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https://sourceware.org/git/glibc.git
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e70c176825
Optimized exp and exp2 implementations using a lookup table for fractional powers of 2. There are several variants, see e_exp_data.c, they can be selected by modifying math_config.h allowing different tradeoffs. The default selection should be acceptable as generic libm code. Worst case error is 0.509 ULP for exp and 0.507 ULP for exp2, on aarch64 the rodata size is 2160 bytes, shared between exp and exp2. On aarch64 .text + .rodata size decreased by 24912 bytes. The non-nearest rounding error is less than 1 ULP even on targets without efficient round implementation (although the error rate is higher in that case). Targets with single instruction, rounding mode independent, to nearest integer rounding and conversion can use them by setting TOINT_INTRINSICS and adding the necessary code to their math_private.h. The __exp1 code uses the same algorithm, so the error bound of pow increased a bit. New double precision error handling code was added following the style of the single precision error handling code. Improvements on Cortex-A72 compared to current glibc master: exp thruput: 1.61x in [-9.9 9.9] exp latency: 1.53x in [-9.9 9.9] exp thruput: 1.13x in [0.5 1] exp latency: 1.30x in [0.5 1] exp2 thruput: 2.03x in [-9.9 9.9] exp2 latency: 1.64x in [-9.9 9.9] For small (< 1) inputs the current exp code uses a separate algorithm so the speed up there is less. Was tested on aarch64-linux-gnu (TOINT_INTRINSICS, fma contraction) and arm-linux-gnueabihf (!TOINT_INTRINSICS, no fma contraction) and x86_64-linux-gnu (!TOINT_INTRINSICS, no fma contraction) and powerpc64le-linux-gnu (!TOINT_INTRINSICS, fma contraction) targets, only non-nearest rounding ulp errors increase and they are within acceptable bounds (ulp updates are in separate patches). * NEWS: Mention exp and exp2 improvements. * math/Makefile (libm-support): Remove t_exp. (type-double-routines): Add math_err and e_exp_data. * sysdeps/aarch64/libm-test-ulps: Update. * sysdeps/arm/libm-test-ulps: Update. * sysdeps/i386/fpu/e_exp_data.c: New file. * sysdeps/i386/fpu/math_err.c: New file. * sysdeps/i386/fpu/t_exp.c: Remove. * sysdeps/ia64/fpu/e_exp_data.c: New file. * sysdeps/ia64/fpu/math_err.c: New file. * sysdeps/ia64/fpu/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/e_exp.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp2.c: Rewrite. * sysdeps/ieee754/dbl-64/e_exp_data.c: New file. * sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Update error bound. * sysdeps/ieee754/dbl-64/eexp.tbl: Remove. * sysdeps/ieee754/dbl-64/math_config.h: New file. * sysdeps/ieee754/dbl-64/math_err.c: New file. * sysdeps/ieee754/dbl-64/t_exp.c: Remove. * sysdeps/ieee754/dbl-64/t_exp2.h: Remove. * sysdeps/ieee754/dbl-64/uexp.h: Remove. * sysdeps/ieee754/dbl-64/uexp.tbl: Remove. * sysdeps/m68k/m680x0/fpu/e_exp_data.c: New file. * sysdeps/m68k/m680x0/fpu/math_err.c: New file. * sysdeps/m68k/m680x0/fpu/t_exp.c: Remove. * sysdeps/powerpc/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Update.
