emFloat — The floating-point library

emFloat is an IEEE 754 compliant floating-point library designed from the ground up for embedded systems.

Overview

Developed and honed for more than two decades, emFloat is a highly optimized component of emRun, SEGGER's C runtime library, and also a part of SEGGER Embedded Studio.

Designed for plug-and-play, emFloat can replace a default floating-point library, delivering better performance with less code. Very fast and very small, it delivers FPU-like performance in pure software. Where available, it even boosts the performance of an FPU for complex mathematical functions.

It is available stand-alone, in source code form, for developers who wish to increase performance or reduce the code size of their application without replacing the entire runtime library supplied with their toolchain.

emFloat can also be licensed for inclusion in third-party IDEs. An example is Microchip choosing to include emFloat in the Microchip XC32 V4.0 Compiler Toolchain.

Benchmarking for both floating-point and runtime libraries can be done quickly and easily using Embedded Studio, which is readily available at no cost for evaluation and non-commercial usage under SEGGER’s Friendly License.

For details on why using a thoughtfully designed runtime library is important, refer to the emRun page.

emFloat floating point library for embedded systems

Key features

Small code size, high performance
Plug-and-play: Can easily replace the default floating point library, delivering better performance with less code.
Flexible licensing, for integration into user applications or toolchains.
C-Variant can be used on any 8/16/32/64-bit CPU.
Hand-coded, assembly-optimized variants for RISC-V and ARM
Fully reentrant
No heap requirements

Licensing

emFloat is available for integration into specific projects by end users, as well as to toolchain providers that want to deliver a top-of-the-line runtime and/or floating-point library to their users.

Licensing options are available to fit any such needs, usually with a single payment and no royalty obligation.

The library is delivered in source code, with optional rights for redistribution in object code form. All delivered C and assembly language source files are fully commented.

SEGGER software is not covered by an open source or required attribution license, and can be integrated into any commercial or proprietary product, without the obligation to disclose the combined source.

Variants

emFloat is available in a universal variant written in C, and specific variants for different CPUs. The specific variants include modules written in assembly language, optimized for the CPU architecture, and deliver a higher performance than the universal C variant.

Universal C Variant:

The universal version is written in C. The performance is highly optimized and much higher than the performance of comparable, C-coded open source implementations.

Supported CPUs: The universal variant can be used on any platform, including 8-, 16-, 32, and 64- bit processors.

Arm Variant:

The ARM-optimized variant is fully coded in Assembly language, conforming to the AEABI.This means it is compatible with any (A)EABI compliant tool chain, including any GCC, LLVM/Clang based tool chains as well as Arm's own compiler (incl. Keil) and IAR and can replace the default runtime library or parts of it.

Supported CPUs: The Arm Variant supports any 32-bit ARM CPU, starting from ARM Architecture V4. This includes Cortex-M, Cortex-A, and Cortex-R.

RISC-V Variant:

The RISC-V Variant is written in assembly language, providing functions compatible with the EABI. It can easily be used to replace the default runtime library of EABI compliant toolchains.

Supported CPUs: The RISC-V Variant supports RV32I and RV32E with architecture-specific acceleration. It supports faster multiply and divide with the M (multiply/divide) extension. It also supports fast division even if if the M extension lacks a divide instruction.

Silicon vendor buyout option

SEGGER offers the possibility to license emFloat for redistribution to your customers under your own terms. Please contact us to complete your offerings with a proven commercial solution.

More information on the Silicon vendor buyout option...

Silicon vendors for emFloat

Implementation and design

emFloat consists of two parts:

Arithmetic functions
implementing functionality similar to that of the FPU, such as floating-point add, subtract, multiply, divide, comparisons, and conversions

Mathematical functions
using the most efficient, modern algorithms, benefiting systems with or without an FPU

While all mathematical functions are written in C, the arithmetic functions for the Arm and RISC-V variants are hand-coded in assembly language. For other processor architectures the library has a portable C implementation.

emFloat is optimized on both, the design level (using efficient algorithms) as well as the implementation level (running on different architectures). The source code contains options to fine-tune it for high performance or small code size or a balance of the two, delivering excellent performance in all cases.

