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chibi-scheme/opt/bignum.c
Alex Shinn 353594a028 fixing some 64-bit bignum arithmetic cases
2009-11-28 16:05:59 +09:00

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/* bignum.c -- bignum support */
/* Copyright (c) 2009 Alex Shinn. All rights reserved. */
/* BSD-style license: http://synthcode.com/license.txt */
#define SEXP_INIT_BIGNUM_SIZE 2
#define sexp_negate(x) \
if (sexp_bignump(x)) \
sexp_bignum_sign(x) = -sexp_bignum_sign(x); \
else if (sexp_fixnump(x)) \
x = sexp_fx_neg(x);
sexp sexp_make_bignum (sexp ctx, sexp_uint_t len) {
sexp_uint_t size = sexp_sizeof(bignum) + len*sizeof(sexp_uint_t);
sexp res = sexp_alloc_tagged(ctx, size, SEXP_BIGNUM);
sexp_bignum_length(res) = len;
sexp_bignum_sign(res) = 1;
return res;
}
sexp sexp_fixnum_to_bignum (sexp ctx, sexp a) {
sexp res = sexp_make_bignum(ctx, 1);
sexp_bignum_data(res)[0] = sexp_unbox_fixnum(sexp_fx_abs(a));
sexp_bignum_sign(res) = sexp_fx_sign(a);
return res;
}
sexp sexp_make_integer (sexp ctx, sexp_sint_t x) {
sexp res;
if ((SEXP_MIN_FIXNUM < x) && (x < SEXP_MAX_FIXNUM)) {
res = sexp_make_fixnum(x);
} else {
res = sexp_make_bignum(ctx, 1);
sexp_bignum_sign(res) = (x < 0 ? -1 : 1);
sexp_bignum_data(res)[0] = x * sexp_bignum_sign(res);
}
return res;
}
#define double_trunc_10s_digit(f) (trunc((f)/10.0)*10.0)
#define double_10s_digit(f) ((f)-double_trunc_10s_digit(f))
sexp sexp_double_to_bignum (sexp ctx, double f) {
int sign;
sexp_gc_var3(res, scale, tmp);
sexp_gc_preserve3(ctx, res, scale, tmp);
res = sexp_fixnum_to_bignum(ctx, sexp_make_fixnum(0));
scale = sexp_fixnum_to_bignum(ctx, sexp_make_fixnum(1));
sign = (f < 0 ? -1 : 1);
for (f=fabs(f); f >= 1.0; f=trunc(f/10)) {
tmp = sexp_bignum_fxmul(ctx, NULL, scale, double_10s_digit(f), 0);
res = sexp_bignum_add(ctx, res, res, tmp);
scale = sexp_bignum_fxmul(ctx, NULL, scale, 10, 0);
}
sexp_bignum_sign(res) = sign;
sexp_gc_release3(ctx);
return res;
}
sexp sexp_copy_bignum (sexp ctx, sexp dst, sexp a, sexp_uint_t len0) {
sexp_uint_t len = (len0 > 0) ? len0 : sexp_bignum_length(a), size;
size = sexp_sizeof(bignum) + len*sizeof(sexp_uint_t);
if (! dst || sexp_bignum_length(dst) < len) {
dst = sexp_alloc_tagged(ctx, size, SEXP_BIGNUM);
memcpy(dst, a, size);
sexp_bignum_length(dst) = len;
} else {
memset(dst->value.bignum.data, 0,
sexp_bignum_length(dst)*sizeof(sexp_uint_t));
memcpy(dst->value.bignum.data, a->value.bignum.data,
sexp_bignum_length(a)*sizeof(sexp_uint_t));
}
return dst;
}
int sexp_bignum_zerop (sexp a) {
int i;
sexp_uint_t *data = sexp_bignum_data(a);