1683 lines
20 KiB
Plaintext
1683 lines
20 KiB
Plaintext
# Begin of automatic generation
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# Maximal error of functions:
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Function: "acos":
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float: 1
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ifloat: 1
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Function: "acos_downward":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "acos_towardzero":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "acos_upward":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "acosh":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: "acosh_downward":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: "acosh_towardzero":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: "acosh_upward":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: "asin":
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float: 1
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ifloat: 1
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Function: "asin_downward":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "asin_towardzero":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "asin_upward":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "asinh":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "asinh_downward":
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double: 3
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float: 3
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idouble: 3
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ifloat: 3
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Function: "asinh_towardzero":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: "asinh_upward":
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double: 3
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float: 3
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idouble: 3
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ifloat: 3
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Function: "atan":
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float: 1
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ifloat: 1
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Function: "atan2":
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float: 1
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ifloat: 1
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Function: "atan2_downward":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: "atan2_towardzero":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: "atan2_upward":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: "atan_downward":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: "atan_towardzero":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "atan_upward":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: "atanh":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: "atanh_downward":
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double: 3
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float: 3
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idouble: 3
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ifloat: 3
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Function: "atanh_towardzero":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: "atanh_upward":
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double: 3
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float: 3
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idouble: 3
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ifloat: 3
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Function: "cabs":
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double: 1
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idouble: 1
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Function: "cabs_downward":
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double: 1
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idouble: 1
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Function: "cabs_towardzero":
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double: 1
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idouble: 1
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Function: "cabs_upward":
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double: 1
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idouble: 1
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Function: Real part of "cacos":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: Imaginary part of "cacos":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: Real part of "cacos_downward":
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double: 3
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float: 2
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idouble: 3
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ifloat: 2
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Function: Imaginary part of "cacos_downward":
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double: 5
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float: 3
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idouble: 5
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ifloat: 3
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Function: Real part of "cacos_towardzero":
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double: 3
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float: 2
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idouble: 3
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ifloat: 2
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Function: Imaginary part of "cacos_towardzero":
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double: 5
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float: 3
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idouble: 5
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ifloat: 3
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Function: Real part of "cacos_upward":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: Imaginary part of "cacos_upward":
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double: 5
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float: 7
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idouble: 5
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ifloat: 7
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Function: Real part of "cacosh":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: Imaginary part of "cacosh":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: Real part of "cacosh_downward":
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double: 5
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float: 3
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idouble: 5
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ifloat: 3
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Function: Imaginary part of "cacosh_downward":
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double: 3
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float: 3
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idouble: 3