It provides a consistent execution environment which ensures that infinities, not-a-number, and zero results with correct sign are accepted as inputs and generated as outputs. To be consistent with floating-point units executing in fast mode, the library elects to flush subnormals to a correctly-signed zero. Because subnormals do not typically occur in embedded systems, this optimization enables significant code size reduction.

Integration and use

emFloat provides all well-known floating-point-related API functions of C standard libraries, as well as floating-point-operation functions defined by the architecture's EABI which are implicitly called and added by the compiler.

The floating-point Library can either be integrated into a toolchain to replace the existing standard library implementation, or it can be used side-by-side. The side-by-side use enables selective calls to the Floating-Point Library, while retaining the toolchain's standard library, which makes the integration and use easy and simple.

Example: To return the sine of a value x:

With the integrated use, call sin(x).
With the side-by-side use, call SEGGER_sin(x).

To multiply two float values A and B without the use of an FPU:

With the integrated use, call A * B, for which the compiler will implicitly call __mulsf3(A, B) or __aeabi_fmul(A, B).
With the side-by-side use, call SEGGER_fmul(A,B)

Configuration options

emFloat is configurable for small code size or increased execution speed or a combination. Optimizing for code-size or execution-speed or a balance of both does not cause any loss of accuracy. Calculated results are identical in all modes.

In the source distribution, the library can be configured and tuned to favor faster or smaller code with different levels of optimization:
-2 - Favor size at the expense of speed
-1 - Favor size over speed
0 - Balanced
+1 - Favor speed over size
+2 - Favor speed at the expense of size

The sections below show the performance of the high-level explicit functions and the low-level implicit floating-point functions of different architectures. For more information please refer to the blog post Floating-point face-off, part 2.

Note: Due to the specific features of each architecture, the performance values should not be compared to each other. Instead these values are generated for comparison with other floating-point libraries.

Architecture-specific optimization

The assembly language variants of the emFloat take advantage of processor-specific features. Each architecture has its own fine-tuned implementation.

In the Arm variant, the floating-point support makes use of the 32-bit Arm and Thumb-2 instruction set and uses divide instructions and extended multiply instructions, when available, which results in a smaller and faster implementation. Pure Thumb instruction sets, such as on Cortex-M0 and Cortex-M23 processors, are, of course, supported entirely, too.

In the RISC-V variant, software floating-point is supported on all RV32I and RV32E architectures. The floating-point implementation takes full advantage of processors that have the M extension, and processors that have the M extension but without a divide instruction. The C extension is supported to select registers that make the best use of the compact instruction encoding, achieving smaller code.

The assembly language versions have multiple implementations of arithmetic operations, using architectural details and tailored algorithms to make the best use of the available instruction set. For instance, for single precision division:

Use a division instruction to iteratively develop a quotient, if available.
If no division instruction, but there is a multiplication instruction, use an initial reciprocal approximation refined by Newton-Raphson iterations with a final correction and multiplication.
If no division and no multiplication instruction, use a non-restoring division algorithm.

Similar optimizations apply to double-precision division.

API functions — Explicit & implicit

Explicit Functions: emFloat implements all standard library functions which are usually exposed through math.h. These functions are always explicitly called by a user application.

With the integrated use of the library, the standard function can simply be called (no prefix), with the side-by-side use, the functions of this library can be called instead of the standard library implementation by adding the prefix "SEGGER_". The API interface is compatible.

Function List:

