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bignum.c
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bignum.c
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/* bignum.c -- bignum support */
/* Copyright (c) 2009-2012 Alex Shinn. All rights reserved. */
/* BSD-style license: http://synthcode.com/license.txt */
#include "chibi/sexp.h"
#if SEXP_USE_BIGNUMS
#define SEXP_INIT_BIGNUM_SIZE 2
static int digit_value (int c) {
return (((c)<='9') ? ((c) - '0') : ((sexp_toupper(c) - 'A') + 10));
}
static int hex_digit (int n) {
return ((n<=9) ? ('0' + n) : ('A' + n - 10));
}
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_lsint_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);
if (x < 0) {
sexp_bignum_sign(res) = -1;
sexp_bignum_data(res)[0] = -x;
} else {
sexp_bignum_sign(res) = 1;
sexp_bignum_data(res)[0] = x;
}
}
return res;
}
sexp sexp_make_unsigned_integer (sexp ctx, sexp_luint_t x) {
sexp res;
if (x <= SEXP_MAX_FIXNUM) {
res = sexp_make_fixnum(x);
} else {
res = sexp_make_bignum(ctx, 1);
sexp_bignum_sign(res) = 1;
sexp_bignum_data(res)[0] = x;
}
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_ZERO);
scale = sexp_fixnum_to_bignum(ctx, SEXP_ONE);
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);
memmove(dst, a, size);
sexp_bignum_length(dst) = len;
} else {
memset(dst->value.bignum.data, 0,
sexp_bignum_length(dst)*sizeof(sexp_uint_t));
memmove(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;
}
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_sint_t i;
sexp_uint_t *data=sexp_bignum_data(a);
for (i=sexp_bignum_hi(a)-1; i>=0; i--)
res = res * ((double)SEXP_UINT_T_MAX+1) + data[i];
return res * sexp_bignum_sign(a);
}
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;
sexp_gc_var1(tmp);
sexp_gc_preserve1(ctx, tmp);
if ((! d) || (sexp_bignum_length(d)+offset < len))
d = tmp = 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;
}
sexp_gc_release1(ctx);
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,
signed 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); sexp_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);
} else {
if (c!='.') sexp_push_char(ctx, c, in); /* push the e back */
res = sexp_read_float_tail(ctx, in, sexp_bignum_to_double(res), (sign==-1));
}
#if SEXP_USE_RATIOS
} else if (c=='/') {
res = sexp_bignum_normalize(res);
res = sexp_make_ratio(ctx, res, SEXP_ONE);
sexp_ratio_denominator(res) = sexp_read_number(ctx, in, 10);
res = sexp_ratio_normalize(ctx, res, in);
#endif
#if SEXP_USE_COMPLEX
} else if (c=='i' || c=='i' || c=='+' || c=='-') {
sexp_push_char(ctx, c, in);
res = sexp_bignum_normalize(res);
res = sexp_read_complex_tail(ctx, in, res);
#endif
} else if ((c!=EOF) && ! sexp_is_separator(c)) {
res = sexp_read_error(ctx, "invalid numeric syntax",
sexp_make_character(c), in);
} else {
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_ZERO);
}
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_ONE);
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_exact(*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_gc_var1(rem);