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ifloat: 3
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Function: Real part of "cacosh_towardzero":
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double: 5
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float: 3
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idouble: 5
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ifloat: 3
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Function: Imaginary part of "cacosh_towardzero":
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double: 3
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float: 2
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idouble: 3
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ifloat: 2
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Function: Real part of "cacosh_upward":
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double: 4
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float: 4
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idouble: 4
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ifloat: 4
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Function: Imaginary part of "cacosh_upward":
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double: 3
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float: 2
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idouble: 3
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ifloat: 2
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Function: "carg":
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float: 1
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ifloat: 1
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Function: "carg_downward":
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double: 1
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float: 2
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idouble: 1
|
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ifloat: 2
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Function: "carg_towardzero":
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double: 1
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float: 2
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idouble: 1
|
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ifloat: 2
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Function: "carg_upward":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: Real part of "casin":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: Imaginary part of "casin":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: Real part of "casin_downward":
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double: 3
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float: 2
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idouble: 3
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ifloat: 2
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Function: Imaginary part of "casin_downward":
|
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double: 5
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float: 3
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idouble: 5
|
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ifloat: 3
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|
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Function: Real part of "casin_towardzero":
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double: 3
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float: 1
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idouble: 3
|
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ifloat: 1
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|
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Function: Imaginary part of "casin_towardzero":
|
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double: 5
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float: 3
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idouble: 5
|
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ifloat: 3
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|
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Function: Real part of "casin_upward":
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double: 3
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float: 2
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idouble: 3
|
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ifloat: 2
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Function: Imaginary part of "casin_upward":
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double: 5
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float: 7
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idouble: 5
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ifloat: 7
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Function: Real part of "casinh":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: Imaginary part of "casinh":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: Real part of "casinh_downward":
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double: 5
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float: 3
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idouble: 5
|
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ifloat: 3
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Function: Imaginary part of "casinh_downward":
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double: 3
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float: 2
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idouble: 3
|
|
ifloat: 2
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|
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Function: Real part of "casinh_towardzero":
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double: 5
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float: 3
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idouble: 5
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ifloat: 3
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|
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Function: Imaginary part of "casinh_towardzero":
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double: 3
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float: 1
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idouble: 3
|
|
ifloat: 1
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Function: Real part of "casinh_upward":
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double: 5
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float: 7
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idouble: 5
|
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ifloat: 7
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Function: Imaginary part of "casinh_upward":
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double: 3
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float: 2
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idouble: 3
|
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ifloat: 2
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Function: Real part of "catan":
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double: 1
