| // whatever return type | |
| typedef struct { float h,l; } f32_pair_t; | |
| f32_pair_t f32_quadratic_hq(float A, float B, float C) | |
| { | |
| double a = (double)A; | |
| double b = (double)B; | |
| double c = (double)C; |
| // if 'f' is the 64-bit input CRC32-C (with 'incoming' 32-bit value of zero) then | |
| // there are 50 bijections (invertiable functions) which are a sum of f | |
| // and a simple xorshift. So the follow two forms: | |
| // | |
| // f(x) ^ (x ^ (x << S)) | |
| // f(x) ^ (x ^ (x >> S)) | |
| // | |
| // and 23 using a rotate instead of a shift: | |
| // |
| // Public Domain under http://unlicense.org, see link for details. | |
| // except: | |
| // * core-math function `cr_cbrtf` (see license below) | |
| // * musl flavored fdlib function `fdlibm_cbrtf` (see license below) | |
| // code and test driver for cube root and it's reciprocal based on: | |
| // "Fast Calculation of Cube and Inverse Cube Roots Using | |
| // a Magic Constant and Its Implementation on Microcontrollers" | |
| // Moroz, Samotyy, Walczyk, Cieslinski, 2021 | |
| // (PDF: https://www.mdpi.com/1996-1073/14/4/1058) |
| ---------------------------------------------------------------------------- | |
| starting: vrecpe_f32 on [3f800000, 40000000] | |
| // min/max ulp -45502 44978 | |
| // abs max ulp 45502.375051 | |
| // correctly: 0.002611% (219) | |
| // faithfully: 0.005555% (466) | |
| // 2 ulp: 0.005436% (456) | |
| // 3 ulp: 0.005460% (458) | |
| // 4 ulp: 0.005329% (447) | |
| // 5 ulp: 0.005531% (464) |
checking on [3f800000,40000000] [1.000000e+00,2.000000e+00]
| func | e | max ULP | CR | FR | 2 ULP | > 2 ULP | CR% | FR% | 2 ULP% | > 2 ULP% |
|---|---|---|---|---|---|---|---|---|---|---|
| vrsqrte_f32 | -- | 4947968 | 103 | 225 | 216 | 8388065 | 0.001228 | 0.002682 | 0.002575 | 99.993515 |
| FRSR_Mon0 | -- | 564177 | 3 | 8 | 6 | 8388592 | 0.000036 | 0.000095 | 0.000072 | 99.999797 |
| FRSR_Deg0 | -- | 403258 | 0 | 0 | 0 | 8388609 | 0.000000 | 0.000000 | 0.000000 | 100.000000 |
| FRSR_Mon1 | -- | 14751 | 230 | 464 | 466 | 8387449 | 0.002742 | 0.005531 | 0.005555 | 99.986172 |
| // Public Domain under http://unlicense.org, see link for details. | |
| #include <stdint.h> | |
| #include <stdlib.h> | |
| #include <stdio.h> | |
| #include <math.h> | |
| #include <string.h> | |
| #include "xmmintrin.h" | |
| #include "wmmintrin.h" |
| // SEE: https://marc-b-reynolds.github.io/math/2019/03/12/FpDiv.html | |
| #include <stdint.h> | |
| #include <stdio.h> | |
| #include <string.h> | |
| #include <math.h> | |
| #define RANDOMIZE | |
| #define TEST_LEN UINT64_C(0x0000000100000000) |
| #include <stdint.h> | |
| #include <stdio.h> | |
| #include <string.h> | |
| #include <math.h> | |
| #define RANDOMIZE | |
| #define TEST_LEN 0x7fffffff | |
| #define VARIANT_FMA |
| 00 : mean=0.000000,variance=0.000000,std-dev=0.000000, count=67108863 on [0.000000,0.000000] | |
| 01 : mean=6.511208,variance=3.084904,std-dev=1.756390, count=67108863 on [2.000000,31.000000] | |
| 02 : mean=6.254943,variance=3.523351,std-dev=1.877059, count=67108863 on [2.000000,30.000000] | |
| 03 : mean=6.142395,variance=3.876341,std-dev=1.968843, count=67108863 on [2.000000,31.000000] | |
| 04 : mean=6.083418,variance=4.125431,std-dev=2.031116, count=67108863 on [2.000000,31.000000] | |
| 05 : mean=6.046452,variance=4.320036,std-dev=2.078470, count=67108863 on [2.000000,31.000000] | |
| 06 : mean=6.018018,variance=4.485348,std-dev=2.117864, count=67108863 on [2.000000,31.000000] | |
| 07 : mean=5.996642,variance=4.607561,std-dev=2.146523, count=67108863 on [2.000000,33.000000] | |
| 08 : mean=5.986188,variance=4.664854,std-dev=2.159827, count=67108863 on [2.000000,32.000000] | |
| 09 : mean=5.987023,variance=4.672484,std-dev=2.161593, count=67108863 on [2.000000,33.000000] |
| // 1) "Tables of linear congruential generators of different sizes and good lattice structure" (1999), Pierre L'Ecuyer | |
| // 2) Pre-print version of (3) (https://arxiv.org/abs/2001.05304) | |
| // 3) "Computationally easy, spectrally good multipliers for congruential pseudorandom number generators" (2021), Guy L. Steele Jr. & Sebastiano Vigna (https://onlinelibrary.wiley.com/doi/epdf/10.1002/spe.3030) | |
| // inline comment number is bit width of constant | |
| const uint32_t lcg_mul_k_table_32[] = | |
| { | |
| // (3) Table 4 LCGs | |
| 0x0000d9f5, // 16 |