for (i=sexp_bignum_length(a)-1; i>=0; i--)
if (data[i])
return 0;
return 1;
}
static sexp_uint_t sexp_bignum_hi (sexp a) {
sexp_uint_t i=sexp_bignum_length(a)-1;
while ((i>0) && ! sexp_bignum_data(a)[i])
i--;
return i+1;
}
sexp_sint_t sexp_bignum_compare_abs (sexp a, sexp b) {
int ai=sexp_bignum_hi(a), bi=sexp_bignum_hi(b);
sexp_uint_t *adata=sexp_bignum_data(a), *bdata=sexp_bignum_data(b);
if (ai != bi)
return ai - bi;
for (--ai; ai >= 0; ai--) {
if (adata[ai] > bdata[ai])
return 1;
else if (adata[ai] < bdata[ai])
return -1;
}
return 0;
}
sexp_sint_t sexp_bignum_compare (sexp a, sexp b) {
if (sexp_bignum_sign(a) != sexp_bignum_sign(b))
return sexp_bignum_sign(a);
return sexp_bignum_compare_abs(a, b);
}
sexp sexp_bignum_normalize (sexp a) {
sexp_uint_t *data;
if ((! sexp_bignump(a)) || (sexp_bignum_hi(a)>1))
return a;
data = sexp_bignum_data(a);
if ((data[0] > SEXP_MAX_FIXNUM)
&& ! ((sexp_bignum_sign(a) == -1) && (data[0] == SEXP_MAX_FIXNUM+1)))
return a;
return sexp_make_fixnum((sexp_sint_t)data[0] * sexp_bignum_sign(a));
}
double sexp_bignum_to_double (sexp a) {
double res = 0;
sexp_uint_t i, *data=sexp_bignum_data(a);
for (i=0; i<sexp_bignum_length(a); i++)
res = res * ((double)SEXP_UINT_T_MAX+1) + data[i];
return res;
}
sexp sexp_bignum_fxadd (sexp ctx, sexp a, sexp_uint_t b) {
sexp_uint_t len=sexp_bignum_hi(a), *data=sexp_bignum_data(a),
carry=b, i=0, n;
do { n = data[i];
data[i] += carry;
carry = (n > (SEXP_UINT_T_MAX - carry));
} while (++i<len && carry);
if (carry) {
a = sexp_copy_bignum(ctx, NULL, a, len+1);
sexp_bignum_data(a)[len] = 1;
}
return a;
}
sexp sexp_bignum_fxsub (sexp ctx, sexp a, sexp_uint_t b) {
sexp_uint_t *data=sexp_bignum_data(a), borrow, i=0, n;
for (borrow=b; borrow; i++) {
n = data[i];
data[i] -= borrow;
borrow = (n < borrow);
}
return a;
}
sexp sexp_bignum_fxmul (sexp ctx, sexp d, sexp a, sexp_uint_t b, int offset) {
sexp_uint_t len=sexp_bignum_length(a), *data, *adata=sexp_bignum_data(a),
carry=0, i;
sexp_luint_t n;
if ((! d) || (sexp_bignum_length(d)+offset < len))
d = sexp_make_bignum(ctx, len);
data = sexp_bignum_data(d);
for (i=0; i<len; i++) {
n = (sexp_luint_t)adata[i]*b + carry;
data[i+offset] = (sexp_uint_t)n;
carry = n >> (sizeof(sexp_uint_t)*8);
}
if (carry) {
if (sexp_bignum_length(d)+offset <= len)
d = sexp_copy_bignum(ctx, NULL, d, len+offset+1);
sexp_bignum_data(d)[len+offset] = carry;
}
return d;
}
sexp_uint_t sexp_bignum_fxdiv (sexp ctx, sexp a, sexp_uint_t b, int offset) {
sexp_uint_t len=sexp_bignum_hi(a), *data=sexp_bignum_data(a), q, r=0;
int i;
sexp_luint_t n = 0;
for (i=len-1; i>=offset; i--) {