int                SEGGER_isinff        (float  x);
int                SEGGER_isinf         (double x);
int                SEGGER_isnanf        (float  x);
int                SEGGER_isnan         (double x);
int                SEGGER_isfinitef     (float  x);
int                SEGGER_isfinite      (double x);
int                SEGGER_isnormalf     (float  x);
int                SEGGER_isnormal      (double x);
int                SEGGER_signbitf      (float  x);
int                SEGGER_signbit       (double x);
int                SEGGER_classifyf     (float  x);
int                SEGGER_classify      (double x);
float              SEGGER_cosf          (float  x);
double             SEGGER_cos           (double x);
float              SEGGER_sinf          (float  x);
double             SEGGER_sin           (double x);
float              SEGGER_tanf          (float  x);
double             SEGGER_tan           (double x);
float              SEGGER_acosf         (float  x);
double             SEGGER_acos          (double x);
float              SEGGER_asinf         (float  x);
double             SEGGER_asin          (double x);
float              SEGGER_atanf         (float  x);
double             SEGGER_atan          (double x);
float              SEGGER_atan2f        (float  y, float  x);
double             SEGGER_atan2         (double y, double x);
float              SEGGER_frexpf        (float  x, int *exp);
double             SEGGER_frexp         (double x, int *exp);
float              SEGGER_ldexpf        (float  x, int exp);
double             SEGGER_ldexp         (double x, int exp);
float              SEGGER_scalbnf       (float  x, int exp);
double             SEGGER_scalbn        (double x, int exp);
float              SEGGER_logf          (float  x);
double             SEGGER_log           (double x);
float              SEGGER_log10f        (float  x);
double             SEGGER_log10         (double x);
float              SEGGER_fmodf         (float  x, float  y);
double             SEGGER_fmod          (double x, double y);
float              SEGGER_modff         (float  x, float  *iptr);
double             SEGGER_modf          (double x, double *iptr);
float              SEGGER_powf          (float  x, float  y);
double             SEGGER_pow           (double x, double y);
float              SEGGER_sqrtf         (float  x);
double             SEGGER_sqrt          (double x);
float              SEGGER_cbrtf         (float  x);
double             SEGGER_cbrt          (double x);
float              SEGGER_ceilf         (float  x);
double             SEGGER_ceil          (double x);
float              SEGGER_fabsf         (float  x);
double             SEGGER_fabs          (double x);
float              SEGGER_fminf         (float  x, float  y);
double             SEGGER_fmin          (double x, double y);
float              SEGGER_fmaxf         (float  x, float  y);
double             SEGGER_fmax          (double x, double y);
float              SEGGER_floorf        (float  x);
double             SEGGER_floor         (double x);
float              SEGGER_hypotf        (float  x, float  y);
double             SEGGER_hypot         (double x, double y);
float              SEGGER_coshf         (float  x);
double             SEGGER_cosh          (double x);
float              SEGGER_sinhf         (float  x);
double             SEGGER_sinh          (double x);
float              SEGGER_tanhf         (float  x);
double             SEGGER_tanh          (double x);
float              SEGGER_expf          (float  x);
double             SEGGER_exp           (double x);
float              SEGGER_expm1f        (float  x);
float              SEGGER_acoshf        (float  x);
double             SEGGER_acosh         (double x);
float              SEGGER_asinhf        (float  x);
double             SEGGER_asinh         (double x);
float              SEGGER_atanhf        (float  x);
double             SEGGER_atanh         (double x);
float              SEGGER_fmaf          (float  x, float  y, float  z);
double             SEGGER_fma           (double x, double y, double z);
float              SEGGER_exp2f         (float  x);
double             SEGGER_exp2          (double x);
float              SEGGER_exp10f        (float  x);
double             SEGGER_exp10         (double x);
float              SEGGER_expm1f        (float  x);
double             SEGGER_expm1         (double x);
float              SEGGER_log1pf        (float  x);
double             SEGGER_log1p         (double x);
float              SEGGER_log2f         (float  x);
double             SEGGER_log2          (double x);
float              SEGGER_logbf         (float  x);
double             SEGGER_logb          (double x);

Implicit Functions: When there is no hardware support for basic operations, such as multiplication of two floats, the compiler adds calls to helper functions emulating the operation with available resources. These are the implicit functions, defined by the toolchain's and architecture's EABI.

With the integrated use of the specific variants of emFloat, the compiler will use its implicit functions. When used side-by-side, the functions can be explicitly called instead of writing the standard operation in code.

