312 lines
12 KiB
C
312 lines
12 KiB
C
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/*
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These functions provide integer arithmetic with integer checking. They do not
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actually raise an exception when an overflow is detected, but rather set a bit
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in the overflow parameter. (This parameter may be re-used across several
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arithmetic operations, so should be or-ed rather than assigned to.)
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The implementation is divided into two parts, the signed and unsigned basecases,
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which is where the magic happens, and a generic template matching a specific
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type to an implementation based on its (c-compile-time) size and signedness.
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When possible, branching is avoided, and preference is given to speed over
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accuracy (a low rate of falsely "detected" overflows are acceptable,
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undetected overflows are not).
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TODO: Hook up checking.
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TODO: Conditionally support 128-bit with intmax_t?
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*/
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/////////////// Common.proto ///////////////
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static int __Pyx_check_twos_complement(void) {
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if ((-1 != ~0)) {
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PyErr_SetString(PyExc_RuntimeError, "Two's complement required for overflow checks.");
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return 1;
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} else if ((sizeof(short) == sizeof(int))) {
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PyErr_SetString(PyExc_RuntimeError, "sizeof(short) < sizeof(int) required for overflow checks.");
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return 1;
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} else {
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return 0;
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}
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}
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#define __PYX_IS_UNSIGNED(type) ((((type) -1) > 0))
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#define __PYX_SIGN_BIT(type) ((((unsigned type) 1) << (sizeof(type) * 8 - 1)))
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#define __PYX_HALF_MAX(type) ((((type) 1) << (sizeof(type) * 8 - 2)))
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#define __PYX_MIN(type) ((__PYX_IS_UNSIGNED(type) ? (type) 0 : 0 - __PYX_HALF_MAX(type) - __PYX_HALF_MAX(type)))
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#define __PYX_MAX(type) ((~__PYX_MIN(type)))
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#define __Pyx_add_no_overflow(a, b, overflow) ((a) + (b))
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#define __Pyx_add_const_no_overflow(a, b, overflow) ((a) + (b))
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#define __Pyx_sub_no_overflow(a, b, overflow) ((a) - (b))
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#define __Pyx_sub_const_no_overflow(a, b, overflow) ((a) - (b))
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#define __Pyx_mul_no_overflow(a, b, overflow) ((a) * (b))
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#define __Pyx_mul_const_no_overflow(a, b, overflow) ((a) * (b))
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#define __Pyx_div_no_overflow(a, b, overflow) ((a) / (b))
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#define __Pyx_div_const_no_overflow(a, b, overflow) ((a) / (b))
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/////////////// Common.init ///////////////
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//@substitute: naming
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// FIXME: Propagate the error here instead of just printing it.
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if (unlikely(__Pyx_check_twos_complement())) {
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PyErr_WriteUnraisable($module_cname);
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}
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/////////////// BaseCaseUnsigned.proto ///////////////
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static CYTHON_INLINE {{UINT}} __Pyx_add_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow);
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static CYTHON_INLINE {{UINT}} __Pyx_sub_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow);
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static CYTHON_INLINE {{UINT}} __Pyx_mul_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow);
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static CYTHON_INLINE {{UINT}} __Pyx_div_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow);
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// Use these when b is known at compile time.
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#define __Pyx_add_const_{{NAME}}_checking_overflow __Pyx_add_{{NAME}}_checking_overflow
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#define __Pyx_sub_const_{{NAME}}_checking_overflow __Pyx_sub_{{NAME}}_checking_overflow
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static CYTHON_INLINE {{UINT}} __Pyx_mul_const_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} constant, int *overflow);
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#define __Pyx_div_const_{{NAME}}_checking_overflow __Pyx_div_{{NAME}}_checking_overflow
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/////////////// BaseCaseUnsigned ///////////////
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static CYTHON_INLINE {{UINT}} __Pyx_add_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow) {
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{{UINT}} r = a + b;
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*overflow |= r < a;
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return r;
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}
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static CYTHON_INLINE {{UINT}} __Pyx_sub_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow) {
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{{UINT}} r = a - b;
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*overflow |= r > a;
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return r;
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}
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static CYTHON_INLINE {{UINT}} __Pyx_mul_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow) {
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if ((sizeof({{UINT}}) < sizeof(unsigned long))) {
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unsigned long big_r = ((unsigned long) a) * ((unsigned long) b);
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{{UINT}} r = ({{UINT}}) big_r;
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*overflow |= big_r != r;
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return r;
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#ifdef HAVE_LONG_LONG
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} else if ((sizeof({{UINT}}) < sizeof(unsigned PY_LONG_LONG))) {
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unsigned PY_LONG_LONG big_r = ((unsigned PY_LONG_LONG) a) * ((unsigned PY_LONG_LONG) b);
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{{UINT}} r = ({{UINT}}) big_r;
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*overflow |= big_r != r;
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return r;
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#endif
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} else {
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{{UINT}} prod = a * b;
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double dprod = ((double) a) * ((double) b);
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// Overflow results in an error of at least 2^sizeof(UINT),
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// whereas rounding represents an error on the order of 2^(sizeof(UINT)-53).
