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ea5c662c62
This patch is a complete rewrite of sincosf. The new version is significantly faster, as well as simple and accurate. The worst-case ULP is 0.5607, maximum relative error is 0.5303 * 2^-23 over all 4 billion inputs. In non-nearest rounding modes the error is 1ULP. The algorithm uses 3 main cases: small inputs which don't need argument reduction, small inputs which need a simple range reduction and large inputs requiring complex range reduction. The code uses approximate integer comparisons to quickly decide between these cases. The small range reducer uses a single reduction step to handle values up to 120.0. It is fastest on targets which support inlined round instructions. The large range reducer uses integer arithmetic for simplicity. It does a 32x96 bit multiply to compute a 64-bit modulo result. This is more than accurate enough to handle the worst-case cancellation for values close to an integer multiple of PI/4. It could be further optimized, however it is already much faster than necessary. sincosf throughput gains on Cortex-A72: * |x| < 0x1p-12 : 1.6x * |x| < M_PI_4 : 1.7x * |x| < 2 * M_PI: 1.5x * |x| < 120.0 : 1.8x * |x| < Inf : 2.3x * math/Makefile: Add s_sincosf_data.c. * sysdeps/ia64/fpu/s_sincosf_data.c: New file. * sysdeps/ieee754/flt-32/s_sincosf.h (abstop12): Add new function. (sincosf_poly): Likewise. (reduce_small): Likewise. (reduce_large): Likewise. * sysdeps/ieee754/flt-32/s_sincosf.c (sincosf): Rewrite. * sysdeps/ieee754/flt-32/s_sincosf_data.c: New file with sincosf data. * sysdeps/m68k/m680x0/fpu/s_sincosf_data.c: New file. * sysdeps/x86_64/fpu/s_sincosf_data.c: New file. |
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| aarch64 | ||
| alpha | ||
| arm | ||
| generic | ||
| gnu | ||
| hppa | ||
| htl | ||
| hurd | ||
| i386 | ||
| ia64 | ||
| ieee754 | ||
| init_array | ||
| m68k | ||
| mach | ||
| microblaze | ||
| mips | ||
| nios2 | ||
| nptl | ||
| posix | ||
| powerpc | ||
| pthread | ||
| riscv | ||
| s390 | ||
| sh | ||
| sparc | ||
| unix | ||
| wordsize-32 | ||
| wordsize-64 | ||
| x86 | ||
| x86_64 | ||