Function List:

float              SEGGER_addf          (float, float);
double             SEGGER_add           (double, double);
float              SEGGER_subf          (float, float);
double             SEGGER_sub           (double, double);
float              SEGGER_mulf          (float, float);
double             SEGGER_mul           (double, double);
float              SEGGER_divf          (float, float);
double             SEGGER_div           (double, double);
int                SEGGER_ltf           (float, float);
int                SEGGER_lt            (double, double);
int                SEGGER_lef           (float, float);
int                SEGGER_le            (double, double);
int                SEGGER_gtf           (float, float);
int                SEGGER_gt            (double, double);
int                SEGGER_gef           (float, float);
int                SEGGER_ge            (double, double);
int                SEGGER_eqf           (float, float);
int                SEGGER_eq            (double, double);
int                SEGGER_nef           (float, float);
int                SEGGER_ne            (double, double);
float              SEGGER_float_int     (int);
double             SEGGER_double_int    (int);
float              SEGGER_float_llong   (long long);
double             SEGGER_double_llong  (long long);
float              SEGGER_float_uint    (unsigned);
double             SEGGER_double_uint   (unsigned);
float              SEGGER_float_ullong  (unsigned long long);
double             SEGGER_double_ullong (unsigned long long);
int                SEGGER_int_float     (float);
int                SEGGER_int_double    (double);
long long          SEGGER_llong_float   (float);
long long          SEGGER_llong_double  (double);
unsigned           SEGGER_uint_float    (float);
unsigned           SEGGER_uint_double   (double);
unsigned long long SEGGER_ullong_float  (float);
unsigned long long SEGGER_ullong_double (double);
float              SEGGER_float_double  (double);
double             SEGGER_double_float  (float);

Explicit function performance

For verification and benchmark of the explicit functions, the IEEE-754 Floating-point Library Benchmark application is available. It measures performance and precision of the implementation. For each function, significant values have been chosen to get best coverage.

The tables below show the results of the benchmark application running the C implementation on different architectures.

Performance on Arm: The benchmark has been done on an Arm Cortex-M4 microcontroller (NXP K66FN2M0), running from RAM. Detailed results and test cases are available on the SEGGER Wiki.

sinf()	Bit Error	Cycles
sin(1e-4)	0.00	21
sin(1e-3)	0.00	55
sin(1e-2)	0.00	55
sin(1e-1)	0.00	54
sin(1)	0.00	139
sin(1.47264147)	0.00	138
sin(1.57079089)	0.00	138
sinf(3.14158154)	0.00	106
sin(39.0735703)	0.00	148
sin(355)	0.00	152
sin(1048582.75)	0.00	176
sin(100000*Pi)	0.00	151
sin(1e10)	0.00	187
sin(1e38)	0.00	186
Total	0.00	1706

cosf()	Bit Error	Cycles
cos(1e-4)	0.00	3
cos(1e-3)	0.00	48
cos(1e-2)	0.00	48
cos(1e-1)	0.00	48
cos(1)	0.00	136
cos(1.47264147)	0.00	103
cos(1.57079780)	0.00	103
cos(6.28319073)	0.00	136
cos(355)	0.00	180
cos(100000*Pi)	0.00	180
cos(1e10)	0.00	183
cos(1e38)	0.00	182
Total	0.00	1350

tanf()	Bit Error	Cycles
tan(1e-4)	0.00	25
tan(1e-3)	0.00	74
tan(1e-2)	0.00	74
tan(1e-1)	0.00	73
tan(1)	0.00	258
tan(6.45840693)	0.00	258
tan(355)	0.00	282
tan(100000*Pi)	0.00	273
tan(1e10)	0.00	304
tan(1e38)	0.00	321
Total	0.00	1942

expf()	Bit Error	Cycles
expf(0)	0.00	3
expf(1e-5)	0.00	44
expf(1e-4)	0.00	44
expf(2e-4)	0.00	44
expf(4e-4)	0.00	43
expf(4.5e-4)	0.00	44
expf(1e-3)	0.00	44
expf(0.25123)	0.00	81
expf(0.55123)	0.00	80
expf(8.1)	0.00	81
expf(16.1)	0.00	81
Total	0.00	589

sinhf()	Bit Error	Cycles
sinhf(1e-5)	0.00	22
sinhf(1e-4)	0.00	23
sinhf(2e-4)	0.00	23
sinhf(4e-4)	0.00	60
sinhf(4.5e-4)	0.00	59
sinhf(1e-3)	0.00	60
sinhf(0.25123)	0.00	60
sinhf(0.55123)	0.00	119
sinhf(8.1)	0.00	121
sinhf(16.1)	0.00	108
Total	0.00	655

