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extern int32_t fastabs(int32_t x);
extern int64_t fastabs64(int64_t x);
#define fpdiv fpdiv_d2
#define isqrt isqrt_d1i
#define fplog2 fplog2_d1i
#define fpexp2 fpexp2_d1i
#define fpcos fpcos_d2
#define fpatan2 fpatan2_d2
#define fpwsinc fpwsinc_d1i
#define fpgauss fpgauss_d0
#define fperfr fperfr_d0
#define fpsin(x) fpcos((x)+0xC0000000)
#define fpsin_d2(x) fpcos_d2((x)+0xC0000000)
#define fpsin_d1i(x) fpcos_d1i((x)+0xC0000000)
#ifndef RL_EXCL_APPROX
extern int32_t log2_ffo32(uint32_t x);
extern int32_t log2_ffo64(uint64_t x);
extern int64_t mulshift (int64_t a, int64_t b, int s);
extern int64_t fpdiv_d2(int32_t y, int32_t x, int32_t outfmt);
extern uint32_t isqrt_d1i(uint64_t x);
extern int32_t fplog2_d1i(uint32_t x);
extern uint32_t fpexp2_d1i(int32_t x);
extern int32_t fppow(uint32_t x, int32_t y, const uint32_t fmt);
extern int32_t fpcos_d2(uint32_t x);
extern int32_t fpcos_d1i(uint32_t x);
extern int64_t fpatan2_d2(int32_t y, int32_t x);
extern int32_t fpwsinc_d1i(int32_t x);
extern int32_t fpgauss_d1i(int32_t x);
extern int32_t fpgauss_d0(int32_t x);
extern int32_t fpgauss_d0_nocheck(int32_t x);
extern int32_t fperfr_d1i(int32_t x);
extern int32_t fperfr_d0(int32_t x);
#else
#define log2_ffo32(x) noop_i("log2_ffo32(x)")
#define log2_ffo64(x) noop_i("log2_ffo64(x)")
#define mulshift(a, b, s) noop_i("mulshift(a, b, s)")
#define fpdiv_d2(y, x, outfmt) noop_i("fpdiv_d2(y, x, outfmt)")
#define isqrt_d1i(x) noop_i("isqrt_d1i(x)")
#define fplog2_d1i(x) noop_i("fplog2_d1i(x)")
#define fpexp2_d1i(x) noop_i("fpexp2_d1i(x)")
#define fppow(x, y, fmt) noop_i("fppow(x, y, fmt)")
#define fpcos_d2(x) noop_i("fpcos_d2(x)")
#define fpcos_d1i(x) noop_i("fpcos_d1i(x)")
#define fpatan2_d2(y, x) noop_i("fpatan2_d2(y, x)")
#define fpwsinc_d1i(x) noop_i("fpwsinc_d1i(x)")
#define fpgauss_d1i(x) noop_i("fpgauss_d1i(x)")
#define fpgauss_d0(x) noop_i("fpgauss_d0(x)")
#define fpgauss_d0_nocheck(x) noop_i("fpgauss_d0_nocheck(x)")
#define fperfr_d1i(x) noop_i("fperfr_d1i(x)")
#define fperfr_d0(x) noop_i("fperfr_d0(x)")
#endif