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atof.c
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atof.c
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/* fast_atof by Peter Miller 23/1/2020
See below for license information.
This atof also returns a "good number" flag so its NOT a drop in replacement for the standard atof.
The code should be robust to anything thrown at it (lots of leading of trailing zeros, extremely large numbers of digits, etc ).
As well as floating point numbers this also accepts NAN and INF (case does not matter).
As the name suggests its also written to be fast (much faster than the built in strtod or atof library functions at least for mingw64 ).
Its round trip exact for doubles when used with ya_sprintf and the built in sprintf functions
ie if you start with a double convert it to a string (with enough digits in it) and then use one of these functions you get exactly (bit wise) the same number as you started with.
*/
#define USE_LD /* if defined use long double rather than pair of doubles for double conversions */
#if 0 /* following not needed by wmawk2 */
#define AFormatSupport /* if defined then support numbers as generated by printf %a ie 0xh.hhhhp+/-d */
#ifdef __SIZEOF_INT128__ /* only allow if compiler supports __float128 & __int128 */
#define ATOF128 /* if defined add support for reading __float128 's */
#define F128_DD /* if defined use "double double" maths (both f128_t) for f128 conversions [ without this there are round-loop conversion errors ] */
#define F128_DD_TABLE /* if defined use powers of 10 table with F128DD, if not defined compute powers of 10 at runtime - my tests show these take almost identical runtimes ! */
#endif
#endif
/*----------------------------------------------------------------------------
* MIT License:
*
* Copyright (c) 2020 Peter Miller
*
* 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 AUTHOR OR COPYRIGHT HOLDER 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.
*--------------------------------------------------------------------------*/
//#define DEBUG
#if defined(DEBUG)
#define __USE_MINGW_ANSI_STDIO 1 /* if this is defined then writing to stdout > NUL is VERY slow (70 secs vs 4 secs) ! Note strtof() etc are still much slower than fast_atof() etc */
#include <stdio.h>
#endif
#include <stdlib.h>
#include <ctype.h>
#include <stdbool.h> /* for bool */
#include <stdint.h> /* for int64_t etc */
#include <math.h> /* for NAN, INFINITY */
#ifndef USE_LD
#include "double-double.h"
#endif
#define STATIC_ASSERT(condition) extern int macro_assert[!!(condition)-1] /* check at compile time and works in a global or function context see https://scaryreasoner.wordpress.com/2009/02/28/checking-sizeof-at-compile-time/ */
STATIC_ASSERT( sizeof(long double) > sizeof(double)); // long double needs more precision than double for the code here to work to full accuracy.
/* the line below defines GCC_OPTIMIZE_AWARE to 1 when we can use # pragma GCC optimize ("-O2") */
#define GCC_OPTIMIZE_AWARE (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 7)) || defined(__clang__)
/* code below cannot be compiled with -Ofast as this makes the compiler break some C rules that we need (even use NAN etc) , so make sure of this here */
#if GCC_OPTIMIZE_AWARE
#pragma GCC optimize ("-O3") /* cannot use Ofast */
#endif
/* ieee floating point maths limits:
double (64 bits) max 1.797 e + 308
min 2.225 e-308
min denormalised 4.94 e-324
sig digits 15-17
float (32 bit) max 3.4e38
min 1.17e-38
min denormalised 1.4e-45
sig digits 6-9
Also note that 0x0fff ffff ffff ffff = 1,152,921,504,606,846,975 , so 18 digits easily fit into a 64 bit unsigned (with 4 bits spare) - which is enough for a double mantissa.
2^64= 18,446,744,073,709,551,616
0xffff ffff = 4,294,967,295 so 9 digits fits with a 32 bit unsigned (with 2 bits spare) which is NOT enough for a float mantissa
*/
double fast_atof(const char *s,bool * not_number);