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*overflow |= fabs(dprod - prod) > (__PYX_MAX({{UINT}}) / 2);
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return prod;
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}
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}
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static CYTHON_INLINE {{UINT}} __Pyx_mul_const_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow) {
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if (b > 1) {
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*overflow |= a > __PYX_MAX({{UINT}}) / b;
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}
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return a * b;
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}
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static CYTHON_INLINE {{UINT}} __Pyx_div_{{NAME}}_checking_overflow({{UINT}} a, {{UINT}} b, int *overflow) {
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if (b == 0) {
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*overflow |= 1;
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return 0;
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}
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return a / b;
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}
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/////////////// BaseCaseSigned.proto ///////////////
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static CYTHON_INLINE {{INT}} __Pyx_add_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow);
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static CYTHON_INLINE {{INT}} __Pyx_sub_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow);
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static CYTHON_INLINE {{INT}} __Pyx_mul_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow);
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static CYTHON_INLINE {{INT}} __Pyx_div_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow);
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// Use when b is known at compile time.
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static CYTHON_INLINE {{INT}} __Pyx_add_const_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow);
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static CYTHON_INLINE {{INT}} __Pyx_sub_const_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow);
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static CYTHON_INLINE {{INT}} __Pyx_mul_const_{{NAME}}_checking_overflow({{INT}} a, {{INT}} constant, int *overflow);
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#define __Pyx_div_const_{{NAME}}_checking_overflow __Pyx_div_{{NAME}}_checking_overflow
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/////////////// BaseCaseSigned ///////////////
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static CYTHON_INLINE {{INT}} __Pyx_add_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow) {
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if ((sizeof({{INT}}) < sizeof(long))) {
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long big_r = ((long) a) + ((long) b);
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{{INT}} r = ({{INT}}) big_r;
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*overflow |= big_r != r;
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return r;
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#ifdef HAVE_LONG_LONG
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} else if ((sizeof({{INT}}) < sizeof(PY_LONG_LONG))) {
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PY_LONG_LONG big_r = ((PY_LONG_LONG) a) + ((PY_LONG_LONG) b);
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{{INT}} r = ({{INT}}) big_r;
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*overflow |= big_r != r;
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return r;
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#endif
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} else {
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// Signed overflow undefined, but unsigned overflow is well defined.
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{{INT}} r = ({{INT}}) ((unsigned {{INT}}) a + (unsigned {{INT}}) b);
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// Overflow happened if the operands have the same sign, but the result
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// has opposite sign.
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// sign(a) == sign(b) != sign(r)
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{{INT}} sign_a = __PYX_SIGN_BIT({{INT}}) & a;
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{{INT}} sign_b = __PYX_SIGN_BIT({{INT}}) & b;
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{{INT}} sign_r = __PYX_SIGN_BIT({{INT}}) & r;
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*overflow |= (sign_a == sign_b) & (sign_a != sign_r);
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return r;
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}
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}
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static CYTHON_INLINE {{INT}} __Pyx_add_const_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow) {
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if (b > 0) {
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*overflow |= a > __PYX_MAX({{INT}}) - b;
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} else if (b < 0) {
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*overflow |= a < __PYX_MIN({{INT}}) - b;
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}
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return a + b;
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}
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static CYTHON_INLINE {{INT}} __Pyx_sub_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow) {
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*overflow |= b == __PYX_MIN({{INT}});
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return __Pyx_add_{{NAME}}_checking_overflow(a, -b, overflow);
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}
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static CYTHON_INLINE {{INT}} __Pyx_sub_const_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow) {
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*overflow |= b == __PYX_MIN({{INT}});
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return __Pyx_add_const_{{NAME}}_checking_overflow(a, -b, overflow);
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}
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static CYTHON_INLINE {{INT}} __Pyx_mul_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow) {
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if ((sizeof({{INT}}) < sizeof(long))) {
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long big_r = ((long) a) * ((long) b);
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{{INT}} r = ({{INT}}) big_r;
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*overflow |= big_r != r;
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return ({{INT}}) r;
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#ifdef HAVE_LONG_LONG
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} else if ((sizeof({{INT}}) < sizeof(PY_LONG_LONG))) {
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PY_LONG_LONG big_r = ((PY_LONG_LONG) a) * ((PY_LONG_LONG) b);
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{{INT}} r = ({{INT}}) big_r;
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*overflow |= big_r != r;
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return ({{INT}}) r;
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#endif
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} else {
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{{INT}} prod = a * b;
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double dprod = ((double) a) * ((double) b);
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// Overflow results in an error of at least 2^sizeof(INT),
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// whereas rounding represents an error on the order of 2^(sizeof(INT)-53).