sexp_gc_preserve1(ctx, rem);
sexp_bignum_quot_rem(ctx, &rem, a, b); /* discard quotient */
sexp_gc_release1(ctx);
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_ONE);
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 sexp_bignum_normalize(res);
}
/************************ ratios ******************************/
#if SEXP_USE_RATIOS
double sexp_ratio_to_double (sexp rat) {
sexp num = sexp_ratio_numerator(rat), den = sexp_ratio_denominator(rat);
return (sexp_bignump(num) ? sexp_bignum_to_double(num)
: sexp_fixnum_to_double(num))
/ (sexp_bignump(den) ? sexp_bignum_to_double(den)
: sexp_fixnum_to_double(den));
}
sexp sexp_double_to_ratio (sexp ctx, double f) {
int sign, i;
sexp_gc_var3(res, whole, scale);
if (f == trunc(f))
return sexp_bignum_normalize(sexp_double_to_bignum(ctx, f));
sexp_gc_preserve3(ctx, res, whole, scale);
whole = sexp_double_to_bignum(ctx, trunc(f));
res = sexp_fixnum_to_bignum(ctx, SEXP_ZERO);
scale = SEXP_ONE;
sign = (f < 0 ? -1 : 1);
for (i=0, f=fabs(f-trunc(f)); f != trunc(f) && i < 15; i++) {
res = sexp_bignum_fxmul(ctx, NULL, res, 10, 0);
f = f * 10;
res = sexp_bignum_fxadd(ctx, res, double_10s_digit(f));
f = f - trunc(f);
scale = sexp_mul(ctx, scale, SEXP_TEN);
}
sexp_bignum_sign(res) = sign;
res = sexp_bignum_normalize(res);
scale = sexp_bignum_normalize(scale);
res = sexp_make_ratio(ctx, res, scale);
res = sexp_ratio_normalize(ctx, res, SEXP_FALSE);
res = sexp_add(ctx, res, whole);
sexp_gc_release3(ctx);
return res;
}
sexp sexp_ratio_add (sexp ctx, sexp a, sexp b) {
sexp_gc_var3(res, num, den);
sexp_gc_preserve3(ctx, res, num, den);
num = sexp_mul(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(b));
den = sexp_mul(ctx, sexp_ratio_numerator(b), sexp_ratio_denominator(a));
num = sexp_add(ctx, num, den);
den = sexp_mul(ctx, sexp_ratio_denominator(a), sexp_ratio_denominator(b));
res = sexp_make_ratio(ctx, num, den);
sexp_gc_release3(ctx);
return sexp_ratio_normalize(ctx, res, SEXP_FALSE);
}
sexp sexp_ratio_mul (sexp ctx, sexp a, sexp b) {
sexp_gc_var3(res, num, den);
sexp_gc_preserve3(ctx, res, num, den);
num = sexp_mul(ctx, sexp_ratio_numerator(a), sexp_ratio_numerator(b));
den = sexp_mul(ctx, sexp_ratio_denominator(a), sexp_ratio_denominator(b));
res = sexp_make_ratio(ctx, num, den);
sexp_gc_release3(ctx);
return sexp_ratio_normalize(ctx, res, SEXP_FALSE);
}
sexp sexp_ratio_div (sexp ctx, sexp a, sexp b) {
sexp_gc_var3(res, num, den);
sexp_gc_preserve3(ctx, res, num, den);
num = sexp_mul(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(b));
den = sexp_mul(ctx, sexp_ratio_denominator(a), sexp_ratio_numerator(b));
res = sexp_make_ratio(ctx, num, den);
sexp_gc_release3(ctx);
return sexp_ratio_normalize(ctx, res, SEXP_FALSE);
}
sexp sexp_ratio_compare (sexp ctx, sexp a, sexp b) {
sexp_gc_var2(a2, b2);
sexp_gc_preserve2(ctx, a2, b2);
a2 = sexp_mul(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(b));
b2 = sexp_mul(ctx, sexp_ratio_numerator(b), sexp_ratio_denominator(a));