double fast_atof_nan(const char *s);// like fast_atof, but returns NAN if whole string is not a valid number
double fast_strtod(const char *s,char ** endptr);
float fast_strtof(const char *s,char **endptr); // if endptr != NULL returns 1st character thats not in the number
static const int maxExponent = 308; /* Largest possible base 10 for a double exponent. (must match array below) */
static const int maxfExponent = 38; /* Largest possible base 10 for a float exponent. (must match array below) */
#ifdef USE_LD
static long double const powersOf10[] =
{
1e0L, 1e1L, 1e2L, 1e3L, 1e4L, 1e5L, 1e6L, 1e7L, 1e8L, 1e9L,
1e10L, 1e11L, 1e12L, 1e13L, 1e14L, 1e15L, 1e16L, 1e17L, 1e18L, 1e19L,
1e20L, 1e21L, 1e22L, 1e23L, 1e24L, 1e25L, 1e26L, 1e27L, 1e28L, 1e29L,
1e30L, 1e31L, 1e32L, 1e33L, 1e34L, 1e35L, 1e36L, 1e37L, 1e38L, 1e39L,
1e40L, 1e41L, 1e42L, 1e43L, 1e44L, 1e45L, 1e46L, 1e47L, 1e48L, 1e49L,
1e50L, 1e51L, 1e52L, 1e53L, 1e54L, 1e55L, 1e56L, 1e57L, 1e58L, 1e59L,
1e60L, 1e61L, 1e62L, 1e63L, 1e64L, 1e65L, 1e66L, 1e67L, 1e68L, 1e69L,
1e70L, 1e71L, 1e72L, 1e73L, 1e74L, 1e75L, 1e76L, 1e77L, 1e78L, 1e79L,
1e80L, 1e81L, 1e82L, 1e83L, 1e84L, 1e85L, 1e86L, 1e87L, 1e88L, 1e89L,
1e90L, 1e91L, 1e92L, 1e93L, 1e94L, 1e95L, 1e96L, 1e97L, 1e98L, 1e99L,
1e100L, 1e101L, 1e102L, 1e103L, 1e104L, 1e105L, 1e106L, 1e107L, 1e108L, 1e109L,
1e110L, 1e111L, 1e112L, 1e113L, 1e114L, 1e115L, 1e116L, 1e117L, 1e118L, 1e119L,
1e120L, 1e121L, 1e122L, 1e123L, 1e124L, 1e125L, 1e126L, 1e127L, 1e128L, 1e129L,
1e130L, 1e131L, 1e132L, 1e133L, 1e134L, 1e135L, 1e136L, 1e137L, 1e138L, 1e139L,
1e140L, 1e141L, 1e142L, 1e143L, 1e144L, 1e145L, 1e146L, 1e147L, 1e148L, 1e149L,
1e150L, 1e151L, 1e152L, 1e153L, 1e154L, 1e155L, 1e156L, 1e157L, 1e158L, 1e159L,
1e160L, 1e161L, 1e162L, 1e163L, 1e164L, 1e165L, 1e166L, 1e167L, 1e168L, 1e169L,
1e170L, 1e171L, 1e172L, 1e173L, 1e174L, 1e175L, 1e176L, 1e177L, 1e178L, 1e179L,
1e180L, 1e181L, 1e182L, 1e183L, 1e184L, 1e185L, 1e186L, 1e187L, 1e188L, 1e189L,
1e190L, 1e191L, 1e192L, 1e193L, 1e194L, 1e195L, 1e196L, 1e197L, 1e198L, 1e199L,
1e200L, 1e201L, 1e202L, 1e203L, 1e204L, 1e205L, 1e206L, 1e207L, 1e208L, 1e209L,
1e210L, 1e211L, 1e212L, 1e213L, 1e214L, 1e215L, 1e216L, 1e217L, 1e218L, 1e219L,
1e220L, 1e221L, 1e222L, 1e223L, 1e224L, 1e225L, 1e226L, 1e227L, 1e228L, 1e229L,
1e230L, 1e231L, 1e232L, 1e233L, 1e234L, 1e235L, 1e236L, 1e237L, 1e238L, 1e239L,
1e240L, 1e241L, 1e242L, 1e243L, 1e244L, 1e245L, 1e246L, 1e247L, 1e248L, 1e249L,
1e250L, 1e251L, 1e252L, 1e253L, 1e254L, 1e255L, 1e256L, 1e257L, 1e258L, 1e259L,
1e260L, 1e261L, 1e262L, 1e263L, 1e264L, 1e265L, 1e266L, 1e267L, 1e268L, 1e269L,
1e270L, 1e271L, 1e272L, 1e273L, 1e274L, 1e275L, 1e276L, 1e277L, 1e278L, 1e279L,
1e280L, 1e281L, 1e282L, 1e283L, 1e284L, 1e285L, 1e286L, 1e287L, 1e288L, 1e289L,
1e290L, 1e291L, 1e292L, 1e293L, 1e294L, 1e295L, 1e296L, 1e297L, 1e298L, 1e299L,
1e300L, 1e301L, 1e302L, 1e303L, 1e304L, 1e305L, 1e306L, 1e307L, 1e308L
};
#else
/* use double double rather than long double */
#include "table10.h" /* powers of 10 table for double doubles */
static void dd_to_power10( double *ohi, double *olo, double dh,double dl, int power ) // power can be +/-500. ASSUMES dh,dl came from a uint64 - this code will not work in general for all values dh,dl.
{
double th,tl; // power10
double xh,xl;
if(power==0)
{*ohi=dh; /* 10^0=1 so can just return d - we expect this special case to be relatively common so worth doing */
*olo=dl;
}
else if(power<-200) // need to do in 2 multiplies rather than 1 as the max -ve exponent for a normalised double is -308. Picked -200 so we keep full precision of double double
{
th=NegPowerOf10_hi[200];
tl=NegPowerOf10_lo[200];
mult_dd_dd(&xh,&xl,th,tl,dh,dl);// xh/l=th/l*d
// there is a risk that the next multiply will end up with denormalised numbers and so can be inexact, so multiply by 2^100 first, do multiply then divide back again
// we have just divided by 10^200 so the multiply by 2^100 (1.3e30) cannot overflow
xh=ldexp(xh,100);// multiply by 2^100
