,
+ 0xdb68c2ca82ed2a06, 0x892179be91d43a44, 0xab69d82e364948d4
+};
- /*
- * find g,e such that f = g*10^e.
- * guess 10-exponent using 2-exponent, then fine tune.
- */
- frexp(f, &e2);
- e = (int)(e2 * .301029995664);
- g = f * pow10(-e);
- while(g < 1) {- e--;
- g = f * pow10(-e);
- }
- while(g >= 10) {- e++;
- g = f * pow10(-e);
- }
+static const int powers_ten_e[] = {+ -1203, -1200, -1196, -1193, -1190, -1186, -1183, -1180, -1176, -1173, -1170,
+ -1166, -1163, -1160, -1156, -1153, -1150, -1146, -1143, -1140, -1136, -1133,
+ -1130, -1127, -1123, -1120, -1117, -1113, -1110, -1107, -1103, -1100, -1097,
+ -1093, -1090, -1087, -1083, -1080, -1077, -1073, -1070, -1067, -1063, -1060,
+ -1057, -1053, -1050, -1047, -1043, -1040, -1037, -1034, -1030, -1027, -1024,
+ -1020, -1017, -1014, -1010, -1007, -1004, -1000, -997, -994, -990, -987, -984,
+ -980, -977, -974, -970, -967, -964, -960, -957, -954, -950, -947, -944, -940,
+ -937, -934, -931, -927, -924, -921, -917, -914, -911, -907, -904, -901, -897,
+ -894, -891, -887, -884, -881, -877, -874, -871, -867, -864, -861, -857, -854,
+ -851, -847, -844, -841, -838, -834, -831, -828, -824, -821, -818, -814, -811,
+ -808, -804, -801, -798, -794, -791, -788, -784, -781, -778, -774, -771, -768,
+ -764, -761, -758, -754, -751, -748, -744, -741, -738, -735, -731, -728, -725,
+ -721, -718, -715, -711, -708, -705, -701, -698, -695, -691, -688, -685, -681,
+ -678, -675, -671, -668, -665, -661, -658, -655, -651, -648, -645, -642, -638,
+ -635, -632, -628, -625, -622, -618, -615, -612, -608, -605, -602, -598, -595,
+ -592, -588, -585, -582, -578, -575, -572, -568, -565, -562, -558, -555, -552,
+ -549, -545, -542, -539, -535, -532, -529, -525, -522, -519, -515, -512, -509,
+ -505, -502, -499, -495, -492, -489, -485, -482, -479, -475, -472, -469, -465,
+ -462, -459, -455, -452, -449, -446, -442, -439, -436, -432, -429, -426, -422,
+ -419, -416, -412, -409, -406, -402, -399, -396, -392, -389, -386, -382, -379,
+ -376, -372, -369, -366, -362, -359, -356, -353, -349, -346, -343, -339, -336,
+ -333, -329, -326, -323, -319, -316, -313, -309, -306, -303, -299, -296, -293,
+ -289, -286, -283, -279, -276, -273, -269, -266, -263, -259, -256, -253, -250,
+ -246, -243, -240, -236, -233, -230, -226, -223, -220, -216, -213, -210, -206,
+ -203, -200, -196, -193, -190, -186, -183, -180, -176, -173, -170, -166, -163,
+ -160, -157, -153, -150, -147, -143, -140, -137, -133, -130, -127, -123, -120,
+ -117, -113, -110, -107, -103, -100, -97, -93, -90, -87, -83, -80, -77, -73,
+ -70, -67, -63, -60, -57, -54, -50, -47, -44, -40, -37, -34, -30, -27, -24, -20,
+ -17, -14, -10, -7, -4, 0, 3, 6, 10, 13, 16, 20, 23, 26, 30, 33, 36, 39, 43, 46,