a2 = sexp_compare(ctx, a2, b2);
sexp_gc_release2(ctx);
return a2;
}
sexp sexp_ratio_round (sexp ctx, sexp a) {
sexp_gc_var2(q, r);
sexp_gc_preserve2(ctx, q, r);
q = sexp_quotient(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(a));
if ((sexp_ratio_denominator(a) == SEXP_TWO) && sexp_oddp(q)) {
q = sexp_add(ctx, q, (sexp_positivep(q) ? SEXP_ONE : SEXP_NEG_ONE));
} else {
r = sexp_remainder(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(a));
r = sexp_mul(ctx, r, SEXP_TWO);
if (sexp_negativep(r)) {sexp_negate(r);}
if (sexp_unbox_fixnum(sexp_compare(ctx, r, sexp_ratio_denominator(a))) > 0)
q = sexp_add(ctx, q, (sexp_positivep(q) ? SEXP_ONE : SEXP_NEG_ONE));
}
sexp_gc_release2(ctx);
return q;
}
sexp sexp_ratio_trunc (sexp ctx, sexp a) {
return sexp_quotient(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(a));
}
sexp sexp_ratio_floor (sexp ctx, sexp a) {
sexp_gc_var1(q);
sexp_gc_preserve1(ctx, q);
q = sexp_quotient(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(a));
if (sexp_negativep(sexp_ratio_numerator(a)))
q = sexp_add(ctx, q, SEXP_NEG_ONE);
sexp_gc_release1(ctx);
return q;
}
sexp sexp_ratio_ceiling (sexp ctx, sexp a) {
sexp_gc_var1(q);
sexp_gc_preserve1(ctx, q);
q = sexp_quotient(ctx, sexp_ratio_numerator(a), sexp_ratio_denominator(a));
if (sexp_positivep(sexp_ratio_numerator(a)))
q = sexp_add(ctx, q, SEXP_ONE);
sexp_gc_release1(ctx);
return q;
}
#endif
/************************ complex numbers ****************************/
#if SEXP_USE_COMPLEX
sexp sexp_complex_add (sexp ctx, sexp a, sexp b) {
sexp_gc_var3(res, real, imag);
sexp_gc_preserve3(ctx, res, real, imag);
real = sexp_add(ctx, sexp_complex_real(a), sexp_complex_real(b));
imag = sexp_add(ctx, sexp_complex_imag(a), sexp_complex_imag(b));
res = sexp_make_complex(ctx, real, imag);
sexp_gc_release3(ctx);
return sexp_complex_normalize(res);
}
sexp sexp_complex_sub (sexp ctx, sexp a, sexp b) {
sexp_gc_var2(res, tmp);
sexp_gc_preserve2(ctx, res, tmp);
tmp = sexp_make_complex(ctx, sexp_complex_real(b), sexp_complex_imag(b));
sexp_negate(sexp_complex_real(tmp));
sexp_negate(sexp_complex_imag(tmp));
res = sexp_complex_add(ctx, a, tmp);
sexp_gc_release2(ctx);
return res;
}
sexp sexp_complex_mul (sexp ctx, sexp a, sexp b) {
sexp_gc_var3(res, real, imag);
sexp_gc_preserve3(ctx, res, real, imag);
real = sexp_mul(ctx, sexp_complex_real(a), sexp_complex_real(b));
res = sexp_mul(ctx, sexp_complex_imag(a), sexp_complex_imag(b));
real = sexp_sub(ctx, real, res);
imag = sexp_mul(ctx, sexp_complex_real(a), sexp_complex_imag(b));
res = sexp_mul(ctx, sexp_complex_imag(a), sexp_complex_real(b));
imag = sexp_add(ctx, imag, res);
res = sexp_make_complex(ctx, real, imag);
sexp_gc_release3(ctx);
return sexp_complex_normalize(res);
}
/* (a + bi) (ac + bd) (bc - ad) */
/* -------- = ----------- + ----------- i */
/* (c + di) (c^2 + d^2) (c^2 + d^2) */
sexp sexp_complex_div (sexp ctx, sexp a, sexp b) {
sexp_gc_var4(res, real, imag, denom);
sexp_gc_preserve4(ctx, res, real, imag, denom);