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float: 1
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idouble: 1
|
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ifloat: 1
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|
Function: Imaginary part of "catan":
|
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double: 1
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float: 1
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idouble: 1
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|
ifloat: 1
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|
Function: Real part of "catan_downward":
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double: 1
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float: 2
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idouble: 1
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|
ifloat: 2
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Function: Imaginary part of "catan_downward":
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double: 2
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float: 2
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idouble: 2
|
|
ifloat: 2
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Function: Real part of "catan_towardzero":
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double: 1
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float: 2
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idouble: 1
|
|
ifloat: 2
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Function: Imaginary part of "catan_towardzero":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: Real part of "catan_upward":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: Imaginary part of "catan_upward":
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double: 3
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float: 3
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idouble: 3
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ifloat: 3
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Function: Real part of "catanh":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: Imaginary part of "catanh":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: Real part of "catanh_downward":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: Imaginary part of "catanh_downward":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: Real part of "catanh_towardzero":
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double: 2
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float: 2
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idouble: 2
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ifloat: 2
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Function: Imaginary part of "catanh_towardzero":
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double: 1
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float: 2
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idouble: 1
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ifloat: 2
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Function: Real part of "catanh_upward":
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double: 4
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float: 4
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idouble: 4
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ifloat: 4
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Function: Imaginary part of "catanh_upward":
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double: 1
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float: 1
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idouble: 1
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ifloat: 1
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Function: "cbrt":
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double: 3
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float: 1
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idouble: 3
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ifloat: 1
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Function: "cbrt_downward":
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double: 4
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float: 1
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idouble: 4
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ifloat: 1
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Function: "cbrt_towardzero":
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double: 3
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float: 1
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idouble: 3
|
|
ifloat: 1
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Function: "cbrt_upward":
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double: 5
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float: 1
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idouble: 5
|
|
ifloat: 1
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|
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Function: Real part of "ccos":
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|
double: 1
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float: 1
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idouble: 1
|
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ifloat: 1
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Function: Imaginary part of "ccos":
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|
double: 1
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|
float: 1
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|
idouble: 1
|
|
ifloat: 1
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|
|
Function: Real part of "ccos_downward":
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|
double: 1
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|
float: 1
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|
idouble: 1
|
|
ifloat: 1
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|
|
Function: Imaginary part of "ccos_downward":
|
|
double: 3
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|
float: 3
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|
idouble: 3
|
|
ifloat: 3
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|
|
Function: Real part of "ccos_towardzero":
|
|
double: 1
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float: 2
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|
idouble: 1
|
|
ifloat: 2
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|
|
Function: Imaginary part of "ccos_towardzero":
|
|
double: 3
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|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Real part of "ccos_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "ccos_upward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "ccosh":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: Imaginary part of "ccosh":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: Real part of "ccosh_downward":
|
|
double: 2
|
|
float: 3
|
|
idouble: 2
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "ccosh_downward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Real part of "ccosh_towardzero":
|
|
double: 2
|
|
float: 3
|
|
idouble: 2