xl=ldexp(xl,100);
th=NegPowerOf10_hi[(-power)-200];
tl=NegPowerOf10_lo[(-power)-200];
mult_dd_dd(&xh,&xl,th,tl,xh,xl);
xh=ldexp(xh,-100);// multiply by 2^-100
xl=ldexp(xl,-100);
*ohi=xh;
*olo=xl;
}
else if(power<0)
{// can do with one double-double multiply
th=NegPowerOf10_hi[-power];
tl=NegPowerOf10_lo[-power];
mult_dd_dd(ohi,olo,th,tl,dh,dl);
}
else if (power>290) // need to do in 2 multiplies rather than 1 as the max exponent for a double is 308 and we may need to multiply by 10^350 here. Picked 290 as thats 18 sf from 308 so keeping full precision of double double
{
th=PosPowerOf10_hi[290];
tl=PosPowerOf10_lo[290];
mult_dd_dd(&xh,&xl,th,tl,dh,dl);// xh/l=th/l*d
th=PosPowerOf10_hi[power-290];
tl=PosPowerOf10_lo[power-290];
mult_dd_dd(ohi,olo,th,tl,xh,xl);
}
else
{// can do with one double-double multiply
th=PosPowerOf10_hi[power];
tl=PosPowerOf10_lo[power];
mult_dd_dd(ohi,olo,th,tl,dh,dl);
}
}
#endif
static double const dblpowersOf10[] = /* always double */
{
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,
1e160, 1e161, 1e162, 1e163, 1e164, 1e165, 1e166, 1e167, 1e168, 1e169,
1e170, 1e171, 1e172, 1e173, 1e174, 1e175, 1e176, 1e177, 1e178, 1e179,
1e180, 1e181, 1e182, 1e183, 1e184, 1e185, 1e186, 1e187, 1e188, 1e189,
1e190, 1e191, 1e192, 1e193, 1e194, 1e195, 1e196, 1e197, 1e198, 1e199,
1e200, 1e201, 1e202, 1e203, 1e204, 1e205, 1e206, 1e207, 1e208, 1e209,
1e210, 1e211, 1e212, 1e213, 1e214, 1e215, 1e216, 1e217, 1e218, 1e219,
1e220, 1e221, 1e222, 1e223, 1e224, 1e225, 1e226, 1e227, 1e228, 1e229,
1e230, 1e231, 1e232, 1e233, 1e234, 1e235, 1e236, 1e237, 1e238, 1e239,
1e240, 1e241, 1e242, 1e243, 1e244, 1e245, 1e246, 1e247, 1e248, 1e249,
1e250, 1e251, 1e252, 1e253, 1e254, 1e255, 1e256, 1e257, 1e258, 1e259,
1e260, 1e261, 1e262, 1e263, 1e264, 1e265, 1e266, 1e267, 1e268, 1e269,
1e270, 1e271, 1e272, 1e273, 1e274, 1e275, 1e276, 1e277, 1e278, 1e279,
1e280, 1e281, 1e282, 1e283, 1e284, 1e285, 1e286, 1e287, 1e288, 1e289,
1e290, 1e291, 1e292, 1e293, 1e294, 1e295, 1e296, 1e297, 1e298, 1e299,
1e300, 1e301, 1e302, 1e303, 1e304, 1e305, 1e306, 1e307, 1e308
};
static float const fltpowersOf10[] = /* always float */
{
1e0f, 1e1f, 1e2f, 1e3f, 1e4f, 1e5f, 1e6f, 1e7f, 1e8f, 1e9f,
1e10f, 1e11f, 1e12f, 1e13f, 1e14f, 1e15f, 1e16f, 1e17f, 1e18f, 1e19f,
1e20f, 1e21f, 1e22f, 1e23f, 1e24f, 1e25f, 1e26f, 1e27f, 1e28f, 1e29f,
1e30f, 1e31f, 1e32f, 1e33f, 1e34f, 1e35f, 1e36f, 1e37f, 1e38f
};
static uint64_t u64powersOf10[]=
{
UINT64_C(1), // 10^ 0
UINT64_C(10), // 10^1
UINT64_C(100), // 10^2
UINT64_C(1000), // 10^3
UINT64_C(10000),// 10^4
UINT64_C(100000),// 5
UINT64_C(1000000),// 6
UINT64_C(10000000),// 7
UINT64_C(100000000),// 8
UINT64_C(1000000000),// 9
UINT64_C(10000000000),// 10
UINT64_C(100000000000),// 11
UINT64_C(1000000000000),// 12
UINT64_C(10000000000000),// 13
UINT64_C(100000000000000),// 14
UINT64_C(1000000000000000), // 15
UINT64_C(10000000000000000), // 16
UINT64_C(100000000000000000), // 17
UINT64_C(1000000000000000000), // 18
UINT64_C(10000000000000000000) // 19 2^64=1.8446744073709551616e+19 so 10^19 should fit into a uint64
};
static uint32_t u32powersOf10[]=
{
UINT32_C(1), // 10^ 0
UINT32_C(10), // 10^1
UINT32_C(100), // 10^2
UINT32_C(1000), // 10^3
UINT32_C(10000),// 10^4
UINT32_C(100000),// 5
UINT32_C(1000000),// 6
UINT32_C(10000000),// 7
UINT32_C(100000000),// 8
UINT32_C(1000000000),// 9 [ largest possible 10^10 gives compiler error (overflow) ]
};
/*
*----------------------------------------------------------------------
*
* double fast_strtod(const char *s,char **endptr)
*
* This procedure converts a floating-point number from an ASCII
* decimal representation to internal double-precision format.
* Also accepts "NaN", "Inf" and "Infinity" (any mix of case) which return NAN and INFINITY
* Results:
* The return value is the floating-point equivalent of string.
* *endptr is set to the first character after the valid number
*
* If endptr == NULL it is ignored.
*
* Side effects:
* None.