/* c^2 + d^2 */
denom = sexp_mul(ctx, sexp_complex_real(b), sexp_complex_real(b));
res = sexp_mul(ctx, sexp_complex_imag(b), sexp_complex_imag(b));
denom = sexp_add(ctx, denom, res);
/* ac + bd */
real = sexp_mul(ctx, sexp_complex_real(a), sexp_complex_real(b));
res = sexp_mul(ctx, sexp_complex_imag(a), sexp_complex_imag(b));
real = sexp_add(ctx, real, res);
real = sexp_div(ctx, real, denom);
/* bc - ad */
imag = sexp_mul(ctx, sexp_complex_imag(a), sexp_complex_real(b));
res = sexp_mul(ctx, sexp_complex_real(a), sexp_complex_imag(b));
imag = sexp_sub(ctx, imag, res);
imag = sexp_div(ctx, imag, denom);
res = sexp_make_complex(ctx, real, imag);
sexp_gc_release4(ctx);
return sexp_complex_normalize(res);
}
static double sexp_to_double (sexp x) {
if (sexp_flonump(x))
return sexp_flonum_value(x);
else if (sexp_fixnump(x))
return sexp_fixnum_to_double(x);
else if (sexp_bignump(x))
return sexp_bignum_to_double(x);
#if SEXP_USE_RATIOS
else if (sexp_ratiop(x))
return sexp_ratio_to_double(x);
#endif
else
return 0.0;
}
static sexp sexp_to_complex (sexp ctx, sexp x) {
#if SEXP_USE_RATIOS
sexp_gc_var1(tmp);
#endif
if (sexp_flonump(x) || sexp_fixnump(x) || sexp_bignump(x)) {
return sexp_make_complex(ctx, x, SEXP_ZERO);
#if SEXP_USE_RATIOS
} else if (sexp_ratiop(x)) {
sexp_gc_preserve1(ctx, tmp);
tmp = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ZERO);
sexp_complex_real(tmp) = sexp_make_flonum(ctx, sexp_to_double(x));
sexp_gc_release1(ctx);
return tmp;
#endif
} else {
return x;
}
}
sexp sexp_complex_exp (sexp ctx, sexp z) {
double e2x = exp(sexp_to_double(sexp_complex_real(z))),
y = sexp_to_double(sexp_complex_imag(z));
sexp_gc_var1(res);
sexp_gc_preserve1(ctx, res);
res = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ZERO);
sexp_complex_real(res) = sexp_make_flonum(ctx, e2x*cos(y));
sexp_complex_imag(res) = sexp_make_flonum(ctx, e2x*sin(y));
sexp_gc_release1(ctx);
return res;
}
sexp sexp_complex_log (sexp ctx, sexp z) {
double x = sexp_to_double(sexp_complex_real(z)),
y = sexp_to_double(sexp_complex_imag(z));
sexp_gc_var1(res);
sexp_gc_preserve1(ctx, res);
res = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ZERO);
sexp_complex_real(res) = sexp_make_flonum(ctx, log(sqrt(x*x + y*y)));
sexp_complex_imag(res) = sexp_make_flonum(ctx, atan2(y, x));
sexp_gc_release1(ctx);
return res;
}
sexp sexp_complex_expt (sexp ctx, sexp a, sexp b) {
sexp_gc_var1(res);
sexp_gc_preserve1(ctx, res);
res = sexp_to_complex(ctx, a);
res = sexp_complex_log(ctx, res);
res = sexp_mul(ctx, b, res);
res = sexp_complex_exp(ctx, res);
sexp_gc_release1(ctx);
return res;
}
#if SEXP_USE_MATH
sexp sexp_complex_sqrt (sexp ctx, sexp z) {
double x = sexp_to_double(sexp_complex_real(z)),
y = sexp_to_double(sexp_complex_imag(z)), r;
sexp_gc_var1(res);
sexp_gc_preserve1(ctx, res);
r = sqrt(x*x + y*y);
res = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ZERO);
sexp_complex_real(res) = sexp_make_flonum(ctx, sqrt((x+r)/2));
sexp_complex_imag(res) = sexp_make_flonum(ctx, (y<0?-1:1)*sqrt((-x+r)/2));
