basic sqrt implementation

This commit is contained in:
bumbread 2022-06-10 13:08:45 +11:00
parent 5890659112
commit 1a834c303d
7 changed files with 185 additions and 16 deletions

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@ -51,4 +51,4 @@ del build\*.obj
:skip_crt_compilation :skip_crt_compilation
echo Compiling test.. echo Compiling test..
clang test\test4.c ciabatta.lib -std=c11 -lkernel32 -luser32 -lshell32 -nostdlib %CIABATTA_OPTIONS% clang test\test5.c ciabatta.lib -std=c11 -lkernel32 -luser32 -lshell32 -nostdlib %CIABATTA_OPTIONS%

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@ -9,21 +9,26 @@
// e.g. f for floats // e.g. f for floats
#define f_nbits (1+f_ebits+f_mbits) #define f_nbits (1+f_ebits+f_mbits)
#define f_emax ((1ULL << (f_ebits-1)) - 1) #define f_emax ((1ULL << (f_ebits-1)) - 1)
#define f_emin (1 - f_emax) #define f_emin (1 - f_emax)
#define f_ebias f_emax
// Extracting fields from the float // Extracting fields from the float
#define f_eoffs (f_mbits) #define f_eoffs (f_mbits)
#define f_soffs (f_mbits+f_ebits) #define f_soffs (f_mbits+f_ebits)
#define f_emask ((1ULL << f_ebits) - 1) #define f_emask ((1ULL << f_ebits) - 1)
#define f_mmask ((1ULL << f_mbits) - 1) #define f_mmask ((1ULL << f_mbits) - 1)
#define f_smask 1ULL #define f_smask 1ULL
#define f_eval(b) (((b) >> f_eoffs) & f_emask) #define f_eval(b) (((b) >> f_eoffs) & f_emask)
#define f_sval(b) (((b) >> f_soffs) & f_smask) #define f_sval(b) (((b) >> f_soffs) & f_smask)
#define f_mval(b) (((b) >> 0) & f_mmask) #define f_mval(b) (((b) >> 0) & f_mmask)
#define f_abs(b) ((b) & ~(f_smask << f_soffs)) #define f_abs(b) ((b) & ~(f_smask << f_soffs))
#define f_exp(b) (f_eval(b) - f_ebias)
#define b_cons(s,e,m) ((s << f_soffs) | (e << f_eoffs) | (m)) #define f_qexp(b) (f_eval(b) - f_ebias - f_mbits)
#define f_qman(b) (((b) & f_mmask) | (f_mmask+1))
#define b_cons(s,e,m) (((itype)s << f_soffs) | ((itype)e << f_eoffs) | (itype)(m))
// Converting float to integer bits // Converting float to integer bits
static inline itype suffix(f_bits)(ftype f) { static inline itype suffix(f_bits)(ftype f) {
@ -35,8 +40,8 @@ static inline itype suffix(f_bits)(ftype f) {
return u.b; return u.b;
} }
static inline itype suffix(f_frombits)(itype b) { static inline ftype suffix(f_frombits)(itype b) {
union _u { union _u {
ftype f; ftype f;
itype b; itype b;
} u; } u;
@ -49,7 +54,7 @@ int suffix(_fpclassify)(ftype f) {
itype bits = suffix(f_bits)(f); itype bits = suffix(f_bits)(f);
itype exp = f_eval(bits); itype exp = f_eval(bits);
itype man = f_mval(bits); itype man = f_mval(bits);
if(exp == f_emax) { if(exp == f_emask) {
if(man == 0) return FP_INFINITE; if(man == 0) return FP_INFINITE;
else return FP_NAN; else return FP_NAN;
} }