n = (n << sizeof(sexp_uint_t)*8) + data[i];
q = n / b;
r = n - (sexp_luint_t)q * b;
data[i] = q;
n = r;
}
return r;
}
sexp sexp_read_bignum (sexp ctx, sexp in, sexp_uint_t init,
char sign, sexp_uint_t base) {
int c, digit;
sexp_gc_var1(res);
sexp_gc_preserve1(ctx, res);
res = sexp_make_bignum(ctx, SEXP_INIT_BIGNUM_SIZE);
sexp_bignum_sign(res) = sign;
sexp_bignum_data(res)[0] = init;
for (c=sexp_read_char(ctx, in); isxdigit(c); c=sexp_read_char(ctx, in)) {
digit = digit_value(c);
if ((digit < 0) || (digit >= base))
break;
res = sexp_bignum_fxmul(ctx, res, res, base, 0);
res = sexp_bignum_fxadd(ctx, res, digit);
}
if (c=='.' || c=='e' || c=='E') {
if (base != 10)
res = sexp_read_error(ctx, "found non-base 10 float", SEXP_NULL, in);
if (c!='.') sexp_push_char(ctx, c, in);
res = sexp_read_float_tail(ctx, in, sexp_bignum_to_double(res), (sign==-1));
} else if ((c!=EOF) && ! is_separator(c)) {
res = sexp_read_error(ctx, "invalid numeric syntax",
sexp_make_character(c), in);
}
sexp_push_char(ctx, c, in);
sexp_gc_release1(ctx);
return sexp_bignum_normalize(res);
}
static int log2i(int v) {
int i;
for (i = 0; i < sizeof(v)*8; i++)
if ((1<<(i+1)) > v)
break;
return i;
}
sexp sexp_write_bignum (sexp ctx, sexp a, sexp out, sexp_uint_t base) {
int i, str_len, lg_base = log2i(base);
char *data;
sexp_gc_var2(b, str);
sexp_gc_preserve2(ctx, b, str);
b = sexp_copy_bignum(ctx, NULL, a, 0);
sexp_bignum_sign(b) = 1;
i = str_len = (sexp_bignum_length(b)*sizeof(sexp_uint_t)*8 + lg_base - 1)
/ lg_base + 1;
str = sexp_make_string(ctx, sexp_make_fixnum(str_len),
sexp_make_character(' '));
data = sexp_string_data(str);
while (! sexp_bignum_zerop(b))
data[--i] = hex_digit(sexp_bignum_fxdiv(ctx, b, base, 0));
if (i == str_len)
data[--i] = '0';
else if (sexp_bignum_sign(a) == -1)
data[--i] = '-';
sexp_write_string(ctx, data + i, out);
sexp_gc_release2(ctx);
return SEXP_VOID;
}
/****************** bignum arithmetic *************************/
sexp sexp_bignum_add_fixnum (sexp ctx, sexp a, sexp b) {
sexp_gc_var1(c);
sexp_gc_preserve1(ctx, c);
c = sexp_copy_bignum(ctx, NULL, a, 0);
if (sexp_bignum_sign(c) == sexp_fx_sign(b))
c = sexp_bignum_fxadd(ctx, c, sexp_unbox_fixnum(sexp_fx_abs(b)));
else
c = sexp_bignum_fxsub(ctx, c, sexp_unbox_fixnum(sexp_fx_abs(b)));
sexp_gc_release1(ctx);
return c;
}
sexp sexp_bignum_sub_digits (sexp ctx, sexp dst, sexp a, sexp b) {
sexp_uint_t alen=sexp_bignum_hi(a), blen=sexp_bignum_hi(b),
borrow=0, i, *adata, *bdata, *cdata;
sexp_gc_var1(c);
if ((alen < blen) || ((alen == blen) && (sexp_bignum_compare_abs(a, b) < 0)))
return sexp_bignum_sub_digits(ctx, dst, b, a);
sexp_gc_preserve1(ctx, c);
c = ((dst && sexp_bignum_hi(dst) >= alen)
? dst : sexp_copy_bignum(ctx, NULL, a, 0));
adata = sexp_bignum_data(a);
bdata = sexp_bignum_data(b);
cdata = sexp_bignum_data(c);
for (i=0; i<blen; i++) {
cdata[i] = adata[i] - bdata[i] - borrow;
borrow = (adata[i] < bdata[i] ? 1 : 0);
}
for ( ; borrow && (i<alen); i++) {
borrow = (cdata[i] == 0 ? 1 : 0);
cdata[i]--;
}
sexp_gc_release1(ctx);
return c;
}
sexp sexp_bignum_add_digits (sexp ctx, sexp dst, sexp a, sexp b) {
sexp_uint_t alen=sexp_bignum_hi(a), blen=sexp_bignum_hi(b),
carry=0, i, n, *adata, *bdata, *cdata;
sexp_gc_var1(c);
if (alen < blen) return sexp_bignum_add_digits(ctx, dst, b, a);
sexp_gc_preserve1(ctx, c);
c = ((dst && sexp_bignum_hi(dst) >= alen)
? dst : sexp_copy_bignum(ctx, NULL, a, 0));
adata = sexp_bignum_data(a);
bdata = sexp_bignum_data(b);
cdata = sexp_bignum_data(c);
for (i=0; i<blen; i++) {
n = adata[i];
cdata[i] = n + bdata[i] + carry;
carry = (n > (SEXP_UINT_T_MAX - bdata[i]) ? 1 : 0);
}
for ( ; carry && (i<alen); i++) {
carry = (cdata[i] == SEXP_UINT_T_MAX-1 ? 1 : 0);
cdata[i]++;
}
if (carry) {
c = sexp_copy_bignum(ctx, NULL, c, alen+1);
sexp_bignum_data(c)[alen] = 1;
}
sexp_gc_release1(ctx);
return c;
}
sexp sexp_bignum_add (sexp ctx, sexp dst, sexp a, sexp b) {
sexp res;
if (sexp_bignum_sign(a) == sexp_bignum_sign(b)) {
res = sexp_bignum_add_digits(ctx, dst, a, b);
sexp_bignum_sign(res) = sexp_bignum_sign(a);
} else {
res = sexp_bignum_sub_digits(ctx, dst, a, b);
sexp_bignum_sign(res)
= sexp_bignum_sign(sexp_bignum_compare_abs(a, b) >= 0 ? a : b);
}
return res;
}
sexp sexp_bignum_sub (sexp ctx, sexp dst, sexp a, sexp b) {
sexp res;
if (sexp_bignum_sign(a) == sexp_bignum_sign(b)) {
res = sexp_bignum_sub_digits(ctx, dst, a, b);
sexp_bignum_sign(res)
= (sexp_bignum_compare_abs(a, b) >= 0 ? sexp_bignum_sign(a)
: -sexp_bignum_sign(a));
} else {
res = sexp_bignum_add_digits(ctx, dst, a, b);
sexp_bignum_sign(res) = sexp_bignum_sign(a);
}
return res;
}
sexp sexp_bignum_mul (sexp ctx, sexp dst, sexp a, sexp b) {
sexp_uint_t alen=sexp_bignum_hi(a), blen=sexp_bignum_hi(b), i,
*bdata=sexp_bignum_data(b);
sexp_gc_var2(c, d);
if (alen < blen) return sexp_bignum_mul(ctx, dst, b, a);
sexp_gc_preserve2(ctx, c, d);
c = (dst ? dst : sexp_make_bignum(ctx, alen+blen+1));
d = sexp_make_bignum(ctx, alen+blen+1);
for (i=0; i<blen; i++) {
d = sexp_bignum_fxmul(ctx, d, a, bdata[i], i);
c = sexp_bignum_add_digits(ctx, NULL, c, d);
sexp_bignum_data(d)[i] = 0;
}
sexp_bignum_sign(c) = sexp_bignum_sign(a) * sexp_bignum_sign(b);
sexp_gc_release2(ctx);
return c;
}
static sexp sexp_bignum_double (sexp ctx, sexp a) {
return sexp_bignum_fxmul(ctx, NULL, a, 2, 0);
}
static sexp quot_step (sexp ctx, sexp *rem, sexp a, sexp b, sexp k, sexp i) {
sexp res;
sexp_gc_var5(x, prod, diff, k2, i2);
if (sexp_bignum_compare(k, a) > 0) {
*rem = a;
return sexp_fixnum_to_bignum(ctx, sexp_make_fixnum(0));
}
sexp_gc_preserve5(ctx, x, prod, diff, k2, i2);
k2 = sexp_bignum_double(ctx, k);
i2 = sexp_bignum_double(ctx, i);
x = quot_step(ctx, rem, a, b, k2, i2);
prod = sexp_bignum_mul(ctx, NULL, x, b);
diff = sexp_bignum_sub_digits(ctx, NULL, a, prod);
if (sexp_bignum_compare(diff, k) >= 0) {
*rem = sexp_bignum_sub_digits(ctx, NULL, diff, k);
res = sexp_bignum_add_digits(ctx, NULL, x, i);
} else {
*rem = diff;
res = x;
}
sexp_gc_release5(ctx);
return res;
}
sexp sexp_bignum_quot_rem (sexp ctx, sexp *rem, sexp a, sexp b) {
sexp res;
sexp_gc_var4(k, i, a1, b1);
sexp_gc_preserve4(ctx, k, i, a1, b1);
a1 = sexp_copy_bignum(ctx, NULL, a, 0);
sexp_bignum_sign(a1) = 1;
b1 = sexp_copy_bignum(ctx, NULL, b, 0);
sexp_bignum_sign(b1) = 1;
k = sexp_copy_bignum(ctx, NULL, b1, 0);
i = sexp_fixnum_to_bignum(ctx, sexp_make_fixnum(1));
res = quot_step(ctx, rem, a1, b1, k, i);
sexp_bignum_sign(res) = sexp_bignum_sign(a) * sexp_bignum_sign(b);
if (sexp_bignum_sign(a) < 0) {
sexp_negate(*rem);
}
sexp_gc_release4(ctx);
return res;
}
sexp sexp_bignum_quotient (sexp ctx, sexp a, sexp b) {
sexp res;
sexp_gc_var1(rem);
sexp_gc_preserve1(ctx, rem);
res = sexp_bignum_quot_rem(ctx, &rem, a, b);
sexp_gc_release1(ctx);
return res;
}
sexp sexp_bignum_remainder (sexp ctx, sexp a, sexp b) {
sexp rem;
sexp_bignum_quot_rem(ctx, &rem, a, b); /* discard quotient */
return rem;
}
sexp sexp_bignum_expt (sexp ctx, sexp a, sexp b) {
sexp_sint_t e = sexp_unbox_fixnum(sexp_fx_abs(b));
sexp_gc_var2(res, acc);
sexp_gc_preserve2(ctx, res, acc);
res = sexp_fixnum_to_bignum(ctx, sexp_make_fixnum(1));
acc = sexp_copy_bignum(ctx, NULL, a, 0);
for (; e; e>>=1, acc=sexp_bignum_mul(ctx, NULL, acc, acc))
if (e & 1)
res = sexp_bignum_mul(ctx, NULL, res, acc);
sexp_gc_release2(ctx);
return res;
}
/****************** generic arithmetic ************************/
enum sexp_number_types {
SEXP_NUM_NOT = 0,
SEXP_NUM_FIX,
SEXP_NUM_FLO,
SEXP_NUM_BIG
};
enum sexp_number_combs {
SEXP_NUM_NOT_NOT = 0,
SEXP_NUM_NOT_FIX,
SEXP_NUM_NOT_FLO,
SEXP_NUM_NOT_BIG,
SEXP_NUM_FIX_NOT,
SEXP_NUM_FIX_FIX,
SEXP_NUM_FIX_FLO,
SEXP_NUM_FIX_BIG,
SEXP_NUM_FLO_NOT,
SEXP_NUM_FLO_FIX,
SEXP_NUM_FLO_FLO,
SEXP_NUM_FLO_BIG,
SEXP_NUM_BIG_NOT,
SEXP_NUM_BIG_FIX,
SEXP_NUM_BIG_FLO,
SEXP_NUM_BIG_BIG
};
static int sexp_number_types[] =
{0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0};
static int sexp_number_type (sexp a) {
return sexp_pointerp(a) ? sexp_number_types[sexp_pointer_tag(a)&15]
: sexp_fixnump(a);
}
sexp sexp_add (sexp ctx, sexp a, sexp b) {
int at=sexp_number_type(a), bt=sexp_number_type(b), t;
sexp r=SEXP_VOID;
if (at > bt) {r=a; a=b; b=r; t=at; at=bt; bt=t;}
switch ((at << 2) + bt) {
case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
r = sexp_type_exception(ctx, "+: not a number", a);
break;
case SEXP_NUM_FIX_FIX:
r = sexp_fx_add(a, b); /* VM catches this case */
break;
case SEXP_NUM_FIX_FLO:
r = sexp_make_flonum(ctx, sexp_fixnum_to_double(a)+sexp_flonum_value(b));
break;
case SEXP_NUM_FIX_BIG:
r = sexp_bignum_normalize(sexp_bignum_add_fixnum(ctx, b, a));
break;
case SEXP_NUM_FLO_FLO:
r = sexp_fp_add(ctx, a, b);
break;
case SEXP_NUM_FLO_BIG:
r = sexp_make_flonum(ctx, sexp_flonum_value(a) + sexp_bignum_to_double(b));
break;
case SEXP_NUM_BIG_BIG:
r = sexp_bignum_normalize(sexp_bignum_add(ctx, NULL, b, a));
break;
}
return r;
}
sexp sexp_sub (sexp ctx, sexp a, sexp b) {
int at=sexp_number_type(a), bt=sexp_number_type(b);
sexp r=SEXP_VOID;
switch ((at << 2) + bt) {
case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
r = sexp_type_exception(ctx, "-: not a number", a);
break;
case SEXP_NUM_FIX_NOT: case SEXP_NUM_FLO_NOT: case SEXP_NUM_BIG_NOT:
r = sexp_type_exception(ctx, "-: not a number", b);
break;
case SEXP_NUM_FIX_FIX:
r = sexp_fx_sub(a, b); /* VM catches this case */
break;
case SEXP_NUM_FIX_FLO:
r = sexp_make_flonum(ctx, sexp_fixnum_to_double(a)-sexp_flonum_value(b));
break;
case SEXP_NUM_FIX_BIG:
r = sexp_bignum_sub(ctx, NULL, b, sexp_fixnum_to_bignum(ctx, a));
sexp_negate(r);
r = sexp_bignum_normalize(r);
break;
case SEXP_NUM_FLO_FIX:
r = sexp_make_flonum(ctx, sexp_fixnum_to_double(b)+sexp_flonum_value(a));
break;
case SEXP_NUM_FLO_FLO:
r = sexp_fp_sub(ctx, a, b);
break;
case SEXP_NUM_FLO_BIG:
r = sexp_make_flonum(ctx, sexp_flonum_value(a) - sexp_bignum_to_double(b));
break;
case SEXP_NUM_BIG_FIX:
r = sexp_bignum_normalize(sexp_bignum_sub(ctx, NULL, a, sexp_fixnum_to_bignum(ctx, b)));
break;
case SEXP_NUM_BIG_FLO:
r = sexp_make_flonum(ctx, sexp_flonum_value(b) - sexp_bignum_to_double(a));
case SEXP_NUM_BIG_BIG:
r = sexp_bignum_normalize(sexp_bignum_sub(ctx, NULL, a, b));
break;
}
return r;
}
sexp sexp_mul (sexp ctx, sexp a, sexp b) {
int at=sexp_number_type(a), bt=sexp_number_type(b), t;
sexp r=SEXP_VOID;
if (at > bt) {r=a; a=b; b=r; t=at; at=bt; bt=t;}
switch ((at << 2) + bt) {
case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
r = sexp_type_exception(ctx, "*: not a number", a);
break;
case SEXP_NUM_FIX_FIX:
r = sexp_fx_mul(a, b);
break;
case SEXP_NUM_FIX_FLO:
r = sexp_make_flonum(ctx, sexp_fixnum_to_double(a)*sexp_flonum_value(b));
break;
case SEXP_NUM_FIX_BIG:
r = sexp_bignum_fxmul(ctx, NULL, b, sexp_unbox_fixnum(sexp_fx_abs(a)), 0);
sexp_bignum_sign(r) = sexp_fx_sign(a) * sexp_bignum_sign(b);
break;
case SEXP_NUM_FLO_FLO:
r = sexp_fp_mul(ctx, a, b);
break;
case SEXP_NUM_FLO_BIG:
r = sexp_make_flonum(ctx, sexp_flonum_value(a) * sexp_bignum_to_double(b));
break;
case SEXP_NUM_BIG_BIG:
r = sexp_bignum_mul(ctx, NULL, a, b);
break;
}
return r;
}
sexp sexp_div (sexp ctx, sexp a, sexp b) {
int at=sexp_number_type(a), bt=sexp_number_type(b);
double f;
sexp r=SEXP_VOID, rem;
switch ((at << 2) + bt) {
case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
r = sexp_type_exception(ctx, "/: not a number", a);
break;
case SEXP_NUM_FIX_NOT: case SEXP_NUM_FLO_NOT: case SEXP_NUM_BIG_NOT:
r = sexp_type_exception(ctx, "/: not a number", b);
break;
case SEXP_NUM_FIX_FIX:
f = sexp_fixnum_to_double(a) / sexp_fixnum_to_double(b);
r = ((f == trunc(f)) ? sexp_make_fixnum((sexp_sint_t)f)
: sexp_make_flonum(ctx, f));
break;
case SEXP_NUM_FIX_FLO:
r = sexp_make_flonum(ctx, sexp_fixnum_to_double(a)/sexp_flonum_value(b));
break;
case SEXP_NUM_FIX_BIG:
r = sexp_make_flonum(ctx, sexp_fixnum_to_double(a)/sexp_bignum_to_double(b));
break;
case SEXP_NUM_FLO_FIX:
r = sexp_make_flonum(ctx, sexp_fixnum_to_double(b)/sexp_flonum_value(a));
break;
case SEXP_NUM_FLO_FLO:
r = sexp_fp_div(ctx, a, b);
break;
case SEXP_NUM_FLO_BIG:
r = sexp_make_flonum(ctx, sexp_flonum_value(a) / sexp_bignum_to_double(b));
break;
case SEXP_NUM_BIG_FIX:
b = sexp_fixnum_to_bignum(ctx, b);
/* ... FALLTHROUGH ... */
case SEXP_NUM_BIG_BIG:
r = sexp_bignum_quot_rem(ctx, &rem, a, b);
if (sexp_bignum_normalize(rem) != sexp_make_fixnum(0))
r = sexp_make_flonum(ctx, sexp_bignum_to_double(a)
/ sexp_fixnum_to_double(b));
else
r = sexp_bignum_normalize(r);
break;
case SEXP_NUM_BIG_FLO:
r = sexp_make_flonum(ctx, sexp_bignum_to_double(a) / sexp_flonum_value(b));
break;
}
return r;
}
sexp sexp_quotient (sexp ctx, sexp a, sexp b) {
int at=sexp_number_type(a), bt=sexp_number_type(b);
sexp r=SEXP_VOID;
switch ((at << 2) + bt) {
case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
r = sexp_type_exception(ctx, "quotient: not a number", a);
break;
case SEXP_NUM_FIX_NOT: case SEXP_NUM_FLO_NOT: case SEXP_NUM_BIG_NOT:
r = sexp_type_exception(ctx, "quotient: not a number", b);
break;
case SEXP_NUM_FLO_FIX: case SEXP_NUM_FLO_FLO: case SEXP_NUM_FLO_BIG:
r = sexp_type_exception(ctx, "quotient: can't take quotient of inexact", a);
break;
case SEXP_NUM_FIX_FLO: case SEXP_NUM_BIG_FLO:
r = sexp_type_exception(ctx, "quotient: can't take quotient of inexact", b);
break;
case SEXP_NUM_FIX_FIX:
r = sexp_fx_div(a, b);
break;
case SEXP_NUM_FIX_BIG:
r = sexp_make_fixnum(0);
break;
case SEXP_NUM_BIG_FIX:
b = sexp_fixnum_to_bignum(ctx, b);
/* ... FALLTHROUGH ... */
case SEXP_NUM_BIG_BIG:
r = sexp_bignum_normalize(sexp_bignum_quotient(ctx, a, b));
break;
}
return r;
}
sexp sexp_remainder (sexp ctx, sexp a, sexp b) {
int at=sexp_number_type(a), bt=sexp_number_type(b);
sexp r=SEXP_VOID;
switch ((at << 2) + bt) {
case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
r = sexp_type_exception(ctx, "remainder: not a number", a);
break;
case SEXP_NUM_FIX_NOT: case SEXP_NUM_FLO_NOT: case SEXP_NUM_BIG_NOT:
r = sexp_type_exception(ctx, "remainder: not a number", b);
break;
case SEXP_NUM_FLO_FIX: case SEXP_NUM_FLO_FLO: case SEXP_NUM_FLO_BIG:
r = sexp_type_exception(ctx, "remainder: can't take quotient of inexact", a);
break;
case SEXP_NUM_FIX_FLO: case SEXP_NUM_BIG_FLO:
r = sexp_type_exception(ctx, "remainder: can't take quotient of inexact", b);
break;
case SEXP_NUM_FIX_FIX:
r = sexp_fx_rem(a, b);
break;
case SEXP_NUM_FIX_BIG:
r = a;
break;
case SEXP_NUM_BIG_FIX:
b = sexp_fixnum_to_bignum(ctx, b);
/* ... FALLTHROUGH ... */
case SEXP_NUM_BIG_BIG:
r = sexp_bignum_normalize(sexp_bignum_remainder(ctx, a, b));
break;
}
return r;
}
sexp sexp_compare (sexp ctx, sexp a, sexp b) {
int at=sexp_number_type(a), bt=sexp_number_type(b);
sexp r=SEXP_VOID;
double f;
if (at > bt) {
r = sexp_compare(ctx, b, a);
sexp_negate(r);
} else {
switch ((at << 2) + bt) {
case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
r = sexp_type_exception(ctx, "compare: not a number", a);
break;
case SEXP_NUM_FIX_FIX:
r = sexp_make_fixnum(sexp_unbox_fixnum(a) - sexp_unbox_fixnum(b));
break;
case SEXP_NUM_FIX_FLO:
f = sexp_fixnum_to_double(a) - sexp_flonum_value(b);
r = sexp_make_fixnum(f > 0.0 ? 1 : f == 0.0 ? 0 : -1);
break;
case SEXP_NUM_FIX_BIG:
r = sexp_make_fixnum(-1);
break;
case SEXP_NUM_FLO_FLO:
f = sexp_flonum_value(a) - sexp_flonum_value(b);
r = sexp_make_fixnum(f > 0.0 ? 1 : f == 0.0 ? 0 : -1);
break;
case SEXP_NUM_FLO_BIG:
f = sexp_flonum_value(a) - sexp_bignum_to_double(b);
r = sexp_make_fixnum(f > 0.0 ? 1 : f == 0.0 ? 0 : -1);
break;
case SEXP_NUM_BIG_BIG:
r = sexp_make_fixnum(sexp_bignum_compare(a, b));
break;
}
}
return r;
}
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