+ 49, 53, 56, 59, 63, 66, 69, 73, 76, 79, 83, 86, 89, 93, 96, 99, 103, 106, 109,
+ 113, 116, 119, 123, 126, 129, 132, 136, 139, 142, 146, 149, 152, 156, 159, 162,
+ 166, 169, 172, 176, 179, 182, 186, 189, 192, 196, 199, 202, 206, 209, 212, 216,
+ 219, 222, 226, 229, 232, 235, 239, 242, 245, 249, 252, 255, 259, 262, 265, 269,
+ 272, 275, 279, 282, 285, 289, 292, 295, 299, 302, 305, 309, 312, 315, 319, 322,
+ 325, 328, 332, 335, 338, 342, 345, 348, 352, 355, 358, 362, 365, 368, 372, 375,
+ 378, 382, 385, 388, 392, 395, 398, 402, 405, 408, 412, 415, 418, 422, 425, 428,
+ 431, 435, 438, 441, 445, 448, 451, 455, 458, 461, 465, 468, 471, 475, 478, 481,
+ 485, 488, 491, 495, 498, 501, 505, 508, 511, 515, 518, 521, 524, 528, 531, 534,
+ 538, 541, 544, 548, 551, 554, 558, 561, 564, 568, 571, 574, 578, 581, 584, 588,
+ 591, 594, 598, 601, 604, 608, 611, 614, 617, 621, 624, 627, 631, 634, 637, 641,
+ 644, 647, 651, 654, 657, 661, 664, 667, 671, 674, 677, 681, 684, 687, 691, 694,
+ 697, 701, 704, 707, 711, 714, 717, 720, 724, 727, 730, 734, 737, 740, 744, 747,
+ 750, 754, 757, 760, 764, 767, 770, 774, 777, 780, 784, 787, 790, 794, 797, 800,
+ 804, 807, 810, 813, 817, 820, 823, 827, 830, 833, 837, 840, 843, 847, 850, 853,
+ 857, 860, 863, 867, 870, 873, 877, 880, 883, 887, 890, 893, 897, 900, 903, 907,
+ 910, 913, 916, 920, 923, 926, 930, 933, 936, 940, 943, 946, 950, 953, 956, 960,
+ 963, 966, 970, 973, 976, 980, 983, 986, 990, 993, 996, 1000, 1003, 1006, 1009,
+ 1013, 1016, 1019, 1023, 1026, 1029, 1033, 1036, 1039, 1043, 1046, 1049, 1053,
+ 1056, 1059, 1063, 1066, 1069, 1073, 1076
+};
- /*
- * convert NSIGNIF digits as a first approximation.
- */
- for(i=0; i<NSIGNIF; i++) {- d = (int)g;
- s[i] = d+'0';
- g = (g-d) * 10;
- }
- s[i] = 0;
+static diy_fp_t cached_power(int k)
+{+ diy_fp_t res;
+ int index = 343 + k;
+ res.f = powers_ten[index];
+ res.e = powers_ten_e[index];
+ return res;
+}
- /*
- * adjust e because s is 314159... not 3.14159...
- */
- e -= NSIGNIF-1;
- js_fmtexp(s+NSIGNIF, e);
+static int k_comp(int e, int alpha, int gamma) {+ return ceil((alpha-e+63) * D_1_LOG2_10);
+}
- /*
- * adjust conversion until strtod(s) == f exactly.
- */
- for(i=0; i<10; i++) {- g = js_strtod(s, NULL);
- if(f > g) {- if(xadd1(s, NSIGNIF)) {- /* gained a digit */
- e--;
- js_fmtexp(s+NSIGNIF, e);
- }
- continue;
- }
- if(f < g) {- if(xsub1(s, NSIGNIF)) {- /* lost a digit */
- e++;
- js_fmtexp(s+NSIGNIF, e);
- }
- continue;
- }
- break;
- }
+static diy_fp_t minus(diy_fp_t x, diy_fp_t y)
+{+ diy_fp_t r;
+ assert(x.e == y.e);
+ assert(x.f >= y.f);
+ r.f = x.f - y.f;
+ r.e = x.e;
+ return r;
+}
- /*
- * play with the decimal to try to simplify.