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "ccosh_towardzero":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Real part of "ccosh_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "ccosh_upward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "cexp":
|
|
double: 2
|
|
float: 1
|
|
idouble: 2
|
|
ifloat: 1
|
|
|
|
Function: Imaginary part of "cexp":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Real part of "cexp_downward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "cexp_downward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Real part of "cexp_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "cexp_towardzero":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Real part of "cexp_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "cexp_upward":
|
|
double: 3
|
|
float: 2
|
|
idouble: 3
|
|
ifloat: 2
|
|
|
|
Function: Real part of "clog":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "clog":
|
|
float: 1
|
|
ifloat: 1
|
|
|
|
Function: Real part of "clog10":
|
|
double: 3
|
|
float: 4
|
|
idouble: 3
|
|
ifloat: 4
|
|
|
|
Function: Imaginary part of "clog10":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "clog10_downward":
|
|
double: 5
|
|
float: 5
|
|
idouble: 5
|
|
ifloat: 5
|
|
|
|
Function: Imaginary part of "clog10_downward":
|
|
double: 2
|
|
float: 4
|
|
idouble: 2
|
|
ifloat: 4
|
|
|
|
Function: Real part of "clog10_towardzero":
|
|
double: 5
|
|
float: 5
|
|
idouble: 5
|
|
ifloat: 5
|
|
|
|
Function: Imaginary part of "clog10_towardzero":
|
|
double: 2
|
|
float: 4
|
|
idouble: 2
|
|
ifloat: 4
|
|
|
|
Function: Real part of "clog10_upward":
|
|
double: 6
|
|
float: 5
|
|
idouble: 6
|
|
ifloat: 5
|
|
|
|
Function: Imaginary part of "clog10_upward":
|
|
double: 2
|
|
float: 4
|
|
idouble: 2
|
|
ifloat: 4
|
|
|
|
Function: Real part of "clog_downward":
|
|
double: 4
|
|
float: 3
|
|
idouble: 4
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "clog_downward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Real part of "clog_towardzero":
|
|
double: 4
|
|
float: 4
|
|
idouble: 4
|
|
ifloat: 4
|
|
|
|
Function: Imaginary part of "clog_towardzero":
|
|
double: 1
|
|
float: 3
|
|
idouble: 1
|
|
ifloat: 3
|
|
|
|
Function: Real part of "clog_upward":
|
|
double: 4
|
|
float: 3
|
|
idouble: 4
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "clog_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "cos":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "cos_downward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "cos_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "cos_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "cosh":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "cosh_downward":
|
|
double: 2
|
|
float: 1
|
|
idouble: 2
|
|
ifloat: 1
|
|
|
|
Function: "cosh_towardzero":
|
|
double: 2
|
|
float: 1
|
|
idouble: 2
|
|
ifloat: 1
|
|
|
|
Function: "cosh_upward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "cpow":
|
|
double: 2
|
|
float: 5
|
|
idouble: 2
|
|
ifloat: 5
|
|
|
|
Function: Imaginary part of "cpow":
|
|
float: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "cpow_downward":
|
|
double: 5
|
|
float: 8
|
|
idouble: 5
|
|
ifloat: 8
|
|
|
|
Function: Imaginary part of "cpow_downward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Real part of "cpow_towardzero":
|
|
double: 5
|
|
float: 8
|
|
idouble: 5
|
|
ifloat: 8
|
|
|
|
Function: Imaginary part of "cpow_towardzero":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Real part of "cpow_upward":
|
|
double: 4
|
|
float: 1
|
|
idouble: 4
|
|
ifloat: 1
|
|
|
|
Function: Imaginary part of "cpow_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Real part of "csin":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: Real part of "csin_downward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "csin_downward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: Real part of "csin_towardzero":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "csin_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: Real part of "csin_upward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "csin_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Real part of "csinh":
|
|
float: 1
|
|
ifloat: 1
|
|
|
|
Function: Imaginary part of "csinh":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: Real part of "csinh_downward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "csinh_downward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Real part of "csinh_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "csinh_towardzero":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Real part of "csinh_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "csinh_upward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "csqrt":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "csqrt":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "csqrt_downward":
|
|
double: 5
|
|
float: 4
|
|
idouble: 5
|
|
ifloat: 4
|
|
|
|
Function: Imaginary part of "csqrt_downward":
|
|
double: 4
|
|
float: 3
|
|
idouble: 4
|
|
ifloat: 3
|
|
|
|
Function: Real part of "csqrt_towardzero":
|
|
double: 4
|
|
float: 3
|
|
idouble: 4
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "csqrt_towardzero":
|
|
double: 4
|
|
float: 3
|
|
idouble: 4
|
|
ifloat: 3
|
|
|
|
Function: Real part of "csqrt_upward":
|
|
double: 5
|
|
float: 4
|
|
idouble: 5
|
|
ifloat: 4
|
|
|
|
Function: Imaginary part of "csqrt_upward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: Real part of "ctan":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: Imaginary part of "ctan":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "ctan_downward":
|
|
double: 6
|
|
float: 5
|
|
idouble: 6
|
|
ifloat: 5
|
|
|
|
Function: Imaginary part of "ctan_downward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "ctan_towardzero":
|
|
double: 5
|
|
float: 3
|
|
idouble: 5
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "ctan_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "ctan_upward":
|
|
double: 2
|
|
float: 4
|
|
idouble: 2
|
|
ifloat: 4
|
|
|
|
Function: Imaginary part of "ctan_upward":
|
|
double: 2
|
|
float: 3
|
|
idouble: 2
|
|
ifloat: 3
|
|
|
|
Function: Real part of "ctanh":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "ctanh":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Real part of "ctanh_downward":
|
|
double: 4
|
|
float: 2
|
|
idouble: 4
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "ctanh_downward":
|
|
double: 6
|
|
float: 5
|
|
idouble: 6
|
|
ifloat: 5
|
|
|
|
Function: Real part of "ctanh_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: Imaginary part of "ctanh_towardzero":
|
|
double: 5
|
|
float: 3
|
|
idouble: 5
|
|
ifloat: 3
|
|
|
|
Function: Real part of "ctanh_upward":
|
|
double: 2
|
|
float: 3
|
|
idouble: 2
|
|
ifloat: 3
|
|
|
|
Function: Imaginary part of "ctanh_upward":
|
|
double: 2
|
|
float: 3
|
|
idouble: 2
|
|
ifloat: 3
|
|
|
|
Function: "erf":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "erf_downward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "erf_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "erf_upward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "erfc":
|
|
double: 3
|
|
float: 2
|
|
idouble: 3
|
|
ifloat: 2
|
|
|
|
Function: "erfc_downward":
|
|
double: 5
|
|
float: 6