*
*----------------------------------------------------------------------
*/
static const int maxdigits=19; // see above this is the largest possible in a uint64
double fast_strtod(const char *s,char **endptr) // if endptr != NULL returns 1st character thats not in the number
{
#ifdef USE_LD
long double dr;
#else
double dh,dl; /* use double double instead of long double */
#endif
bool sign=false,expsign=false,got_number=false;
uint64_t r=0; // mantissa
int exp=0,rexp=0;
int nos_mant_digits=0;
const char *se=s; // string end - candidate for endptr
#ifdef DEBUG
fprintf(stderr,"strtod(%s):\n",s);
#endif
while(isspace(*s)) ++s; // skip initial whitespace
// deal with leading sign
if(*s=='+') ++s;
else if(*s=='-')
{sign=true;
++s;
}
// NAN is a special case - NAN is signed in the input but always returns NAN
if((*s=='n' || *s=='N') && (s[1]=='a' || s[1]=='A') && (s[2]=='n' || s[2]=='N'))
{if(endptr!=NULL) *endptr=(char *)s+3;// 3 for NAN
return NAN;
}
// INF or Infinity is a special case - and is signed
if((*s=='i' || *s=='I') && (s[1]=='n' || s[1]=='N') && (s[2]=='f' || s[2]=='F'))
{s+=3;// INF
if((*s=='i' || *s=='I') && (s[1]=='n' || s[1]=='N') && (s[2]=='i' || s[2]=='I') && (s[3]=='t' || s[3]=='T') && (s[4]=='y' || s[4]=='Y') )
s+=5; // "Infinity" is 5 more chars (inity) than "inf"
if(endptr!=NULL) *endptr=(char *)s;
if(sign) return -INFINITY;
return INFINITY;
}
#ifdef AFormatSupport
/* support hex floating point numbers of the format 0xh.hhhhp+/-d as generated by printf %a */
if(*s=='0' && (s[1]=='x' || s[1] =='X'))
{ // got hex number
double h;
s+=2; // skip 0x
// no need to skip leading zero's as we can just check is ms 4 bits of r are not zero
while(isxdigit(*s))
{got_number=true; // have a valid number
if((r & UINT64_C(0xf000000000000000))==0)
{ if(*s<='9')
r=r*16+(*s-'0'); // 0..9
else
r=r*16+(tolower(*s)-'a'+10); // a-f or A-F
}
else if(exp<2048)
exp+=4; // cannot actually capture digits beyond 16 but keep track of decimal point, trap ensures we don't overflow exp when given a number with a silly number of digits (that would overflow a double)
++s;
}
// now look for optional decimal point (and fractional bit of mantissa)
if(*s=='.')
{ // got decimal point, skip and then look for fractional bit
++s;
while(isxdigit(*s))
{got_number=true; // have a valid number
if((r & UINT64_C(0xf000000000000000))==0)
{ if(*s<='9')
r=r*16+(*s-'0'); // 0..9
else
r=r*16+(tolower(*s)-'a'+10); // a-f or A-F
exp-=4;
}
// if we have too many digits after dp just ignore them
++s;
}
}
// got all of mantissa - see if its a valid number, if not we are done
if(!got_number)
{if(endptr!=NULL) *endptr=(char *)se;
#ifdef DEBUG
fprintf(stderr," strtod returns 0 (invalid hex number)\n");
#endif
return 0;
}
se=s; // update to reflect end of a valid mantissa
// now see if we have an exponent
if(*s=='p' || *s=='P')
{// have exponent, optional sign is 1st
++s ; // skip 'p'
if(*s=='+') ++s;
else if(*s=='-')
{expsign=true;
++s;
}
while(isdigit(*s))
{if(rexp<=2048)
rexp=rexp*10+(*s - '0'); // if statement clips at a value that will result in +/-inf but will not overflow int
++s;
se=s; // update to reflect end of a valid exponent (p[+-]digit+)
}
}
if(endptr!=NULL) *endptr=(char *)se; // we now know the end of the number - so save it now (means we can have multiple returns going forward without having to worry about this)
if(expsign) rexp=-rexp;
rexp+=exp; // add in correct to exponent from mantissa processing
h=ldexp((double)r,rexp); // combine mantissa and exponent
if(sign) h=-h;
#ifdef DEBUG
fprintf(stderr," strtod (0x) returns %.18g [0x%.16A] (rexp=%d, exp=%d)\n",h,h,rexp,exp);
#endif
return h; // all done
}
#endif
// skip leading zeros
while(*s=='0')
{got_number=true; // have a number (0)
++s;
}
// now read rest of the mantissa
while(isdigit(*s))
{ got_number=true; // have a valid number
if(nos_mant_digits<maxdigits)
{ r=r*10+(*s-'0');
nos_mant_digits++;
}
else
{
if(nos_mant_digits==maxdigits)
{if(*s >='5') r++; // use 1st "ignored digit" to round to nearest
nos_mant_digits++;
}
if(exp<2*maxExponent)
exp++; // cannot actually capture digits as more than 18 but keep track of decimal point, trap at 2*maxExponent ensures we don't overflow exp when given a number with a silly number of digits (that would overflow a double)
}
++s;
}
// now look for optional decimal point (and fractional bit of mantissa)
if(*s=='.')
{ // got decimal point, skip and then look for fractional bit
++s;
if(r==0)
{// number is zero at present, so deal with leading zeros in fractional bit of mantissa
while(*s=='0')
{got_number=true;
++s;
if(exp > -2*maxExponent)
exp--; // test avoids issues with silly number of leading zeros
}
}
// now process the rest of the fractional bit of the mantissa
while(isdigit(*s))
{got_number=true;
#if 1
// see if the whole remaining fractional bit is "0", if so can just skip. This speeds up some conversions (and slows others) but more importantly it ensures 1, 1.0, 1.00 & 1.15, 1.150, 1.1500 etc give exactly the same result
if(*s=='0')
{// got a zero, see if all remaining numbers in mantissa are zero
const char *s0=s;
while(*s0=='0') ++s0;
if(!isdigit(*s0))
{// was all zero's, just skip them
s=s0;
break;
}
}
#endif
if(nos_mant_digits<maxdigits)
{ r=r*10+(*s-'0');
nos_mant_digits++;
exp--;
}
else
{ // cannot actually capture digits as more than 18, so just ignore them (except for next digit which we use for rounding)
if(nos_mant_digits==maxdigits )
{if(*s >='5') r++; // use 1st "ignored digit" to round to nearest
nos_mant_digits++;
}
}
++s;
}
}
// got all of mantissa - see if its a valid number, if not we are done
if(!got_number)
{if(endptr!=NULL) *endptr=(char *)se;
#ifdef DEBUG
fprintf(stderr," strtod returns 0 (invalid number)\n");
#endif
return 0;
}
se=s; // update to reflect end of a valid mantissa
// now see if we have an exponent
if(*s=='e' || *s=='E')
{// have exponent, optional sign is 1st
++s ; // skip 'e'
if(*s=='+') ++s;
else if(*s=='-')
{expsign=true;
++s;
}
while(isdigit(*s))
{if(rexp<=2*maxExponent)
rexp=rexp*10+(*s - '0'); // if statement clips at a value that will result in +/-inf but will not overflow int
++s;
se=s; // update to reflect end of a valid exponent (e[+-]digit+)
}
}
if(endptr!=NULL) *endptr=(char *)se; // we now know the end of the number - so save it now (means we can have multiple returns going forward without having to worry about this)
if(expsign) rexp=-rexp;
rexp+=exp; // add in correct to exponent from mantissa processing
#if 1 /* if 0 removes the optimisations which just results in slower code - there is no loss of accuracy with these optimisations */
if(rexp>0 && rexp+nos_mant_digits<=maxdigits)
{// optimisation: can do all calculations using uint64 which is fastish and exact
r*=u64powersOf10[rexp];
rexp=0;// will just convert to double and return
}
else if(rexp<0 && rexp >= -15 && nos_mant_digits<=15 )
{// in this region we can use double rather than long double as 10^15 is exact as a double (another speed optimisation, but one than thats common and therefore worthwhile)
if(sign) return -(r/dblpowersOf10[-rexp]); // negative exponent means we divide by powers of 10
else return r/dblpowersOf10[-rexp];
}
#endif
#ifdef USE_LD
// calculate dr=(long double)r*powl(10,rexp), but by using a lookup table of powers of 10 for speed and accuracy, and using long doubles to ensure accuracy.
if(rexp>0)
{if(rexp>maxExponent)
{// we have defininaly overflowed
if(sign) return -INFINITY;
return INFINITY;
}
dr=r;
dr*=powersOf10[rexp]; // as mantissa >= 1 this may overflow, but thats OK.
}
else if(rexp<0)
{// need to take care here as mantissa is > 1 so even dividing by 10^maxExponent may not be enough, here we all division by upto 10^2*maxExponet is is by far enough
rexp= -rexp;
exp=rexp;
if(rexp>maxExponent)
{
rexp=maxExponent;
exp-=maxExponent; // any excess which we will also need to divide by (if its > 0)
}
else exp=0;
dr=r;
dr/=powersOf10[rexp]; // negative exponent means we divide by powers of 10
if(exp>0)
{dr/=powersOf10[exp]; // divide by some more, we should only be dividing by max 10^18 as we only have 18 sig figs in mantissa (plus a few more if we consider creation of denormalised numbers)
}
}
else
{// special case, rexp==0
// do not need to use long double here, so we use double for speed.
if(sign) return -((double)r); // r is unsigned so cannot do -r !
else return (double) r;
}
if(sign) dr= -dr;
#ifdef DEBUG
// while this is the normal return there are several earlier return possibilities, which this will not print for (sorry).
fprintf(stderr," strtod returns %.18g (rexp=%d, exp=%d)\n",(double)dr,rexp,exp);
#endif
return (double)dr; // this should be only rounding [it will be round to even] - to this point we have used integer maths (exact) or long doubles (very nearly exact).
}
#else
/* use double double. Input is mantissa as uint64 (r) and exponent as rexp */
/* special cases */
if(rexp>maxExponent)
{// we have defininaly overflowed as mantissa is >=1
if(sign) return -INFINITY;
return INFINITY;
}
if(rexp<-500)
{// we have defininaly underflowed as mantissa is uint64 max ~ 1e19
if(sign) return -0.0;
return 0.0;
}
U64toDD(r,&dh,&dl);/* convert uint64 to double double */
#ifdef DEBUG
printf("%llu => %g + %g\n",r,dh,dl);
#endif
dd_to_power10( &dh, &dl, dh, dl, rexp ) ;// d *10^rexp
if(sign) return -dh; // we only return a double so dl is not needed now
return dh;
}
#endif
/*
*----------------------------------------------------------------------
*
* double fast_atof(const char *s,bool * not_number) :
*
* This procedure converts a floating-point number from an ASCII
* decimal representation to internal double-precision format.
* Also accepts "NaN", "Inf" and "Infinity" (any mix of case) which return NAN and INFINITY
* Results:
* The return value is the floating-point equivalent of string.
* If a terminating character is found before any floating-point
* digits, then zero is returned and *not_number is set to true (otherwise its set to false);
*
* If not_number == NULL it is ignored.
*
* Side effects:
* None.
*
*----------------------------------------------------------------------
*/
double fast_atof(const char *s,bool * not_number)
{char *se;
double r;
r=fast_strtod(s,&se);
if(not_number != NULL) *not_number = (se==(char *)s); // if strtod found no number not_number is set to true
return r;
}
double fast_atof_nan(const char *s)// like fast_atof, but returns NAN if the string does not start with a valid number (fast_atof returns 0)
{char *se;
double r;
r=fast_strtod(s,&se);
if(se==s) return NAN; // if string does not contain a number return NAN
return r;
}
/*
*----------------------------------------------------------------------
*
* float fast_strtof(const char *s,char **endptr)
*
* This procedure converts a floating-point number from an ASCII
* decimal representation to internal single-precision format.
* Also accepts "NaN", "Inf" and "Infinity" (any mix of case) which return NAN and INFINITY
* Results:
* The return value is the floating-point equivalent of string.
* *endptr is set to the first character after the valid number
*
* If endptr == NULL it is ignored.
*
* Side effects:
* None.
*
*----------------------------------------------------------------------
*/
#if defined(__SIZEOF_POINTER__ ) && __SIZEOF_POINTER__ == 8 /* compiling for x86_64 , this is defined for gcc, if its not defined the build version uisng u32's which is the best default */
/* could also have used __WIN64__, WIN64, __WIN64, __X86_64__ which all appear to only be defined for 64 bit compiles */
/* version of fast_strtof() using uint64 - this passes the test suite with no errors */
/* tests with nsort show this is faster than the version below which tries to use uint32's as much as possible when compiled for x64
When compiled for 64 bits, this code takes 1.203 secs to sort demo1M.csv, whereas the code below based on u32's takes 1.406 secs.
When compiled for 32 bits, this version using u64 takes 2.093 secs, while the version using u32 takes 1.532 secs
above #if statement should automatically compile the fastest version.
*/
const int fast_strtof_u=64; // tell rest of system we are using u64's (only useful for diagnostics/debugging)
static const int maxfdigits=18; // see above this is the largest possible in a uint64
float fast_strtof(const char *s,char **endptr) // if endptr != NULL returns 1st character thats not in the number
{
double dr; // may need to use double precision to get an accurate float - we try hard below to avoid this either by uisng just a uint32, or just by using float's
bool sign=false,expsign=false,got_number=false;
uint64_t r=0; // mantissa, uint32 can hold 9 digits which is NOT enough for a float
int exp=0,rexp=0;
int nos_mant_digits=0;
const char *se=s; // string end - candidate for endptr
#ifdef DEBUG
fprintf(stderr,"strtof(%s):\n",s);
#endif
while(isspace(*s)) ++s; // skip initial whitespace
// deal with leading sign
if(*s=='+') ++s;
else if(*s=='-')
{sign=true;
++s;
}
// NAN is a special case - NAN is signed in the input but always returns NAN
if((*s=='n' || *s=='N') && (s[1]=='a' || s[1]=='A') && (s[2]=='n' || s[2]=='N'))
{if(endptr!=NULL) *endptr=(char *)s+3;// 3 for NAN
return NAN;
}
// INF or Infinity is a special case - and is signed
if((*s=='i' || *s=='I') && (s[1]=='n' || s[1]=='N') && (s[2]=='f' || s[2]=='F'))
{s+=3;// INF
if((*s=='i' || *s=='I') && (s[1]=='n' || s[1]=='N') && (s[2]=='i' || s[2]=='I') && (s[3]=='t' || s[3]=='T') && (s[4]=='y' || s[4]=='Y') )
s+=5; // "Infinity" is 5 more chars (inity) than "inf"
if(endptr!=NULL) *endptr=(char *)s;
if(sign) return -INFINITY;
return INFINITY;
}
#ifdef AFormatSupport
/* support hex floating point numbers of the format 0xh.hhhhp+/-d as generated by printf %a */
if(*s=='0' && (s[1]=='x' || s[1] =='X'))
{ // got hex number
float h;
s+=2; // skip 0x
// no need to skip leading zero's as we can just check is ms 4 bits of r are not zero
while(isxdigit(*s))
{got_number=true; // have a valid number
if((r & UINT64_C(0xf000000000000000))==0)
{ if(*s<='9')
r=r*16+(*s-'0'); // 0..9
else
r=r*16+(tolower(*s)-'a'+10); // a-f or A-F
}
else if(exp<2048)
exp+=4; // cannot actually capture digits beyond 16 but keep track of decimal point, trap ensures we don't overflow exp when given a number with a silly number of digits (that would overflow a double)
++s;
}
// now look for optional decimal point (and fractional bit of mantissa)
if(*s=='.')
{ // got decimal point, skip and then look for fractional bit
++s;
while(isxdigit(*s))
{got_number=true; // have a valid number
if((r & UINT64_C(0xf000000000000000))==0)
{ if(*s<='9')
r=r*16+(*s-'0'); // 0..9
else
r=r*16+(tolower(*s)-'a'+10); // a-f or A-F
exp-=4;
}
// if we have too many digits after dp just ignore them
++s;
}
}
// got all of mantissa - see if its a valid number, if not we are done
if(!got_number)
{if(endptr!=NULL) *endptr=(char *)se;
#ifdef DEBUG
fprintf(stderr," strtof returns 0 (invalid hex number)\n");
#endif
return 0;
}
se=s; // update to reflect end of a valid mantissa
// now see if we have an exponent
if(*s=='p' || *s=='P')
{// have exponent, optional sign is 1st
++s ; // skip 'p'
if(*s=='+') ++s;
else if(*s=='-')
{expsign=true;
++s;
}
while(isdigit(*s))
{if(rexp<=2048)
rexp=rexp*10+(*s - '0'); // if statement clips at a value that will result in +/-inf but will not overflow int
++s;
se=s; // update to reflect end of a valid exponent (p[+-]digit+)
}
}
if(endptr!=NULL) *endptr=(char *)se; // we now know the end of the number - so save it now (means we can have multiple returns going forward without having to worry about this)
if(expsign) rexp=-rexp;
rexp+=exp; // add in correct to exponent from mantissa processing
h=ldexpf((float)r,rexp); // combine mantissa and exponent
if(sign) h=-h;
#ifdef DEBUG
fprintf(stderr," strtof (0x) returns %.18g [0x%.16A] (rexp=%d, exp=%d)\n",h,h,rexp,exp);
#endif
return h; // all done
}
#endif
// skip leading zeros
while(*s=='0')
{got_number=true; // have a number (0)
++s;
}
// now read rest of the mantissa
while(isdigit(*s))
{ got_number=true; // have a valid number
if(nos_mant_digits<maxfdigits)
{ r=r*10+(*s-'0');
nos_mant_digits++;
}
else
{ if(exp<2*maxfExponent)
exp++; // cannot actually capture digits as more than 9 but keep track of decimal point, trap at 2*maxExponent ensures we don't overflow exp when given a number with a silly number of digits (that would overflow a double)
}
++s;
}
// now look for optional decimal point (and fractional bit of mantissa)
if(*s=='.')
{ // got decimal point, skip and then look for fractional bit
++s;
if(r==0)
{// number is zero at present, so deal with leading zeros in fractional bit of mantissa
while(*s=='0')
{got_number=true;
++s;
if(exp > -2*maxfExponent)
exp--; // test avoids issues with silly number of leading zeros
}
}
// now process the rest of the fractional bit of the mantissa
while(isdigit(*s))
{got_number=true;
if(nos_mant_digits<maxfdigits)
{ r=r*10+(*s-'0');
nos_mant_digits++;
exp--;
}
else
{ // cannot actually capture digits as more than 9, so just ignore them
}
++s;
}
}
// got all of mantissa - see if its a valid number, if not we are done
if(!got_number)
{if(endptr!=NULL) *endptr=(char *)se;
#ifdef DEBUG
fprintf(stderr," strtof returns 0 (invalid number)\n");
#endif
return 0;
}
se=s; // update to reflect end of a valid mantissa
// now see if we have an exponent
if(*s=='e' || *s=='E')
{// have exponent, optional sign is 1st
++s ; // skip 'e'
if(*s=='+') ++s;
else if(*s=='-')
{expsign=true;
++s;
}
while(isdigit(*s))
{if(rexp<=2*maxfExponent)
rexp=rexp*10+(*s - '0'); // if statement clips at a value that will result in +/-inf but will not overflow int
++s;
se=s; // update to reflect end of a valid exponent (e[+-]digit+)
}
}
if(endptr!=NULL) *endptr=(char *)se; // we now know the end of the number - so save it now (means we can have multiple returns going forward without having to worry about this)
if(expsign) rexp=-rexp;
rexp+=exp; // add in correct to exponent from mantissa processing
#if 1 /* if 0 removes the optimisations which just results in slower code - there is no loss of accuracy with these optimisations */
if(rexp>0 && rexp+nos_mant_digits<=9)
{// optimisation: can do all calculations using uint32 which is exact and fast
uint32_t r32=r;
r32*=u32powersOf10[rexp];
if(sign) return -((float)r32); // negative exponent means we divide by powers of 10
else return (float)r32;
}
else if(rexp<0 && rexp >= -6 && nos_mant_digits<=6 )
{// in this region we can use float rather than double as 10^6 is exact as a float (another speed optimisation, but one than thats common and therefore worthwhile)
if(sign) return -((float)r/fltpowersOf10[-rexp]); // negative exponent means we divide by powers of 10
else return (float)r/fltpowersOf10[-rexp];
}
#endif
// calculate dr=(float)r*pow(10,rexp), but by using a lookup table of powers of 10 for speed and accuracy, and using doubles to ensure accuracy.
if(rexp>0)
{if(rexp>maxfExponent)
{// we have defininaly overflowed
if(sign) return -INFINITY;
return INFINITY;
}
dr=(double)r*dblpowersOf10[rexp]; // as mantissa >= 1 this may overflow, but thats OK.
}
else if(rexp<0)
{// need to take care here as mantissa is > 1 so even dividing by 10^maxExponent may not be enough, here we all division by upto 10^2*maxExponet is is by far enough
rexp= -rexp;
exp=rexp;
if(rexp>maxfExponent)
{
rexp=maxfExponent;
exp-=maxfExponent; // any excess which we will also need to divide by (if its > 0)
}
else exp=0;
dr=(double)r/dblpowersOf10[rexp]; // negative exponent means we divide by powers of 10
if(exp>0)
{dr/=dblpowersOf10[exp]; // divide by some more, we should only be dividing by max 10^18 as we only have 18 sig figs in mantissa (plus a few more if we consider creation of denormalised numbers)
}
}
else
{// special case, rexp==0
// do not need to use double here, so we use float for speed.
if(sign) return -((float)r); // r is unsigned so cannot do -r !
else return (float) r;
}
if(sign) dr= -dr;
#ifdef DEBUG
// while this is the normal return there are several earlier return possibilities, which this will not print for (sorry).
fprintf(stderr," strtof returns %.18g (rexp=%d, exp=%d)\n",(double)dr,rexp,exp);
#endif
return (float)dr;
}
#else
/* version of fast_strtof() using unit32 */
/* ======================================*/
/* I could not get this to work to full accuracy by just using a uint32 mantissa, so the code below uses a uint32 for as long as possible then swaps to a uint64 */
/* this reduces the number of uint64 multiplies and additions and so is faster that just using a uint64 all the time */
const int fast_strtof_u=32; // tell rest of system we are using u32's (only useful for diagnostics/debugging)
static const int maxfdigits=18; // see above this is the largest possible in a uint32
float fast_strtof(const char *s,char **endptr) // if endptr != NULL returns 1st character thats not in the number
{
double dr; // may need to use double precision to get an accurate float - we try hard below to avoid this either by uisng just a uint32, or just by using float's
bool sign=false,expsign=false,got_number=false;
uint_fast32_t r32=0; // mantissa, uint32 can hold 9 digits
uint_fast64_t r64=0; // if we get too many digits in mantissa then we swap to using this
bool usingr64=false; // set to true when we use r64
int_fast16_t exp=0,rexp=0;
int_fast16_t nos_mant_digits=0;
const char *se=s; // string end - candidate for endptr
#ifdef DEBUG
fprintf(stderr,"strtof(%s):\n",s);
#endif
while(isspace(*s)) ++s; // skip initial whitespace
// deal with leading sign
if(*s=='+') ++s;
else if(*s=='-')
{sign=true;
++s;
}
// NAN is a special case - NAN is signed in the input but always returns NAN
if((*s=='n' || *s=='N') && (s[1]=='a' || s[1]=='A') && (s[2]=='n' || s[2]=='N'))
{if(endptr!=NULL) *endptr=(char *)s+3;// 3 for NAN
return NAN;
}
// INF or Infinity is a special case - and is signed
if((*s=='i' || *s=='I') && (s[1]=='n' || s[1]=='N') && (s[2]=='f' || s[2]=='F'))
{s+=3;// INF
if((*s=='i' || *s=='I') && (s[1]=='n' || s[1]=='N') && (s[2]=='i' || s[2]=='I') && (s[3]=='t' || s[3]=='T') && (s[4]=='y' || s[4]=='Y') )
s+=5; // "Infinity" is 5 more chars (inity) than "inf"
if(endptr!=NULL) *endptr=(char *)s;
if(sign) return -INFINITY;
return INFINITY;
}
#ifdef AFormatSupport
/* support hex floating point numbers of the format 0xh.hhhhp+/-d as generated by printf %a */
if(*s=='0' && (s[1]=='x' || s[1] =='X'))
{ // got hex number
float h;
uint_fast64_t r=0;// always use a 64 bit mantissa as we only do shitfs and adds here on mantissa so these should be fast enough on 64 bits.
s+=2; // skip 0x
// no need to skip leading zero's as we can just check is ms 4 bits of r are not zero
while(isxdigit(*s))
{got_number=true; // have a valid number
if((r & UINT64_C(0xf000000000000000))==0)
{ if(*s<='9')
r=r*16+(*s-'0'); // 0..9
else
r=r*16+(tolower(*s)-'a'+10); // a-f or A-F
}
else if(exp<2048)
exp+=4; // cannot actually capture digits beyond 16 but keep track of decimal point, trap ensures we don't overflow exp when given a number with a silly number of digits (that would overflow a double)
++s;
}
// now look for optional decimal point (and fractional bit of mantissa)
if(*s=='.')
{ // got decimal point, skip and then look for fractional bit
++s;
while(isxdigit(*s))
{got_number=true; // have a valid number
if((r & UINT64_C(0xf000000000000000))==0)
{ if(*s<='9')
r=r*16+(*s-'0'); // 0..9
else
r=r*16+(tolower(*s)-'a'+10); // a-f or A-F
exp-=4;
}
// if we have too many digits after dp just ignore them
++s;
}
}
// got all of mantissa - see if its a valid number, if not we are done
if(!got_number)
{if(endptr!=NULL) *endptr=(char *)se;
#ifdef DEBUG
fprintf(stderr," strtof returns 0 (invalid hex number)\n");
#endif
return 0;
}
se=s; // update to reflect end of a valid mantissa
// now see if we have an exponent
if(*s=='p' || *s=='P')
{// have exponent, optional sign is 1st
++s ; // skip 'p'
if(*s=='+') ++s;
else if(*s=='-')
{expsign=true;
++s;
}
while(isdigit(*s))
{if(rexp<=2048)
rexp=rexp*10+(*s - '0'); // if statement clips at a value that will result in +/-inf but will not overflow int
++s;
se=s; // update to reflect end of a valid exponent (p[+-]digit+)
}
}
if(endptr!=NULL) *endptr=(char *)se; // we now know the end of the number - so save it now (means we can have multiple returns going forward without having to worry about this)
if(expsign) rexp=-rexp;
rexp+=exp; // add in correct to exponent from mantissa processing
h=ldexpf((float)r,rexp); // combine mantissa and exponent
if(sign) h=-h;
#ifdef DEBUG
fprintf(stderr," strtof (0x) returns %.18g [0x%.16A] (rexp=%d, exp=%d)\n",h,h,rexp,exp);
#endif
return h; // all done
}
#endif
// skip leading zeros
while(*s=='0')
{got_number=true; // have a number (0)
++s;
}