- */
+static diy_fp_t multiply(diy_fp_t x, diy_fp_t y)
+{+ uint64_t a,b,c,d,ac,bc,ad,bd,tmp;
+ diy_fp_t r; uint64_t M32 = 0xFFFFFFFF;
+ a = x.f >> 32; b = x.f & M32;
+ c = y.f >> 32; d = y.f & M32;
+ ac = a*c; bc = b*c; ad = a*d; bd = b*d;
+ tmp = (bd>>32) + (ad&M32) + (bc&M32);
+ tmp += 1U << 31;
+ r.f = ac+(ad>>32)+(bc>>32)+(tmp >>32);
+ r.e = x.e + y.e + 64;
+ return r;
+}
- /*
- * bump last few digits up to 9 if we can
- */
- for(i=NSIGNIF-1; i>=NSIGNIF-3; i--) {- c = s[i];
- if(c != '9') {- s[i] = '9';
- g = js_strtod(s, NULL);
- if(g != f) {- s[i] = c;
- break;
- }
- }
- }
+typedef union {+ double d;
+ uint64_t n;
+} converter_t;
- /*
- * add 1 in hopes of turning 9s to 0s
- */
- if(s[NSIGNIF-1] == '9') {- strcpy(tmp, s);
- ee = e;
- if(xadd1(tmp, NSIGNIF)) {- ee--;
- js_fmtexp(tmp+NSIGNIF, ee);
- }
- g = js_strtod(tmp, NULL);
- if(g == f) {- strcpy(s, tmp);
- e = ee;
- }
+static uint64_t double_to_uint64(double d) { converter_t tmp; tmp.d = d; return tmp.n; }+
+#define DP_SIGNIFICAND_SIZE 52
+#define DP_EXPONENT_BIAS (0x3FF + DP_SIGNIFICAND_SIZE)
+#define DP_MIN_EXPONENT (-DP_EXPONENT_BIAS)
+#define DP_EXPONENT_MASK 0x7FF0000000000000
+#define DP_SIGNIFICAND_MASK 0x000FFFFFFFFFFFFF
+#define DP_HIDDEN_BIT 0x0010000000000000
+
+static diy_fp_t double2diy_fp(double d)
+{+ uint64_t d64 = double_to_uint64(d);
+ int biased_e = (d64 & DP_EXPONENT_MASK) >> DP_SIGNIFICAND_SIZE;
+ uint64_t significand = (d64 & DP_SIGNIFICAND_MASK);
+ diy_fp_t res;
+ if (biased_e != 0) {+ res.f = significand + DP_HIDDEN_BIT;
+ res.e = biased_e - DP_EXPONENT_BIAS;
+ } else {+ res.f = significand;
+ res.e = DP_MIN_EXPONENT + 1;
}
+ return res;
+}
- /*
- * bump last few digits down to 0 as we can.
- */
- for(i=NSIGNIF-1; i>=NSIGNIF-3; i--) {- c = s[i];
- if(c != '0') {- s[i] = '0';
- g = js_strtod(s, NULL);
- if(g != f) {- s[i] = c;
- break;
- }
- }
+static diy_fp_t normalize_boundary(diy_fp_t in)
+{+ diy_fp_t res = in;
+ /* Normalize now */
+ /* the original number could have been a denormal. */
+ while (! (res.f & (DP_HIDDEN_BIT << 1))) {+ res.f <<= 1;
+ res.e--;
}
+ /* do the final shifts in one go. Don't forget the hidden bit (the '-1') */
+ res.f <<= (DIY_SIGNIFICAND_SIZE - DP_SIGNIFICAND_SIZE - 2);
+ res.e = res.e - (DIY_SIGNIFICAND_SIZE - DP_SIGNIFICAND_SIZE - 2);
+ return res;
+}
- /*
- * remove trailing zeros.