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*overflow |= fabs(dprod - prod) > (__PYX_MAX({{INT}}) / 2);
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return prod;
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}
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}
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static CYTHON_INLINE {{INT}} __Pyx_mul_const_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow) {
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if (b > 1) {
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*overflow |= a > __PYX_MAX({{INT}}) / b;
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*overflow |= a < __PYX_MIN({{INT}}) / b;
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} else if (b == -1) {
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*overflow |= a == __PYX_MIN({{INT}});
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} else if (b < -1) {
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*overflow |= a > __PYX_MIN({{INT}}) / b;
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*overflow |= a < __PYX_MAX({{INT}}) / b;
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}
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return a * b;
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}
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static CYTHON_INLINE {{INT}} __Pyx_div_{{NAME}}_checking_overflow({{INT}} a, {{INT}} b, int *overflow) {
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if (b == 0) {
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*overflow |= 1;
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return 0;
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}
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*overflow |= (a == __PYX_MIN({{INT}})) & (b == -1);
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return a / b;
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}
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/////////////// SizeCheck.init ///////////////
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//@substitute: naming
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// FIXME: Propagate the error here instead of just printing it.
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if (unlikely(__Pyx_check_sane_{{NAME}}())) {
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PyErr_WriteUnraisable($module_cname);
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}
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/////////////// SizeCheck.proto ///////////////
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static int __Pyx_check_sane_{{NAME}}(void) {
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if (((sizeof({{TYPE}}) <= sizeof(int)) ||
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#ifdef HAVE_LONG_LONG
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(sizeof({{TYPE}}) == sizeof(PY_LONG_LONG)) ||
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#endif
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(sizeof({{TYPE}}) == sizeof(long)))) {
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return 0;
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} else {
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PyErr_Format(PyExc_RuntimeError, \
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"Bad size for int type %.{{max(60, len(TYPE))}}s: %d", "{{TYPE}}", (int) sizeof({{TYPE}}));
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return 1;
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}
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}
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/////////////// Binop.proto ///////////////
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static CYTHON_INLINE {{TYPE}} __Pyx_{{BINOP}}_{{NAME}}_checking_overflow({{TYPE}} a, {{TYPE}} b, int *overflow);
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/////////////// Binop ///////////////
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static CYTHON_INLINE {{TYPE}} __Pyx_{{BINOP}}_{{NAME}}_checking_overflow({{TYPE}} a, {{TYPE}} b, int *overflow) {
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if ((sizeof({{TYPE}}) < sizeof(int))) {
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return __Pyx_{{BINOP}}_no_overflow(a, b, overflow);
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} else if (__PYX_IS_UNSIGNED({{TYPE}})) {
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if ((sizeof({{TYPE}}) == sizeof(unsigned int))) {
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return ({{TYPE}}) __Pyx_{{BINOP}}_unsigned_int_checking_overflow(a, b, overflow);
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} else if ((sizeof({{TYPE}}) == sizeof(unsigned long))) {
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return ({{TYPE}}) __Pyx_{{BINOP}}_unsigned_long_checking_overflow(a, b, overflow);
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#ifdef HAVE_LONG_LONG
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} else if ((sizeof({{TYPE}}) == sizeof(unsigned PY_LONG_LONG))) {
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return ({{TYPE}}) __Pyx_{{BINOP}}_unsigned_long_long_checking_overflow(a, b, overflow);
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#endif
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} else {
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abort(); return 0; /* handled elsewhere */
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}
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} else {
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if ((sizeof({{TYPE}}) == sizeof(int))) {
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return ({{TYPE}}) __Pyx_{{BINOP}}_int_checking_overflow(a, b, overflow);
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} else if ((sizeof({{TYPE}}) == sizeof(long))) {
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return ({{TYPE}}) __Pyx_{{BINOP}}_long_checking_overflow(a, b, overflow);
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#ifdef HAVE_LONG_LONG
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} else if ((sizeof({{TYPE}}) == sizeof(PY_LONG_LONG))) {
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return ({{TYPE}}) __Pyx_{{BINOP}}_long_long_checking_overflow(a, b, overflow);
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#endif
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} else {
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abort(); return 0; /* handled elsewhere */
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}
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}
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}
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/////////////// LeftShift.proto ///////////////
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static CYTHON_INLINE {{TYPE}} __Pyx_lshift_{{NAME}}_checking_overflow({{TYPE}} a, {{TYPE}} b, int *overflow) {
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*overflow |=
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#if {{SIGNED}}
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(b < 0) |
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#endif
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(b > ({{TYPE}}) (8 * sizeof({{TYPE}}))) | (a > (__PYX_MAX({{TYPE}}) >> b));
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return a << b;
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}
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#define __Pyx_lshift_const_{{NAME}}_checking_overflow __Pyx_lshift_{{NAME}}_checking_overflow
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/////////////// UnaryNegOverflows.proto ///////////////
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//FIXME: shouldn't the macro name be prefixed by "__Pyx_" ? Too late now, I guess...
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// from intobject.c
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#define UNARY_NEG_WOULD_OVERFLOW(x) \
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(((x) < 0) & ((unsigned long)(x) == 0-(unsigned long)(x)))
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