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@ -16,6 +16,7 @@ enum Ordering {
#define f_mbits 23 #define f_mbits 23
#define suffix(n) n ## f #define suffix(n) n ## f
#include "ieee754.h" #include "ieee754.h"
#include "pow.h"
#undef suffix #undef suffix
#undef f_mbits #undef f_mbits
#undef f_ebits #undef f_ebits
@ -28,6 +29,7 @@ enum Ordering {
#define f_mbits 52 #define f_mbits 52
#define suffix(n) n #define suffix(n) n
#include "ieee754.h" #include "ieee754.h"
#include "pow.h"
#undef suffix #undef suffix
#undef f_mbits #undef f_mbits
#undef f_ebits #undef f_ebits
@ -42,7 +44,8 @@ _Static_assert(sizeof(long double) == sizeof(double),
#define f_ebits 11 #define f_ebits 11
#define f_mbits 52 #define f_mbits 52
#define suffix(n) n ## l #define suffix(n) n ## l
//#include "ieee754.h" #include "ieee754.h"
#include "pow.h"
#undef suffix #undef suffix
#undef f_mbits #undef f_mbits
#undef f_ebits #undef f_ebits

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@ -0,0 +1,95 @@
#include <errno.h>
#if !defined(_isqrt_defined)
#define _isqrt_defined
static uint64_t _isqrt(uint64_t num, uint64_t *remp) {
// To find a square root of a number
// We get rid of zero
if(num == 0) {
*remp = 0;
return 0;
}
// Then, starting from the bottom, split num into 2-digit pairs
// and find the top-most non-zero pair
uint64_t i = 0;
while(i != (sizeof(uint64_t)*8) && (num >> i) != 0) {
i += 2;
}
// Then we start taking guesses such that at each step
// sqrt^2 <= number made of consequent pairs of exausted integers
uint64_t sqrt = 0;
uint64_t rem = 0;
// Repeat until remainder is equal to zero:
do {
i -= 2;
// Bring the next two digits of the number to our remainder
rem = (rem << 2) | ((num >> i) & 0x3);
// Find d such that d(2sqrt+d) <= rem
// Since d could be either 0 or 1 we simply check 1, otherwise its 0
uint64_t d = 1;
uint64_t t = ((sqrt<<2)|1);
if(t <= rem) {
rem -= t;
}
else {
d = 0;
}
// Append the digit to sqrt from the right
sqrt = (sqrt<<1)|d;
} while(i != 0);
*remp = rem;
return sqrt;
}
#endif
// For all it's worth this shit is simply equivalent to
// _isqrt((uint64)x)
// I hate porgaming.
ftype suffix(sqrt)(ftype x) {
if(x < 0) {
#if math_errhandling & MATH_ERRNO
errno = EDOM;
#endif
return NAN;
}
if(x == 0 || isinf(x)) {
return x;
}
if(isnan(x)) {
return NAN;
}
itype bits = suffix(f_bits)(x);
itype exp = f_qexp(bits);
itype man = f_qman(bits);
// Get lots of precision by shifting man right by max bits
// and subtracting this from the exponent
itype bit = 0; // highest set-bit of man
while((man >> (bit+1)) != 0) ++bit;
itype prec_shift_n = f_nbits - bit - 3;
man <<= prec_shift_n;
exp -= prec_shift_n;
// Now do the sqrt of 2^exp * man
// If exp is odd then 2^{2k+1}*sqrt(man) = 2^{2k}*sqrt{2*man}
if((2 + (exp % 2)) % 2 != 0) {
man <<= 1;
}
// Take exp sqrt
exp >>= 1;
// Take sqrt of mantissa
uint64_t rem;
man = (itype)_isqrt(man, &rem);
// Now sqrt(x) = 2^exp * man
// we need to normalize this shit
bit = 0; // highest set-bit of man
while((man >> (bit+1)) != 0) ++bit;
exp += bit;
man <<= f_nbits-bit;
exp += f_ebias;
man >>= f_nbits-f_mbits;
man &= f_mmask;
// Cons it back
bits = b_cons(0, exp, man);
return suffix(f_frombits)(bits);
}

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@ -1,3 +1,7 @@
//TODO: verify printf("%d", 0). From the code it looked like it would print
// an empty string.
// NOTE: this file doesn't exist in a vacuum, it's a template for generating // NOTE: this file doesn't exist in a vacuum, it's a template for generating
// the formatted print, you should define FMT_CHAR_TYPE before including it // the formatted print, you should define FMT_CHAR_TYPE before including it
inline static int FMT_FUNC_NAME (void *ctx, OutputFunc out, const FMT_CHAR_TYPE *fmt, va_list args) { inline static int FMT_FUNC_NAME (void *ctx, OutputFunc out, const FMT_CHAR_TYPE *fmt, va_list args) {
@ -83,6 +87,9 @@ inline static int FMT_FUNC_NAME (void *ctx, OutputFunc out, const FMT_CHAR_TYPE
} }
FMT_CHAR_TYPE ch = *fmt++; FMT_CHAR_TYPE ch = *fmt++;
const char* characters = "0123456789abcdef";
if (ch == 'X') characters = "0123456789ABCDEF";
switch (ch) { switch (ch) {
case 'c': { case 'c': {
const char chr = va_arg(args, int); const char chr = va_arg(args, int);
@ -90,6 +97,45 @@ inline static int FMT_FUNC_NAME (void *ctx, OutputFunc out, const FMT_CHAR_TYPE
full_length ++; full_length ++;
break; break;
} }
case 'f':
case 'L': {
double d = va_arg(args, double);
if(isinf(d)) {
out(ctx, sizeof"inf"-1, "inf");
break;
}
else if(isnan(d)) {
out(ctx, sizeof"nan"-1, "nan");
break;
}
if(d < 0) { // TODO: negative zero
out(ctx, 1, "-");
d = -d;
}
uint64_t w = (uint64_t)d;
d -= w;
FMT_CHAR_TYPE buffer[20];
size_t len = sizeof(buffer);
do {
buffer[--len] = characters[w % 10];
w /= 10;
} while(w != 0);
out(ctx, sizeof(buffer) - (len * sizeof(FMT_CHAR_TYPE)), buffer + len);
char dot = '.';
out(ctx, 1, &dot);
for(int i = 0; i != 6; ++i) {
d *= 10;
int dv = (int)d;
d -= dv;
char digit = characters[dv];
out(ctx, 1, &digit);
}
} break;
case 's': { case 's': {
const FMT_CHAR_TYPE *str = va_arg(args, FMT_CHAR_TYPE*); const FMT_CHAR_TYPE *str = va_arg(args, FMT_CHAR_TYPE*);
size_t len = FMT_STRLEN_S(str, precision ? precision : SIZE_MAX); size_t len = FMT_STRLEN_S(str, precision ? precision : SIZE_MAX);
@ -114,9 +160,6 @@ inline static int FMT_FUNC_NAME (void *ctx, OutputFunc out, const FMT_CHAR_TYPE
default: base = 10; break; default: base = 10; break;
} }
const char* characters = "0123456789abcdef";
if (ch == 'X') characters = "0123456789ABCDEF";
uintmax_t i; uintmax_t i;
if (ch == 'd' || ch == 'i') { if (ch == 'd' || ch == 'i') {
intmax_t num = 0; intmax_t num = 0;

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@ -2,6 +2,7 @@
#include <stdarg.h> #include <stdarg.h>
#include <ctype.h> #include <ctype.h>
#include <stdbool.h> #include <stdbool.h>
#include <math.h>
#include <_os.h> #include <_os.h>

22
test/test5.c Normal file
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@ -0,0 +1,22 @@
#include <stdio.h>
#include <math.h>
void test_sqrt(float f) {
float s = sqrtf(f);
printf("sqrt of %f is %f\n", f, s);
}
int main() {
test_sqrt(0.0f);
test_sqrt(1.0f);
test_sqrt(2.0f);
test_sqrt(3.0f);
test_sqrt(4.0f);
test_sqrt(7.0f);
test_sqrt(9.0f);
test_sqrt(16.0f);
test_sqrt(256.0f);
test_sqrt(257.0f);
return 0;
}