- */
- ndigit = NSIGNIF;
- while(ndigit > 1 && s[ndigit-1] == '0'){- e++;
- --ndigit;
+static void normalized_boundaries(double d, diy_fp_t* out_m_minus, diy_fp_t* out_m_plus)
+{+ diy_fp_t v = double2diy_fp(d);
+ diy_fp_t pl, mi;
+ int significand_is_zero = v.f == DP_HIDDEN_BIT;
+ pl.f = (v.f << 1) + 1; pl.e = v.e - 1;
+ pl = normalize_boundary(pl);
+ if (significand_is_zero) {+ mi.f = (v.f << 2) - 1;
+ mi.e = v.e - 2;
+ } else {+ mi.f = (v.f << 1) - 1;
+ mi.e = v.e - 1;
}
- s[ndigit] = 0;
- *exp = e;
- *ns = ndigit;
- errno = oerrno;
+ mi.f <<= mi.e - pl.e;
+ mi.e = pl.e;
+ *out_m_plus = pl;
+ *out_m_minus = mi;
}
-static inline ulong
-umuldiv(ulong a, ulong b, ulong c)
+#define TEN2 100
+static void digit_gen(diy_fp_t Mp, diy_fp_t delta, char* buffer, int* len, int* K)
{- double d;
+ uint32_t div; int d,kappa; diy_fp_t one;
+ one.f = ((uint64_t) 1) << -Mp.e; one.e = Mp.e;
+ uint32_t p1 = Mp.f >> -one.e;
+ uint64_t p2 = Mp.f & (one.f - 1);
+ *len = 0; kappa = 3; div = TEN2;
+ while (kappa > 0) {+ d = p1 / div;
+ if (d || *len) buffer[(*len)++] = '0' + d;
+ p1 %= div; kappa--; div /= 10;
+ if ((((uint64_t)p1)<<-one.e)+p2 <= delta.f) {+ *K += kappa; return;
+ }
+ }
+ do {+ p2 *= 10;
+ d = p2 >> -one.e;
+ if (d || *len) buffer[(*len)++] = '0' + d;
+ p2 &= one.f - 1; kappa--; delta.f *= 10;
+ } while (p2 > delta.f);
+ *K += kappa;
+}
- d = ((double)a * (double)b) / (double)c;
- if(d >= 4294967295.)
- d = 4294967295.;
- return (ulong)d;
+int
+js_grisu2(double v, char *buffer, int *K)
+{+ int length;
+ diy_fp_t w_m, w_p;
+ int q = 64, alpha = -59, gamma = -56;
+ normalized_boundaries(v, &w_m, &w_p);
+ int mk = k_comp(w_p.e + q, alpha, gamma);
+ diy_fp_t c_mk = cached_power(mk);
+ diy_fp_t Wp = multiply(w_p, c_mk);
+ diy_fp_t Wm = multiply(w_m, c_mk);
+ Wm.f++; Wp.f--;
+ diy_fp_t delta = minus(Wp, Wm);
+ *K = -mk;
+ digit_gen(Wp, delta, buffer, &length, K);
+ return length;
}
/*
- * This routine will convert to arbitrary precision
- * floating point entirely in multi-precision fixed.
- * The answer is the closest floating point number to
- * the given decimal number. Exactly half way are
- * rounded ala ieee rules.
- * Method is to scale input decimal between .500 and .999...
- * with external power of 2, then binary search for the
- * closest mantissa to this decimal number.
- * Nmant is is the required precision. (53 for ieee dp)
- * Nbits is the max number of bits/word. (must be <= 28)
- * Prec is calculated - the number of words of fixed mantissa.
+ * strtod.c
+ *
+ * Copyright (c) 1988-1993 The Regents of the University of California.
+ * Copyright (c) 1994 Sun Microsystems, Inc.
+ *
+ * Permission to use, copy, modify, and distribute this software and its
+ * documentation for any purpose and without fee is hereby granted, provided
+ * that the above copyright notice appear in all copies. The University of
+ * California makes no representations about the suitability of this software
+ * for any purpose. It is provided "as is" without express or implied warranty.
*/
-enum
-{- Nbits = 28, /* bits safely represented in a ulong */
- Nmant = 53, /* bits of precision required */
- Prec = (Nmant+Nbits+1)/Nbits, /* words of Nbits each to represent mantissa */
- Sigbit = 1<<(Prec*Nbits-Nmant), /* first significant bit of Prec-th word */
- Ndig = 1500,
- One = (ulong)(1<<Nbits),
- Half = (ulong)(One>>1),
- Maxe = 310,
- Fsign = 1<<0, /* found - */
- Fesign = 1<<1, /* found e- */
- Fdpoint = 1<<2, /* found . */
+/* Largest possible base 10 exponent. Any exponent larger than this will
+ * already produce underflow or overflow, so there's no need to worry about
+ * additional digits.
+ */
+static int maxExponent = 511;
- S0 = 0, /* _ _S0 +S1 #S2 .S3 */
- S1, /* _+ #S2 .S3 */
- S2, /* _+# #S2 .S4 eS5 */
- S3, /* _+. #S4 */
- S4, /* _+#.# #S4 eS5 */
- S5, /* _+#.#e +S6 #S7 */
- S6, /* _+#.#e+ #S7 */
- S7 /* _+#.#e+# #S7 */
+/* Table giving binary powers of 10. Entry
+ * is 10^2^i. Used to convert decimal
+ * exponents into floating-point numbers.