sexp_gc_release1(ctx);
return res;
}
sexp sexp_complex_sin (sexp ctx, sexp z) {
double x = sexp_to_double(sexp_complex_real(z)),
y = sexp_to_double(sexp_complex_imag(z));
sexp_gc_var1(res);
sexp_gc_preserve1(ctx, res);
res = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ZERO);
sexp_complex_real(res) = sexp_make_flonum(ctx, sin(x)*cosh(y));
sexp_complex_imag(res) = sexp_make_flonum(ctx, cos(x)*sinh(y));
sexp_gc_release1(ctx);
return res;
}
sexp sexp_complex_cos (sexp ctx, sexp z) {
double x = sexp_to_double(sexp_complex_real(z)),
y = sexp_to_double(sexp_complex_imag(z));
sexp_gc_var1(res);
sexp_gc_preserve1(ctx, res);
res = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ZERO);
sexp_complex_real(res) = sexp_make_flonum(ctx, cos(x)*cosh(y));
sexp_complex_imag(res) = sexp_make_flonum(ctx, -sin(x)*sinh(y));
sexp_gc_release1(ctx);
return res;
}
sexp sexp_complex_tan (sexp ctx, sexp z) {
sexp res;
sexp_gc_var2(sin, cos);
sexp_gc_preserve2(ctx, sin, cos);
sin = sexp_complex_sin(ctx, z);
cos = sexp_complex_cos(ctx, z);
res = sexp_complex_div(ctx, sin, cos);
sexp_gc_release2(ctx);
return res;
}
sexp sexp_complex_asin (sexp ctx, sexp z) {
sexp_gc_var2(res, tmp);
sexp_gc_preserve2(ctx, res, tmp);
res = sexp_complex_mul(ctx, z, z);
tmp = sexp_make_complex(ctx, SEXP_ONE, SEXP_ZERO);
res = sexp_complex_sub(ctx, tmp, res);
res = sexp_complex_sqrt(ctx, res);
/* tmp = iz */
sexp_complex_real(tmp) = sexp_complex_imag(z);
sexp_negate(sexp_complex_real(tmp));
sexp_complex_imag(tmp) = sexp_complex_real(z);
res = sexp_complex_add(ctx, tmp, res);
tmp = sexp_complex_log(ctx, res);
/* res = -i*tmp */
sexp_complex_real(res) = sexp_complex_imag(tmp);
sexp_complex_imag(res) = sexp_complex_real(tmp);
sexp_negate(sexp_complex_imag(res));
sexp_gc_release2(ctx);
return res;
}
sexp sexp_complex_acos (sexp ctx, sexp z) {
sexp_gc_var2(res, tmp);
sexp_gc_preserve2(ctx, res, tmp);
res = sexp_complex_asin(ctx, z);
tmp = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ZERO);
sexp_complex_real(tmp) = sexp_make_flonum(ctx, acos(-1)/2);
res = sexp_sub(ctx, tmp, res);
sexp_gc_release2(ctx);
return res;
}
sexp sexp_complex_atan (sexp ctx, sexp z) {
sexp_gc_var3(res, tmp1, tmp2);
sexp_gc_preserve3(ctx, res, tmp1, tmp2);
tmp1 = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ONE);
tmp1 = sexp_complex_mul(ctx, z, tmp1);
res = sexp_make_complex(ctx, SEXP_ONE, SEXP_ZERO);
res = sexp_complex_sub(ctx, res, tmp1);
res = sexp_complex_log(ctx, res);
tmp2 = sexp_make_complex(ctx, SEXP_ONE, SEXP_ZERO);
tmp2 = sexp_complex_add(ctx, tmp2, tmp1);
tmp2 = sexp_complex_log(ctx, tmp2);
res = sexp_complex_sub(ctx, res, tmp2);
tmp1 = sexp_make_complex(ctx, SEXP_ZERO, SEXP_ONE);
sexp_complex_imag(tmp1) = sexp_make_flonum(ctx, 0.5);
res = sexp_complex_mul(ctx, res, tmp1);
sexp_gc_release3(ctx);
return res;
}
#endif
#endif
/****************** generic arithmetic ************************/
enum sexp_number_types {
SEXP_NUM_NOT = 0,
SEXP_NUM_FIX,
SEXP_NUM_FLO,
SEXP_NUM_BIG,