|
|
idouble: 5
|
|
ifloat: 6
|
|
|
|
Function: "erfc_towardzero":
|
|
double: 3
|
|
float: 4
|
|
idouble: 3
|
|
ifloat: 4
|
|
|
|
Function: "erfc_upward":
|
|
double: 5
|
|
float: 6
|
|
idouble: 5
|
|
ifloat: 6
|
|
|
|
Function: "exp":
|
|
float: 1
|
|
ifloat: 1
|
|
|
|
Function: "exp10":
|
|
double: 2
|
|
idouble: 2
|
|
|
|
Function: "exp10_downward":
|
|
double: 3
|
|
float: 1
|
|
idouble: 3
|
|
ifloat: 1
|
|
|
|
Function: "exp10_towardzero":
|
|
double: 3
|
|
float: 1
|
|
idouble: 3
|
|
ifloat: 1
|
|
|
|
Function: "exp10_upward":
|
|
double: 2
|
|
float: 1
|
|
idouble: 2
|
|
ifloat: 1
|
|
|
|
Function: "exp2":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "exp2_downward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "exp2_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "exp2_upward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "exp_downward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "exp_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "exp_upward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "expm1":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "expm1_downward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "expm1_towardzero":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "expm1_upward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "gamma":
|
|
double: 4
|
|
float: 4
|
|
idouble: 4
|
|
ifloat: 4
|
|
|
|
Function: "gamma_downward":
|
|
double: 5
|
|
float: 4
|
|
idouble: 5
|
|
ifloat: 4
|
|
|
|
Function: "gamma_towardzero":
|
|
double: 5
|
|
float: 4
|
|
idouble: 5
|
|
ifloat: 4
|
|
|
|
Function: "gamma_upward":
|
|
double: 5
|
|
float: 5
|
|
idouble: 5
|
|
ifloat: 5
|
|
|
|
Function: "hypot":
|
|
double: 1
|
|
idouble: 1
|
|
|
|
Function: "hypot_downward":
|
|
double: 1
|
|
idouble: 1
|
|
|
|
Function: "hypot_towardzero":
|
|
double: 1
|
|
idouble: 1
|
|
|
|
Function: "hypot_upward":
|
|
double: 1
|
|
idouble: 1
|
|
|
|
Function: "j0":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "j0_downward":
|
|
double: 2
|
|
float: 4
|
|
idouble: 2
|
|
ifloat: 4
|
|
|
|
Function: "j0_towardzero":
|
|
double: 3
|
|
float: 2
|
|
idouble: 3
|
|
ifloat: 2
|
|
|
|
Function: "j0_upward":
|
|
double: 3
|
|
float: 2
|
|
idouble: 3
|
|
ifloat: 2
|
|
|
|
Function: "j1":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "j1_downward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "j1_towardzero":
|
|
double: 3
|
|
float: 2
|
|
idouble: 3
|
|
ifloat: 2
|
|
|
|
Function: "j1_upward":
|
|
double: 3
|
|
float: 5
|
|
idouble: 3
|
|
ifloat: 5
|
|
|
|
Function: "jn":
|
|
double: 4
|
|
float: 4
|
|
idouble: 4
|
|
ifloat: 4
|
|
|
|
Function: "jn_downward":
|
|
double: 5
|
|
float: 5
|
|
idouble: 5
|
|
ifloat: 5
|
|
|
|
Function: "jn_towardzero":
|
|
double: 5
|
|
float: 5
|
|
idouble: 5
|
|
ifloat: 5
|
|
|
|
Function: "jn_upward":
|
|
double: 5
|
|
float: 5
|
|
idouble: 5
|
|
ifloat: 5
|
|
|
|
Function: "lgamma":
|
|
double: 4
|
|
float: 4
|
|
idouble: 4
|
|
ifloat: 4
|
|
|
|
Function: "lgamma_downward":
|
|
double: 5
|
|
float: 4
|
|
idouble: 5
|
|
ifloat: 4
|
|
|
|
Function: "lgamma_towardzero":
|
|
double: 5
|
|
float: 4
|
|
idouble: 5
|
|
ifloat: 4
|
|
|
|
Function: "lgamma_upward":
|
|
double: 5
|
|
float: 5
|
|
idouble: 5
|
|
ifloat: 5
|
|
|
|
Function: "log":
|
|
float: 1
|
|
ifloat: 1
|
|
|
|
Function: "log10":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "log10_downward":
|
|
double: 2
|
|
float: 3
|
|
idouble: 2
|
|
ifloat: 3
|
|
|
|
Function: "log10_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "log10_upward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "log1p":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "log1p_downward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "log1p_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "log1p_upward":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "log2":
|
|
double: 2
|
|
float: 1
|
|
idouble: 2
|
|
ifloat: 1
|
|
|
|
Function: "log2_downward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "log2_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "log2_upward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "log_downward":
|
|
float: 2
|
|
ifloat: 2
|
|
|
|
Function: "log_towardzero":
|
|
float: 2
|
|
ifloat: 2
|
|
|
|
Function: "log_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "pow":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "pow_downward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "pow_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "pow_upward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "sin":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "sin_downward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "sin_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "sin_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "sincos":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "sincos_downward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "sincos_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "sincos_upward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "sinh":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "sinh_downward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "sinh_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "sinh_upward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "tan":
|
|
float: 1
|
|
ifloat: 1
|
|
|
|
Function: "tan_downward":
|
|
double: 1
|
|
float: 2
|
|
idouble: 1
|
|
ifloat: 2
|
|
|
|
Function: "tan_towardzero":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "tan_upward":
|
|
double: 1
|
|
float: 1
|
|
idouble: 1
|
|
ifloat: 1
|
|
|
|
Function: "tanh":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "tanh_downward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "tanh_towardzero":
|
|
double: 2
|
|
float: 2
|
|
idouble: 2
|
|
ifloat: 2
|
|
|
|
Function: "tanh_upward":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "tgamma":
|
|
double: 5
|
|
float: 4
|
|
idouble: 5
|
|
ifloat: 4
|
|
|
|
Function: "tgamma_downward":
|
|
double: 5
|
|
float: 5
|
|
idouble: 5
|
|
ifloat: 5
|
|
|
|
Function: "tgamma_towardzero":
|
|
double: 5
|
|
float: 4
|
|
idouble: 5
|
|
ifloat: 4
|
|
|
|
Function: "tgamma_upward":
|
|
double: 4
|
|
float: 4
|
|
idouble: 4
|
|
ifloat: 4
|
|
|
|
Function: "y0":
|
|
double: 2
|
|
float: 1
|
|
idouble: 2
|
|
ifloat: 1
|
|
|
|
Function: "y0_downward":
|
|
double: 3
|
|
float: 4
|
|
idouble: 3
|
|
ifloat: 4
|
|
|
|
Function: "y0_towardzero":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "y0_upward":
|
|
double: 3
|
|
float: 5
|
|
idouble: 3
|
|
ifloat: 5
|
|
|
|
Function: "y1":
|
|
double: 3
|
|
float: 2
|
|
idouble: 3
|
|
ifloat: 2
|
|
|
|
Function: "y1_downward":
|
|
double: 3
|
|
float: 2
|
|
idouble: 3
|
|
ifloat: 2
|
|
|
|
Function: "y1_towardzero":
|
|
double: 3
|
|
float: 2
|
|
idouble: 3
|
|
ifloat: 2
|
|
|
|
Function: "y1_upward":
|
|
double: 7
|
|
float: 2
|
|
idouble: 7
|
|
ifloat: 2
|
|
|
|
Function: "yn":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "yn_downward":
|
|
double: 3
|
|
float: 4
|
|
idouble: 3
|
|
ifloat: 4
|
|
|
|
Function: "yn_towardzero":
|
|
double: 3
|
|
float: 3
|
|
idouble: 3
|
|
ifloat: 3
|
|
|
|
Function: "yn_upward":
|
|
double: 4
|
|
float: 5
|
|
idouble: 4
|
|
ifloat: 5
|
|
|
|
# end of automatic generation
|