+ */
+static double powersOf10[] = {+ 10.,
+ 100.,
+ 1.0e4,
+ 1.0e8,
+ 1.0e16,
+ 1.0e32,
+ 1.0e64,
+ 1.0e128,
+ 1.0e256
};
-static int xcmp(char*, char*);
-static int fpcmp(char*, ulong*);
-static void frnorm(ulong*);
-static void divascii(char*, int*, int*, int*);
-static void mulascii(char*, int*, int*, int*);
-
-typedef struct Tab Tab;
-struct Tab
-{- int bp;
- int siz;
- char* cmp;
-};
-
+/* Parse a decimal ASCII floating-point number, optionally preceded by white
+ * space. Must have form "-I.FE-X", where I is the integer part of the
+ * mantissa, F is the fractional part of the mantissa, and X is the exponent.
+ * Either of the signs may be "+", "-", or omitted. Either I or F may be
+ * omitted, or both. The decimal point isn't necessary unless F is present.
+ * The "E" may actually be an "e". E and X may both be omitted (but not just
+ * one).
+ */
double
-js_strtod(const char *as, char **aas)
+js_strtod(const char *string, char **endPtr)
{- int na, ex, dp, bp, c, i, flag, state;
- ulong low[Prec], hig[Prec], mid[Prec];
- double d;
- char *s, a[Ndig];
+ int sign, expSign = FALSE;
+ double fraction, dblExp, *d;
+ register const char *p;
+ register int c;
- flag = 0; /* Fsign, Fesign, Fdpoint */
- na = 0; /* number of digits of a[] */
- dp = 0; /* na of decimal point */
- ex = 0; /* exonent */
+ /* Exponent read from "EX" field. */
+ int exp = 0;
- state = S0;
- for(s=(char*)as;; s++) {- c = *s;
- if(c >= '0' && c <= '9') {- switch(state) {- case S0:
- case S1:
- case S2:
- state = S2;
- break;
- case S3:
- case S4:
- state = S4;
- break;
+ /* Exponent that derives from the fractional part. Under normal
+ * circumstances, it is the negative of the number of digits in F.
+ * However, if I is very long, the last digits of I get dropped
+ * (otherwise a long I with a large negative exponent could cause an
+ * unnecessary overflow on I alone). In this case, fracExp is
+ * incremented one for each dropped digit.
+ */
+ int fracExp = 0;
- case S5:
- case S6:
- case S7:
- state = S7;
- ex = ex*10 + (c-'0');
- continue;
- }
- if(na == 0 && c == '0') {- dp--;
- continue;
- }
- if(na < Ndig-50)
- a[na++] = c;
- continue;
- }
- switch(c) {- case '\t':
- case '\n':
- case '\v':
- case '\f':
- case '\r':
- case ' ':
- if(state == S0)
- continue;
- break;
- case '-':
- if(state == S0)
- flag |= Fsign;
- else
- flag |= Fesign;
- /* fall through */
- case '+':
- if(state == S0)
- state = S1;
- else
- if(state == S5)
- state = S6;
- else
- break; /* syntax */
- continue;
- case '.':
- flag |= Fdpoint;
- dp = na;
- if(state == S0 || state == S1) {- state = S3;
- continue;
- }
- if(state == S2) {- state = S4;
- continue;
- }
- break;
- case 'e':
- case 'E':
- if(state == S2 || state == S4) {- state = S5;
- continue;
- }
- break;
- }
- break;
- }
+ /* Number of digits in mantissa. */
+ int mantSize;
- /*
- * clean up return char-pointer
- */
- switch(state) {- case S0:
- if(xcmp(s, "nan") == 0) {- if(aas != NULL)
- *aas = s+3;
- goto retnan;
- }
- /* fall through */
- case S1:
- if(xcmp(s, "infinity") == 0) {- if(aas != NULL)
- *aas = s+8;
- goto retinf;
- }
- if(xcmp(s, "inf") == 0) {- if(aas != NULL)
- *aas = s+3;
- goto retinf;
- }
- /* fall through */
- case S3:
- if(aas != NULL)
- *aas = (char*)as;
- goto ret0; /* no digits found */
- case S6:
- s--; /* back over +- */
- /* fall through */
- case S5:
- s--; /* back over e */
- break;
- }
- if(aas != NULL)
- *aas = s;
+ /* Number of mantissa digits BEFORE decimal point. */
+ int decPt;
- if(flag & Fdpoint)
- while(na > 0 && a[na-1] == '0')
- na--;
- if(na == 0)
- goto ret0; /* zero */
- a[na] = 0;
- if(!(flag & Fdpoint))
- dp = na;
- if(flag & Fesign)
- ex = -ex;
- dp += ex;
- if(dp < -Maxe){- errno = ERANGE;
- goto ret0; /* underflow by exp */
- } else
- if(dp > +Maxe)
- goto retinf; /* overflow by exp */
+ /* Temporarily holds location of exponent in string. */
+ const char *pExp;
/*
- * normalize the decimal ascii number
- * to range .[5-9][0-9]* e0
+ * Strip off leading blanks and check for a sign.
*/
- bp = 0; /* binary exponent */
- while(dp > 0)
- divascii(a, &na, &dp, &bp);
- while(dp < 0 || a[0] < '5')
- mulascii(a, &na, &dp, &bp);
- /* close approx by naive conversion */
- mid[0] = 0;
- mid[1] = 1;
- for(i=0; (c=a[i]) != '\0'; i++) {- mid[0] = mid[0]*10 + (c-'0');
- mid[1] = mid[1]*10;
- if(i >= 8)
- break;
+ p = string;
+ while (*p == ' ' || *p == '\t' || *p == '\n' || *p == '\r') {+ p += 1;
}
- low[0] = umuldiv(mid[0], One, mid[1]);
- hig[0] = umuldiv(mid[0]+1, One, mid[1]);
- for(i=1; i<Prec; i++) {- low[i] = 0;
- hig[i] = One-1;
+ if (*p == '-') {+ sign = TRUE;
+ p += 1;
+ } else {+ if (*p == '+') {+ p += 1;
+ }
+ sign = FALSE;
}
- /* binary search for closest mantissa */
- for(;;) {- /* mid = (hig + low) / 2 */
- c = 0;
- for(i=0; i<Prec; i++) {- mid[i] = hig[i] + low[i];
- if(c)
- mid[i] += One;
- c = mid[i] & 1;
- mid[i] >>= 1;
- }
- frnorm(mid);
+ /*
+ * Count the number of digits in the mantissa (including the decimal
+ * point), and also locate the decimal point.
+ */
- /* compare */
- c = fpcmp(a, mid);
- if(c > 0) {- c = 1;
- for(i=0; i<Prec; i++)
- if(low[i] != mid[i]) {- c = 0;
- low[i] = mid[i];
- }
- if(c)
- break; /* between mid and hig */
- continue;
+ decPt = -1;
+ for (mantSize = 0; ; mantSize += 1)
+ {+ c = *p;
+ if (!(c>='0'&&c<='9')) {+ if ((c != '.') || (decPt >= 0)) {+ break;
+ }
+ decPt = mantSize;
}
- if(c < 0) {- for(i=0; i<Prec; i++)
- hig[i] = mid[i];
- continue;
- }
-
- /* only hard part is if even/odd roundings wants to go up */
- c = mid[Prec-1] & (Sigbit-1);
- if(c == Sigbit/2 && (mid[Prec-1]&Sigbit) == 0)
- mid[Prec-1] -= c;
- break; /* exactly mid */
+ p += 1;
}
- /* normal rounding applies */
- c = mid[Prec-1] & (Sigbit-1);
- mid[Prec-1] -= c;
- if(c >= Sigbit/2) {- mid[Prec-1] += Sigbit;
- frnorm(mid);
- }
- goto out;
-
-ret0:
- if(flag & Fsign)
- return -0.0;
- return 0;
-
-retnan:
- return NAN;
-
-retinf:
/*
- * Unix strtod requires these. Plan 9 would return Inf(0) or Inf(-1). */
- errno = ERANGE;
- if(flag & Fsign)
- return -HUGE_VAL;
- return HUGE_VAL;
+ * Now suck up the digits in the mantissa. Use two integers to
+ * collect 9 digits each (this is faster than using floating-point).
+ * If the mantissa has more than 18 digits, ignore the extras, since
+ * they can't affect the value anyway.
+ */
-out:
- d = 0;
- for(i=0; i<Prec; i++)
- d = d*One + mid[i];
- if(flag & Fsign)
- d = -d;
- d = ldexp(d, bp - Prec*Nbits);
- if(d == 0){ /* underflow */- errno = ERANGE;
+ pExp = p;
+ p -= mantSize;
+ if (decPt < 0) {+ decPt = mantSize;
+ } else {+ mantSize -= 1; /* One of the digits was the point. */
}
- return d;
-}
-
-static void
-frnorm(ulong *f)
-{- int i, c;
-
- c = 0;
- for(i=Prec-1; i>0; i--) {- f[i] += c;
- c = f[i] >> Nbits;
- f[i] &= One-1;
+ if (mantSize > 18) {+ fracExp = decPt - 18;
+ mantSize = 18;
+ } else {+ fracExp = decPt - mantSize;
}
- f[0] += c;
-}
-
-static int
-fpcmp(char *a, ulong* f)
-{- ulong tf[Prec];
- int i, d, c;
-
- for(i=0; i<Prec; i++)
- tf[i] = f[i];
-
- for(;;) {- /* tf *= 10 */
- for(i=0; i<Prec; i++)
- tf[i] = tf[i]*10;
- frnorm(tf);
- d = (tf[0] >> Nbits) + '0';
- tf[0] &= One-1;
-
- /* compare next digit */
- c = *a;
- if(c == 0) {- if('0' < d)- return -1;
- if(tf[0] != 0)
- goto cont;
- for(i=1; i<Prec; i++)
- if(tf[i] != 0)
- goto cont;
- return 0;
+ if (mantSize == 0) {+ fraction = 0.0;
+ p = string;
+ goto done;
+ } else {+ int frac1, frac2;
+ frac1 = 0;
+ for ( ; mantSize > 9; mantSize -= 1)
+ {+ c = *p;
+ p += 1;
+ if (c == '.') {+ c = *p;
+ p += 1;
+ }
+ frac1 = 10*frac1 + (c - '0');
}
- if(c > d)
- return +1;
- if(c < d)
- return -1;
- a++;
- cont:;
+ frac2 = 0;
+ for (; mantSize > 0; mantSize -= 1)
+ {+ c = *p;
+ p += 1;
+ if (c == '.') {+ c = *p;
+ p += 1;
+ }
+ frac2 = 10*frac2 + (c - '0');
+ }
+ fraction = (1.0e9 * frac1) + frac2;
}
-}
-static inline void
-divby(char *a, int *na, int b)
-{- int n, c;
- char *p;
+ /*
+ * Skim off the exponent.
+ */
- p = a;
- n = 0;
- while(n>>b == 0) {- c = *a++;
- if(c == 0) {- while(n) {- c = n*10;
- if(c>>b)
- break;
- n = c;
+ p = pExp;
+ if ((*p == 'E') || (*p == 'e')) {+ p += 1;
+ if (*p == '-') {+ expSign = TRUE;
+ p += 1;
+ } else {+ if (*p == '+') {+ p += 1;
}
- goto xx;
+ expSign = FALSE;
}
- n = n*10 + c-'0';
- (*na)--;
+ while ((*p >= 0) && (*p <= '9')) {+ exp = exp * 10 + (*p - '0');
+ p += 1;
+ }
}
- for(;;) {- c = n>>b;
- n -= c<<b;
- *p++ = c + '0';
- c = *a++;
- if(c == 0)
- break;
- n = n*10 + c-'0';
+ if (expSign) {+ exp = fracExp - exp;
+ } else {+ exp = fracExp + exp;
}
- (*na)++;
-xx:
- while(n) {- n = n*10;
- c = n>>b;
- n -= c<<b;
- *p++ = c + '0';
- (*na)++;
- if (*na >= Ndig) break; /* abort if overflowing */
- }
- *p = 0;
-}
-static Tab tab1[] =
-{- { 1, 0, "" },- { 3, 1, "7" },- { 6, 2, "63" },- { 9, 3, "511" },- { 13, 4, "8191" },- { 16, 5, "65535" },- { 19, 6, "524287" },- { 23, 7, "8388607" },- { 26, 8, "67108863" },- { 27, 9, "134217727" },-};
+ /*
+ * Generate a floating-point number that represents the exponent.
+ * Do this by processing the exponent one bit at a time to combine
+ * many powers of 2 of 10. Then combine the exponent with the
+ * fraction.
+ */
-static void
-divascii(char *a, int *na, int *dp, int *bp)
-{- int b, d;
- Tab *t;
-
- d = *dp;
- if(d >= (int)(nelem(tab1)))
- d = (int)(nelem(tab1))-1;
- t = tab1 + d;
- b = t->bp;
- if(memcmp(a, t->cmp, t->siz) > 0)
- d--;
- *dp -= d;
- *bp += b;
- divby(a, na, b);
-}
-
-static inline void
-mulby(char *a, char *p, char *q, int b)
-{- int n, c;
-
- n = 0;
- *p = 0;
- for(;;) {- q--;
- if(q < a)
- break;
- c = *q - '0';
- c = (c<<b) + n;
- n = c/10;
- c -= n*10;
- p--;
- *p = c + '0';
+ if (exp < 0) {+ expSign = TRUE;
+ exp = -exp;
+ } else {+ expSign = FALSE;
}
- while(n) {- c = n;
- n = c/10;
- c -= n*10;
- p--;
- *p = c + '0';
+ if (exp > maxExponent) {+ exp = maxExponent;
+ errno = ERANGE;
}
-}
+ dblExp = 1.0;
+ for (d = powersOf10; exp != 0; exp >>= 1, d += 1) {+ if (exp & 01) {+ dblExp *= *d;
+ }
+ }
+ if (expSign) {+ fraction /= dblExp;
+ } else {+ fraction *= dblExp;
+ }
-static Tab tab2[] =
-{- { 1, 1, "" }, /* dp = 0-0 */- { 3, 3, "125" },- { 6, 5, "15625" },- { 9, 7, "1953125" },- { 13, 10, "1220703125" },- { 16, 12, "152587890625" },- { 19, 14, "19073486328125" },- { 23, 17, "11920928955078125" },- { 26, 19, "1490116119384765625" },- { 27, 19, "7450580596923828125" }, /* dp 8-9 */-};
+done:
+ if (endPtr != NULL) {+ *endPtr = (char *) p;
+ }
-static void
-mulascii(char *a, int *na, int *dp, int *bp)
-{- char *p;
- int d, b;
- Tab *t;
-
- d = -*dp;
- if(d >= (int)(nelem(tab2)))
- d = (int)(nelem(tab2))-1;
- t = tab2 + d;
- b = t->bp;
- if(memcmp(a, t->cmp, t->siz) < 0)
- d--;
- p = a + *na;
- *bp -= b;
- *dp += d;
- *na += d;
- mulby(a, p+d, p, b);
-}
-
-static int
-xcmp(char *a, char *b)
-{- int c1, c2;
-
- while((c1 = *b++) != '\0') {- c2 = *a++;
- if(c2 >= 'A' && c2 <= 'Z')
- c2 = c2 - 'A' + 'a';
- if(c1 != c2)
- return 1;
+ if (sign) {+ return -fraction;
}
- return 0;
+ return fraction;
}
--- a/jsi.h
+++ b/jsi.h
@@ -87,7 +87,7 @@
/* Portable strtod and printf float formatting */
void js_fmtexp(char *p, int e);
-void js_dtoa(double f, char *digits, int *exp, int *neg, int *ndigits);
+int js_grisu2(double v, char *buffer, int *K);
double js_strtod(const char *as, char **aas);
/* Private stack functions */
--- a/jsvalue.c
+++ b/jsvalue.c
@@ -220,16 +220,16 @@
const char *jsV_numbertostring(js_State *J, char buf[32], double f)
{char digits[32], *p = buf, *s = digits;
- int exp, neg, ndigits, point;
+ int exp, ndigits, point;
if (isnan(f)) return "NaN";
if (isinf(f)) return f < 0 ? "-Infinity" : "Infinity";
if (f == 0) return "0";
- js_dtoa(f, digits, &exp, &neg, &ndigits);
+ ndigits = js_grisu2(f, digits, &exp);
point = ndigits + exp;
- if (neg)
+ if (signbit(f))
*p++ = '-';
if (point < -5 || point > 21) {