#if SEXP_USE_RATIOS
SEXP_NUM_RAT,
#endif
#if SEXP_USE_COMPLEX
SEXP_NUM_CPX,
#endif
};
enum sexp_number_combs {
SEXP_NUM_NOT_NOT = 0,
SEXP_NUM_NOT_FIX,
SEXP_NUM_NOT_FLO,
SEXP_NUM_NOT_BIG,
#if SEXP_USE_RATIOS
SEXP_NUM_NOT_RAT,
#endif
#if SEXP_USE_COMPLEX
SEXP_NUM_NOT_CPX,
#endif
SEXP_NUM_FIX_NOT,
SEXP_NUM_FIX_FIX,
SEXP_NUM_FIX_FLO,
SEXP_NUM_FIX_BIG,
#if SEXP_USE_RATIOS
SEXP_NUM_FIX_RAT,
#endif
#if SEXP_USE_COMPLEX
SEXP_NUM_FIX_CPX,
#endif
SEXP_NUM_FLO_NOT,
SEXP_NUM_FLO_FIX,
SEXP_NUM_FLO_FLO,
SEXP_NUM_FLO_BIG,
#if SEXP_USE_RATIOS
SEXP_NUM_FLO_RAT,
#endif
#if SEXP_USE_COMPLEX
SEXP_NUM_FLO_CPX,
#endif
SEXP_NUM_BIG_NOT,
SEXP_NUM_BIG_FIX,
SEXP_NUM_BIG_FLO,
SEXP_NUM_BIG_BIG,
#if SEXP_USE_RATIOS
SEXP_NUM_BIG_RAT,
#endif
#if SEXP_USE_COMPLEX
SEXP_NUM_BIG_CPX,
#endif
#if SEXP_USE_RATIOS
SEXP_NUM_RAT_NOT,
SEXP_NUM_RAT_FIX,
SEXP_NUM_RAT_FLO,
SEXP_NUM_RAT_BIG,
SEXP_NUM_RAT_RAT,
#if SEXP_USE_COMPLEX
SEXP_NUM_RAT_CPX,
#endif
#endif
#if SEXP_USE_COMPLEX
SEXP_NUM_CPX_NOT,
SEXP_NUM_CPX_FIX,
SEXP_NUM_CPX_FLO,
SEXP_NUM_CPX_BIG,
#if SEXP_USE_RATIOS
SEXP_NUM_CPX_RAT,
#endif
SEXP_NUM_CPX_CPX,
#endif
};
static int sexp_number_types[] =
#if SEXP_USE_RATIOS && SEXP_USE_COMPLEX
{0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 4, 5, 0, 0};
#else
#if SEXP_USE_RATIOS || SEXP_USE_COMPLEX
{0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 4, 0, 0, 0};
#else
{0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0};
#endif
#endif
#define SEXP_NUM_NUMBER_TYPES (4 + SEXP_USE_RATIOS + SEXP_USE_COMPLEX)
static int sexp_number_type (sexp a) {
return sexp_pointerp(a) ?
(sexp_pointer_tag(a)<(sizeof(sexp_number_types)/sizeof(sexp_number_types[0]))
? sexp_number_types[sexp_pointer_tag(a)] : 0)
#if SEXP_USE_IMMEDIATE_FLONUMS
: sexp_flonump(a) ? 2
#endif
: sexp_fixnump(a);
}
sexp sexp_add (sexp ctx, sexp a, sexp b) {
sexp_sint_t sum;
int at=sexp_number_type(a), bt=sexp_number_type(b), t;
sexp r=SEXP_VOID;
sexp_gc_var1(tmp);
sexp_gc_preserve1(ctx, tmp);
if (at > bt) {r=a; a=b; b=r; t=at; at=bt; bt=t;}
switch ((at * SEXP_NUM_NUMBER_TYPES) + bt) {
case SEXP_NUM_NOT_NOT: case SEXP_NUM_NOT_FIX:
case SEXP_NUM_NOT_FLO: case SEXP_NUM_NOT_BIG:
#if SEXP_USE_RATIOS
case SEXP_NUM_NOT_RAT:
#endif
#if SEXP_USE_COMPLEX
case SEXP_NUM_NOT_CPX:
#endif
r = sexp_type_exception(ctx, NULL, SEXP_NUMBER, a);
break;
case SEXP_NUM_FIX_FIX:
sum = sexp_unbox_fixnum(a) + sexp_unbox_fixnum(b);
if ((sum < SEXP_MIN_FIXNUM) || (sum > SEXP_MAX_FIXNUM))
r = sexp_add(ctx, tmp=sexp_fixnum_to_bignum(ctx, a), b);
else
r = sexp_make_fixnum(sum);
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;
#if SEXP_USE_RATIOS
case SEXP_NUM_FLO_RAT:
r = sexp_make_flonum(ctx, sexp_flonum_value(a) + sexp_ratio_to_double(b));
break;
case SEXP_NUM_FIX_RAT:
case SEXP_NUM_BIG_RAT:
a = tmp = sexp_make_ratio(ctx, a, SEXP_ONE);
/* ... FALLTHROUGH ... */
case SEXP_NUM_RAT_RAT:
r = sexp_ratio_add(ctx, a, b);
break;
#endif
#if SEXP_USE_COMPLEX
#if SEXP_USE_RATIOS
case SEXP_NUM_RAT_CPX:
#endif
case SEXP_NUM_FLO_CPX:
case SEXP_NUM_FIX_CPX: