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/*
fp_trig.c: floating-point math routines for the Linux-m68k
floating point emulator.
Copyright (c) 1998-1999 David Huggins-Daines / Roman Zippel.
I hereby give permission, free of charge, to copy, modify, and
redistribute this software, in source or binary form, provided that
the above copyright notice and the following disclaimer are included
in all such copies.
THIS SOFTWARE IS PROVIDED "AS IS", WITH ABSOLUTELY NO WARRANTY, REAL
OR IMPLIED.
*/
#include "fp_emu.h"
static const struct fp_ext fp_one =
{
.exp = 0x3fff,
};
extern struct fp_ext *fp_fadd(struct fp_ext *dest, const struct fp_ext *src);
extern struct fp_ext *fp_fdiv(struct fp_ext *dest, const struct fp_ext *src);
struct fp_ext *
fp_fsqrt(struct fp_ext *dest, struct fp_ext *src)
{
struct fp_ext tmp, src2;
int i, exp;
dprint(PINSTR, "fsqrt\n");
fp_monadic_check(dest, src);
if (IS_ZERO(dest))
return dest;
if (dest->sign) {
fp_set_nan(dest);
return dest;
}
if (IS_INF(dest))
return dest;
/*
* sqrt(m) * 2^(p) , if e = 2*p
* sqrt(m*2^e) =
* sqrt(2*m) * 2^(p) , if e = 2*p + 1
*
* So we use the last bit of the exponent to decide wether to
* use the m or 2*m.
*
* Since only the fractional part of the mantissa is stored and
* the integer part is assumed to be one, we place a 1 or 2 into
* the fixed point representation.
*/
exp = dest->exp;
dest->exp = 0x3FFF;
if (!(exp & 1)) /* lowest bit of exponent is set */
dest->exp++;
fp_copy_ext(&src2, dest);
/*
* The taylor row around a for sqrt(x) is:
* sqrt(x) = sqrt(a) + 1/(2*sqrt(a))*(x-a) + R
* With a=1 this gives:
* sqrt(x) = 1 + 1/2*(x-1)
* = 1/2*(1+x)
*/
fp_fadd(dest, &fp_one);
dest->exp--; /* * 1/2 */
/*
* We now apply the newton rule to the function
* f(x) := x^2 - r
* which has a null point on x = sqrt(r).
*
* It gives:
* x' := x - f(x)/f'(x)
* = x - (x^2 -r)/(2*x)
* = x - (x - r/x)/2
* = (2*x - x + r/x)/2
* = (x + r/x)/2
*/
for (i = 0; i < 9; i++) {
fp_copy_ext(&tmp, &src2);
fp_fdiv(&tmp, dest);
fp_fadd(dest, &tmp);
dest->exp--;
}
dest->exp += (exp - 0x3FFF) / 2;
return dest;
}
struct fp_ext *
fp_fetoxm1(struct fp_ext *dest, struct fp_ext *src)
{
uprint("fetoxm1\n");
fp_monadic_check(dest, src);
return dest;
}
struct fp_ext *
fp_fetox(struct fp_ext *dest, struct fp_ext *src)
{
uprint("fetox\n");
fp_monadic_check(dest, src);
return dest;
}
struct fp_ext *
fp_ftwotox(struct fp_ext *dest, struct fp_ext *src)
{
uprint("ftwotox\n");
fp_monadic_check(dest, src);
return dest;
}
struct fp_ext *
fp_ftentox(struct fp_ext *dest, struct fp_ext *src)
{
uprint("ftentox\n");
fp_monadic_check(dest, src);
return dest;
}
struct fp_ext *
fp_flogn(struct fp_ext *dest, struct fp_ext *src)
{
uprint("flogn\n");
fp_monadic_check(dest, src);
return dest;
}
struct fp_ext *
fp_flognp1(struct fp_ext *dest, struct fp_ext *src)
{
uprint("flognp1\n");
fp_monadic_check(dest, src);
return dest;
}
struct fp_ext *
fp_flog10(struct fp_ext *dest, struct fp_ext *src)
{
uprint("flog10\n");
fp_monadic_check(dest, src);
return dest;
}
struct fp_ext *
fp_flog2(struct fp_ext *dest, struct fp_ext *src)
{
uprint("flog2\n");
fp_monadic_check(dest, src);
return dest;
}
struct fp_ext *
fp_fgetexp(struct fp_ext *dest, struct fp_ext *src)
{
dprint(PINSTR, "fgetexp\n");
fp_monadic_check(dest, src);
if (IS_INF(dest)) {
fp_set_nan(dest);
return dest;
}
if (IS_ZERO(dest))
return dest;
fp_conv_long2ext(dest, (int)dest->exp - 0x3FFF);
fp_normalize_ext(dest);
return dest;
}
struct fp_ext *
fp_fgetman(struct fp_ext *dest, struct fp_ext *src)
{
dprint(PINSTR, "fgetman\n");
fp_monadic_check(dest, src);
if (IS_ZERO(dest))
return dest;
if (IS_INF(dest))
return dest;
dest->exp = 0x3FFF;
return dest;
}
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