coshf()	Bit Error	Cycles
coshf(1e-5)	0.00	28
coshf(1e-4)	0.00	28
coshf(2e-4)	0.00	29
coshf(4e-4)	0.00	48
coshf(4.5e-4)	0.00	48
coshf(1e-3)	0.00	47
coshf(0.25123)	0.00	48
coshf(0.55123)	0.00	111
coshf(8.1)	0.00	114
coshf(16.1)	0.00	100
Total	0.00	601

tanhf()	Bit Error	Cycles
tanhf(0.25)	0.00	66
tanhf(1)	0.00	108
tanhf(10)	0.00	18
Total	0.00	192

logf()	Bit Error	Cycles
logf(1e-5)	0.00	158
logf(1024)	0.00	100
logf(4177.25)	0.00	140
Total	0.00	398

Performance on RISC-V: The benchmark has been done on an RISC-V RV32IMAC microcontroller (GigaDevice GD32VF103), running from RAM. Detailed results and test cases are available on the SEGGER Wiki.

sinf()	Bit Error	Cycles
sin(1e-4)	0.00	8
sin(1e-3)	0.00	70
sin(1e-2)	0.00	67
sin(1e-1)	0.00	67
sin(1)	0.00	182
sin(1.47264147)	0.00	193
sin(1.57079089)	0.00	196
sinf(3.14158154)	0.00	153
sin(39.0735703)	0.00	193
sin(355)	0.00	219
sin(1048582.75)	0.00	236
sin(100000*Pi)	0.00	214
sin(1e10)	0.00	255
sin(1e38)	0.00	248
Total	0.00	2301

cosf()	Bit Error	Cycles
cos(1e-4)	0.00	10
cos(1e-3)	0.00	50
cos(1e-2)	0.00	43
cos(1e-1)	0.00	43
cos(1)	0.00	186
cos(1.47264147)	0.00	158
cos(1.57079780)	0.00	161
cos(6.28319073)	0.00	190
cos(355)	0.00	252
cos(100000*Pi)	0.00	251
cos(1e10)	0.00	245
cos(1e38)	0.00	257
Total	0.00	1846

tanf()	Bit Error	Cycles
tan(1e-4)	0.00	7
tan(1e-3)	0.00	92
tan(1e-2)	0.00	87
tan(1e-1)	0.00	86
tan(1)	0.00	403
tan(6.45840693)	0.00	397
tan(355)	0.00	444
tan(100000*Pi)	0.00	430
tan(1e10)	0.00	458
tan(1e38)	0.00	483
Total	0.00	2887

expf()	Bit Error	Cycles
expf(0)	0.00	10
expf(1e-5)	0.00	45
expf(1e-4)	0.00	41
expf(2e-4)	0.00	38
expf(4e-4)	0.00	38
expf(4.5e-4)	0.00	38
expf(1e-3)	0.00	38
expf(0.25123)	0.00	86
expf(0.55123)	0.00	89
expf(8.1)	0.00	88
expf(16.1)	0.00	86
Total	0.00	597

sinhf()	Bit Error	Cycles
sinhf(1e-5)	0.00	14
sinhf(1e-4)	0.00	14
sinhf(2e-4)	0.00	13
sinhf(4e-4)	0.00	67
sinhf(4.5e-4)	0.00	59
sinhf(1e-3)	0.00	59
sinhf(0.25123)	0.00	59
sinhf(0.55123)	0.00	137
sinhf(8.1)	0.00	133
sinhf(16.1)	0.00	112
Total	0.00	667

coshf()	Bit Error	Cycles
coshf(1e-5)	0.00	26
coshf(1e-4)	0.00	24
coshf(2e-4)	0.00	24
coshf(4e-4)	0.00	50
coshf(4.5e-4)	0.00	50
coshf(1e-3)	0.00	50
coshf(0.25123)	0.00	50
coshf(0.55123)	0.00	140
coshf(8.1)	0.00	139
coshf(16.1)	0.00	126
Total	0.00	679

tanhf()	Bit Error	Cycles
tanhf(0.25)	0.00	89
tanhf(1)	0.00	145
tanhf(10)	0.00	14
Total	0.00	248

logf()	Bit Error	Cycles
logf(1e-5)	0.00	265
logf(1024)	0.00	183
logf(4177.25)	0.00	240
Total	0.00	688

Implicit function performance

The following tables show the performance and code size of the Arm and RISC-V EABI floating-point functions.

The performance benchmark runs the speed-optimized implementation of the floating-point library (__SEGGER_RTL_OPTIMIZE +2).
The code size has been measured with size optimization (__SEGGER_RTL_OPTIMIZE -2). The speed-optimized configuration requires slightly more code.

Performance on Arm: The benchmarks have been done on an Arm Cortex-M4 microcontroller (NXP K66FN2M0), running from RAM, compiled with Embedded Studio (GCC).

Function		Average Cycles
Float, Math	__aeabi_fadd	31.0
	__aeabi_fsub	39.9
	__aeabi_frsub	39.9
	__aeabi_fmul	26.0
	__aeabi_fdiv	53.0
Float, Compare	__aeabi_fcmplt	13.0
	__aeabi_fcmple	13.0
	__aeabi_fcmpgt	13.0
	__aeabi_fcmpge	13.0
	__aeabi_fcmpeq	7.0
Double, Math	__aeabi_dadd	54.5
	__aeabi_dsub	71.2
	__aeabi_drsub	71.2
	__aeabi_dmul	56.4
	__aeabi_ddiv	134.0
Double, Compare	__aeabi_dcmplt	14.0
	__aeabi_dcmple	14.0
	__aeabi_dcmpgt	14.0
	__aeabi_dcmpge	14.0
	__aeabi_dcmpeq	14.0
Float, Conversion	__aeabi_f2iz	9.0
	__aeabi_f2uiz	6.0
	__aeabi_f2lz	13.5
	__aeabi_f2ulz	12.0
	__aeabi_i2f	10.5
	__aeabi_ui2f	7.5
	__aeabi_l2f	19.0
	__aeabi_ul2f	13.8
	__aeabi_f2d	9.0
Double, Conversion	__aeabi_d2iz	10.0
	__aeabi_d2uiz	8.0
	__aeabi_d2lz	16.5
	__aeabi_d2ulz	13.5
	__aeabi_i2d	12.0
	__aeabi_ui2d	8.0
	__aeabi_l2d	17.9
	__aeabi_ul2d	12.9
	__aeabi_d2f	11.0

EABI function performance on RISC-V

The benchmarks have been done on a GD32VD107 (RV32IMAC), running from Flash, compiled with Embedded Studio (GCC), optimized for speed.

Function		Cycles, Min	Cycles, Max	Cycles, Avg
Float, Math	__addsf3	45	60	49.5
	__subsf3	42	84	62.2
	__mulsf3	37	57	39.3
	__divsf3	67	70	67.0
Float, Compare	__ltsf2	11	15	11.0
	__lesf2	10	14	10.0
	__gtsf2	10	17	10.0
	__gesf2	11	14	11.0
	__eqsf2	10	13	10.0
	__nesf2	10	10	10.0
Double, Math	__adddf3	52	89	62.8
	__subdf3	60	123	82.8
	__muldf3	68	88	75.0
	__divdf3	192	204	197.2
Double, Compare	__ltdf2	15	20	16.0
	__ledf2	15	19	16.0
	__gtdf2	15	20	16.1
	__gedf2	15	19	16.1
	__eqdf2	14	17	14.0
	__nedf2	14	14	14.0
Float, Conversion	__fixsfsi	14	14	14.0
	__fixunssfsi	13	13	13.0
	__fixsfdi	20	29	23.2
	__fixunssfdi	15	23	18.9
	__floatsisf	28	47	32.6
	__floatunsisf	28	42	33.0
	__floatdisf	39	66	49.1
	__floatundisf	35	58	44.1
	__extendsfdf2	14	18	14.1
Double, Conversion	__fixdfsi	9	20	16.8
	__fixunsdfsi	9	14	13.8
	__fixdfdi	9	34	26.9
	__fixunsdfdi	9	25	21.5
	__floatsidf	28	47	31.6
	__floatunsidf	19	32	23.9
	__floatdidf	30	73	45.1
	__floatundidf	27	62	39.3
	__truncdfsf2	25	36	25.1

EABI function code size on RISC-V

For function code size, the floating-point library has been compiled with optimization for size, targeting RV32IMC.

Function		Code Size [Bytes]
Float, Math	__addsf3	410
	__subsf3	10
	__mulsf3	178
	__divsf3	184
Float, Compare	__ltsf2	58
	__lesf2	54
	__gtsf2	50
	__gesf2	62
	__eqsf2	44
	__nesf2	--
Double, Math	__adddf3	724
	__subdf3	10
	__muldf3	286
	__divdf3	278
Double, Compare	__ltdf2	70
	__ledf2	70
	__gtdf2	70
	__gedf2	70
	__eqdf2	52
	__nedf2	--
Float, Conversion	__fixsfsi	74
	__fixunssfsi	50
	__fixsfdi	146
	__fixunssfdi	98
	__floatsisf	66
	__floatunsisf	52
	__floatdisf	96
	__floatundisf	70
	__extendsfdf2	64
Double, Conversion	__fixdfsi	84
	__fixunsdfsi	54
	__fixdfdi	146
	__fixunsdfdi	96
	__floatsidf	46
	__floatunsidf	34
	__floatdidf	128
	__floatundidf	106
	__truncdfsf2	130

Notes: __subsf3 tail-calls __addsf3, __subdf3 tail-calls __adddf3. __nesf2 is an alias of __eqsf2, __nedf2 is an alias of __eqdf2.

Size comparison

To demonstrate how competitive the floating-point library is from a size perspective, a level -playing-field benchmark is available. Quite simply, it calls a selection of the explicit floating-point library functions from main().

For the Arm variant and similarly for RISC-V, a single application and startup code can successfully link against multiple vendor-provided runtime systems thanks to all compilers conforming to the core-specific EABI. This simplifies the swapping of libraries both in the benchmark and in other projects.

The benchmark project uses exactly the same object modules with different runtimes for each vendor. The project uses Embedded Studio and a standard project template to build for different architectures.

The Arm applications are built with the SEGGER Compiler and the SEGGER Linker. The RISC-V applications use the GNU tools which are included in Embedded Studio.

#include "math.h"

volatile float  vf;
volatile double vd;

int main(void) {
  float f;
  double d;
  //
  f = vf;
  //
  f = sinf(f);
  f = cosf(f);
  f = tanf(f);
  f = asinf(f);
  f = acosf(f);
  f = atanf(f);
  f = sinhf(f);
  f = coshf(f);
  f = tanhf(f);
  f = asinhf(f);
  f = acoshf(f);
  f = atanhf(f);
  vf = f;
  //
  d = vd;
  d = sin(d);
  d = cos(d);
  d = tan(d);
  d = asin(d);
  d = acos(d);
  d = atan(d);
  d = sinh(d);
  d = cosh(d);
  d = tanh(d);
  d = asinh(d);
  d = acosh(d);
  d = atanh(d);
  vd = d;
  //
  return 0;
}

Size comparison on Arm

emFloat has been tested against:

IAR Embedded Workbench 8.50
GNU Arm Embedded 9-2020-q2-update
Arm Compiler 6.14, standard Arm libraries (flush-to-zero mode)
Arm Compiler 6.14, MicroLib (non-conforming IEEE implementation)
TI Code Composer 20.2.1 LTS

The table shows the results for ARMv7M with full software floating point.

Library	ROM Usage
SEGGER	10,628 bytes
IAR	17,656 bytes
AC6 MicroLib	18,668 bytes
AC6	21,514 bytes
GNU	33,809 bytes
CCS	34,274 bytes

The overhead from the benchmark application is 306 bytes Flash.

Size comparison on RISC-V

For RISC-V emFloat has been tested against:

standard 2019-08-gcc-8.3.0 toolset (maintained by SiFive)

These are the results for RV32IMC.

Library	ROM Usage
SEGGER	12,644 bytes
GNU	47,176 bytes

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